Compound M can convert to two products, X and Y

CHEMISTRY · Single correct · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

Compound M can convert to two products, X and Y. Kinetic data and thermodynamic data are provided: • At 298 K298\,\text{K}: kX=3.0×10−3 s−1k_X = 3.0 \times 10^{-3}\,\text{s}^{-1}, kY=1.5×10−5 s−1k_Y = 1.5 \times 10^{-5}\,\text{s}^{-1} • At 373 K373\,\text{K}: kX=4.8×10−2 s−1k_X = 4.8 \times 10^{-2}\,\text{s}^{-1}, kY=1.0×10−2 s−1k_Y = 1.0 \times 10^{-2}\,\text{s}^{-1} • Standard Gibbs free energies relative to M: ΔGX∘=+2 kJ mol−1\Delta G^{\circ}_X = +2\,\text{kJ}\,\text{mol}^{-1}; ΔGY∘=−18 kJ mol−1\Delta G^{\circ}_Y = -18\,\text{kJ}\,\text{mol}^{-1} A solution of M is heated at 373 K373\,\text{K} for 2 h2\,\text{h} and then allowed to cool while remaining closed to further reaction until equilibrium is reached. Which statement best predicts the composition of the final mixture? (a) X will predominate because its rate constant is greater than that of Y at every temperature studied, so the faster product dominates the mixture. (b) Y will predominate because it is more stable and the elevated temperature allows equilibrium to be attained despite its slower initial rate. (c) Approximately equal amounts of X and Y will be present because the values of kXk_X and kYk_Y at 373 K373\,\text{K} are of the same order of magnitude. (d) X will predominate because its ΔG∘\Delta G^{\circ} value is closer to zero, indicating it is the more stable product under standard conditions.

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