Consider a mixture of 1 mole of CO2(g) and 6 moles of N2(g) at 300 K and 1 bar. This is a crude model for the flue gas that escapes a modern power plant that burns coal. One proposal for lowering the amount of CO2(g) in the atmosphere is to separate the carbon dioxide gas from the mixture and then to sequester it in underground cavities under pressure. Lets calculate the minimum amount of energy required to accomplish these two steps and then compare this to the energy produced by burning the fuel.

a) Calculate DG for unmixing this system to obtain 1 mole of pure CO2(g) and 6 moles of pure N2(g), all at 1 bar and 300 K. Explain why this is equal to the minimum amount of non-PV work that can be performed in the surroundings to accomplish this separation. You can assume ideal gases.

b) Calculate the minimum amount of work required to compress 1 mole of pure CO2(g) at 300 K by a factor of 140. For simplicity, assume that carbon dioxide is an ideal gas for this process even though this isnt very accurate.

c) Add together your two work values, and divide by the electrical energy that is produced by burning 1 mole of pure carbon (coal) (this is roughly 145 kJ). Note that each mole of carbon produces 1 mole of carbon dioxide. Your answer should be a dimensionless fraction this is a lower bound on the fraction of the electrical energy produced by the power plant that must be used to sequester the carbon dioxide that is produced. It is a lower bound on the actual fraction because we have assumed reversible processes in parts a and b