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 $kJ$)

For the following reaction $Fe_2O_{3(s)} + 3 CO_{(g)} \longrightarrow 2 Fe_{(s)} + 3 CO_{2(g)}$,$\Delta H^{\circ} = -29.8 \ kJ$ and $\Delta S^{\circ} = 15 \ JK^{-1}$. What is the value of $\Delta S_{\text{total}}$ at $298 \ K$ (in $JK^{-1}$)?

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 = $122 \ g/mol$)

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature:
$(a)$ $|w_{reversible}|$ for expansion in infinite stage.
$(b)$ $|w_{irreversible}|$ for expansion in single stage.
$(c)$ $|w_{reversible}|$ for compression in infinite stage.
$(d)$ $|w_{irreversible}|$ for compression in single stage.
Choose the correct answer from the options given below:

Find the enthalpy of neutralisation of $NH_4OH$ and $HCN$ in aqueous solution if the enthalpy of ionisation of $NH_4OH$ and $HCN$ are $7 \ kJ/mol$ and $8 \ kJ/mol$ respectively. Also,the enthalpy of neutralisation of $H^{+}$ and $OH^{-}$ is $-57.3 \ kJ/mol$.

For which of the following thermodynamic processes is $\Delta U = 0$?