For the reaction $X_2O_{4(g)} \to 2XO_{2(g)}$,given $\Delta U = 2.1 \, kcal$ and $\Delta S = 20 \, cal \, K^{-1}$ at $300 \, K$. Calculate $\Delta G$ in $kcal$.

Match List-$I$ with List-$II$. Given $V_1$ and $V_2$ are initial and final volumes respectively.

List-$I$ (Isothermal process)	List-$II$ (Expression)
$A$. Reversible expansion	$I$. $q = 0$
$B$. Free expansion	$II$. $q = nRT \ln \frac{V_2}{V_1}$
$C$. Irreversible Compression	$III$. $w = -P_{ext}(V_1 - V_2)$
$D$. Cyclic reversible	$IV$. $\frac{q_{rev}}{T} = 0$

$2 \ mol$ of $Hg_{(g)}$ is combusted in a fixed volume bomb calorimeter with excess of $O_2$ at $298 \ K$ and $1 \ atm$ into $HgO_{(s)}$. During the reaction,temperature increases from $298.0 \ K$ to $312.8 \ K$. If heat capacity of the bomb calorimeter and enthalpy of formation of $Hg_{(g)}$ are $20.00 \ kJ \ K^{-1}$ and $61.32 \ kJ \ mol^{-1}$ at $298 \ K$,respectively,the calculated standard molar enthalpy of formation of $HgO_{(s)}$ at $298 \ K$ is $X \ kJ \ mol^{-1}$. The value of $|X|$ is. . . . . [Given : Gas constant $R = 8.3 \ J \ K^{-1} \ mol^{-1}$]

Calculate $\Delta H_f^o$ of $SiH_2$ from the following reactions:
$Si_2H_{6(g)} + H_{2(g)} \to 2SiH_{4(g)}, \Delta H = -11.7 \ kJ/mol$
$SiH_{4(g)} \to SiH_{2(g)} + H_{2(g)}, \Delta H = +239.7 \ kJ/mol$
$\Delta H_f^o(Si_2H_{6(g)}) = 80.3 \ kJ/mol$

Calculate the difference between heat of combustion of carbon monoxide gas at constant pressure and at constant volume at $27^{\circ} C$ (in $cal$)? $(R = 2 \ cal \ K^{-1} \ mol^{-1})$

Considering the reaction $C_{(s)} + O_{2(g)} \longrightarrow CO_{2(g)} + 393.5 \ kJ$,the signs of $\Delta H, \Delta S$,and $\Delta G$ respectively are: