Standard entropies for $H_2, Cl_2$ and $HCl$ are $60, 40$ and $60 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $H_2 + Cl_2 \rightleftharpoons 2HCl$,with $\Delta H = +30 \ kJ$,the temperature at which the reaction will be at equilibrium is $..... \ K$.

Match the transformations in Column-$I$ with the appropriate options in Column-$II$.

Column-$I$	Column-$II$
$(A) \; CO_{2(s)} \to CO_{2(g)}$	$(p) \; \text{Transition state}$
$(B) \; CaCO_{3(s)} \to CaO_{(s)} + CO_{2(g)}$	$(q) \; \text{Allotropic change}$
$(C) \; 2H^{\cdot} \to H_{2(g)}$	$(r) \; \Delta H > 0$
$(D) \; P_{\text{(white solid)}} \to P_{\text{(red solid)}}$	$(s) \; \Delta S > 0$
	$(t) \; \Delta S < 0$

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?

If $100$ mole of $H_2O_2$ decomposes at $1$ bar and $300$ $K$,the work done $(kJ)$ by $50$ mole of $O_{2(g)}$ as it expands against $1$ bar pressure is............. $kJ$
$2H_2O_{2(l)} \rightleftharpoons 2H_2O_{(l)} + O_{2(g)}$
$(R = 8.3 \ J \ K^{-1} \ mol^{-1})$

One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27\,^oC$. If the work done during the process is $3\,kJ$,the final temperature will be equal to $(C_v = 20\,J\,K^{-1} \, mol^{-1})$

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 $R = 8.3 \, J \, \text{mol}^{-1} \, K^{-1}$)