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A crude model for the molecular distribution of atmospheric gases above Earth's surface (denoted by height $h$ ) can be obtained by considering the potential energy due to gravity:
$$
P(h)=e^{-m g h / k T}
$$
In this expression $m$ is the per-particle mass of the gas, $g$ is the acceleration due to gravity, $k$ is a constant equal to $1.38 \times 10^{-23} \mathrm{~J} \mathrm{~K}^{-1}$, and $T$ is temperature. Determine $\langle h\rangle$ for methane $\left(\mathrm{CH}_4\right)$ using this distribution function. | 1.6 | 1.6 | $10^4 \mathrm{~m}$ | thermo | 12.32 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA crude model for the molecular distribution of atmospheric gases above Earth's surface (denoted by height $h$ ) can be obtained by considering the potential energy due to gravity:\r\n$$\r\nP(h)=e^{-m g h / k T}\r\n$$\r\nIn this expression $m$ is the per-particle mass of the gas, $g$ is the acceleration due to gravity, $k$ is a constant equal to $1.38 \\times 10^{-23} \\mathrm{~J} \\mathrm{~K}^{-1}$, and $T$ is temperature. Determine $\\langle h\\rangle$ for methane $\\left(\\mathrm{CH}_4\\right)$ using this distribution function.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.6",
"unit": " $10^4 \\mathrm{~m}$"
},
"style": "rule"
} | {
"index": 100,
"split": "train"
} |
||
A camper stranded in snowy weather loses heat by wind convection. The camper is packing emergency rations consisting of $58 \%$ sucrose, $31 \%$ fat, and $11 \%$ protein by weight. Using the data provided in Problem P4.32 and assuming the fat content of the rations can be treated with palmitic acid data and the protein content similarly by the protein data in Problem P4.32, how much emergency rations must the camper consume in order to compensate for a reduction in body temperature of $3.5 \mathrm{~K}$ ? Assume the heat capacity of the body equals that of water. Assume the camper weighs $67 \mathrm{~kg}$. | 49 | 49 | $\mathrm{~g}$ | thermo | 4.33 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA camper stranded in snowy weather loses heat by wind convection. The camper is packing emergency rations consisting of $58 \\%$ sucrose, $31 \\%$ fat, and $11 \\%$ protein by weight. Using the data provided in Problem P4.32 and assuming the fat content of the rations can be treated with palmitic acid data and the protein content similarly by the protein data in Problem P4.32, how much emergency rations must the camper consume in order to compensate for a reduction in body temperature of $3.5 \\mathrm{~K}$ ? Assume the heat capacity of the body equals that of water. Assume the camper weighs $67 \\mathrm{~kg}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "49",
"unit": " $\\mathrm{~g}$"
},
"style": "rule"
} | {
"index": 101,
"split": "train"
} |
||
At 303 . K, the vapor pressure of benzene is 120 . Torr and that of hexane is 189 Torr. Calculate the vapor pressure of a solution for which $x_{\text {benzene }}=0.28$ assuming ideal behavior. | 170 | 170 | $\mathrm{Torr}$ | thermo | 9.8 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nAt 303 . K, the vapor pressure of benzene is 120 . Torr and that of hexane is 189 Torr. Calculate the vapor pressure of a solution for which $x_{\\text {benzene }}=0.28$ assuming ideal behavior.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "170",
"unit": " $\\mathrm{Torr}$"
},
"style": "rule"
} | {
"index": 102,
"split": "train"
} |
||
Determine the molar standard Gibbs energy for ${ }^{35} \mathrm{Cl}^{35} \mathrm{Cl}$ where $\widetilde{\nu}=560 . \mathrm{cm}^{-1}, B=0.244 \mathrm{~cm}^{-1}$, and the ground electronic state is nondegenerate. | -57.2 | -57.2 | $\mathrm{~kJ} \mathrm{~mol}^{-1}$ | thermo | 15.45 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nDetermine the molar standard Gibbs energy for ${ }^{35} \\mathrm{Cl}^{35} \\mathrm{Cl}$ where $\\widetilde{\\nu}=560 . \\mathrm{cm}^{-1}, B=0.244 \\mathrm{~cm}^{-1}$, and the ground electronic state is nondegenerate.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-57.2",
"unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$"
},
"style": "rule"
} | {
"index": 103,
"split": "train"
} |
||
For the reaction $\mathrm{C}($ graphite $)+\mathrm{H}_2 \mathrm{O}(g) \rightleftharpoons$ $\mathrm{CO}(g)+\mathrm{H}_2(g), \Delta H_R^{\circ}=131.28 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298.15 \mathrm{~K}$. Use the values of $C_{P, m}^{\circ}$ at $298.15 \mathrm{~K}$ in the data tables to calculate $\Delta H_R^{\circ}$ at $125.0^{\circ} \mathrm{C}$. | 132.9 | 132.9 | $\mathrm{~kJ} \mathrm{~mol}^{-1}$ | thermo | 6.12 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor the reaction $\\mathrm{C}($ graphite $)+\\mathrm{H}_2 \\mathrm{O}(g) \\rightleftharpoons$ $\\mathrm{CO}(g)+\\mathrm{H}_2(g), \\Delta H_R^{\\circ}=131.28 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ at $298.15 \\mathrm{~K}$. Use the values of $C_{P, m}^{\\circ}$ at $298.15 \\mathrm{~K}$ in the data tables to calculate $\\Delta H_R^{\\circ}$ at $125.0^{\\circ} \\mathrm{C}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "132.9",
"unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$"
},
"style": "rule"
} | {
"index": 104,
"split": "train"
} |
||
Calculate the mean ionic activity of a $0.0350 \mathrm{~m} \mathrm{Na}_3 \mathrm{PO}_4$ solution for which the mean activity coefficient is 0.685 . | 0.0547 | 0.0547 | thermo | 10.6 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the mean ionic activity of a $0.0350 \\mathrm{~m} \\mathrm{Na}_3 \\mathrm{PO}_4$ solution for which the mean activity coefficient is 0.685 .\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.0547",
"unit": " "
},
"style": "rule"
} | {
"index": 105,
"split": "train"
} |
|||
Consider the transition between two forms of solid tin, $\mathrm{Sn}(s$, gray $) \rightarrow \mathrm{Sn}(s$, white $)$. The two phases are in equilibrium at 1 bar and $18^{\circ} \mathrm{C}$. The densities for gray and white tin are 5750 and $7280 \mathrm{~kg} \mathrm{~m}^{-3}$, respectively, and the molar entropies for gray and white tin are 44.14 and $51.18 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, respectively. Calculate the temperature at which the two phases are in equilibrium at 350. bar. | -3.5 | -3.5 | $^{\circ} \mathrm{C}$ | thermo | 8.43 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\n Consider the transition between two forms of solid tin, $\\mathrm{Sn}(s$, gray $) \\rightarrow \\mathrm{Sn}(s$, white $)$. The two phases are in equilibrium at 1 bar and $18^{\\circ} \\mathrm{C}$. The densities for gray and white tin are 5750 and $7280 \\mathrm{~kg} \\mathrm{~m}^{-3}$, respectively, and the molar entropies for gray and white tin are 44.14 and $51.18 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$, respectively. Calculate the temperature at which the two phases are in equilibrium at 350. bar.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-3.5",
"unit": " $^{\\circ} \\mathrm{C}$"
},
"style": "rule"
} | {
"index": 106,
"split": "train"
} |
||
The densities of pure water and ethanol are 997 and $789 \mathrm{~kg} \mathrm{~m}^{-3}$, respectively. For $x_{\text {ethanol }}=0.35$, the partial molar volumes of ethanol and water are 55.2 and $17.8 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1}$, respectively. Calculate the change in volume relative to the pure components when $2.50 \mathrm{~L}$ of a solution with $x_{\text {ethanol }}=0.35$ is prepared. | -0.10 | -0.10 | $\mathrm{~L}$ | thermo | 9.22 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe densities of pure water and ethanol are 997 and $789 \\mathrm{~kg} \\mathrm{~m}^{-3}$, respectively. For $x_{\\text {ethanol }}=0.35$, the partial molar volumes of ethanol and water are 55.2 and $17.8 \\times 10^{-3} \\mathrm{~L} \\mathrm{~mol}^{-1}$, respectively. Calculate the change in volume relative to the pure components when $2.50 \\mathrm{~L}$ of a solution with $x_{\\text {ethanol }}=0.35$ is prepared.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-0.10",
"unit": " $\\mathrm{~L}$"
},
"style": "rule"
} | {
"index": 107,
"split": "train"
} |
||
For $\mathrm{N}_2$ at $298 \mathrm{~K}$, what fraction of molecules has a speed between 200. and $300 . \mathrm{m} / \mathrm{s}$ ? | 0.132 | 0.132 | thermo | 16.15 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor $\\mathrm{N}_2$ at $298 \\mathrm{~K}$, what fraction of molecules has a speed between 200. and $300 . \\mathrm{m} / \\mathrm{s}$ ?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.132",
"unit": " "
},
"style": "rule"
} | {
"index": 108,
"split": "train"
} |
|||
Calculate the pressure exerted by Ar for a molar volume of $1.31 \mathrm{~L} \mathrm{~mol}^{-1}$ at $426 \mathrm{~K}$ using the van der Waals equation of state. The van der Waals parameters $a$ and $b$ for Ar are 1.355 bar dm ${ }^6 \mathrm{~mol}^{-2}$ and $0.0320 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, respectively. Is the attractive or repulsive portion of the potential dominant under these conditions?
