Qualitative Analysis - Result Question 23
####23. For the equilibrium, $2 H _2 O \rightleftharpoons H _3 O^{+}+OH^{-}$, the value of $\Delta G^{\circ}$ at $298 K$ is approximately $\quad$ (2019 Main 11 Jan II)
(a) $-80 kJ mol^{-1}$
(b) $100 kJ mol^{-1}$
(c) $80 kJ mol^{-1}$
(d) $-100 kJ mol^{-1}$
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Answer:
Correct Answer: 23. (c)
Solution:
- We know that,
$$ \Delta G^{\circ}=-2.303 R T \log K $$
Also, given equilibrium is
$$ \begin{aligned} & \quad 2 H _2 O \rightleftharpoons H _3 O^{+}+\overline{O} H \\ & {\left[H^{+}\right]\left[OH^{-}\right]=10^{-14} \text { or } K=10^{-14}} \\ & \therefore \quad \Delta G^{\circ}=-2.303 \times 8.314 JK^{-1} mol^{-1} \times 298 K \times \log 10^{-14} \\ & = \\ & =79881.8 J mol^{-1}=79.8 kJ \approx 80 kJ mol^{-1} \end{aligned} $$
