Calculate $\Delta S_{total}$ for the following reaction at $300 \ K$.
$NH_4NO_{3(s)} \longrightarrow NH_4^+{(aq)} + NO_3^-{(aq)}$ $(\Delta H = 28.1 \ kJ \ mol^{-1}, \Delta S_{sys} = 108.7 \ J \ K^{-1} \ mol^{-1})$

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 $0 \ K$]

Identify the incorrect statements from the following.
$I$. For adiabatic process,$\Delta U = w_{ad}$
$II$. Enthalpy is an intensive property
$III$. For the process,$H_2O_{(l)} \rightarrow H_2O_{(s)}$,the entropy increases

$10 \ g$ each of $NH_3, N_2, Cl_2$ and $H_2S$ are expanded isothermally and reversibly at the same temperature. Identify the gas that performs maximum work.

In the reaction at $300 \ K$:
$C_6H_6(\ell) + \frac{15}{2}O_{2(g)} \to 6CO_{2(g)} + 3H_2O(\ell) \quad \Delta H = -3271 \ kJ$
What is the value of $\Delta U$ for the combustion of $1.5 \ mol$ of benzene at $27 \ ^oC$? $..... \ kJ$

The heat liberated when $1.89 \ g$ of benzoic acid is burnt in a bomb calorimeter at $25 \ ^\circ C$ increases the temperature of $18.94 \ kg$ of water by $0.632 \ ^\circ C$. If the specific heat of water at $25 \ ^\circ C$ is $0.998 \ cal/g \cdot ^\circ C$,the value of the heat of combustion of benzoic acid is .... $kcal/mol$. (Molar mass of benzoic acid = $122 \ g/mol$)