At 17°C, 1.5 mol of a prefect gas was compressed reversibly and isothermally from a pressure of  $2.02\times {10}^3{\mathrm{Nm}}^{-2}\text{ to }8.08\times {10}^4{\mathrm{Nm}}^{-2}$  the value of work done and that of free energy would be.

(a) n=1.5 mol, T=17+273=290 K, R=8.314 J/K mol, ${\mathrm{P}}_1=2.02\times {10}^3{\mathrm{Nm}}^{-2}$,${\mathrm{P}}_2=8.08\times {10}^4{\mathrm{Nm}}^{-2}$.For isothermal reversible process , work done is negative.

So, $\mathrm{W}=-2.303\mathrm{nRTlog}\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}=-2.303\times 1.5 \mathrm{mol}\times 8.314 \mathrm{J}/\mathrm{Kmol}\times 290 \mathrm{Klog}\frac{2.02\times {10}^3}{8.08\times {10}^4}$

$=-8329\mathrm{J}\left(\log \frac{1}{40.4}\right)=-8329(\log 1-\log 40.4)\mathrm{J}=-8329(0-1.6064)=+13379.7\mathrm{J}=13.38 \mathrm{kJ}$

(b) we know  ${\mathrm{W}}_{\mathrm{rev}}$  is a measure of free energy change, $\mathrm{\Delta G}$.

So:    $-\mathrm{\Delta G}=-{\mathrm{W}}_{\mathrm{rev}}-{\mathrm{W}}_{\max }=+13.38\mathrm{kJ}$