The $C_p$ of an ideal gas is $10.314 \ J \ mol^{-1} \ K^{-1}$. One mole of this gas is expanded against a constant pressure of $p \ atm$. The change in temperature during expansion is $1.0 \ K$. The values of $q$ (in $J$) and $\Delta H$ (in $J \ mol^{-1}$) are respectively

The molar heat of formation of $NH_4NO_{3(s)}$ is $-367.54 \ kJ \ mol^{-1}$ and those of $N_2O_{(g)}$ and $H_2O_{(l)}$ are $+81.46 \ kJ \ mol^{-1}$ and $-285.78 \ kJ \ mol^{-1}$ respectively at $25 \ ^oC$ and $1.0 \ atm$ pressure. Calculate $\Delta U$ at $25 \ ^oC$ for the reaction:
$NH_4NO_{3(s)} \rightarrow N_2O_{(g)} + 2H_2O_{(l)}$ (in $kJ$)

Match the thermodynamic processes given under Column $I$ with the expression given under Column $II$:

Column $I$	Column $II$
$A$. Freezing of water at $273 \ K$ and $1 \ atm$	$P$. $q=0$
$B$. Expansion of $1 \ mol$ of an ideal gas into a vacuum under isolated conditions	$Q$. $w=0$
$C$. Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container	$R$. $\Delta S_{sys} < 0$
$D$. Reversible heating of $H_{2(g)}$ at $1 \ atm$ from $300 \ K$ to $600 \ K$,followed by reversible cooling to $300 \ K$ at $1 \ atm$	$S$. $\Delta U=0$
	$T$. $\Delta G=0$

For a certain thermochemical reaction $M \rightarrow N$ at $T = 400 \ K$,$\Delta H^{\ominus} = 77.2 \ kJ \ mol^{-1}$ and $\Delta S = 122 \ J \ K^{-1} \ mol^{-1}$,the value of $\log K$ is $ . . . . . . \times 10^{-1}$.

For the reaction $2X_{(s)} + 2Y_{(s)} \to 2C_{(\ell)} + D_{(g)}$,the value of $q_p$ is $-28 \, \text{kcal mol}^{-1}$ at $2700 \, ^\circ\text{C}$. Calculate the value of $q_v$ in $\text{kcal mol}^{-1}$.

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 $kcal$.