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 $T_2/T_1$ . 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

Answer: (A), (C)

$A\rightleftharpoons P$
given $T_2>T_1$
$\frac{\ln K_1}{\ln K_2}>\frac{T_2}{T_1}$
$\Rightarrow T_1\ln k_1>T_2\ln k_2$
$\Rightarrow -\Delta G_1^{\circ }>-\Delta G_2^{\circ }$
$\Rightarrow \left(-\Delta H^{\circ }+T_1\Delta S^{\circ }\right)>\left(-\Delta H^{\circ }+T_2\Delta S^{\circ }\right)$
$\Rightarrow T_1\Delta S^{\circ }>T_2\Delta S^{\circ }$
$\Rightarrow \Delta S^{\circ }<0$