Ch.18 - Free Energy and Thermodynamics

Tro - Chemistry: A Molecular Approach 4th Edition

Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook

Tro 4th Edition

Ch.18 - Free Energy and Thermodynamics

Problem 71

Chapter 18, Problem 71

Consider the reaction: CH3OH(g) → CO(g) + 2 H2(g). Calculate ΔG for this reaction at 25 °C under the following conditions: i. PCH3OH = 0.855 atm ii. PCO = 0.125 atm iii. PH2 = 0.183 atm.

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

Verified step by step guidance

Identify the reaction: CH3OH(g) → CO(g) + 2 H2(g). This is a decomposition reaction where methanol decomposes into carbon monoxide and hydrogen gas.

Use the equation for Gibbs free energy change under non-standard conditions: \( \Delta G = \Delta G^\circ + RT \ln Q \), where \( R \) is the gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, and \( Q \) is the reaction quotient.

Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 = 298.15 \text{ K} \).

Calculate the reaction quotient \( Q \) using the partial pressures: \( Q = \frac{P_{CO} \cdot (P_{H_2})^2}{P_{CH_3OH}} = \frac{0.125 \cdot (0.183)^2}{0.855} \).

Substitute the values into the Gibbs free energy equation: \( \Delta G = \Delta G^\circ + (8.314 \times 298.15) \ln Q \). Note that \( \Delta G^\circ \) (standard Gibbs free energy change) needs to be provided or looked up in a table of standard values.

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.

Reaction Quotient (Q)

The reaction quotient (Q) is a ratio that compares the concentrations or partial pressures of the products to the reactants at any point in a reaction. It is used to determine the direction in which a reaction will proceed to reach equilibrium. For the given reaction, Q can be calculated using the partial pressures of the gases involved.

Standard Gibbs Free Energy Change (ΔG°)

The standard Gibbs free energy change (ΔG°) is the change in Gibbs free energy for a reaction under standard conditions (1 atm pressure, 25 °C). It serves as a reference point for calculating ΔG under non-standard conditions using the equation ΔG = ΔG° + RT ln(Q), where R is the gas constant and T is the temperature in Kelvin.

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Related Practice

Textbook Question

Consider the reaction: CO₂(g) + CCl₄(g) ⇌ 2 COCl₂(g) Calculate ΔG for this reaction at 25 °C under the following conditions: i. P_CO2 = 0.112 atm ii. P_CCl4 = 0.174 atm iii. P_COCl2 = 0.744 atm

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)

Consider the evaporation of methanol at 25.0 °C : CH₃OH(l) → CH₃OH(g) b. Find ΔG_r at 25.0 °C under the following nonstandard conditions: i. P_CH3OH = 150.0 mmHg ii. P_CH3OH= 100.0 mmHg iii. P_CH3OH = 10.0 mmHg

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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) c. Explain why methanol spontaneously evaporates in open air at 25.0 °C

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Textbook Question

Use data from Appendix IIB to calculate the equilibrium constants at 25 °C for each reaction. b. 2 H₂S(g) ⇌ 2 H₂(g) + S₂(g)

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