Question

At 300 k the vapour pressure of an ideal solution containing 3 moles of a and 2 moles of b is 600 torr.At the same temperature if 1.5 mole of a and 0.5 of c is added to the solution the vapour presssure decreases by 30 torr. What is the value of p0b

Answer 1

Answer: the value of $p_B^0$ is 1037.25 torr

Explanation: According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.

$p_1=x_1p_1^0$ and $p_2=x_2P_2^0$

where, x = mole fraction

$p^0$ = pressure in the pure state

$x_A=\frac{3}{3+2}=\frac{3}{5}=0.6$

$x_B=\frac{2}{3+2}=\frac{2}{5}=0.4$

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_1+p_2$

$p_{total}=x_Ap_A^0+x_BP_B^0$

$600torr=0.6\times p_A^0+0.4\times p_B^0$     (1)

Also: when 1.5 mole of A and 0.5 mole of B is added to the above solution

$x_A=\frac{4.5}{4.5+2.5}=0.64$

$x_B=\frac{2.5}{4.5+2.5}=0.36$

$570=0.64\times p_A^0+0.36\times p_B^0$        (2)

Solving 1 and 2

$p_B^0=1037.25torr$