For the reaction,$X_2O_{4(l)} \to 2XO_{2(g)}$,$\Delta U = 2.1 \ kcal$ and $\Delta S = 20 \ cal \ K^{-1}$ at $300 \ K$. Calculate $\Delta G$ in $kcal$.

Total enthalpy change for freezing of $1 \ mol$ of water at $10^{\circ} C$ to ice at $-10^{\circ} C$ is $..........$ (Given : $\Delta_{fus} H = x \ kJ / mol$,$C_{p}[H_2O_{(l)}] = y \ J \ mol^{-1} \ K^{-1}$,$C_{p}[H_2O_{(s)}] = z \ J \ mol^{-1} \ K^{-1}$)

How much $kJ$ energy is released when $6 \ mol$ of octane is burnt in air? Given $\Delta H_f^o$ for $CO_{2(g)}$,$H_2O_{(g)}$ and $C_8H_{18(l)}$ respectively are $-490$,$-240$,and $+160 \ kJ/mol$.

The molar heats of fusion and vaporisation of benzene are $10.9$ and $31.0 \ kJ \ mol^{-1}$ respectively. The changes in entropy for the solid $\rightarrow$ liquid and liquid $\rightarrow$ vapour transitions for benzene are $x$ and $y \ JK^{-1} \ mol^{-1}$,respectively. The value of $(y-x)$ (in $JK^{-1} \ mol^{-1}$) is (At $1 \ atm$,benzene melts at $5.5^{\circ} C$ and boils at $80^{\circ} C$).

Match the following processes with their corresponding entropy changes:

Process	Entropy Change
$(a)$ Liquid to vapor conversion	$(1)$ $\Delta S = 0$
$(b)$ Process not spontaneous at any temperature	$(2)$ $\Delta S = (+)$
$(c)$ Reversible expansion of an ideal gas	$(3)$ $\Delta S = (-)$

The heat of combustion of $CO$ at $290 \ K$ and constant volume is $-280.5 \ kJ$. What will be the heat of combustion at constant pressure in $kJ$?