| 26.9 | 26.9 | $\mathrm{~bar}$ | thermo | 1.3 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the pressure exerted by Ar for a molar volume of $1.31 \\mathrm{~L} \\mathrm{~mol}^{-1}$ at $426 \\mathrm{~K}$ using the van der Waals equation of state. The van der Waals parameters $a$ and $b$ for Ar are 1.355 bar dm ${ }^6 \\mathrm{~mol}^{-2}$ and $0.0320 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$, respectively. Is the attractive or repulsive portion of the potential dominant under these conditions?\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "26.9",
"unit": "$\\mathrm{~bar}$"
},
"style": "rule"
} | {
"index": 109,
"split": "train"
} |
||
For water, $\Delta H_{\text {vaporization }}$ is $40.656 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and the normal boiling point is $373.12 \mathrm{~K}$. Calculate the boiling point for water on the top of Mt. Everest (elevation $8848 \mathrm{~m}$ ), where the barometric pressure is 253 Torr. | 344 | 344 | $\mathrm{~K}$ | thermo | 8.25 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor water, $\\Delta H_{\\text {vaporization }}$ is $40.656 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$, and the normal boiling point is $373.12 \\mathrm{~K}$. Calculate the boiling point for water on the top of Mt. Everest (elevation $8848 \\mathrm{~m}$ ), where the barometric pressure is 253 Torr.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "344",
"unit": " $\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 110,
"split": "train"
} |
||
An ideal solution is formed by mixing liquids $\mathrm{A}$ and $B$ at $298 \mathrm{~K}$. The vapor pressure of pure A is 151 Torr and that of pure B is 84.3 Torr. If the mole fraction of $\mathrm{A}$ in the vapor is 0.610 , what is the mole fraction of $\mathrm{A}$ in the solution? | 0.466 | 0.466 | thermo | 9.24 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nAn ideal solution is formed by mixing liquids $\\mathrm{A}$ and $B$ at $298 \\mathrm{~K}$. The vapor pressure of pure A is 151 Torr and that of pure B is 84.3 Torr. If the mole fraction of $\\mathrm{A}$ in the vapor is 0.610 , what is the mole fraction of $\\mathrm{A}$ in the solution?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.466",
"unit": " "
},
"style": "rule"
} | {
"index": 111,
"split": "train"
} |
|||
The mean solar flux at Earth's surface is $\sim 2.00 \mathrm{~J}$ $\mathrm{cm}^{-2} \mathrm{~min}^{-1}$. In a nonfocusing solar collector, the temperature reaches a value of $79.5^{\circ} \mathrm{C}$. A heat engine is operated using the collector as the hot reservoir and a cold reservoir at $298 \mathrm{~K}$. Calculate the area of the collector needed to produce 1000. W. Assume that the engine operates at the maximum Carnot efficiency. | 19.4 | 19.4 | $\mathrm{~m}^2$ | thermo | 5.42 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe mean solar flux at Earth's surface is $\\sim 2.00 \\mathrm{~J}$ $\\mathrm{cm}^{-2} \\mathrm{~min}^{-1}$. In a nonfocusing solar collector, the temperature reaches a value of $79.5^{\\circ} \\mathrm{C}$. A heat engine is operated using the collector as the hot reservoir and a cold reservoir at $298 \\mathrm{~K}$. Calculate the area of the collector needed to produce 1000. W. Assume that the engine operates at the maximum Carnot efficiency.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "19.4",
"unit": " $\\mathrm{~m}^2$"
},
"style": "rule"
} | {
"index": 112,
"split": "train"
} |
||
A hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations that if completely metabolized will release $35 \mathrm{~kJ}$ of heat per gram of rations consumed. How much rations must the hiker consume to avoid a reduction in body temperature of $2.5 \mathrm{~K}$ as a result of heat loss? Assume the heat capacity of the body equals that of water and that the hiker weighs $51 \mathrm{~kg}$. | 15 | 15 | $\mathrm{~g}$ | thermo | 2.4 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations that if completely metabolized will release $35 \\mathrm{~kJ}$ of heat per gram of rations consumed. How much rations must the hiker consume to avoid a reduction in body temperature of $2.5 \\mathrm{~K}$ as a result of heat loss? Assume the heat capacity of the body equals that of water and that the hiker weighs $51 \\mathrm{~kg}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "15",
"unit": "$\\mathrm{~g}$"
},
"style": "rule"
} | {
"index": 113,
"split": "train"
} |
||
Calculate the degree of dissociation of $\mathrm{N}_2 \mathrm{O}_4$ in the reaction $\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g)$ at 300 . $\mathrm{K}$ and a total pressure of 1.50 bar. Do you expect the degree of dissociation to increase or decrease as the temperature is increased to 550 . K? Assume that $\Delta H_R^{\circ}$ is independent of temperature. | 0.241 | 0.241 | thermo | 6.30 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the degree of dissociation of $\\mathrm{N}_2 \\mathrm{O}_4$ in the reaction $\\mathrm{N}_2 \\mathrm{O}_4(g) \\rightleftharpoons 2 \\mathrm{NO}_2(g)$ at 300 . $\\mathrm{K}$ and a total pressure of 1.50 bar. Do you expect the degree of dissociation to increase or decrease as the temperature is increased to 550 . K? Assume that $\\Delta H_R^{\\circ}$ is independent of temperature.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.241",
"unit": " "
},
"style": "rule"
} | {
"index": 114,
"split": "train"
} |
|||
Calculate $\Delta G$ for the isothermal expansion of $2.25 \mathrm{~mol}$ of an ideal gas at $325 \mathrm{~K}$ from an initial pressure of 12.0 bar to a final pressure of 2.5 bar. | -9.54 | -9.54 | $10^3 \mathrm{~J}$ | thermo | 6.20 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate $\\Delta G$ for the isothermal expansion of $2.25 \\mathrm{~mol}$ of an ideal gas at $325 \\mathrm{~K}$ from an initial pressure of 12.0 bar to a final pressure of 2.5 bar.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-9.54",
"unit": " $10^3 \\mathrm{~J}$"
},
"style": "rule"
} | {
"index": 115,
"split": "train"
} |
||
Determine the total collisional frequency for $\mathrm{CO}_2$ at $1 \mathrm{~atm}$ and $298 \mathrm{~K}$. | 8.44 | 8.44 | $10^{34} \mathrm{~m}^{-3} \mathrm{~s}^{-1}$ | thermo | 16.30 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nDetermine the total collisional frequency for $\\mathrm{CO}_2$ at $1 \\mathrm{~atm}$ and $298 \\mathrm{~K}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "8.44",
"unit": " $10^{34} \\mathrm{~m}^{-3} \\mathrm{~s}^{-1}$"
},
"style": "rule"
} | {
"index": 116,
"split": "train"
} |
||
The volatile liquids $A$ and $\mathrm{B}$, for which $P_A^*=165$ Torr and $P_B^*=85.1$ Torr are confined to a piston and cylinder assembly. Initially, only the liquid phase is present. As the pressure is reduced, the first vapor is observed at a total pressure of 110 . Torr. Calculate $x_{\mathrm{A}}$ | 0.312 | 0.312 | thermo | 9.9 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe volatile liquids $A$ and $\\mathrm{B}$, for which $P_A^*=165$ Torr and $P_B^*=85.1$ Torr are confined to a piston and cylinder assembly. Initially, only the liquid phase is present. As the pressure is reduced, the first vapor is observed at a total pressure of 110 . Torr. Calculate $x_{\\mathrm{A}}$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.312",
"unit": " "
},
"style": "rule"
} | {
"index": 117,
"split": "train"
} |
|||
The osmotic pressure of an unknown substance is measured at $298 \mathrm{~K}$. Determine the molecular weight if the concentration of this substance is $31.2 \mathrm{~kg} \mathrm{~m}^{-3}$ and the osmotic pressure is $5.30 \times 10^4 \mathrm{~Pa}$. The density of the solution is $997 \mathrm{~kg} \mathrm{~m}^{-3}$. | 1.45 | 1.45 | $10^3 \mathrm{~g} \mathrm{~mol}^{-1}$ | thermo | 9.7 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe osmotic pressure of an unknown substance is measured at $298 \\mathrm{~K}$. Determine the molecular weight if the concentration of this substance is $31.2 \\mathrm{~kg} \\mathrm{~m}^{-3}$ and the osmotic pressure is $5.30 \\times 10^4 \\mathrm{~Pa}$. The density of the solution is $997 \\mathrm{~kg} \\mathrm{~m}^{-3}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.45",
"unit": " $10^3 \\mathrm{~g} \\mathrm{~mol}^{-1}$"
},
"style": "rule"
} | {
"index": 118,
"split": "train"
} |
||
One mole of Ar initially at 310 . K undergoes an adiabatic expansion against a pressure $P_{\text {external }}=0$ from a volume of $8.5 \mathrm{~L}$ to a volume of $82.0 \mathrm{~L}$. Calculate the final temperature using the ideal gas | 310 | 310 | $\mathrm{~K}$ | thermo | 7.4 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\n One mole of Ar initially at 310 . K undergoes an adiabatic expansion against a pressure $P_{\\text {external }}=0$ from a volume of $8.5 \\mathrm{~L}$ to a volume of $82.0 \\mathrm{~L}$. Calculate the final temperature using the ideal gas\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "310",
