Question

Two liquids, A and B have the same molecular weights and form an ideal solution. The solution of composition $x_A$ has the vapour pressure 700 mm Hg at 80°C. The above solution is distilled without reflux till 3/4 of the solution is collected as condensate. The composition of the condensate is $x_A^{'}$= 0.75 and that of residue is $x_A$ = 0.3. If the vapour pressure of the residue at 80°C is 600 mm Hg, calculate $x_A$, $P_A^0$ and $P_B^0$.

Answer 1

$x_A = 0.6375$

$P_A^0 = \frac{2180}{27}$ mm Hg

$P_B^0 = \frac{460}{9}$ mm Hg

Answer 2

Here's a detailed explanation of the solution:

1. Calculate the initial mole fraction $x_A$ using the conservation of moles of component A during simple distillation, given the initial amount distilled and the compositions of condensate and residue.
2. Apply Raoult's Law for ideal solutions, $P_{total} = x_A P_A^0 + x_B P_B^0$.
3. Set up a system of two linear equations using Raoult's Law for the initial solution and for the residue, with $P_A^0$ and $P_B^0$ as unknowns.
4. Solve the system of equations to find the values of $P_A^0$ and $P_B^0$.