Answer to Question #144924 in General Chemistry for sssss

Question

liquids A and B form an ideal solution at 25 degrees Celsius . the vapor pressure of pure A is 300 torr and that of B is 125 torr . calculate the mole fraction of B in the solution when the vapor pressure of both A and B are equal at 25 degrees Celsius .

Answer 1

P_A=X_AP⁰_A

P_B=X_BP⁰_B

Where, P_A=new vapor pressure of A

P_B=new vapor pressure of B

X_A=mole fraction of A

X_B=mole fraction of B

P⁰_A=Vapor pressure of pure A

P⁰_B=Vapor pressure of pure B

P⁰_A=300torr

P⁰_B=125torr

According to the question, P⁰_B= P_B

Therefore, X_AP⁰_A=X_BP⁰_B

If mole fraction of A is X_A then, mole fraction of B can be expressed as (1-X_A)

300X_A=125(1-X_A)

300X_A=125- 125X_A

300X_A+125X_A=125

425X_A=125

X_A=5/17

X_B= (1-X_A)=(1-5/17)

mole fraction of B= 12/17