For an ideal solution with $p_{A}^{o} > p_{B}^{o}$ , which of the following is true?

{(x_{A})}_{l i q u i d} = {(x_{A})}_{v a p o u r}

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{(x_{A})}_{l i q u i d} > {(x_{A})}_{v a p o u r}

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{(x_{A})}_{l i q u i d} < {(x_{A})}_{v a p o u r}

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{(x_{A})}_{l i q u i d}

and

{(x_{A})}_{v a p o u r}

cannot be correlated with each other.

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Solution

The correct option is C ${(x_{A})}_{l i q u i d} < {(x_{A})}_{v a p o u r}$
As we know the Partial pressure of A is greater than B in pure state means A is more volatile than B, Therefore A is more in the vapour state.

From Raoult's law, $P_{A} = P_{A}^{0} \times x_{A}$

In vapour phase,
$x_{A} > x_{B}$ $[∵ B . P ._{A} < B . P ._{B}]$
In liquid phase,
$x_{B} > x_{A}$
Comparing A itself in liquid and vapour phase
$x_{A} (v a p o u r) > x_{A} (l i q u i d)$

The correct option is C.

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P_{T o t a l} = P_{A}^{o} \times X_{A} + P_{B}^{o} \times X_{B}

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