I am studying Chemistry by Zumdahl and Zumdahl (9th edition) and I have come across a question in Chapter 11 that I can't figure out the explanation for:
Liquid A has vapor pressure x , and liquid B has vapor pressure y . What is the mole fraction of the liquid mixture if the vapor above the solution is 30% A by moles?
I know that Raoult's Law tells us that the total vapor pressure is χx + (1-χ)y in this case. I also assume that the total vapor must be 0.3x + 0.7y given the other constraint of the question. This would mean the answer should be:
0.3x + 0.7y = χx + (1-χ)y
However this leads to the answer χ = 0.3, whereas the text gives the answer as 0.3y/(0.7x+0.3y)
What have I got wrong? (Also sorry for not formatting it properly but I'm a noob here and I can't figure out the equation formatting).