| {"id": 5, "assessment_name": "missouri_eoc", "assessment_type": "standalone", "subject": "maths", "domain": "Statistics and Probability", "context": "Mrs. Krum's class consists of freshmen and sophomores. She asked each student which social media platform they preferred and compiled the data into a two- way frequency table.\n\nSocial Media Preference in Mrs. Krum's Class\n\n<table><tr><td></td><td>Social Media A</td><td>Social Media B</td><td>Total</td></tr><tr><td>Freshmen</td><td>5</td><td>3</td><td>8</td></tr><tr><td>Sophomore</td><td>7</td><td>10</td><td>17</td></tr><tr><td>Total</td><td>12</td><td>13</td><td>25</td></tr></table>\n\nEnter the answers in the boxes.\n\nFor freshmen, what is the probability that they prefer Social Media A?", "table_context": null, "table": "| | Social Media A | Social Media B | Total |\n| --- | --- | --- | --- |\n| Freshmen | 5 | 3 | 8 |\n| Sophomore | 7 | 10 | 17 |\n| Total | 12 | 13 | 25 |", "question": "For freshmen, what is the probability that they prefer Social Media A?", "answer": "$\\frac{5}{8}$", "split": "val", "answer_type": "numerical_value", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 174, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "redox", "context": "Aluminum is a highly reducing metal.\n\nThe standard reduction potentials for Al³⁺(aq) and Fe³⁺(aq) are\n\nAl³⁺ (aq) + 3 e⁻ → Al (s) E°red = -1.66 V\nFe³⁺ (aq) + 3 e⁻ → Fe (s) E°red = -0.04 V\n\nand the standard S° values for these species are", "table_context": null, "table": "| species | S° (J/mol K) |\n| --- | --- |\n| Al (s) | 28 |\n| Fe (s) | 27 |\n| Al³⁺ (aq) | -293.3 |\n| Fe³⁺ (aq) | -313.8 |", "question": "Calculate ΔG° for the reduction of Fe³⁺(aq) by Al at 25°C.", "answer": "E° = E°red − E°anode\nΔG° = −nFE°\nE° = 0.04 V − (−1.66 V)\nΔG° = −3 × (96500 J mol⁻¹ V⁻¹) × 1.70 V\nE° = 1.70 V\nΔG° = −492150 J mol⁻¹ ≈ −492 kJ mol⁻¹", "split": "val", "answer_type": "equation_or_expression", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 175, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "redox", "context": "Aluminum is a highly reducing metal.\n\nThe standard reduction potentials for Al³⁺(aq) and Fe³⁺(aq) are\n\nAl³⁺ (aq) + 3 e⁻ → Al (s) E°red = -1.66 V\nFe³⁺ (aq) + 3 e⁻ → Fe (s) E°red = -0.04 V\n\nand the standard S° values for these species are", "table_context": null, "table": "| species | S° (J/mol K) |\n| --- | --- |\n| Al (s) | 28 |\n| Fe (s) | 27 |\n| Al³⁺ (aq) | -293.3 |\n| Fe³⁺ (aq) | -313.8 |", "question": "Calculate ΔS° for the reduction of Fe³⁺(aq) by Al.", "answer": "ΔS° = S°Al³⁺ + S°Fe − [S°Al + S°Fe³⁺]\nΔS° = −293.3 + 27 − [28 − 313.8]\nΔS° = −266.3 − [−285.8]\nΔS° = 19.5 J mol⁻¹ K⁻¹", "split": "val", "answer_type": "equation_or_expression", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 176, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "redox", "context": "Aluminum is a highly reducing metal.\n\nThe standard reduction potentials for Al³⁺(aq) and Fe³⁺(aq) are\n\nAl³⁺ (aq) + 3 e⁻ → Al (s) E°red = -1.66 V\nFe³⁺ (aq) + 3 e⁻ → Fe (s) E°red = -0.04 V\n\nand the standard S° values for these species are", "table_context": null, "table": "| species | S° (J/mol K) |\n| --- | --- |\n| Al (s) | 28 |\n| Fe (s) | 27 |\n| Al³⁺ (aq) | -293.3 |\n| Fe³⁺ (aq) | -313.8 |", "question": "Calculate ΔH° for the reduction of Fe³⁺(aq) by Al at 25°C.", "answer": "ΔG° = ΔH° − TΔS°\nΔH° = ΔG° + TΔS°\nΔH° = −468990 J + 298 K × 19.5 J K⁻¹\nΔH° = −463179 J mol⁻¹\nΔH° = −463.2 kJ mol⁻¹", "split": "val", "answer_type": "equation_or_expression", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 185, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "thermochemistry_thermodynamics", "context": "For