The equilibrium constant for the reaction given below is $2.0\times {10}^{-7}$ at $300 \mathrm{K}$. Calculate the standard free energy change for the reaction:

${\mathrm{PCl}}_5 \left(\mathrm{g}\right)\rightleftharpoons {\mathrm{PCl}}_3 \left(\mathrm{g}\right)+{\mathrm{Cl}}_{2 }\left(\mathrm{g}\right)$

An ideal mono-atomic gas was at $1$ $\mathrm{atm}$ and $300 \mathrm{K}$. If one mole of such ideal gas is allowed to expand adiabatically against a constant pressure of $0.3$ $\mathrm{atm}$ till double its volume, determine $∆\mathrm{S}$ in ${\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$ for the process.

Given: $\log 2=0.3; \log 3=0.48; \log 5=0.7$

The value of ${\log }_{10} \mathrm{K}$ for a reaction $\mathrm{A}\rightleftharpoons \mathrm{B}$ is

(Given ${\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^{\mathrm{o}}}_{298 \mathrm{K}}=-54.07 \mathrm{kJ} {\mathrm{mol}}^{-1}, {\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{S}}^{\mathrm{o}}}_{298 \mathrm{K}}=10 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$ and $\mathrm{R}=8.314 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}; 2.303\times 8.314\times 298=5705$)

Predict which of the following reaction(s) has a positive entropy change?

$\left(\mathrm{I}\right) {\mathrm{Ag}}^{+ }\left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-} \left(\mathrm{aq}\right)\to \mathrm{AgCl} \left(\mathrm{s}\right)$

$\left(\mathrm{II}\right) {\mathrm{NH}}_4\mathrm{Cl} \left(\mathrm{s}\right)\to {\mathrm{NH}}_3 \left(\mathrm{g}\right)+\mathrm{HCl} \left(\mathrm{g}\right)$

$\left(\mathrm{III}\right) 2{\mathrm{NH}}_3\left(\mathrm{g}\right)\to {\mathrm{N}}_2 \left(\mathrm{g}\right)+3{\mathrm{H}}_2 \left(\mathrm{g}\right)$