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Addition of a Volatile Solute to a Volatile Solvent, Both of which are Miscible

Let XA and XB are the mole fractions of two volatile miscible liquids A and B having vapor pressures Description: 44991.png and Description: 45000.png, respectively, at temperature T kelvin. Therefore, vapor pressure of solution is given by
PTotal = PA + PB = Description: 45008.png + (1 – XA)Description: 45015.png
A plot between PTotal and XA is linear with slope equal to Description: 45026.png and intercept equal to Description: 45034.png Thus, the total pressure increases with increase in XA.

Graphical representation

If Description: 45041.png and Description: 45049.png are the mole fractions of A and B in the vapor phase, then according to Dalton’s law of partial pressure, we can write
Description: 45056.png
∴ Description: 45065.png
and Description: 45074.png
Description: 45149.png
Now, the vapors above the solution are collected and condensed. The condensed liquid is brought to the same temperature at which original liquid mixture was kept. Then, the vapor pressure (PTotal) of the resulting solution is given by
Description: 45082.png
where Description: 45091.png and Description: 45099.png are partial vapor pressures of A and B, respectively, in the resulting solution.
Description: 45110.png
Let Description: 45119.png and Description: 45127.png be the mole fractions of A and B in the vapors formed above the condensed liquid kept at the same temperature. Therefore,
Description: 45139.png

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