Question

The incorrect expression among the following is

• A. $\frac{\Delta G_{\text{system}}}{\Delta G_{\text{total}}}=-T$
• B. in isothermal process, $W_{\text{reveisible}} =-nRT\,ln\frac{V_{f}}{v_{f}}$
• C. $ln\, K=\frac{\Delta H-T\Delta S^{\circ}}{RT}$
• D. $K=e^{-\Delta G^{\circ}/RT}$

Answer 1

Answer: (C)

According to Gibbs Helmholtz equation, $\Delta G=\Delta H-T\Delta S$
For a system, total entropy change $=\Delta S_{\text{total}}$
$\Delta H_{\text{total}}=0$
$\therefore \Delta G_{\text{system}}=-T\Delta S_{\text{total}}$
$\therefore \frac{\Delta G_{\text{system}}}{\Delta S_{\text{total}}}=-T$
Thus, (a) is correct.
For isothermal reversible process, $\Delta E = 0$
By first law of thermodynamics, $\Delta E=q+W$
$\therefore W_{\text{reversible}}=-q=-\int_{V_f}^{V_{f}} PdV$
$\Rightarrow W_{\text{reversible}}=-nRTln \frac{V_{f}}{V_{f}}$