Standard entropies of $X_2$,$Y_2$ and $XY_3$ are $60$,$40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2} X_2 + \frac{3}{2} Y_2 \rightarrow XY_3$,the enthalpy change is $\Delta H = -30 \ kJ \ mol^{-1}$. At what temperature will the reaction be at equilibrium (in $K$)?

Calculate the work done for the following reaction at $27^{\circ}C$: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$ $(R = 8.314 \text{ J K}^{-1} \text{mol}^{-1})$ (in $\text{ J}$)

Water vapor is an ideal gas. Calculate the internal energy change $(\Delta U)$ when $1 \, \text{mol}$ of water is vaporized at $1 \, \text{bar}$ pressure and $100 \, ^{\circ}C$. (Given: Molar enthalpy of vaporization of water at $1 \, \text{bar}$ and $373 \, K = 41 \, kJ \, \text{mol}^{-1}$ and $R = 8.3 \, J \, \text{mol}^{-1} \, K^{-1}$)

For the combustion of $1 \ mol$ of liquid benzene at $298 \ K$,the heat of reaction at constant pressure is $-3268 \ kJ \ mol^{-1}$. What is the heat of combustion at constant volume? $(R = 8.314 \times 10^{-3} \ kJ \ K^{-1} \ mol^{-1})$

If the standard enthalpy change $\left(\Delta_{r} H^{\theta}\right)$ for a certain reaction at $298 \ K$ and constant pressure is $-1860 \ kJ \ mol^{-1}$,and the standard entropy change $\left(\Delta_{\text{sys}} S^{\theta}\right)$ of the same reaction is $-550 \ J \ K^{-1} \ mol^{-1}$,which one of the following statements is correct?

Three moles of an ideal gas are expanded isothermally from a volume of $300 \ cm^3$ to $2.5 \ L$ at $300 \ K$ against a constant external pressure of $1.9 \ atm$. The work done in joules is: