For the reaction at $25^{\circ} C$, $X_2O_{4(l)} \longrightarrow 2 XO_{2(g)}$, $\Delta U$ and $\Delta S$ are $2.1 \ kCal$ and $20 \ cal \ K^{-1}$ respectively. What is $\Delta G$ for the reaction at the same temperature? $(R = 2 \ cal \ K^{-1} \ mol^{-1})$

$A$ swimmer coming out from a pool is covered with a film of water weighing about $18 \ g$. How much heat must be supplied to evaporate this water at $298 \ K$? Calculate the internal energy of vaporisation at $298 \ K$. Given: $\Delta_{vap} H^{\ominus}$ for water at $298 \ K = 44.01 \ kJ \ mol^{-1}$.

In an irreversible process taking place at constant $T$ and $P$ and in which only pressure-volume work is being done,the change in Gibbs free energy $(dG)$ and change in entropy $(dS)$ satisfy the criteria:

$C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} + 400 \; kJ$
$C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)} + 100 \; kJ$
When coal of purity $60 \%$ is allowed to burn in the presence of insufficient oxygen,$60 \%$ of carbon is converted into $CO$ and the remaining is converted into $CO_2$.
The heat generated when $0.6 \; kg$ of coal is burnt is (in $; kJ$)

Match the transformations in column $I$ with appropriate options in column $II$.

Column $I$	Column $II$
$A$. $CO_{2(s)} \rightarrow CO_{2(g)}$	$p$. phase transition
$B$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$	$q$. allotropic change
$C$. $2H_{(g)} \rightarrow H_{2(g)}$	$r$. $\Delta H$ is positive
$D$. $P_{(\text{white, solid})} \rightarrow P_{(\text{red, solid})}$	$s$. $\Delta S$ is positive
	$t$. $\Delta S$ is negative

For the following reaction $Fe_2O_{3(s)} + 3 CO_{(g)} \longrightarrow 2 Fe_{(s)} + 3 CO_{2(g)}$,$\Delta H^{\circ} = -29.8 \ kJ$ and $\Delta S^{\circ} = 15 \ JK^{-1}$. What is the value of $\Delta S_{\text{total}}$ at $298 \ K$ (in $JK^{-1}$)?