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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

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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.>