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  4. The plot of total vapour pressure as a function of mole fraction of the components of an ideal solution formed by mixing liquids X and Y is

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Q. The plot of total vapour pressure as a function of mole fraction of the components of an ideal solution formed by mixing liquids $X$ and $Y$ is

KVPYKVPY 2018

Solution:

According to Raoult's law,
$p=p^{0} \chi$
According to Dalton's law of partial pressure,
$p_{T} =p_{x}+p_{y}$
$p_{T} =p^{0} x \chi_{x}+p^{0}{ }_{y} \chi_{y} $
$=p^{0} x \chi_{x}+p^{0} y\left(1-\chi_{x}\right) $
$p_{T} =p^{0}{ }_{Y}+\left(p^{0}{ }_{x}-p^{0} y\right) \chi_{x}$
Thus, total vapour pressure of solution varies linearly with mole fraction of component $X$.
Case I, at $\chi_{X}=0$
$p_{T}=p^{0} Y$
Case II, at $X_{X}=1$
$p_{T} =p^{0} Y+p^{0} X-p^{0} Y $
$p_{T} =p_{X}^{0}$