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Ch.18 - Free Energy and Thermodynamics
Chapter 18, Problem 75

Consider the reaction: CO(g) + 2 H2(g) ⇌ CH3OH(g) with Kp = 2.26 * 10^4 at 25°C. Calculate ΔG°rxn for the reaction at 25°C under each of the following conditions: a. standard conditions b. at equilibrium c. PCH3OH = 1.0 atm; PCO = PH2 = 0.010 atm

Verified step by step guidance
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insert step 1> Calculate \( \Delta G^\circ_{rxn} \) using the relation \( \Delta G^\circ_{rxn} = -RT \ln K_p \) where \( R = 8.314 \times 10^{-3} \) kJ/mol·K and \( T = 298 \) K.
insert step 2> For part (a), under standard conditions, \( \Delta G^\circ_{rxn} \) is calculated using the formula from step 1.
insert step 3> For part (b), at equilibrium, \( \Delta G_{rxn} = 0 \) because the reaction is at equilibrium.
insert step 4> For part (c), use the reaction quotient \( Q_p = \frac{P_{CH_3OH}}{P_{CO} \cdot (P_{H_2})^2} \) to find \( Q_p \) with given pressures.
insert step 5> Calculate \( \Delta G_{rxn} \) using \( \Delta G_{rxn} = \Delta G^\circ_{rxn} + RT \ln Q_p \) with \( Q_p \) from step 4.

Key Concepts

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

Gibbs Free Energy (ΔG°rxn)

Gibbs Free Energy is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The standard change in Gibbs Free Energy (ΔG°rxn) for a reaction indicates the spontaneity of the reaction under standard conditions. A negative ΔG°rxn suggests that the reaction is spontaneous, while a positive value indicates non-spontaneity.
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Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a dimensionless number that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction CO(g) + 2 H2(g) ⇌ CH3OH(g), Kp = 2.26 * 10^4 indicates that at equilibrium, the concentration of methanol is significantly higher than that of carbon monoxide and hydrogen, suggesting that the reaction favors product formation.
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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, compared to the equilibrium state. It is calculated using the same expression as Kp but with the current partial pressures. By comparing Q to Kp, one can determine the direction in which the reaction will proceed to reach equilibrium: if Q < Kp, the reaction will shift to the right (toward products), and if Q > Kp, it will shift to the left (toward reactants).
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