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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 76
Chapter 19, Problem 76

Consider the reaction: CO2(g) + CCl4(g) ⇌ 2 COCl2(g) Calculate ΔG for this reaction at 25 °C under the following conditions: i. PCO2 = 0.112 atm ii. PCCl4 = 0.174 atm iii. PCOCl2 = 0.744 atm

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1
Identify the reaction: CO_2(g) + CCl_4(g) ⇌ 2 COCl_2(g).
Use the formula for the reaction quotient, Q: Q = \frac{{(P_{COCl_2})^2}}{{P_{CO_2} \cdot P_{CCl_4}}}.
Substitute the given partial pressures into the expression for Q: P_{CO_2} = 0.112 \text{ atm}, P_{CCl_4} = 0.174 \text{ atm}, P_{COCl_2} = 0.744 \text{ atm}.
Calculate the standard Gibbs free energy change, \Delta G^\circ, using the equation \Delta G = \Delta G^\circ + RT \ln Q, where R = 8.314 \text{ J/mol·K} and T = 298 \text{ K}.
Determine \Delta G by substituting the calculated Q and known values into the equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is a crucial concept in predicting the spontaneity of a reaction; a negative ΔG indicates that a reaction can occur spontaneously, while a positive ΔG suggests non-spontaneity. The relationship between ΔG, enthalpy, and entropy is given by the equation ΔG = ΔH - TΔS.
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Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction CO2(g) + CCl4(g) ⇌ 2 COCl2(g), K can be calculated using the partial pressures of the gases involved. Understanding K is essential for calculating ΔG, as the relationship ΔG = ΔG° + RT ln(Q) connects the standard Gibbs free energy change (ΔG°) to the reaction quotient (Q) and K.
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Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any point in time, calculated using the same expression as the equilibrium constant (K). It helps determine the direction in which a reaction will proceed to reach equilibrium. If Q < K, the reaction will shift to the right (toward products), while if Q > K, it will shift to the left (toward reactants). In this question, Q is calculated using the given partial pressures.
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Related Practice
Textbook Question

Consider the evaporation of methanol at 25.0 °C : CH3OH(l) → CH3OH(g) a. Find ΔG°r at 25.0 °C.

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Textbook Question

Consider the evaporation of methanol at 25.0 °C : CH3OH(l) → CH3OH(g) b. Find ΔGr at 25.0 °C under the following nonstandard conditions: i. PCH3OH = 150.0 mmHg ii. PCH3OH = 100.0 mmHg iii. PCH3OH = 10.0 mmHg

Textbook Question

Consider the evaporation of methanol at 25.0 °C : CH3OH(l) → CH3OH(g) c. Explain why methanol spontaneously evaporates in open air at 25.0 °C

Textbook Question

Use data from Appendix IIB to calculate the equilibrium constants at 25 °C for each reaction. a. 2 CO(g) + O2(g) ⇌ 2 CO2(g)

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