Question

An ideal mixture of liquids A and B with 2 moles of A and 2 moles of B has a total vapour pressure of 1 atm at a certain temperature. Another mixture with 1 mole of A and 3 moles of B has a vapour pressure P which is greater than 1 atm. But if 4 moles of C are added to the second mixture, the vapour pressure comes down to 1 atm. Vapour pressure of C, $P_C^o=0.8$ atm. What is the value of P?

Answer 1

When 2 moles of A and 2 moles of B are mixed $\frac{P_A^0}{2}+\frac{P_B^0}{2}=1atm$ $\Rightarrow P_A^0+P_B^0=2atm$
When 1 moles of A, 3 moles of B and 4 moles of C are mixed
$\frac{P_A^0}{8}+\frac{3P_B^0}{8}+\frac{4P_C^0}{8}=1atm$ $\Rightarrow P_A^0+3P_B^0+4P_C^0=8atm$
As $P_C^0=0.8atm$ So, $P_A^0+3P_B^0=4.8atm$
Hence the solution containing 1 moles A and 3 moles of B
$\frac{P_A^o}{4}+\frac{3P_B^o}{4}=\frac{4.8}{4}=1.20$