Question

For a reaction, \({A \rightleftharpoons P}\), the plots of [A] and [P] with time at temperatures \(T_1\) and \(T_2\) are given below. If \(T_2 > T_1\), the correct statement(s) is (are) (Assume \(\Delta H^{\ominus}\) and \(\Delta S^{\ominus}\) are independent of temperature and ratio of lnK at \(T_1\) to lnK at \(T_2\) is greater than \(\frac{T_2}{T_1}\) . Here \(H, S, G\) and \(K\) are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

• A. $\Delta H^{\ominus} < 0 , \Delta S^{\ominus} < 0 $
• B. $\Delta G^{\ominus} < 0 , \Delta H^{\ominus} > 0 $
• C. $\Delta G^{\ominus} < 0 , \Delta S^{\ominus} < 0 $
• D. $\Delta G^{\ominus} < 0 , \Delta S^{\ominus} > 0 $

Answer 1

The Correct Option is C

The correct answer is option (C) : \(\Delta G^{\ominus} < 0 , \Delta S^{\ominus} < 0\)
\({A \rightleftharpoons P}\) 
given \(T_2 > T_1\)
\(\frac{In K_{1}}{In K_{2}} > \frac{T_{2}}{T_{1} }\)
\(\Rightarrow T_{1} In k_{1} > T_{2} In k_{2}\)
\(\Rightarrow - \Delta G^{\circ}_{1} > - \Delta G^{\circ}_{2}\)
\(\Rightarrow \left(-\Delta H^{\circ} + T_{1}\Delta S^{\circ}\right) > \left( - \Delta H^{\circ} + T_{2} \Delta S^{\circ} \right)\)
\(\Rightarrow T_{1} \Delta S^{\circ} > T_{2} \Delta S^{\circ}\)
\(\Rightarrow \Delta S^{\circ} < 0\)