Take R = 8.314 J mol^-1 K^-1. A reaction has Delta H deg = -92.0 kJ mol^-1 and Delta S deg = -199 J mol^-1 K^-1, both assumed independent of temperature. The value of log_10K at 500 K is closest to

JEE Advanced levelSingle correct optionDifficulty 3 of 3ce155

Take $R = 8.314 J mo l^{- 1} K^{- 1}$ . A reaction has $Δ H^{\circ} = - 92.0 kJ mo l^{- 1}$ and $Δ S^{\circ} = - 199 J mo l^{- 1} K^{- 1}$ , both assumed independent of temperature. The value of $lo g_{10} K$ at $500 K$ is closest to

Δ G^{\circ} (500 K) = Δ H^{\circ} - T Δ S^{\circ} = - 92000 - 500 (- 199) = + 7500 J mo l^{- 1}

lo g_{10} K = - Δ G^{\circ} / (2.303 RT) = - 7500/ (2.303 \times 8.314 \times 500) = - 0.78

. Using

Δ G^{\circ}

298 K

gives 3.42, and a wrong sign on the

T Δ S^{\circ}

term gives 20.0.