QuestionMay 24, 2025

A chemist fills a reaction vessel with 7,40 atm methanol (CH_(3)OH) gas, 5.16 atm oxygen (O_(2)) gas, 6.11 atm carbon dioxide (CO_(2)) gas, and 6.99 atm water (H_(2)O) gas at a temperature of 25.0^circ C Under these conditions, calculate the reaction free energy Delta G for the following chemical reaction: 2CH_(3)OH(g)+3O_(2)(g)leftharpoons 2CO_(2)(g)+4H_(2)O(g) Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule.

A chemist fills a reaction vessel with 7,40 atm methanol (CH_(3)OH) gas, 5.16 atm oxygen (O_(2)) gas, 6.11 atm carbon dioxide (CO_(2)) gas, and 6.99 atm water (H_(2)O) gas at a temperature of 25.0^circ C Under these conditions, calculate the reaction free energy Delta G for the following chemical reaction: 2CH_(3)OH(g)+3O_(2)(g)leftharpoons 2CO_(2)(g)+4H_(2)O(g) Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule.
A chemist fills a reaction vessel with 7,40 atm methanol (CH_(3)OH) gas, 5.16 atm oxygen (O_(2)) gas, 6.11 atm carbon dioxide (CO_(2)) gas, and 6.99 atm water
(H_(2)O) gas at a temperature of 25.0^circ C
Under these conditions, calculate the reaction free energy Delta G for the following chemical reaction:
2CH_(3)OH(g)+3O_(2)(g)leftharpoons 2CO_(2)(g)+4H_(2)O(g)
Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule.

Solution
4.5(260 votes)

Answer

\Delta G \approx -1369 \, kJ Explanation 1. Write the Reaction Quotient Q Q = \frac{(P_{CO_2})^2 (P_{H_2O})^4}{(P_{CH_3OH})^2 (P_{O_2})^3} where P represents partial pressures. 2. Calculate Q Substitute given pressures: Q = \frac{(6.11)^2 (6.99)^4}{(7.40)^2 (5.16)^3}. 3. Use \Delta G = \Delta G^\circ + RT \ln Q Given T = 298 K, R = 8.314 \, J/(mol \cdot K), and \Delta G^\circ = -1370 \, kJ/mol (from data tab). 4. Calculate \ln Q Compute Q from Step 2, then find \ln Q. 5. Calculate \Delta G \Delta G = -1370 \times 1000 + 8.314 \times 298 \times \ln Q. 6. Convert to kJ Divide result by 1000 to convert from J to kJ.

Explanation

1. Write the Reaction Quotient $Q$<br /> $Q = \frac{(P_{CO_2})^2 (P_{H_2O})^4}{(P_{CH_3OH})^2 (P_{O_2})^3}$ where $P$ represents partial pressures.<br /><br />2. Calculate $Q$<br /> Substitute given pressures: $Q = \frac{(6.11)^2 (6.99)^4}{(7.40)^2 (5.16)^3}$.<br /><br />3. Use $\Delta G = \Delta G^\circ + RT \ln Q$<br /> Given $T = 298 K$, $R = 8.314 \, J/(mol \cdot K)$, and $\Delta G^\circ = -1370 \, kJ/mol$ (from data tab).<br /><br />4. Calculate $\ln Q$<br /> Compute $Q$ from Step 2, then find $\ln Q$.<br /><br />5. Calculate $\Delta G$<br /> $\Delta G = -1370 \times 1000 + 8.314 \times 298 \times \ln Q$.<br /><br />6. Convert to kJ<br /> Divide result by 1000 to convert from J to kJ.
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