A gaseous mixture at $1$ bar and $300 \: K$ consists of $20 \text{ mol } \% \: CO_2$ and $80 \text{ mol } \%$ inert gas.
Assume the gases to be ideal. Take $R=8.314 \text{ J mol}^{-1} K^{-1}$.
The magnitude of minimum work required to separate $100 \text{ mol}$ of this mixture at $1$ bar and $300 \: K$ into pure $CO_2$ and inert gas at the same temperature and pressure is ________ $\text{kJ}$ (round off to nearest integer)