liquid benzene, $\\Delta H^\\circ_{\\text{combustion}}=-3273\\ \\text{kJ mol}^{-1}$. Complete combustion produces $\\text{CO}_2$ and $\\text{H}_2\\text{O}$.", "table_context": "Bond energies used in the benzene combustion estimate.", "table": "| Bond | C-H | C-O | C=O | C≡O | H-O | O-O | O=O |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| Energy, kJ/mol | 414 | 351 | 799 | 1070 | 464 | 142 | 498 |", "question": "Use the bond energies below to calculate an estimated bond energy of the carbon-carbon bonds in benzene.", "answer": "$$\\Delta H_{\\text{comb}} = 12 \\text{ BE}_{C=O} + 6 \\text{ BE}_{HO} + [6 \\text{ BE}_{C-H} + 6 \\text{ BE}_{C-C} + 7.5 \\text{ BE}_{O=O}]$$\n$$-3273 = - [12(799) + 6(464)] + [6(414) + 6 \\text{ BE}_{C-C} + 7.5(498)]$$\n$$-3273 = - [9588 + 2784] + [2484 + 3735 + 6 \\text{ BE}_{C-C}]$$\n$$-3273 = - 12372 + [6219 + 6 \\text{ BE}_{C-C}]$$\n$$-3273 + 12372 - 6219 = 6 \\text{ BE}_{C-C}$$\n$$6 \\text{ BE}_{C-C} = 2880$$\n$$\\text{BE}_{C-C} = 480$$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 186, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "thermochemistry_thermodynamics", "context": "The combustion enthalpy of liquid benzene is given in the accompanying thermodynamic table.", "table_context": "Standard enthalpy of formation, standard entropy, and combustion enthalpy data for liquid and gaseous benzene.", "table": "| | \\Delta H_f^\\circ , kJ/mol | S^\\circ , \\text{J}\\cdot\\text{mol}^{-1}\\cdot\\text{K}^{-1} | \\Delta H^\\circ_{\\text{combustion}} , kJ/mol |\n| --- | --- | --- | --- |\n| \\text{C}_6\\text{H}_6(l) | 48.7 | 173.3 | -3273 |\n| \\text{C}_6\\text{H}_6(g) | 82.9 | 269.0 | NA |", "question": "1.50 g of benzene is burned in a bomb calorimeter with a heat capacity of 5.99 kJ/$^\\circ\\text{C}$ submerged in 1.00 kg of water at 22.50 $^\\circ\\text{C}$. Determine the final temperature of the system. [Specific heat of $\\text{H}_2\\text{O}(l)$ = 4.18 $\\text{J}\\cdot\\text{g}^{-1}\\cdot{}^\\circ\\text{C}^{-1}$]", "answer": "$$1.50 \\text{ g } C_6H_6 \\times \\frac{\\text{mol}}{78.11 \\text{ g}} = 0.0192 \\text{ mol}$$\n$$0.0192 \\text{ mol} \\times 3273 \\text{ kJ/mol} = 62.8 \\text{ kJ released}$$\n$$5.99 \\text{ kJ}/^\\circ\\text{C} + 4.18 \\text{ kJ}/^\\circ\\text{C} = 10.17 \\text{ kJ}/^\\circ\\text{C}$$\n$$62.8 \\text{ kJ} \\times \\frac{1^\\circ\\text{C}}{10.17 \\text{ kJ}} = 6.18^\\circ\\text{C}$$\n$$22.50^\\circ\\text{C} + 6.18^\\circ\\text{C} = 28.68^\\circ\\text{C} \\text{ final T}$$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 187, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "solutions_mixtures", "context": "Solution 1 consists of chloroform and carbon tetrachloride, which form an ideal solution at 25 $^\\circ\\text{C}$.", "table_context": "Pure-component vapor pressures at 25 °C.", "table": "| Substance | \\text{CCl}_4 | \\text{CHCl}_3 | \\text{CH}_3\\text{C(O)CH}_3 |\n| --- | --- | --- | --- |\n| Vapor pressure at 25^\\circ\\text{C} , torr | 98.8 | 172.5 | 222 |", "question": "Sketch a graph of vapor pressure vs. mole fraction $\\text{CHCl}_3$ for a $\\text{CHCl}_3$-$\\text{CCl}_4$ solution at 25 $^\\circ\\text{C}$ and predict the vapor pressure at mole fraction $\\text{CHCl}_3=0.30$.", "answer": "$$\\text{VP} = (.30 \\times 172.5) + (0.70 \\times 98.8)$$ $$\\text{VP} = 51.75 + 69.16$$ $$\\text{VP} = 120.9 \\text{ mmHg}$$", "split": "val", "answer_type": "equation_or_expression", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 188, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "solutions_mixtures", "context": "Solution 1 consists of chloroform and carbon