[poppinjoshi]

This is a multi-choice question. I am typing in the exact text.

Q) An equimolar saturated vapor mixture of A (more volatile) and B at 1 atm, is subjected to equilibrium condensation to yield 50 mol% of the feed as liquid. If the relative volatility is constant, the mole fraction of A in the equilibrium liquid phase shall be: relative volatility = alpha

let (just for easy typing): under-root(alpha)=k

a] k/(1+k)  b] k  c] 1/(1+k) d] (1+k)/k

Correct option is known. I'm not sure if I should tell it write now.
I have looked back at the basic definition of alpha many times now, (to solve this) expressed in terms of partial pressures; and I have tried to use Raoult's law, and played around with the partial pressures.

Please give an explained solution if its not too much trouble; (if its not a one line answer) since I'm not sure which concept I may be missing out on.
Referring- Treybal and McCabe-Smith-Hariott

Thank you 

[poppinjoshi]

May i please know why no one is replying!...the answer is C

[curiouscat]

It's an interesting problem. c is correct but I want to see your working a bit more. You don't need partial pressures.

Show me your equations.

[poppinjoshi]

Thank you for asking me to show my working, I was writing it down more neatly;and I got the solution.

Basically for component A, material balance leads to
(assuming F=100 mol)
1=mole fraction in liquid+mole fraction in vapor ....eq1

and then we can substitute y=1-x in relative volatility equation to get a quadratic equation, from where x was determined by the root.

I think I need to keep in mind that I have to first search for two equations always-material balance and equilibrium.
In above case I  was trying to solve using only equilibrium relationship.