The heat of combustion of naphthalene $(C_{10}H_8(s))$ at constant volume is $-5133 \, kJ \, mol^{-1}$. The value of enthalpy change is .... $J$ $(R = 8.314 \, J \, K^{-1} \, mol^{-1}, T = 298 \, K)$.

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)

$A$ solution of $500 \ mL$ of $2 \ M \ KOH$ is added to $500 \ mL$ of $2 \ M \ HCl$ and the mixture is well shaken. The rise in temperature $T_1$ is noted. The experiment is then repeated using $250 \ mL$ of each solution and the rise in temperature $T_2$ is again noted. Assume all heat is absorbed by the solution.

$20.0 \ dm^{3}$ of an ideal gas '$X$' at $600 \ K$ and $0.5 \ MPa$ undergoes isothermal reversible expansion until the pressure of the gas is $0.2 \ MPa$. Which of the following options is correct? (Given: $\log\,2=0.3010$ and $\log\,5=0.6989$)

The enthalpy of vaporization of a liquid at $500 \, K$ and $1 \, atm$ pressure is $10 \, kcal \, mol^{-1}$. The change in internal energy $(\Delta U)$ for $3 \, moles$ of the liquid at the same temperature and pressure is ............ $kcal$.

The amount of heat evolved when $500 \ cm^{3}$ of $0.1 \ M \ HCl$ is mixed with $200 \ cm^{3}$ of $0.2 \ M \ NaOH$ is (in $kJ$)