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

1. 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.
2. insert step 2> For part (a), under standard conditions, \( \Delta G^\circ_{rxn} \) is calculated using the formula from step 1.
3. insert step 3> For part (b), at equilibrium, \( \Delta G_{rxn} = 0 \) because the reaction is at equilibrium.
4. 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.
5. 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

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.

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.

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).