"unit": "$\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 119,
"split": "train"
} |
||
A refrigerator is operated by a $0.25-\mathrm{hp}(1 \mathrm{hp}=$ 746 watts) motor. If the interior is to be maintained at $4.50^{\circ} \mathrm{C}$ and the room temperature on a hot day is $38^{\circ} \mathrm{C}$, what is the maximum heat leak (in watts) that can be tolerated? Assume that the coefficient of performance is $50 . \%$ of the maximum theoretical value. | 773 | 773 | $\mathrm{~J} \mathrm{~s}^{-1}$ | thermo | 5.33 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA refrigerator is operated by a $0.25-\\mathrm{hp}(1 \\mathrm{hp}=$ 746 watts) motor. If the interior is to be maintained at $4.50^{\\circ} \\mathrm{C}$ and the room temperature on a hot day is $38^{\\circ} \\mathrm{C}$, what is the maximum heat leak (in watts) that can be tolerated? Assume that the coefficient of performance is $50 . \\%$ of the maximum theoretical value.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "773",
"unit": " $\\mathrm{~J} \\mathrm{~s}^{-1}$"
},
"style": "rule"
} | {
"index": 120,
"split": "train"
} |
||
In order to get in shape for mountain climbing, an avid hiker with a mass of $60 . \mathrm{kg}$ ascends the stairs in the world's tallest structure, the $828 \mathrm{~m}$ tall Burj Khalifa in Dubai, United Arab Emirates. Assume that she eats energy bars on the way up and that her body is $25 \%$ efficient in converting the energy content of the bars into the work of climbing. How many energy bars does she have to eat if a single bar produces $1.08 \times 10^3 \mathrm{~kJ}$ of energy upon metabolizing? | 1.8 | 1.8 | thermo | 4.34 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nIn order to get in shape for mountain climbing, an avid hiker with a mass of $60 . \\mathrm{kg}$ ascends the stairs in the world's tallest structure, the $828 \\mathrm{~m}$ tall Burj Khalifa in Dubai, United Arab Emirates. Assume that she eats energy bars on the way up and that her body is $25 \\%$ efficient in converting the energy content of the bars into the work of climbing. How many energy bars does she have to eat if a single bar produces $1.08 \\times 10^3 \\mathrm{~kJ}$ of energy upon metabolizing?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.8",
"unit": " "
},
"style": "rule"
} | {
"index": 121,
"split": "train"
} |
|||
The half-life of ${ }^{238} \mathrm{U}$ is $4.5 \times 10^9$ years. How many disintegrations occur in $1 \mathrm{~min}$ for a $10 \mathrm{mg}$ sample of this element? | 1.43 | 1.43 | $10^{24}$ | thermo | 18.14 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe half-life of ${ }^{238} \\mathrm{U}$ is $4.5 \\times 10^9$ years. How many disintegrations occur in $1 \\mathrm{~min}$ for a $10 \\mathrm{mg}$ sample of this element?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.43",
"unit": " $10^{24}$"
},
"style": "rule"
} | {
"index": 122,
"split": "train"
} |
||
Calculate the ionic strength in a solution that is 0.0750 $m$ in $\mathrm{K}_2 \mathrm{SO}_4, 0.0085 \mathrm{~m}$ in $\mathrm{Na}_3 \mathrm{PO}_4$, and $0.0150 \mathrm{~m}$ in $\mathrm{MgCl}_2$. | 0.321 | 0.321 | $\mathrm{~mol} \mathrm{~kg}^{-1}$ | thermo | 10.13 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the ionic strength in a solution that is 0.0750 $m$ in $\\mathrm{K}_2 \\mathrm{SO}_4, 0.0085 \\mathrm{~m}$ in $\\mathrm{Na}_3 \\mathrm{PO}_4$, and $0.0150 \\mathrm{~m}$ in $\\mathrm{MgCl}_2$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.321",
"unit": " $\\mathrm{~mol} \\mathrm{~kg}^{-1}$"
},
"style": "rule"
} | {
"index": 123,
"split": "train"
} |
||
The interior of a refrigerator is typically held at $36^{\circ} \mathrm{F}$ and the interior of a freezer is typically held at $0.00^{\circ} \mathrm{F}$. If the room temperature is $65^{\circ} \mathrm{F}$, by what factor is it more expensive to extract the same amount of heat from the freezer than from the refrigerator? Assume that the theoretical limit for the performance of a reversible refrigerator is valid in this case. | 2.4 | 2.4 | thermo | 5.17 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe interior of a refrigerator is typically held at $36^{\\circ} \\mathrm{F}$ and the interior of a freezer is typically held at $0.00^{\\circ} \\mathrm{F}$. If the room temperature is $65^{\\circ} \\mathrm{F}$, by what factor is it more expensive to extract the same amount of heat from the freezer than from the refrigerator? Assume that the theoretical limit for the performance of a reversible refrigerator is valid in this case.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2.4",
"unit": " "
},
"style": "rule"
} | {
"index": 124,
"split": "train"
} |
|||
Calculate the rotational partition function for $\mathrm{SO}_2$ at $298 \mathrm{~K}$ where $B_A=2.03 \mathrm{~cm}^{-1}, B_B=0.344 \mathrm{~cm}^{-1}$, and $B_C=0.293 \mathrm{~cm}^{-1}$ | 5840 | 5840 | thermo | 14.16 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the rotational partition function for $\\mathrm{SO}_2$ at $298 \\mathrm{~K}$ where $B_A=2.03 \\mathrm{~cm}^{-1}, B_B=0.344 \\mathrm{~cm}^{-1}$, and $B_C=0.293 \\mathrm{~cm}^{-1}$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "5840",
"unit": " "
},
"style": "rule"
} | {
"index": 125,
"split": "train"
} |
|||
For a two-level system where $v=1.50 \times 10^{13} \mathrm{~s}^{-1}$, determine the temperature at which the internal energy is equal to $0.25 \mathrm{Nhv}$, or $1 / 2$ the limiting value of $0.50 \mathrm{Nhv}$. | 655 | 655 | $\mathrm{~K}$ | thermo | 15.2 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor a two-level system where $v=1.50 \\times 10^{13} \\mathrm{~s}^{-1}$, determine the temperature at which the internal energy is equal to $0.25 \\mathrm{Nhv}$, or $1 / 2$ the limiting value of $0.50 \\mathrm{Nhv}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "655",
"unit": " $\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 126,
"split": "train"
} |
||
Calculate $K_P$ at $600 . \mathrm{K}$ for the reaction $\mathrm{N}_2 \mathrm{O}_4(l) \rightleftharpoons 2 \mathrm{NO}_2(g)$ assuming that $\Delta H_R^{\circ}$ is constant over the interval 298-725 K. | 4.76 | 4.76 | $10^6$ | thermo | 6.10 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate $K_P$ at $600 . \\mathrm{K}$ for the reaction $\\mathrm{N}_2 \\mathrm{O}_4(l) \\rightleftharpoons 2 \\mathrm{NO}_2(g)$ assuming that $\\Delta H_R^{\\circ}$ is constant over the interval 298-725 K.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "4.76",
"unit": " $10^6$"
},
"style": "rule"
} | {
"index": 127,
"split": "train"
} |
||
Count Rumford observed that using cannon boring machinery a single horse could heat $11.6 \mathrm{~kg}$ of ice water $(T=273 \mathrm{~K})$ to $T=355 \mathrm{~K}$ in 2.5 hours. Assuming the same rate of work, how high could a horse raise a $225 \mathrm{~kg}$ weight in 2.5 minutes? Assume the heat capacity of water is $4.18 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~g}^{-1}$. | 30 | 30 | $\mathrm{~m}$ | thermo | 2.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCount Rumford observed that using cannon boring machinery a single horse could heat $11.6 \\mathrm{~kg}$ of ice water $(T=273 \\mathrm{~K})$ to $T=355 \\mathrm{~K}$ in 2.5 hours. Assuming the same rate of work, how high could a horse raise a $225 \\mathrm{~kg}$ weight in 2.5 minutes? Assume the heat capacity of water is $4.18 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~g}^{-1}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "30",
"unit": "$\\mathrm{~m}$"
},
"style": "rule"
} | {
"index": 128,
"split": "train"
} |
||
The vibrational frequency of $I_2$ is $208 \mathrm{~cm}^{-1}$. At what temperature will the population in the first excited state be half that of the ground state? | 432 | 432 | $\mathrm{~K}$ | thermo | 13.22 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe vibrational frequency of $I_2$ is $208 \\mathrm{~cm}^{-1}$. At what temperature will the population in the first excited state be half that of the ground state?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "432",
"unit": " $\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 129,
"split": "train"
} |
||
One mole of $\mathrm{H}_2 \mathrm{O}(l)$ is compressed from a state described by $P=1.00$ bar and $T=350$. K to a state described by $P=590$. bar and $T=750$. K. In addition, $\beta=2.07 \times 10^{-4} \mathrm{~K}^{-1}$ and the density can be assumed to be constant at the value $997 \mathrm{~kg} \mathrm{~m}^{-3}$. Calculate $\Delta S$ for this transformation, assuming that $\kappa=0$.
