Two liquids A and B form an ideal solution. The solution has a vapor pressure of 700 torr at 80 deg C. It is distilled till 2/3 rd of the total solution is collected as the condensate.
The composition of the condensate is x_A' = 0.75 and that of the residue is x_A 0.30. If the vapor pressure of the residue at 80 deg C is 600 torr, Which of the following is/ are true ?
A) The composition of the original liquid was x_A = 0.6
B) The composition of the original liquid was x_A = 0.4
C) vapor pressure of pure solution of A is 2500/3 torr
D) vapor pressure of pure solution of B is 500 torr.
Answers
Assume X_A = 0.6
P = 0.6 P_A + 0.4 P_B = 700 torr
P" = 0.3 P_A + 0.7 P_B = 600 torr
Solving the two equations , P_B = 500 torr and P_A=2500/3 torr
Let there be N total number of moles in the total solution initially. Let y*N number of moles of B be present in the condensate. So as mole fraction of A is 0.75, there are 3yN moles of A in condensate.
So in the residue we have (0.6 - 3y) N moles of A and (0.4 -y)N moles of B.
mole fraction in residue of A: (0.6-3y) / [0.4 -y +0.6-3y] = 0.30
solving that y = 1/6
So initially, there are 0.6N moles of A, 0.4N moles of B. In the condensate there are N/2 moles of A and N/6 moles of B. Then in the residue there are 0.1N moles of A and 7N/30 moles of B.
Condensate size = 2/3N moles. residue : 1N/3 moles The data matches with given facts.
As the numbers are consistent, that assumption is true.
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checking by volumes. V = volume of solution. VA = volume per mole of A.
V/N = 0.6 VA + 0.4 VB V'/N = 0.5 VA + VB/6 V"/N = 0.1 VA + 7 VB/30
given, V' = 2 * V" => 0.5 VA + VB/6 = 0.2 VA + 7/15 VB
=> VA = VB => V = VA * N = VB * N
Then V' = 2/3 V and V" = 1/3 V So consistent.