Calculate the work done in $kJ$ when $3$ moles of an ideal gas at $27^{\circ} C$ expand isothermally and reversibly from $10 \ atm$ to $1 \ atm$ $[R=8.314 \ J \ K^{-1} \ mol^{-1}]$

At the temperature $T$ $(K)$ for the reaction: $X_2O_{4(l)} \rightarrow 2XO_{2(g)}$,given $\Delta U = x \ kJ \ mol^{-1}$ and $\Delta S = y \ J \ K^{-1} \ mol^{-1}$. The Gibbs energy change for the reaction is: (Assume $X_2O_4$ and $XO_2$ are ideal gases)

The standard enthalpies of formation of $1,3-butadiene(g)$,$CO_{2(g)}$,and $H_2O_{(l)}$ at $298 \ K$ are $-30$,$-94$,and $-68 \ kcal/mol$ respectively. If the magnitude of resonance enthalpies of $1,3-butadiene$ and $CO_2$ are $10$ and $20 \ kcal/mol$ respectively,the enthalpy of combustion of $1,3-butadiene(g)$ at $298 \ K$ is $........ \ kcal/mol$. (Enthalpy of vaporization of $H_2O_{(l)}$ at $298 \ K = 10 \ kcal/mol$)

When $1 \ g$ of $NH_4NO_3$ is decomposed in a bomb calorimeter,the temperature of the calorimeter increases by $6.12 \ K$. If the heat capacity of the system is $1.23 \ kJ/K$,the molar enthalpy of decomposition of $NH_4NO_3$ is ........ $kJ/mol$.

$2.4 \ g$ coal is burnt in a bomb calorimeter in excess of oxygen at $298 \ K$ and $1 \ atm$ pressure. The temperature of the calorimeter rises from $298 \ K$ to $300 \ K$. The enthalpy change during the combustion of coal is $-x \ kJ \ mol^{-1}$. The value of $x$ is. (Nearest Integer) (Given: Heat capacity of bomb calorimeter $20.0 \ kJ \ K^{-1}$. Assume coal to be pure carbon)

The heat of combustion of carbon to $CO_2$ is $-393.5 \text{ kJ/mol}$. The heat released upon formation of $35.2 \text{ g}$ of $CO_2$ from carbon and oxygen gas is