Compound A can react by two competing

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

Compound A can react by two competing, irreversible, first-order pathways to form either product B or product C. • Pathway 1 (A → B): activation energy Ea1=45 kJ mol−1E_{a1}=45\,\text{kJ mol}^{-1} and identical frequency factor A1=A2A_1=A_2. • Pathway 2 (A → C): activation energy Ea2=60 kJ mol−1E_{a2}=60\,\text{kJ mol}^{-1}. • The standard Gibbs free energies of formation at 298 K are ΔGf∘(B)=−10 kJ mol−1\Delta G_f^{\circ}(\text{B})=-10\,\text{kJ mol}^{-1} and ΔGf∘(C)=−25 kJ mol−1\Delta G_f^{\circ}(\text{C})=-25\,\text{kJ mol}^{-1}. Assume the pre-exponential factors for both pathways are equal and temperature-independent. (a) Calculate the ratio of the initial rates rateBrateC\dfrac{\text{rate}_{\text{B}}}{\text{rate}_{\text{C}}} at 298 K. Use the gas constant R=8.314 J mol−1 K−1R=8.314\,\text{J mol}^{-1}\,\text{K}^{-1}. (b) Based on your calculation in part (a), identify which product is favored kinetically at 298 K and justify your answer. (c) Without repeating the calculation in detail, predict whether the same product would still be kinetically favored at 500 K. Explain your reasoning qualitatively. (d) Using the given standard Gibbs free energies, determine which product is thermodynamically favored at 298 K and justify your choice.

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