$2.2 \, g$ of nitrous oxide $(N_{2}O)$ gas is cooled at a constant pressure of $1 \, atm$ from $310 \, K$ to $270 \, K$ causing the compression of the gas from $217.1 \, mL$ to $167.75 \, mL$. The change in internal energy of the process,$\Delta U$ is $-x \, J$. The value of $x$ is $....$ [nearest integer] (Given: atomic mass of $N = 14 \, g \, mol^{-1}$ and of $O = 16 \, g \, mol^{-1}$. Molar heat capacity of $N_{2}O$ is $100 \, J \, K^{-1} \, mol^{-1}$)

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 $kJ$)

$500 \ J$ of energy is transferred as heat to $0.5 \ mol$ of Argon gas at $298 \ K$ and $1.00 \ atm$. The final temperature and the change in internal energy respectively are $:$ Given $: R = 8.3 \ J \ K^{-1} \ mol^{-1}$

The ${\Delta _c}{U^\circ}$ of combustion of $CH_{4(g)}$ at a certain temperature is $-100 \ kJ/mol$. The value of ${\Delta _c}{H^\circ}$ 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 $kcal$.

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at $1 \ bar$ pressure is given. $S_T$ and $S_0$ are entropies of the phases at temperatures $T$ and $0 \ K$,respectively.
The transition temperature for $\alpha$ to $\beta$ phase change is $600 \ K$ and $C_{p, \beta} - C_{p, \alpha} = 1 \ J \ mol^{-1} \ K^{-1}$. Assume $(C_{p, \beta} - C_{p, \alpha})$ is independent of temperature in the range of $200$ to $700 \ K$. $C_{p, \alpha}$ and $C_{p, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases,respectively.
$(1)$ The value of entropy change,$S_{\beta} - S_{\alpha}$ (in $J \ mol^{-1} \ K^{-1}$),at $300 \ K$ is. . . . . . .
$(2)$ The value of enthalpy change,$H_{\beta} - H_{\alpha}$ (in $J \ mol^{-1}$),at $300 \ K$ is.
[Use : $\ln 2 = 0.69$,Given : $S_{\beta} - S_{\alpha} = 0$ at $0 \ K$]