First slide

Theory of dilute solutions

Question

Two components A and B form an ideal solution. The mole fraction of A and B in ideal solution are X_Aand X_B while that of in vapour phase, these components have their mole fractions as Y_A and Y_{B .}Then, the slope and intercept of plot of $\frac{1}{Y_{A}}$ vs $\frac{1}{X_{A}}$ will be:

Moderate

A

$\frac{P_{A} °}{P_{B} °}, \frac{P_{B} ° - P_{A} °}{P_{B} °}$
B

$\frac{P_{B} °}{P_{A} °}, \frac{P_{A} ° - P_{B} °}{P_{A} °}$
C

$\frac{P_{B} °}{P_{A} °}, \frac{P_{B} °}{P_{B} ° - P_{A} °}$
D

$P_{A} ° - P_{B} °, \frac{P_{A} °}{P_{B} °}$

Solution

$P_{A} = P °_{A} X_{A} (P °_{A} a n d P °_{B} = V . P o f p u r e A a n d B) P_{B} = P °_{B} X_{B} Y_{A} = \frac{P_{A}}{P_{A} + P_{B}} \Rightarrow \frac{P °_{A} X_{A}}{P °_{A} X_{A} + P_{B} ° (1 - X_{A})} \Rightarrow Y_{A} = \frac{P °_{A} X_{A}}{X_{A} (P °_{A} - P_{B} °) + P °_{B}} \Rightarrow \frac{1}{Y_{A}} = (\frac{P °_{A} - P_{B} °}{P °_{A}}) + \frac{P °_{B}}{P °_{A}} . \frac{1}{X_{A}} S o, s l o p e i s \frac{P °_{B}}{P °_{A}} a n d i n t e r c e p t = \frac{P °_{A} - P_{B} °}{P °_{A}}$

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