(i) Define change in entropy.

(ii) Predict sign of $\mathrm{\Delta S}$ for the following changes.

(a) ${\mathrm{H}}_2\left(\mathrm{g}\right)\to 2\mathrm{H}\left(\mathrm{g}\right)$
(b) ${\mathrm{AgNO}}_3\left(\mathrm{s}\right)\to {\mathrm{AgNO}}_3\left(\mathrm{aq}\right)$
(c) $\mathrm{C}$ (graphite) $\to \mathrm{C}$ (diamond)
(d) ${\mathrm{I}}_2\left(\mathrm{s}\right)\to {\mathrm{I}}_2\left(\mathrm{\ell }\right)$

(a) Write any three alternative statements of $2^{\mathrm{nd}}$ law of thermodynamics?

Calculate the entropy change $(\mathrm{J}/\mathrm{mol}/\mathrm{K})$ of the given reaction. The molar entropies $[\mathrm{J}/\mathrm{K}-\mathrm{mol}]$ are given in brackets after each substance.

$2\mathrm{PbS}\left(\mathrm{s}\right)[91.2]+3{\mathrm{O}}_2\left(\mathrm{g}\right)[205.1]⟶2\mathrm{PbO}\left(\mathrm{s}\right)[66.5]+2{\mathrm{SO}}_2\left(\mathrm{g}\right)[248.2]$

$2 \mathrm{A}\left(\mathrm{g}\right) + \mathrm{B}\left(\mathrm{g}\right) \to 2\mathrm{D}\left(\mathrm{g}\right)$ 

Calculate $∆\mathrm{G}°$ for the reaction, and predict whether the reaction may occur spontaneously.

(a) Calculate standard entropy change for reaction $\mathrm{X}\rightleftharpoons \mathrm{Y}$  if $\mathrm{\Delta H}°=25 \mathrm{KJ}$ and $\mathrm{Keq}$ is ${10}^{-7}$ at $300 \mathrm{K}$.

(b) Derive following expression for ideal gas $\mathrm{\Delta S}={\mathrm{nC}}_{\mathrm{v}}\ln \frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}+\mathrm{nRln}\frac{{\mathrm{V}}_2}{{\mathrm{V}}_1}$