| 57.2 | 57.2 | $\mathrm{~K}^{-1}$ | thermo | 5.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nOne mole of $\\mathrm{H}_2 \\mathrm{O}(l)$ is compressed from a state described by $P=1.00$ bar and $T=350$. K to a state described by $P=590$. bar and $T=750$. K. In addition, $\\beta=2.07 \\times 10^{-4} \\mathrm{~K}^{-1}$ and the density can be assumed to be constant at the value $997 \\mathrm{~kg} \\mathrm{~m}^{-3}$. Calculate $\\Delta S$ for this transformation, assuming that $\\kappa=0$.\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "57.2",
"unit": " $\\mathrm{~K}^{-1}$"
},
"style": "rule"
} | {
"index": 130,
"split": "train"
} |
||
A mass of $34.05 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(s)$ at $273 \mathrm{~K}$ is dropped into $185 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(l)$ at $310 . \mathrm{K}$ in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equilibrium has been reached. Assume that $C_{P, m}$ for $\mathrm{H}_2 \mathrm{O}(l)$ is constant at its values for $298 \mathrm{~K}$ throughout the temperature range of interest. | 292 | 292 | $\mathrm{~K}$ | thermo | 3.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA mass of $34.05 \\mathrm{~g}$ of $\\mathrm{H}_2 \\mathrm{O}(s)$ at $273 \\mathrm{~K}$ is dropped into $185 \\mathrm{~g}$ of $\\mathrm{H}_2 \\mathrm{O}(l)$ at $310 . \\mathrm{K}$ in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equilibrium has been reached. Assume that $C_{P, m}$ for $\\mathrm{H}_2 \\mathrm{O}(l)$ is constant at its values for $298 \\mathrm{~K}$ throughout the temperature range of interest.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "292",
"unit": "$\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 131,
"split": "train"
} |
||
Calculate $\Delta H_f^{\circ}$ for $N O(g)$ at $975 \mathrm{~K}$, assuming that the heat capacities of reactants and products are constant over the temperature interval at their values at $298.15 \mathrm{~K}$. | 91.7 | 91.7 | $\mathrm{~kJ} \mathrm{~mol}^{-1}$ | thermo | 4.4 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate $\\Delta H_f^{\\circ}$ for $N O(g)$ at $975 \\mathrm{~K}$, assuming that the heat capacities of reactants and products are constant over the temperature interval at their values at $298.15 \\mathrm{~K}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "91.7",
"unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$"
},
"style": "rule"
} | {
"index": 132,
"split": "train"
} |
||
A two-level system is characterized by an energy separation of $1.30 \times 10^{-18} \mathrm{~J}$. At what temperature will the population of the ground state be 5 times greater than that of the excited state? | 5.85 | 5.85 | $10^4$ | thermo | 13.27 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA two-level system is characterized by an energy separation of $1.30 \\times 10^{-18} \\mathrm{~J}$. At what temperature will the population of the ground state be 5 times greater than that of the excited state?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "5.85",
"unit": " $10^4$"
},
"style": "rule"
} | {
"index": 133,
"split": "train"
} |
||
At what temperature are there Avogadro's number of translational states available for $\mathrm{O}_2$ confined to a volume of 1000. $\mathrm{cm}^3$ ? | 0.068 | 0.068 | $\mathrm{~K}$ | thermo | 14.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nAt what temperature are there Avogadro's number of translational states available for $\\mathrm{O}_2$ confined to a volume of 1000. $\\mathrm{cm}^3$ ?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.068",
"unit": " $\\mathrm{~K}$"
},
"style": "rule"
} | {
"index": 134,
"split": "train"
} |
||
The half-cell potential for the reaction $\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_2 \mathrm{O}(l)$ is $+1.03 \mathrm{~V}$ at $298.15 \mathrm{~K}$ when $a_{\mathrm{O}_2}=1.00$. Determine $a_{\mathrm{H}^{+}}$ | 4.16 | 4.16 | $10^{-4}$ | thermo | 11.25 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe half-cell potential for the reaction $\\mathrm{O}_2(g)+4 \\mathrm{H}^{+}(a q)+4 \\mathrm{e}^{-} \\rightarrow 2 \\mathrm{H}_2 \\mathrm{O}(l)$ is $+1.03 \\mathrm{~V}$ at $298.15 \\mathrm{~K}$ when $a_{\\mathrm{O}_2}=1.00$. Determine $a_{\\mathrm{H}^{+}}$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "4.16",
"unit": " $10^{-4}$"
},
"style": "rule"
} | {
"index": 135,
"split": "train"
} |
||
The partial molar volumes of water and ethanol in a solution with $x_{\mathrm{H}_2 \mathrm{O}}=0.45$ at $25^{\circ} \mathrm{C}$ are 17.0 and $57.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively, at this temperature. | -8 | -8 | $\mathrm{~cm}^3$ | thermo | 9.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe partial molar volumes of water and ethanol in a solution with $x_{\\mathrm{H}_2 \\mathrm{O}}=0.45$ at $25^{\\circ} \\mathrm{C}$ are 17.0 and $57.5 \\mathrm{~cm}^3 \\mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \\mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \\mathrm{~g} \\mathrm{~cm}^{-3}$, respectively, at this temperature.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-8",
"unit": " $\\mathrm{~cm}^3$"
},
"style": "rule"
} | {
"index": 136,
"split": "train"
} |
||
Use the $D_0$ value of $\mathrm{H}_2(4.478 \mathrm{eV})$ and the $D_0$ value of $\mathrm{H}_2^{+}(2.651 \mathrm{eV})$ to calculate the first ionization energy of $\mathrm{H}_2$ (that is, the energy needed to remove an electron from $\mathrm{H}_2$ ). | 15.425 | 15.425 | $\mathrm{eV}$ | quan | 13.3 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nUse the $D_0$ value of $\\mathrm{H}_2(4.478 \\mathrm{eV})$ and the $D_0$ value of $\\mathrm{H}_2^{+}(2.651 \\mathrm{eV})$ to calculate the first ionization energy of $\\mathrm{H}_2$ (that is, the energy needed to remove an electron from $\\mathrm{H}_2$ ).\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "15.425",
"unit": " $\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 137,
"split": "train"
} |
||
Calculate the energy of one mole of UV photons of wavelength $300 \mathrm{~nm}$ and compare it with a typical single-bond energy of $400 \mathrm{~kJ} / \mathrm{mol}$. | 399 | 399 | $\mathrm{~kJ} / \mathrm{mol}$ | quan | 1.3 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the energy of one mole of UV photons of wavelength $300 \\mathrm{~nm}$ and compare it with a typical single-bond energy of $400 \\mathrm{~kJ} / \\mathrm{mol}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "399",
"unit": " $\\mathrm{~kJ} / \\mathrm{mol}$"
},
"style": "rule"
} | {
"index": 138,
"split": "train"
} |
||
Calculate the magnitude of the spin angular momentum of a proton. Give a numerical answer. | 9.13 | 9.13 | $10^{-35} \mathrm{~J} \mathrm{~s}$ | quan | 10.1 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the magnitude of the spin angular momentum of a proton. Give a numerical answer. \n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "9.13",
"unit": " $10^{-35} \\mathrm{~J} \\mathrm{~s}$"
},
"style": "rule"
} | {
"index": 139,
"split": "train"
} |
||
The ${ }^7 \mathrm{Li}^1 \mathrm{H}$ ground electronic state has $D_0=2.4287 \mathrm{eV}, \nu_e / c=1405.65 \mathrm{~cm}^{-1}$, and $\nu_e x_e / c=23.20 \mathrm{~cm}^{-1}$, where $c$ is the speed of light. (These last two quantities are usually designated $\omega_e$ and $\omega_e x_e$ in the literature.) Calculate $D_e$ for ${ }^7 \mathrm{Li}^1 \mathrm{H}$. | 2.5151 | 2.5151 | $\mathrm{eV}$ | quan | 13.5 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe ${ }^7 \\mathrm{Li}^1 \\mathrm{H}$ ground electronic state has $D_0=2.4287 \\mathrm{eV}, \\nu_e / c=1405.65 \\mathrm{~cm}^{-1}$, and $\\nu_e x_e / c=23.20 \\mathrm{~cm}^{-1}$, where $c$ is the speed of light. (These last two quantities are usually designated $\\omega_e$ and $\\omega_e x_e$ in the literature.) Calculate $D_e$ for ${ }^7 \\mathrm{Li}^1 \\mathrm{H}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2.5151",
"unit": " $\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 140,
"split": "train"
} |
||
The positron has charge $+e$ and mass equal to the electron mass. Calculate in electronvolts the ground-state energy of positronium-an "atom" that consists of a positron and an electron. | -6.8 | -6.8 | $\mathrm{eV}$ | quan | 6.22 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe positron has charge $+e$ and mass equal to the electron mass. Calculate in electronvolts the ground-state energy of positronium-an \"atom\" that consists of a positron and an electron.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": " -6.8",
"unit": "$\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 141,
"split": "train"
} |
||
What is the value of the angular-momentum quantum number $l$ for a $t$ orbital? | 14 | 14 | quan | 6.29 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nWhat is the value of the angular-momentum quantum number $l$ for a $t$ orbital?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "14",
"unit": " "
},
"style": "rule"
} | {
"index": 142,
"split": "train"
} |
|||
How many states belong to the carbon configurations $1 s^2 2 s^2 2 p^2$? | 15 | 15 | quan | 11.22 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nHow many states belong to the carbon configurations $1 s^2 2 s^2 2 p^2$?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "15",
"unit": " "
},
"style": "rule"
} | {
"index": 143,
"split": "train"
} |
|||
