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

The heats of combustion of $C_{(s)}$,$H_{2(g)}$,and $C_{2}H_{6(g)}$ are $-x_{1}$,$-x_{2}$,and $-x_{3}$ respectively. The heat of formation of $C_{2}H_{6(g)}$ is:

Match the following:

$A$. Isothermal process	$i$. $q = \Delta U$
$B$. Adiabatic process	$ii$. $W = - P \times \Delta V$
$C$. Isobaric process	$iii$. $W = \Delta U$
$D$. Isochoric process	$iv$. $W = - nRT \ln \left(\frac{v_f}{v_i}\right)$

$A$ sample of argon at $1 \text{ atm}$ pressure and $300 \text{ K}$ expands reversibly and adiabatically from $1.25 \text{ dm}^3$ to $2.5 \text{ dm}^3$. Calculate the approximate enthalpy change (in $\text{J}$).
$(I)$ $C_V$ for argon is $12.48 \text{ J K}^{-1} \text{ mol}^{-1}$
$(II)$ Assume argon to be an ideal gas
$(III)$ $\Delta T = 111.5 \text{ K}$ (temperature decrease)

The heat evolved during the combination of $24 \, g$ of $C$ and $128 \, g$ of $S$ according to the reaction $C + 2S \to CS_2$ with $\Delta H = 22.0 \, kcal$ is:

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