For an ideal mixture of two liquids ‘A’ and ‘B’ in which, mole fraction of ‘A’ (XA) is 0.5 and given that PA0PB0 is 53. Find how many repeated distillations are necessary to get a small quantity of the distillate containing at least 80% of A.

PA0PB0×XAXB=PAPBi) 53×0.50.5=53 ∴ XA1 in the first condensate is 58ii) 111'y 53×5/83/8=259 is XA11 in the second condensate 2534(74%)iii) 53×25/349/34=12527iv) X4111 in the third condensation is 125152vi) %A=125152×100=82

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For an ideal mixture of two liquids ‘A’ and ‘B’ in which, mole fraction of ‘A’ $(X_{A})$ is 0.5 and given that $\frac{P_{A}^{0}}{P_{B}^{0}}$ is $\frac{5}{3}$ . Find how many repeated distillations are necessary to get a small quantity of the distillate containing at least 80% of A.

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Detailed Solution

$\frac{P_{A}^{0}}{P_{B}^{0}} \times \frac{X_{A}}{X_{B}} = \frac{P_{A}}{P_{B}}$

i) $\frac{5}{3} \times \frac{0.5}{0.5} = \frac{5}{3}$
$∴ X_{A}^{1}$ in the first condensate is $\frac{5}{8}$
ii) $111^{'} y \frac{5}{3} \times \frac{5 / 8}{3 / 8} = \frac{25}{9}$ is $X_{A}^{11}$ in the second condensate $\frac{25}{34} (74 %)$
iii) $\frac{5}{3} \times \frac{25 / 34}{9 / 34} = \frac{125}{27}$
iv) $X_{4}^{111}$ in the third condensation is $\frac{125}{152}$
vi) $% A = \frac{125}{152} \times 100 = 82$