The free energy for a reaction having $\Delta H = 31400 \, cal$ and $\Delta S = 32 \, cal \, K^{-1} \, mol^{-1}$ at $1000 \, ^oC$ is ....... $cal$.

Calculate the work done if $1 \ mole$ of a certain gas is compressed isothermally and reversibly at $300 \ K$ from an initial pressure $x \ bar$ to a final pressure $2x \ bar$ $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$. (in $kJ$)

For a reaction at $25^o C$,$\Delta H > 0$ and $\Delta S > 0$. Under what conditions will this reaction become spontaneous?

Calculate the work done if $1 \ mole$ of an ideal gas is compressed isothermally and reversibly from $12 \ dm^3$ to $6 \ dm^3$ at $300 \ K$. $\left[R = 8.314 \ J \ K^{-1} \ mol^{-1}\right]$ (in $kJ$)

Calculate the Gibbs energy change for a reaction having $\Delta H = 31400 \ J$ and $\Delta S = 32 \ J \ K^{-1}$ at $1000^{\circ} C$. (in $J$)

Compare the following criteria for spontaneity of a reaction based on the values of $\Delta_{\text{r}}H^0$,$\Delta_{\text{r}}S^0$,and $\Delta_{\text{r}}G^0$:

$\Delta_{\text{r}}H^0$	$\Delta_{\text{r}}S^0$	$\Delta_{\text{r}}G^0$	Description
$(a) (+)$	$(-)$	$(+)$	$(i) \text{ Non-spontaneous at all temperatures}$
$(b) (-)$	$(-)$	$(-)$	$(ii) \text{ Spontaneous at low temperatures}$
$(c) (-)$	$(+)$	$(-)$	$(iii) \text{ Spontaneous at all temperatures}$