Calculate the energy needed to compress three carbon-carbon single bonds and stretch three carbon-carbon double bonds to the benzene bond length $1.397 Å$. Assume a harmonicoscillator potential-energy function for bond stretching and compression. Typical carboncarbon single- and double-bond lengths are 1.53 and $1.335 Å$; typical stretching force constants for carbon-carbon single and double bonds are 500 and $950 \mathrm{~N} / \mathrm{m}$. | 27 | 27 | $\mathrm{kcal} / \mathrm{mol}$ | quan | 17.9 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the energy needed to compress three carbon-carbon single bonds and stretch three carbon-carbon double bonds to the benzene bond length $1.397 Å$. Assume a harmonicoscillator potential-energy function for bond stretching and compression. Typical carboncarbon single- and double-bond lengths are 1.53 and $1.335 Å$; typical stretching force constants for carbon-carbon single and double bonds are 500 and $950 \\mathrm{~N} / \\mathrm{m}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "27",
"unit": " $\\mathrm{kcal} / \\mathrm{mol}$"
},
"style": "rule"
} | {
"index": 144,
"split": "train"
} |
|
When a particle of mass $9.1 \times 10^{-28} \mathrm{~g}$ in a certain one-dimensional box goes from the $n=5$ level to the $n=2$ level, it emits a photon of frequency $6.0 \times 10^{14} \mathrm{~s}^{-1}$. Find the length of the box. | 1.8 | 1.8 | $\mathrm{~nm}$ | quan | 2.13 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nWhen a particle of mass $9.1 \\times 10^{-28} \\mathrm{~g}$ in a certain one-dimensional box goes from the $n=5$ level to the $n=2$ level, it emits a photon of frequency $6.0 \\times 10^{14} \\mathrm{~s}^{-1}$. Find the length of the box.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.8",
"unit": "$\\mathrm{~nm}$"
},
"style": "rule"
} | {
"index": 145,
"split": "train"
} |
||
Use the normalized Numerov-method harmonic-oscillator wave functions found by going from -5 to 5 in steps of 0.1 to estimate the probability of being in the classically forbidden region for the $v=0$ state. | 0.16 | 0.16 | quan | 4.42 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nUse the normalized Numerov-method harmonic-oscillator wave functions found by going from -5 to 5 in steps of 0.1 to estimate the probability of being in the classically forbidden region for the $v=0$ state.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.16",
"unit": " "
},
"style": "rule"
} | {
"index": 146,
"split": "train"
} |
|||
Calculate the de Broglie wavelength of an electron moving at 1/137th the speed of light. (At this speed, the relativistic correction to the mass is negligible.) | 0.332 | 0.332 | $\mathrm{~nm}$ | quan | 1.6 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the de Broglie wavelength of an electron moving at 1/137th the speed of light. (At this speed, the relativistic correction to the mass is negligible.)\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.332",
"unit": "$\\mathrm{~nm}$"
},
"style": "rule"
} | {
"index": 147,
"split": "train"
} |
||
Calculate the angle that the spin vector $S$ makes with the $z$ axis for an electron with spin function $\alpha$. | 54.7 | 54.7 | $^{\circ}$ | quan | 10.2 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the angle that the spin vector $S$ makes with the $z$ axis for an electron with spin function $\\alpha$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "54.7",
"unit": " $^{\\circ}$"
},
"style": "rule"
} | {
"index": 148,
"split": "train"
} |
||
The AM1 valence electronic energies of the atoms $\mathrm{H}$ and $\mathrm{O}$ are $-11.396 \mathrm{eV}$ and $-316.100 \mathrm{eV}$, respectively. For $\mathrm{H}_2 \mathrm{O}$ at its AM1-calculated equilibrium geometry, the AM1 valence electronic energy (core-core repulsion omitted) is $-493.358 \mathrm{eV}$ and the AM1 core-core repulsion energy is $144.796 \mathrm{eV}$. For $\mathrm{H}(g)$ and $\mathrm{O}(g), \Delta H_{f, 298}^{\circ}$ values are 52.102 and $59.559 \mathrm{kcal} / \mathrm{mol}$, respectively. Find the AM1 prediction of $\Delta H_{f, 298}^{\circ}$ of $\mathrm{H}_2 \mathrm{O}(g)$. | -59.24 | -59.24 | $\mathrm{kcal} / \mathrm{mol}$ | quan | 17.29 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe AM1 valence electronic energies of the atoms $\\mathrm{H}$ and $\\mathrm{O}$ are $-11.396 \\mathrm{eV}$ and $-316.100 \\mathrm{eV}$, respectively. For $\\mathrm{H}_2 \\mathrm{O}$ at its AM1-calculated equilibrium geometry, the AM1 valence electronic energy (core-core repulsion omitted) is $-493.358 \\mathrm{eV}$ and the AM1 core-core repulsion energy is $144.796 \\mathrm{eV}$. For $\\mathrm{H}(g)$ and $\\mathrm{O}(g), \\Delta H_{f, 298}^{\\circ}$ values are 52.102 and $59.559 \\mathrm{kcal} / \\mathrm{mol}$, respectively. Find the AM1 prediction of $\\Delta H_{f, 298}^{\\circ}$ of $\\mathrm{H}_2 \\mathrm{O}(g)$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-59.24",
"unit": " $\\mathrm{kcal} / \\mathrm{mol}$"
},
"style": "rule"
} | {
"index": 149,
"split": "train"
} |
||
Given that $D_e=4.75 \mathrm{eV}$ and $R_e=0.741 Å$ for the ground electronic state of $\mathrm{H}_2$, find $U\left(R_e\right)$ for this state. | -31.95 | -31.95 | $\mathrm{eV}$ | quan | 14.35 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nGiven that $D_e=4.75 \\mathrm{eV}$ and $R_e=0.741 Å$ for the ground electronic state of $\\mathrm{H}_2$, find $U\\left(R_e\\right)$ for this state.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": " -31.95",
"unit": " $\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 150,
"split": "train"
} |
|
For $\mathrm{NaCl}, R_e=2.36 Å$. The ionization energy of $\mathrm{Na}$ is $5.14 \mathrm{eV}$, and the electron affinity of $\mathrm{Cl}$ is $3.61 \mathrm{eV}$. Use the simple model of $\mathrm{NaCl}$ as a pair of spherical ions in contact to estimate $D_e$. [One debye (D) is $3.33564 \times 10^{-30} \mathrm{C} \mathrm{m}$.] | 4.56 | 4.56 | $\mathrm{eV}$ | quan | 14.5 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor $\\mathrm{NaCl}, R_e=2.36 Å$. The ionization energy of $\\mathrm{Na}$ is $5.14 \\mathrm{eV}$, and the electron affinity of $\\mathrm{Cl}$ is $3.61 \\mathrm{eV}$. Use the simple model of $\\mathrm{NaCl}$ as a pair of spherical ions in contact to estimate $D_e$. [One debye (D) is $3.33564 \\times 10^{-30} \\mathrm{C} \\mathrm{m}$.]\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": " 4.56",
"unit": " $\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 151,
"split": "train"
} |
|
Find the number of CSFs in a full CI calculation of $\mathrm{CH}_2 \mathrm{SiHF}$ using a 6-31G** basis set. | 1.86 | 1.86 | $10^{28} $ | quan | 16.1 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFind the number of CSFs in a full CI calculation of $\\mathrm{CH}_2 \\mathrm{SiHF}$ using a 6-31G** basis set.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.86",
"unit": "$10^{28} $"
},
"style": "rule"
} | {
"index": 152,
"split": "train"
} |
||
Calculate the ratio of the electrical and gravitational forces between a proton and an electron. | 2 | 2 | $10^{39}$ | quan | 6.15 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the ratio of the electrical and gravitational forces between a proton and an electron.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2",
"unit": " $10^{39}$"
},
"style": "rule"
} | {
"index": 153,
"split": "train"
} |
||
A one-particle, one-dimensional system has the state function
$$
\Psi=(\sin a t)\left(2 / \pi c^2\right)^{1 / 4} e^{-x^2 / c^2}+(\cos a t)\left(32 / \pi c^6\right)^{1 / 4} x e^{-x^2 / c^2}
$$
where $a$ is a constant and $c=2.000 Å$. If the particle's position is measured at $t=0$, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$. | 0.000216 | 0.000216 | quan | 1.13 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA one-particle, one-dimensional system has the state function\r\n$$\r\n\\Psi=(\\sin a t)\\left(2 / \\pi c^2\\right)^{1 / 4} e^{-x^2 / c^2}+(\\cos a t)\\left(32 / \\pi c^6\\right)^{1 / 4} x e^{-x^2 / c^2}\r\n$$\r\nwhere $a$ is a constant and $c=2.000 Å$. If the particle's position is measured at $t=0$, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.000216",
"unit": " "
},
"style": "rule"
} | {
"index": 154,
"split": "train"
} |
||
The $J=2$ to 3 rotational transition in a certain diatomic molecule occurs at $126.4 \mathrm{GHz}$, where $1 \mathrm{GHz} \equiv 10^9 \mathrm{~Hz}$. Find the frequency of the $J=5$ to 6 absorption in this molecule. | 252.8 | 252.8 | $\mathrm{GHz}$ | quan | 6.10 | Approximated answer | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe $J=2$ to 3 rotational transition in a certain diatomic molecule occurs at $126.4 \\mathrm{GHz}$, where $1 \\mathrm{GHz} \\equiv 10^9 \\mathrm{~Hz}$. Find the frequency of the $J=5$ to 6 absorption in this molecule.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": " 252.8",
"unit": " $\\mathrm{GHz}$"
},
"style": "rule"
} | {
"index": 155,
"split": "train"
} |
|
Assume that the charge of the proton is distributed uniformly throughout the volume of a sphere of radius $10^{-13} \mathrm{~cm}$. Use perturbation theory to estimate the shift in the ground-state hydrogen-atom energy due to the finite proton size. The potential energy experienced by the electron when it has penetrated the nucleus and is at distance $r$ from the nuclear center is $-e Q / 4 \pi \varepsilon_0 r$, where $Q$ is the amount of proton charge within the sphere of radius $r$. The evaluation of the integral is simplified by noting that the exponential factor in $\psi$ is essentially equal to 1 within the nucleus.
| 1.2 | 1.2 | $10^{-8} \mathrm{eV}$ | quan | 9.9 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nAssume that the charge of the proton is distributed uniformly throughout the volume of a sphere of radius $10^{-13} \\mathrm{~cm}$. Use perturbation theory to estimate the shift in the ground-state hydrogen-atom energy due to the finite proton size. The potential energy experienced by the electron when it has penetrated the nucleus and is at distance $r$ from the nuclear center is $-e Q / 4 \\pi \\varepsilon_0 r$, where $Q$ is the amount of proton charge within the sphere of radius $r$. The evaluation of the integral is simplified by noting that the exponential factor in $\\psi$ is essentially equal to 1 within the nucleus.\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.2",
"unit": " $10^{-8} \\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 156,
"split": "train"
} |
||
An electron in a three-dimensional rectangular box with dimensions of $5.00 Å, 3.00 Å$, and $6.00 Å$ makes a radiative transition from the lowest-lying excited state to the ground state. Calculate the frequency of the photon emitted. | 7.58 | 7.58 | $10^{14} \mathrm{~s}^{-1}$ | quan | 3.35 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nAn electron in a three-dimensional rectangular box with dimensions of $5.00 Å, 3.00 Å$, and $6.00 Å$ makes a radiative transition from the lowest-lying excited state to the ground state. Calculate the frequency of the photon emitted.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "7.58",
"unit": " $10^{14} \\mathrm{~s}^{-1}$"
},
"style": "rule"
} | {
"index": 157,
"split": "train"
} |
|
Do $\mathrm{HF} / 6-31 \mathrm{G}^*$ geometry optimizations on one conformers of $\mathrm{HCOOH}$ with $\mathrm{OCOH}$ dihedral angle of $0^{\circ}$. Calculate the dipole moment. | 1.41 | 1.41 | $\mathrm{D}$ | quan | 15.57 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nDo $\\mathrm{HF} / 6-31 \\mathrm{G}^*$ geometry optimizations on one conformers of $\\mathrm{HCOOH}$ with $\\mathrm{OCOH}$ dihedral angle of $0^{\\circ}$. Calculate the dipole moment.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.41",
"unit": " $\\mathrm{D}$"
},
"style": "rule"
} | {
"index": 158,
"split": "train"
} |
||
Frozen-core $\mathrm{SCF} / \mathrm{DZP}$ and CI-SD/DZP calculations on $\mathrm{H}_2 \mathrm{O}$ at its equilibrium geometry gave energies of -76.040542 and -76.243772 hartrees. Application of the Davidson correction brought the energy to -76.254549 hartrees. Find the coefficient of $\Phi_0$ in the normalized CI-SD wave function. | 0.9731 | 0.9731 | quan | 16.3 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFrozen-core $\\mathrm{SCF} / \\mathrm{DZP}$ and CI-SD/DZP calculations on $\\mathrm{H}_2 \\mathrm{O}$ at its equilibrium geometry gave energies of -76.040542 and -76.243772 hartrees. Application of the Davidson correction brought the energy to -76.254549 hartrees. Find the coefficient of $\\Phi_0$ in the normalized CI-SD wave function.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.9731",
"unit": " "
},
"style": "rule"
} | {
"index": 159,
"split": "train"
} |
|||
Let $w$ be the variable defined as the number of heads that show when two coins are tossed simultaneously. Find $\langle w\rangle$. | 1 | 1 | quan | 5.8 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nLet $w$ be the variable defined as the number of heads that show when two coins are tossed simultaneously. Find $\\langle w\\rangle$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1",
"unit": " "
},
"style": "rule"
} | {
"index": 160,
"split": "train"
} |
|||
Calculate the force on an alpha particle passing a gold atomic nucleus at a distance of $0.00300 Å$. | 0.405 | 0.405 | $\mathrm{~N}$ | quan | 1.31 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the force on an alpha particle passing a gold atomic nucleus at a distance of $0.00300 Å$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.405",
"unit": " $\\mathrm{~N}$"
},
"style": "rule"
} | {
"index": 161,
"split": "train"
} |
||
When an electron in a certain excited energy level in a one-dimensional box of length $2.00 Å$ makes a transition to the ground state, a photon of wavelength $8.79 \mathrm{~nm}$ is emitted. Find the quantum number of the initial state. | 4 | 4 | quan | 2.13 | Angstrom | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nWhen an electron in a certain excited energy level in a one-dimensional box of length $2.00 Å$ makes a transition to the ground state, a photon of wavelength $8.79 \\mathrm{~nm}$ is emitted. Find the quantum number of the initial state.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "4",
"unit": ""
},
"style": "rule"
} | {
"index": 162,
"split": "train"
} |
||
For a macroscopic object of mass $1.0 \mathrm{~g}$ moving with speed $1.0 \mathrm{~cm} / \mathrm{s}$ in a one-dimensional box of length $1.0 \mathrm{~cm}$, find the quantum number $n$. | 3 | 3 | $10^{26}$ | quan | 2.11 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor a macroscopic object of mass $1.0 \\mathrm{~g}$ moving with speed $1.0 \\mathrm{~cm} / \\mathrm{s}$ in a one-dimensional box of length $1.0 \\mathrm{~cm}$, find the quantum number $n$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3",
"unit": "$10^{26}$"
},
"style": "rule"
} | {
"index": 163,
"split": "train"
} |
||
For the $\mathrm{H}_2$ ground electronic state, $D_0=4.4781 \mathrm{eV}$. Find $\Delta H_0^{\circ}$ for $\mathrm{H}_2(g) \rightarrow 2 \mathrm{H}(g)$ in $\mathrm{kJ} / \mathrm{mol}$ | 432.07 | 432.07 | $\mathrm{~kJ} / \mathrm{mol}$ | quan | 13.2 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor the $\\mathrm{H}_2$ ground electronic state, $D_0=4.4781 \\mathrm{eV}$. Find $\\Delta H_0^{\\circ}$ for $\\mathrm{H}_2(g) \\rightarrow 2 \\mathrm{H}(g)$ in $\\mathrm{kJ} / \\mathrm{mol}$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "432.07",
"unit": " $\\mathrm{~kJ} / \\mathrm{mol}$"
},
"style": "rule"
} | {
"index": 164,
"split": "train"
} |
||
The contribution of molecular vibrations to the molar internal energy $U_{\mathrm{m}}$ of a gas of nonlinear $N$-atom molecules is (zero-point vibrational energy not included) $U_{\mathrm{m}, \mathrm{vib}}=R \sum_{s=1}^{3 N-6} \theta_s /\left(e^{\theta_s / T}-1\right)$, where $\theta_s \equiv h \nu_s / k$ and $\nu_s$ is the vibrational frequency of normal mode $s$. Calculate the contribution to $U_{\mathrm{m}, \text { vib }}$ at $25^{\circ} \mathrm{C}$ of a normal mode with wavenumber $\widetilde{v} \equiv v_s / c$ of $900 \mathrm{~cm}^{-1}$. | 0.14 | 0.14 | $\mathrm{kJ} / \mathrm{mol}$ | quan | 15.39 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe contribution of molecular vibrations to the molar internal energy $U_{\\mathrm{m}}$ of a gas of nonlinear $N$-atom molecules is (zero-point vibrational energy not included) $U_{\\mathrm{m}, \\mathrm{vib}}=R \\sum_{s=1}^{3 N-6} \\theta_s /\\left(e^{\\theta_s / T}-1\\right)$, where $\\theta_s \\equiv h \\nu_s / k$ and $\\nu_s$ is the vibrational frequency of normal mode $s$. Calculate the contribution to $U_{\\mathrm{m}, \\text { vib }}$ at $25^{\\circ} \\mathrm{C}$ of a normal mode with wavenumber $\\widetilde{v} \\equiv v_s / c$ of $900 \\mathrm{~cm}^{-1}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.14",
"unit": " $\\mathrm{kJ} / \\mathrm{mol}$"
},
"style": "rule"
} | {
"index": 165,
"split": "train"
} |
||
Calculate the magnitude of the spin magnetic moment of an electron. | 1.61 | 1.61 | $10^{-23} \mathrm{~J} / \mathrm{T}$ | quan | 10.17 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the magnitude of the spin magnetic moment of an electron.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.61",
"unit": " $10^{-23} \\mathrm{~J} / \\mathrm{T}$"
},
"style": "rule"
} | {
"index": 166,
"split": "train"
} |
||
A particle is subject to the potential energy $V=a x^4+b y^4+c z^4$. If its ground-state energy is $10 \mathrm{eV}$, calculate $\langle V\rangle$ for the ground state. | $3 rac{1}{3}$ | 3.333333333 | $\mathrm{eV}$ | quan | 14.29 | screenshot answer is weird | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA particle is subject to the potential energy $V=a x^4+b y^4+c z^4$. If its ground-state energy is $10 \\mathrm{eV}$, calculate $\\langle V\\rangle$ for the ground state.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3.333333333",
"unit": " $\\mathrm{eV}$"
},
"style": "rule"
} | {
"index": 167,
"split": "train"
} |
|
For an electron in a certain rectangular well with a depth of $20.0 \mathrm{eV}$, the lowest energy level lies $3.00 \mathrm{eV}$ above the bottom of the well. Find the width of this well. Hint: Use $\tan \theta=\sin \theta / \cos \theta$ | 0.264 | 0.264 | $\mathrm{~nm}$ | quan | 2.27 | hint | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nFor an electron in a certain rectangular well with a depth of $20.0 \\mathrm{eV}$, the lowest energy level lies $3.00 \\mathrm{eV}$ above the bottom of the well. Find the width of this well. Hint: Use $\\tan \\theta=\\sin \\theta / \\cos \\theta$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.264",
"unit": "$\\mathrm{~nm}$"
},
"style": "rule"
} | {
"index": 168,
"split": "train"
} |
|
Calculate the uncertainty $\Delta L_z$ for the hydrogen-atom stationary state: $2 p_z$. | 0 | 0 | quan | 7.56 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the uncertainty $\\Delta L_z$ for the hydrogen-atom stationary state: $2 p_z$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0",
"unit": " "
},
"style": "rule"
} | {
"index": 169,
"split": "train"
} |
|||
Calculate the de Broglie wavelength for an electron with a kinetic energy of $100 \mathrm{eV}$ | 0.123 | 0.123 | nm | chemmc | 1-38 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the de Broglie wavelength for an electron with a kinetic energy of $100 \\mathrm{eV}$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.123",
"unit": "nm "
},
"style": "rule"
} | {
"index": 170,
"split": "train"
} |
||
The threshold wavelength for potassium metal is $564 \mathrm{~nm}$. What is its work function?
| 3.52 | 3.52 | $10^{-19} \mathrm{~J}$ | chemmc | 1-18 | Only the first part, the work function is taken | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe threshold wavelength for potassium metal is $564 \\mathrm{~nm}$. What is its work function? \r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3.52",
"unit": "$10^{-19} \\mathrm{~J}$"
},
"style": "rule"
} | {
"index": 171,
"split": "train"
} |
|
Evaluate the series
$$
S=\sum_{n=0}^{\infty} \frac{1}{3^n}
$$ | 3 / 2 | 1.5 | chemmc | D-7 | Math Part D (after chapter 4) | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nEvaluate the series\r\n$$\r\nS=\\sum_{n=0}^{\\infty} \\frac{1}{3^n}\r\n$$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.5",
"unit": " "
},
"style": "rule"
} | {
"index": 172,
"split": "train"
} |
||
The relationship introduced in Problem $1-48$ has been interpreted to mean that a particle of mass $m\left(E=m c^2\right)$ can materialize from nothing provided that it returns to nothing within a time $\Delta t \leq h / m c^2$. Particles that last for time $\Delta t$ or more are called real particles; particles that last less than time $\Delta t$ are called virtual particles. The mass of the charged pion, a subatomic particle, is $2.5 \times 10^{-28} \mathrm{~kg}$. What is the minimum lifetime if the pion is to be considered a real particle? | 2.9 | 2.9 | $10^{-23} \mathrm{~s}$ | chemmc | 1-49 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe relationship introduced in Problem $1-48$ has been interpreted to mean that a particle of mass $m\\left(E=m c^2\\right)$ can materialize from nothing provided that it returns to nothing within a time $\\Delta t \\leq h / m c^2$. Particles that last for time $\\Delta t$ or more are called real particles; particles that last less than time $\\Delta t$ are called virtual particles. The mass of the charged pion, a subatomic particle, is $2.5 \\times 10^{-28} \\mathrm{~kg}$. What is the minimum lifetime if the pion is to be considered a real particle?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2.9",
"unit": "$10^{-23} \\mathrm{~s}$ "
},
"style": "rule"
} | {
"index": 173,
"split": "train"
} |
||
A household lightbulb is a blackbody radiator. Many lightbulbs use tungsten filaments that are heated by an electric current. What temperature is needed so that $\lambda_{\max }=550 \mathrm{~nm}$ ? | 5300 | 5300 | $\mathrm{~K}$
| chemmc | 1-17 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA household lightbulb is a blackbody radiator. Many lightbulbs use tungsten filaments that are heated by an electric current. What temperature is needed so that $\\lambda_{\\max }=550 \\mathrm{~nm}$ ?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "5300",
"unit": " $\\mathrm{~K}$\r\n"
},
"style": "rule"
} | {
"index": 174,
"split": "train"
} |
||
Evaluate the series
$$
S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots
$$
| 1 | 1 | chemmc | D-6 | Math Part D (after chapter 4) | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nEvaluate the series\r\n$$\r\nS=\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{16}+\\cdots\r\n$$\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1",
"unit": " "
},
"style": "rule"
} | {
"index": 175,
"split": "train"
} |
||
Through what potential must a proton initially at rest fall so that its de Broglie wavelength is $1.0 \times 10^{-10} \mathrm{~m}$ ? | 0.082 | 0.082 | V | chemmc | 1-40 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThrough what potential must a proton initially at rest fall so that its de Broglie wavelength is $1.0 \\times 10^{-10} \\mathrm{~m}$ ?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.082",
"unit": "V "
},
"style": "rule"
} | {
"index": 176,
"split": "train"
} |
||
Example 5-3 shows that a Maclaurin expansion of a Morse potential leads to
$$
V(x)=D \beta^2 x^2+\cdots
$$
Given that $D=7.31 \times 10^{-19} \mathrm{~J} \cdot$ molecule ${ }^{-1}$ and $\beta=1.81 \times 10^{10} \mathrm{~m}^{-1}$ for $\mathrm{HCl}$, calculate the force constant of $\mathrm{HCl}$. | 479 | 479 | $\mathrm{~N} \cdot \mathrm{m}^{-1}$ | chemmc | 5-9 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nExample 5-3 shows that a Maclaurin expansion of a Morse potential leads to\r\n$$\r\nV(x)=D \\beta^2 x^2+\\cdots\r\n$$\r\nGiven that $D=7.31 \\times 10^{-19} \\mathrm{~J} \\cdot$ molecule ${ }^{-1}$ and $\\beta=1.81 \\times 10^{10} \\mathrm{~m}^{-1}$ for $\\mathrm{HCl}$, calculate the force constant of $\\mathrm{HCl}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "479",
"unit": "$\\mathrm{~N} \\cdot \\mathrm{m}^{-1}$ "
},
"style": "rule"
} | {
"index": 177,
"split": "train"
} |
||
A line in the Lyman series of hydrogen has a wavelength of $1.03 \times 10^{-7} \mathrm{~m}$. Find the original energy level of the electron. | 3 | 3 | chemmc | 1-25 | no units | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA line in the Lyman series of hydrogen has a wavelength of $1.03 \\times 10^{-7} \\mathrm{~m}$. Find the original energy level of the electron.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3",
"unit": " "
},
"style": "rule"
} | {
"index": 178,
"split": "train"
} |
||
A helium-neon laser (used in supermarket scanners) emits light at $632.8 \mathrm{~nm}$. Calculate the frequency of this light. | 4.738 | 4.738 | $10^{14} \mathrm{~Hz}$ | chemmc | 1-15 | just the first part is taken: frequency of light | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA helium-neon laser (used in supermarket scanners) emits light at $632.8 \\mathrm{~nm}$. Calculate the frequency of this light.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "4.738",
"unit": "$10^{14} \\mathrm{~Hz}$ "
},
"style": "rule"
} | {
"index": 179,
"split": "train"
} |
|
What is the uncertainty of the momentum of an electron if we know its position is somewhere in a $10 \mathrm{pm}$ interval? | 6.6 | 6.6 | $10^{-23} \mathrm{~kg} \cdot \mathrm{m} \cdot \mathrm{s}^{-1}$ | chemmc | 1-47 | discard the second part of the answer | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nWhat is the uncertainty of the momentum of an electron if we know its position is somewhere in a $10 \\mathrm{pm}$ interval?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": " 6.6",
"unit": " $10^{-23} \\mathrm{~kg} \\cdot \\mathrm{m} \\cdot \\mathrm{s}^{-1}$"
},
"style": "rule"
} | {
"index": 180,
"split": "train"
} |
|
Using the Bohr theory, calculate the ionization energy (in electron volts and in $\mathrm{kJ} \cdot \mathrm{mol}^{-1}$ ) of singly ionized helium. | 54.394 | 54.394 | $\mathrm{eV}$ | chemmc | 1-34 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nUsing the Bohr theory, calculate the ionization energy (in electron volts and in $\\mathrm{kJ} \\cdot \\mathrm{mol}^{-1}$ ) of singly ionized helium.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "54.394",
"unit": "$\\mathrm{eV}$ "
},
"style": "rule"
} | {
"index": 181,
"split": "train"
} |
||
When an excited nucleus decays, it emits a $\gamma$ ray. The lifetime of an excited state of a nucleus is of the order of $10^{-12} \mathrm{~s}$. What is the uncertainty in the energy of the $\gamma$ ray produced? | 7 | 7 | $10^{-22} \mathrm{~J}$ | chemmc | 1-51 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nWhen an excited nucleus decays, it emits a $\\gamma$ ray. The lifetime of an excited state of a nucleus is of the order of $10^{-12} \\mathrm{~s}$. What is the uncertainty in the energy of the $\\gamma$ ray produced?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "7",
"unit": "$10^{-22} \\mathrm{~J}$ "
},
"style": "rule"
} | {
"index": 182,
"split": "train"
} |
||
Calculate the wavelength and the energy of a photon associated with the series limit of the Lyman series. | 91.17 | 91.17 | nm | chemmc | 1-28 | only the first part of the question, the wavelength | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the wavelength and the energy of a photon associated with the series limit of the Lyman series.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "91.17",
"unit": "nm "
},
"style": "rule"
} | {
"index": 183,
"split": "train"
} |
|
Given a context information that there is also an uncertainty principle for energy and time:
$$
\Delta E \Delta t \geq h
$$, another application of the relationship has to do with the excitedstate energies and lifetimes of atoms and molecules. If we know that the lifetime of an excited state is $10^{-9} \mathrm{~s}$, then what is the uncertainty in the energy of this state? | 7 | 7 | $10^{-25} \mathrm{~J}$ | chemmc | 1-50 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nGiven a context information that there is also an uncertainty principle for energy and time:\n$$\n\\Delta E \\Delta t \\geq h\n$$, another application of the relationship has to do with the excitedstate energies and lifetimes of atoms and molecules. If we know that the lifetime of an excited state is $10^{-9} \\mathrm{~s}$, then what is the uncertainty in the energy of this state?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "7",
"unit": " $10^{-25} \\mathrm{~J}$"
},
"style": "rule"
} | {
"index": 184,
"split": "train"
} |
||
One of the most powerful modern techniques for studying structure is neutron diffraction. This technique involves generating a collimated beam of neutrons at a particular temperature from a high-energy neutron source and is accomplished at several accelerator facilities around the world. If the speed of a neutron is given by $v_{\mathrm{n}}=\left(3 k_{\mathrm{B}} T / m\right)^{1 / 2}$, where $m$ is the mass of a neutron, then what temperature is needed so that the neutrons have a de Broglie wavelength of $50 \mathrm{pm}$ ? | 2500 | 2500 | $\mathrm{K}$ | chemmc | 1-42 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nOne of the most powerful modern techniques for studying structure is neutron diffraction. This technique involves generating a collimated beam of neutrons at a particular temperature from a high-energy neutron source and is accomplished at several accelerator facilities around the world. If the speed of a neutron is given by $v_{\\mathrm{n}}=\\left(3 k_{\\mathrm{B}} T / m\\right)^{1 / 2}$, where $m$ is the mass of a neutron, then what temperature is needed so that the neutrons have a de Broglie wavelength of $50 \\mathrm{pm}$ ?\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2500",
"unit": "$\\mathrm{K}$ "
},
"style": "rule"
} | {
"index": 185,
"split": "train"
} |
||
The temperature of the fireball in a thermonuclear explosion can reach temperatures of approximately $10^7 \mathrm{~K}$. What value of $\lambda_{\max }$ does this correspond to? | 3 | 3 | $10^{-10} \mathrm{~m}$
| chemmc | 1-8 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe temperature of the fireball in a thermonuclear explosion can reach temperatures of approximately $10^7 \\mathrm{~K}$. What value of $\\lambda_{\\max }$ does this correspond to? \n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3",
"unit": " $10^{-10} \\mathrm{~m}$\r\n"
},
"style": "rule"
} | {
"index": 186,
"split": "train"
} |
||
Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit
$$
\lim _{x \rightarrow 0} \frac{\ln (1+x)-x}{x^2}
$$
both ways and report the final result. | -1/2 | -0.5 | chemmc | D-21 | Math Part D (after chapter 4) | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nShow that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit\r\n$$\r\n\\lim _{x \\rightarrow 0} \\frac{\\ln (1+x)-x}{x^2}\r\n$$\r\nboth ways and report the final result.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "-0.5",
"unit": " "
},
"style": "rule"
} | {
"index": 187,
"split": "train"
} |
||
Evaluate the series
$$
S=\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2^n}
$$ | 1/3 | 0.3333333 | chemmc | D-8 | Math Part D (after chapter 4) | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nEvaluate the series\r\n$$\r\nS=\\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{2^n}\r\n$$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.3333333",
"unit": " "
},
"style": "rule"
} | {
"index": 188,
"split": "train"
} |
||
Calculate the percentage difference between $\ln (1+x)$ and $x$ for $x=0.0050$ | 0.249 | 0.249 | % | chemmc | D-4 | Math Part D (after chapter 4) | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the percentage difference between $\\ln (1+x)$ and $x$ for $x=0.0050$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.249",
"unit": " %"
},
"style": "rule"
} | {
"index": 189,
"split": "train"
} |
|
Calculate the reduced mass of a nitrogen molecule in which both nitrogen atoms have an atomic mass of 14.00. | 7.00 | 7.00 | chemmc | 1-30 | no units | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the reduced mass of a nitrogen molecule in which both nitrogen atoms have an atomic mass of 14.00.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "7.00",
"unit": " "
},
"style": "rule"
} | {
"index": 190,
"split": "train"
} |
||
Two narrow slits are illuminated with red light of wavelength $694.3 \mathrm{~nm}$ from a laser, producing a set of evenly placed bright bands on a screen located $3.00 \mathrm{~m}$ beyond the slits. If the distance between the bands is $1.50 \mathrm{~cm}$, then what is the distance between the slits?
| 0.139 | 0.139 | mm | chemmc | 1-45 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nTwo narrow slits are illuminated with red light of wavelength $694.3 \\mathrm{~nm}$ from a laser, producing a set of evenly placed bright bands on a screen located $3.00 \\mathrm{~m}$ beyond the slits. If the distance between the bands is $1.50 \\mathrm{~cm}$, then what is the distance between the slits?\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "0.139",
"unit": "mm "
},
"style": "rule"
} | {
"index": 191,
"split": "train"
} |
||
Calculate the energy associated with an $\alpha$ particle that has fallen through a potential difference of $4.0 \mathrm{~V}$. Take the mass of an $\alpha$ particle to be $6.64 \times 10^{-27} \mathrm{~kg}$. | 1.3 | 1.3 | $10^{-18} \mathrm{~J} / \alpha \text {-particle}$ | chemmc | 1-41 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the energy associated with an $\\alpha$ particle that has fallen through a potential difference of $4.0 \\mathrm{~V}$. Take the mass of an $\\alpha$ particle to be $6.64 \\times 10^{-27} \\mathrm{~kg}$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.3",
"unit": "$10^{-18} \\mathrm{~J} / \\alpha \\text {-particle}$"
},
"style": "rule"
} | {
"index": 192,
"split": "train"
} |
||
Calculate the number of photons in a $2.00 \mathrm{~mJ}$ light pulse at (a) $1.06 \mu \mathrm{m}$
| 1.07 | 1.07 | $10^{16}$ photons | chemmc | 1-13 | part (a) only | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nCalculate the number of photons in a $2.00 \\mathrm{~mJ}$ light pulse at (a) $1.06 \\mu \\mathrm{m}$\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.07",
"unit": " $10^{16}$ photons"
},
"style": "rule"
} | {
"index": 193,
"split": "train"
} |
|
The force constant of ${ }^{35} \mathrm{Cl}^{35} \mathrm{Cl}$ is $319 \mathrm{~N} \cdot \mathrm{m}^{-1}$. Calculate the fundamental vibrational frequency | 556 | 556 | $\mathrm{~cm}^{-1}$ | chemmc | 5-14 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nThe force constant of ${ }^{35} \\mathrm{Cl}^{35} \\mathrm{Cl}$ is $319 \\mathrm{~N} \\cdot \\mathrm{m}^{-1}$. Calculate the fundamental vibrational frequency\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "556",
"unit": " $\\mathrm{~cm}^{-1}$"
},
"style": "rule"
} | {
"index": 194,
"split": "train"
} |
||
$$
\text {Calculate the energy of a photon for a wavelength of } 100 \mathrm{pm} \text { (about one atomic diameter). }
$$
| 2 | 2 | $10^{-15} \mathrm{~J}$ | chemmc | 1-11 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\n$$\r\n\\text {Calculate the energy of a photon for a wavelength of } 100 \\mathrm{pm} \\text { (about one atomic diameter). }\r\n$$\r\n\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "2",
"unit": " $10^{-15} \\mathrm{~J}$"
},
"style": "rule"
} | {
"index": 195,
"split": "train"
} |
||
A proton and a negatively charged $\mu$ meson (called a muon) can form a short-lived species called a mesonic atom. The charge of a muon is the same as that on an electron and the mass of a muon is $207 m_{\mathrm{e}}$. Assume that the Bohr theory can be applied to such a mesonic atom and calculate the frequency associated with the $n=1$ to $n=2$ transition in a mesonic atom. | 1.69 | 4.59 | $10^{17} \mathrm{~Hz}$ | chemmc | 1-37 | only the ground state energy is there | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nA proton and a negatively charged $\\mu$ meson (called a muon) can form a short-lived species called a mesonic atom. The charge of a muon is the same as that on an electron and the mass of a muon is $207 m_{\\mathrm{e}}$. Assume that the Bohr theory can be applied to such a mesonic atom and calculate the frequency associated with the $n=1$ to $n=2$ transition in a mesonic atom.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "4.59",
"unit": "$10^{17} \\mathrm{~Hz}$"
},
"style": "rule"
} | {
"index": 196,
"split": "train"
} |
|
$$
\beta=2 \pi c \tilde{\omega}_{\mathrm{obs}}\left(\frac{\mu}{2 D}\right)^{1 / 2}
$$
Given that $\tilde{\omega}_{\mathrm{obs}}=2886 \mathrm{~cm}^{-1}$ and $D=440.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{H}^{35} \mathrm{Cl}$, calculate $\beta$. | 1.81 | 1.81 | $10^{10} \mathrm{~m}^{-1}$ | chemmc | 5-10 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\n$$\r\n\\beta=2 \\pi c \\tilde{\\omega}_{\\mathrm{obs}}\\left(\\frac{\\mu}{2 D}\\right)^{1 / 2}\r\n$$\r\nGiven that $\\tilde{\\omega}_{\\mathrm{obs}}=2886 \\mathrm{~cm}^{-1}$ and $D=440.2 \\mathrm{~kJ} \\cdot \\mathrm{mol}^{-1}$ for $\\mathrm{H}^{35} \\mathrm{Cl}$, calculate $\\beta$.\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "1.81",
"unit": " $10^{10} \\mathrm{~m}^{-1}$"
},
"style": "rule"
} | {
"index": 197,
"split": "train"
} |
||
Two narrow slits separated by $0.10 \mathrm{~mm}$ are illuminated by light of wavelength $600 \mathrm{~nm}$. If a detector is located $2.00 \mathrm{~m}$ beyond the slits, what is the distance between the central maximum and the first maximum? | 12 | 12 | mm | chemmc | 1-44 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\nTwo narrow slits separated by $0.10 \\mathrm{~mm}$ are illuminated by light of wavelength $600 \\mathrm{~nm}$. If a detector is located $2.00 \\mathrm{~m}$ beyond the slits, what is the distance between the central maximum and the first maximum?\n<|im_end|>\n<|im_start|>assistant\n<think>",
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| logic | {
"ground_truth": {
"answer_number": "12",
"unit": " mm"
},
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} | {
"index": 198,
"split": "train"
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||
$$
\text { If we locate an electron to within } 20 \mathrm{pm} \text {, then what is the uncertainty in its speed? }
$$ | 3.7 | 3.7 | $10^7 \mathrm{~m} \cdot \mathrm{s}^{-1}$ | chemmc | 1-46 | scibench | [
{
"content": "<|im_start|>system\nA conversation between User and Assistant. The user asks a question, and the assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>.\n<|im_end|>\n<|im_start|>user\n$$\r\n\\text { If we locate an electron to within } 20 \\mathrm{pm} \\text {, then what is the uncertainty in its speed? }\r\n$$\n<|im_end|>\n<|im_start|>assistant\n<think>",
"role": "user"
}
]
| logic | {
"ground_truth": {
"answer_number": "3.7",
"unit": "$10^7 \\mathrm{~m} \\cdot \\mathrm{s}^{-1}$ "
},
"style": "rule"
} | {
"index": 199,
"split": "train"
} |
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