Answer
(a) $12.7\,JK^{-1}mol^{-1}$
Solid is changed to aqueous state which increases the randomness and therefore entropy increases. $\Delta_{r}S^{\circ}$ is positive because of this increase.
(b) $-102.56\,JK^{-1}mol^{-1}$
Gas is changed to solid-state which decreases mobility and randomness and therefore entropy decreases. $\Delta_{r}S^{\circ}$ is negative because of this decrease.
(c) $93.3\,JK^{-1}mol^{-1}$
The liquid is changed to gaseous state which results in increased mobility and randomness and therefore entropy increases. $\Delta_{r}S^{\circ}$ is positive because of this increase.
(d) $-129.7\,JK^{-1}mol^{-1}$
Gas is changed to aqueous state which decreases mobility and randomness and therefore entropy decreases. $\Delta_{r}S^{\circ}$ is negative because of this decrease.
Work Step by Step
Recall: $\Delta_{r} S^{\circ}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$
(a) $\Delta_{r} S^{\circ}=[S^{\circ}(KOH,aq)]-[S^{\circ}(KOH,s)]$
$=(91.6\,JK^{-1}mol^{-1})-(78.9\,JK^{-1}mol^{-1})$
$=12.7\,JK^{-1}mol^{-1}$
Solid is changed to aqueous state which increases the randomness and therefore entropy increases. $\Delta_{r}S^{\circ}$ is positive because of this increase.
(b) $\Delta_{r} S^{\circ}=[S^{\circ}(Na,s)]-[S^{\circ}(Na,g)]$
$=(51.21\,JK^{-1}mol^{-1})-(153.765\,JK^{-1}mol^{-1})$
$=-102.56\,JK^{-1}mol^{-1}$
Gas is changed to solid-state which decreases mobility and randomness and therefore entropy decreases. $\Delta_{r}S^{\circ}$ is negative because of this decrease.
(c) $\Delta_{r} S^{\circ}=[S^{\circ}(Br_{2},g)]-[S^{\circ}(Br_{2},l)]$
$=(245.47\,JK^{-1}mol^{-1})-(152.2\,JK^{-1}mol^{-1})$
$=93.3\,JK^{-1}mol^{-1}$
The liquid is changed to gaseous state which results in increased mobility and randomness and therefore entropy increases. $\Delta_{r}S^{\circ}$ is positive because of this increase.
(d) $\Delta_{r} S^{\circ}=[S^{\circ}(HCl,aq)]-[S^{\circ}(HCl,g)]$
$=(56.5\,JK^{-1}mol^{-1})-(186.2\,JK^{-1}mol^{-1})$
$=-129.7\,JK^{-1}mol^{-1}$
Gas is changed to aqueous state which decreases mobility and randomness and therefore entropy decreases. $\Delta_{r}S^{\circ}$ is negative because of this decrease.
