Question

A gaseous mixture at 1 bar and 300 K consists of 20 mol% CO₂ and 80 mol% inert gas. Assume the gases to be ideal. Take R = 8.314 J mol\(^{-1}\) K\(^{-1}\). The magnitude of minimum work required to separate 100 mol of this mixture at 1 bar and 300 K into pure CO₂ and inert gas at the same temperature and pressure is \(\underline{\hspace{1cm}}\) kJ (round off to nearest integer).

Hint:

For separation work, use the Gibbs free energy expression and mole fraction logarithms.

Answer 1

Correct Answer: 124

To calculate the minimum work, we use the formula for minimum work of separation: \[ W_{\text{min}} = -RT \left(\sum x_i \ln x_i\right) \] Substitute values for \(x_{\text{CO}_2} = 0.2\) and \(x_{\text{inert}} = 0.8\): \[ W_{\text{min}} = -8.314 \times 300 \times (0.2 \ln 0.2 + 0.8 \ln 0.8) \] Final answer: 124 to 126 kJ.