Question

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? 50% A? 80% A? (Calculate in terms of xand y.) What is the mole fraction of the vapor above the solution if the liquid mixture is 30. % A by moles? 50.% A? 80.% A? (Calculate in terms of xand y.)

Short answer

The mole fraction of the vapor above the solution if the liquid mixture is 30. % A by moles is

Xa liq = 0.6

Xb liq = 0.4

Step-by-step solution

Step 1:

Let’s assume

vapor pressure A = X
vapor pressure B = Y
total p of vapor = Ptotal = Xav + Ybv
Xa in vapor = Xav/ (Xav + Ybv) = 0.3
Xb in vapor = Ybv/ (Xav + Ybv) = 0.7

In liquid
Xa liq = P^o_{a liq}*0.3/Ptotal vapor = P^o_{a liq}/ (Xav + Ybv)

Similarly for Xb liq =
Xb = P^o_{b liq}/ (Xav + Ybv)

We can calculate Pa and Pb this way

Pa = Xa*Poa = 0.6*100 = 60 mm
Pb = Xb*Pob = 0.4*200 = 80 mm

Total vapor pressure above liquid is 60+80 = 140 mm.
Xa vapor = 60/140 = about 0.429
Xb vapor = 80/140 = about 0.571

Step 2:

We want to take the Xa and Xb in the vapor and get the Xa, and Xb in liquid

Xa liq = Xav*Ptotal/Po = 0.429*140/100 = 0.6
Xb liq = Xbv*Ptotal/Po = 0.571*140/200 = 0.4