tetrachloride, which form an ideal solution at 25 $^\\circ\\text{C}$.", "table_context": "Pure-component vapor pressures at 25 °C.", "table": "| Substance | \\text{CCl}_4 | \\text{CHCl}_3 | \\text{CH}_3\\text{C(O)CH}_3 |\n| --- | --- | --- | --- |\n| Vapor pressure at 25^\\circ\\text{C} , torr | 98.8 | 172.5 | 222 |", "question": "Describe how the composition of the vapor over this solution compares with the composition of the solution. Justify your answer.", "answer": "Vapor will be richer in $\\text{CHCl}_3$ than solution because $\\text{CHCl}_3$ has a higher VP.", "split": "val", "answer_type": "equation_or_expression", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 207, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "thermochemistry_thermodynamics", "context": "The Mond process purifies nickel metal from impurities such as iron and cobalt by forming volatile nickel tetracarbonyl:\n\n$$\\text{Ni}(s) + 4\\text{CO}(g) \\rightarrow \\text{Ni}(\\text{CO})_4(g)$$", "table_context": "Standard enthalpies of formation and standard molar entropies for Ni(s), Ni(g), CO(g), and Ni(CO)4(g).", "table": "| | Ni(s) | Ni(g) | CO(g) | Ni(CO) 4 (g) |\n| --- | --- | --- | --- | --- |\n| \\Delta H^\\circ_f (\\text{kJ mol}^{-1}) | 0 | 430.1 | -110.5 | -607 |\n| S^\\circ (\\text{J mol}^{-1} \\text{ K}^{-1}) | 30 | 182.2 | 198 | 417 |", "question": "Calculate the average bond dissociation enthalpy for the nickel-carbon bonds in $\\text{Ni}(\\text{CO})_4(g)$.", "answer": "For the gas-phase reaction\n$$\\mathrm{Ni}(\\mathrm{CO})_{4}(g) \\rightarrow \\mathrm{Ni}(g) + 4 \\mathrm{CO}(g)$$\n$$\\Delta H^\\circ = 4 \\cdot (-110.5 \\mathrm{ kJ} \\mathrm{ mol}^{-1}) + 430 \\mathrm{ kJ} \\mathrm{ mol}^{-1} - (-607 \\mathrm{ kJ} \\mathrm{ mol}^{-1}) = 595 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$$\n\nSince this reaction involves breaking four nickel-CO bonds, the average BDE is $(595 \\mathrm{ kJ} \\mathrm{ mol}^{-1})/4 = 149 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$.", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 208, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "thermochemistry_thermodynamics", "context": "The Mond process purifies nickel metal from impurities such as iron and cobalt by forming volatile nickel tetracarbonyl:\n\n$$\\text{Ni}(s) + 4\\text{CO}(g) \\rightarrow \\text{Ni}(\\text{CO})_4(g)$$", "table_context": "Standard enthalpies of formation and standard molar entropies for Ni(s), Ni(g), CO(g), and Ni(CO)4(g).", "table": "| | Ni(s) | Ni(g) | CO(g) | Ni(CO) 4 (g) |\n| --- | --- | --- | --- | --- |\n| \\Delta H^\\circ_f (\\text{kJ mol}^{-1}) | 0 | 430.1 | -110.5 | -607 |\n| S^\\circ (\\text{J mol}^{-1} \\text{ K}^{-1}) | 30 | 182.2 | 198 | 417 |", "question": "Calculate $\\Delta H^\\circ_{\\text{rxn}}$ and $\\Delta S^\\circ_{\\text{rxn}}$ for the production of $\\text{Ni}(\\text{CO})_4(g)$ by the Mond process.", "answer": "$\\Delta H^\\circ_{\\mathrm{rxn}} = (-607 \\mathrm{ kJ} \\mathrm{ mol}^{-1}) - 4 \\cdot (-110.5 \\mathrm{ kJ} \\mathrm{ mol}^{-1}) = -165 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$ \n$$\\Delta S^\\circ_{\\mathrm{rxn}} = (417 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}) - 4 \\cdot (198 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}) - 30 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1} = -405 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}$$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 209, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "thermochemistry_thermodynamics", "context": "The Mond process purifies nickel metal from impurities such as iron and cobalt by forming volatile nickel