For a dimerization reaction,$2 A_{(g)} \rightarrow A_{2(g)}$ at $298 \ K$,$\Delta U^{\ominus} = -20 \ kJ \ mol^{-1}$,$\Delta S^{\ominus} = -30 \ J \ K^{-1} \ mol^{-1}$,then the $\Delta G^{\ominus}$ will be........ $J$

When $50 \ cm^3$ of $0.2 \ N \ H_2SO_4$ is mixed with $50 \ cm^3$ of $1 \ N \ KOH$,the heat liberated is

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

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

The $\Delta E^o$ of combustion of $2-$methylpropene is $-X \ kJ \ mol^{-1}$. The value of $\Delta H^o$ is

$A$ calorimeter contains $0.2 \ kg$ of water at $30^{\circ} C$. $0.1 \ kg$ of water at $60^{\circ} C$ is added to it,the mixture is well stirred and the resulting temperature is found to be $35^{\circ} C$. The water equivalent of the calorimeter is $:-$ (in $J / K$)

$A$ gas at $10 \, atm$ pressure and $300 \, K$ temperature undergoes adiabatic reversible expansion to $5 \, atm$ pressure and $290 \, K$ temperature. The molar heat capacity $C_v$ of the gas in $cal \, mol^{-1} \, K^{-1}$ is: