Vapor-Liquid Equilibrium Calculations

[runningman19]

Hi Everyone,
I am having trouble grasping the concept of Raoult's law, partial pressures etc. One problem in specific is: A system contains 3 moles of methanol and 7 moles of water at 25 degrees celsius. The temperature is raised until there is 40 mol% methanol in the gas phase. How much is left in the liquid phase?
The Txy diagram is attached.
Thanks so much guys,
Nick

 

[Chestermiller]

This is strictly a mass balance problem. Let L represent the total number of moles in the liquid and W represent the number of moles in the vapor. So, $$L+V = 10$$

From the diagram, there is 40 mol% methanol in the gas phase ( y = 0.4) when the temperature is 88 C. And the mole percent in the liquid at this state is 10 % (x = 0.1). So, the mass balance on the methanol is $$L(0.1)+V(0.4)=3$$So, solving these equations simultaneously for L and V, we obtain:$$L=\frac{10}{3}$$and $$V=\frac{20}{3}$$So the amount of methanol remaining in the liquid is $\frac{10}{3}(0.1)=\frac{1}{3}\ mole$.