tetracarbonyl:\n\n$$\\text{Ni}(s) + 4\\text{CO}(g) \\rightarrow \\text{Ni}(\\text{CO})_4(g)$$", "table_context": "Standard enthalpies of formation and standard molar entropies for Ni(s), Ni(g), CO(g), and Ni(CO)4(g).", "table": "| | Ni(s) | Ni(g) | CO(g) | Ni(CO) 4 (g) |\n| --- | --- | --- | --- | --- |\n| \\Delta H^\\circ_f (\\text{kJ mol}^{-1}) | 0 | 430.1 | -110.5 | -607 |\n| S^\\circ (\\text{J mol}^{-1} \\text{ K}^{-1}) | 30 | 182.2 | 198 | 417 |", "question": "The boiling point of $\\text{Ni}(\\text{CO})_4$ at 1 bar pressure is $42^\\circ\\text{C}$ and its heat of vaporization is $29.0\\text{ kJ mol}^{-1}$. Calculate $\\Delta H_f^\\circ$ and $S^\\circ$ for $\\text{Ni}(\\text{CO})_4(l)$.", "answer": "For:\n$$\\mathrm{Ni}(\\mathrm{CO})_{4}(l) \\rightarrow \\mathrm{Ni}(\\mathrm{CO})_{4}(g)$$\n\n$\\Delta G^\\circ_{\\mathrm{vap}} = 0$ at the boiling point at 1 bar pressure and $T = 315 \\mathrm{ K}$. $\\Delta H^\\circ_{\\mathrm{vap}} = 29.0 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$.\n\nSo:\n$$0 = 29000 \\mathrm{ J} \\mathrm{ mol}^{-1} - (315 \\mathrm{ K})(\\Delta S^\\circ_{\\mathrm{vap}})$$\n$$\\Delta S^\\circ_{\\mathrm{vap}} = 92.1 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}$$\n$$\\Delta H^\\circ_{\\mathrm{f}}(\\mathrm{Ni}(\\mathrm{CO})_{4}(g)) - \\Delta H^\\circ_{\\mathrm{f}}(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = \\Delta H^\\circ_{\\mathrm{vap}}$$\n$$-607 \\mathrm{ kJ} \\mathrm{ mol}^{-1} - \\Delta H^\\circ_{\\mathrm{f}}(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = 29.0 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$$\n$$\\Delta H^\\circ_{\\mathrm{f}}(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = -636 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$$\n$$S^\\circ(\\mathrm{Ni}(\\mathrm{CO})_{4}(g)) - S^\\circ(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = \\Delta S^\\circ_{\\mathrm{vap}}$$\n$$417 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1} - S^\\circ(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = 92.1 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}$$\n$$S^\\circ(\\mathrm{Ni}(\\mathrm{CO})_{4}(l)) = 325 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}$$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 210, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "equilibrium", "context": "The Mond process purifies nickel metal from impurities such as iron and cobalt by forming volatile nickel tetracarbonyl:\n\n$$\\text{Ni}(s) + 4\\text{CO}(g) \\rightarrow \\text{Ni}(\\text{CO})_4(g)$$", "table_context": "Standard enthalpies of formation and standard molar entropies for Ni(s), Ni(g), CO(g), and Ni(CO)4(g).", "table": "| | Ni(s) | Ni(g) | CO(g) | Ni(CO) 4 (g) |\n| --- | --- | --- | --- | --- |\n| \\Delta H^\\circ_f (\\text{kJ mol}^{-1}) | 0 | 430.1 | -110.5 | -607 |\n| S^\\circ (\\text{J mol}^{-1} \\text{ K}^{-1}) | 30 | 182.2 | 198 | 417 |", "question": "After the $\\text{Ni}(\\text{CO})_4$ vapor has been separated from the solid impurities, Ni metal is recovered by heating the $\\text{Ni}(\\text{CO})_4$ to high temperature, causing it to re-form nickel metal and carbon monoxide. At $230^\\circ\\text{C}$, what is the equilibrium pressure of $\\text{Ni}(\\text{CO})_4(g)$ in the presence of nickel metal, assuming that the carbon monoxide pressure is maintained at 0.10 bar?", "answer": "At $230^\\circ\\mathrm{C} = 503 \\mathrm{ K}$, $\\Delta G^\\circ_{\\mathrm{rxn}} = -165 \\mathrm{ kJ} \\mathrm{ mol}^{-1} - (503 \\mathrm{ K})(-405 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1}) = 39 \\mathrm{ kJ} \\mathrm{ mol}^{-1}$ \n$$K_{\\mathrm{eq}} = e^{-(39000 \\mathrm{ J} \\mathrm{ mol}^{-1})/(503 \\mathrm{ K} \\cdot 8.314 \\mathrm{ J} \\mathrm{ mol}^{-1} \\mathrm{ K}^{-1})} = 9.5 \\times 10^{-5}$$\n$$9.5 \\times 10^{-5} = \\frac{p(\\mathrm{Ni}(\\mathrm{CO})_{4})}{p(\\mathrm{CO})^{4}} = \\frac{p(\\mathrm{Ni}(\\mathrm{CO})_{4})}{(0.1)^{4}}$$\n$$p(\\mathrm{Ni}(\\mathrm{CO})_{4}) = 9.5 \\times 10^{-9} \\mathrm{ bar}$$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 211, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "redox", "context": "A solution is made by adding some $CuSO_4\\cdot5H_2O$ to water, followed by enough sulfuric acid to make the pH 1.00. Two platinum electrodes are placed in the 0.500 L solution, which is electrolyzed at a constant current of 0.120 A while gases evolved at the electrodes are captured separately. Initially, gas is evolved at the anode but not at the cathode. After 10.0 min, gas evolution begins at the cathode, and eventually the total volume of gas evolved at the cathode equals that evolved at the anode.", "table_context": "Standard reduction potentials for copper, oxygen, hydrogen peroxide, water, and hydrogen half-reactions.", "table": "| Half-Reaction | E^\\circ , V | Half-Reaction | E^\\circ , V |\n| --- | --- | --- | --- |\n| Cu^+(aq) + e^- \\rightarrow Cu(s) | 0.518 | Cu^{2+}(aq) + 2e^- \\rightarrow Cu(s) | 0.337 |\n| O_2(g) + 2H^+(aq) + 2e^- \\rightarrow H_2O_2(aq) | 1.780 | O_2(g) + 4H^+(aq) + 4e^- \\rightarrow 2H_2O(l) | 1.229 |\n| 2H^+(aq) + e^- \\rightarrow H_2(g) | 0.000 | | |", "question": "Write the balanced reaction that takes place initially in this electrolytic cell.", "answer": "$2 \\text{Cu}^{2+}(\\text{aq}) + 2 \\text{H}_2\\text{O}(\\ell) \\rightarrow 2 \\text{Cu}(\\text{s}) + \\text{O}_2(\\text{g}) + 4 \\text{H}^{+}(\\text{aq})$", "split": "val", "answer_type": "brief_explanation", "context_policy": "context_first_then_domain_knowledge"} |
| {"id": 212, "assessment_name": "olympiad", "assessment_type": "final", "subject": "chemistry", "domain": "redox", "context": "A solution is made by adding some $CuSO_4\\cdot5H_2O$ to water, followed by enough sulfuric acid to make the pH 1.00. Two platinum electrodes are placed in the 0.500 L solution, which is electrolyzed at a constant current of 0.120 A while gases evolved at the electrodes are captured separately. Initially, gas is evolved at the anode but not at the cathode. After 10.0 min, gas evolution begins at the cathode, and eventually the total volume of gas evolved at the cathode equals that evolved at the anode.", "table_context": "Standard reduction potentials for copper, oxygen, hydrogen peroxide, water, and hydrogen half-reactions.", "table": "| Half-Reaction | E^\\circ , V | Half-Reaction | E^\\circ , V |\n| --- | --- | --- | --- |\n| Cu^+(aq) + e^- \\rightarrow Cu(s) | 0.518 | Cu^{2+}(aq) + 2e^- \\rightarrow Cu(s) | 0.337 |\n| O_2(g) + 2H^+(aq) + 2e^- \\rightarrow H_2O_2(aq) | 1.780 | O_2(g) + 4H^+(aq) + 4e^- \\rightarrow 2H_2O(l) | 1.229 |\n| 2H^+(aq) + e^- \\rightarrow H_2(g) | 0.000 | | |", "question": "What is the initial cell potential for this reaction at 298 K? (In air, the partial pressure of $O_2(g)$ is 0.20 bar and the partial pressure of $H_2(g)$ may be taken to be $10^{-4}$ bar.)", "answer": "$E^\\circ = 0.337 \\text{ V} - 1.229 \\text{ V} = -0.892 \\text{ V}$ From the Nernst equation, $E = E^\\circ - (RT/nF)\\ln([P_{\\text{O}_2}][\\text{H}^{+}]^4/[\\text{Cu}^{2+}]^2)$ $= -0.892 \\text{ V} - (0.0591/4)\\log([0.20][0.1]^4/[7.46 \\times 10^{-4}]^2)$ $= -0.915 \\text{ V}$", "split": "val", "answer_type": "calculation_with_work", "context_policy": "context_first_then_domain_knowledge"} |
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