The theoretical minimum work required to separate one mole of a liquid mixture at 1 atm, containing 50 mole % each of n- heptane and n- octane into pure compounds each at 1 atm is

A. -2 RT ln 0.5

B. -RT ln 0.5

C. 0.5 RT

D. 2 RT

Answer: Option B

Solution(By Examveda Team)

Entropy of mixing is
$$\eqalign{ & = - R\sum {{X_i}\ln {x_i}} \cr & = - R\left[ {0.5\,\ln \,0.5 + 0.5\,\ln \,0.5} \right] \cr} $$
Since, work $$ = T\Delta S = - RT\,\ln \,0.5.$$