Question

Calculate the change in free energy when $1$ mole of an ideal gas is compressed from $10$L of $1$l at ${27}^o$C. ($2.303$ $nRTlog$ $\frac{V_i}{V_f}$)

Answer 1

As we know that,

$\Delta G=2.303nRT\log \frac{V_i}{V_f}.....\left(1\right)$

Whereas,

$\Delta G=$ Change in free energy $=?$

$n=$ No. of moles $=1\text{mole}$

$T=$ Temperature $=27℃=(27+273)=300K$

$V_i=$ Initial volume $=10L$

$V_f=$ Final volume $=1L$

Substituting all these values in ${eq}^n\left(1\right)$, we have

$\Delta G=2.303\times 1\times 8.314\times 300\times \log \frac{10}{1}$

$\Rightarrow \Delta G=5744.14J=5.74kJ$

Hence the value of change in free enrgy is $5.74kJ$.