An ideal solution has two components A and B- A is more volatile than B- i-e- PA-PB- and also PA-Ptotal- If XA and YA are mole fractions of components A in liquid and vapour phases- then -

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D/L Nomenclature

An ideal solu...

Question

An ideal solution has two components $A$ and $B$ . $A$ is more volatile than $B$ , i.e., $P_{A}^{\circ} > P_{B}^{\circ}$ and also $P_{A}^{\circ} > P_{t o t a l}$ . If $X_{A}$ and $Y_{A}$ are mole fractions of components $A$ in liquid and vapour phases, then :

X_{A} = Y_{A}

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X_{A} > Y_{A}

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X_{A} < Y_{A}

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Data insufficient

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Solution

The correct option is C $X_{A} < Y_{A}$
According to Raoult's law, the partial pressure of a component of solution is equal to its mole fraction in the solution multiplied by its vapour pressure in pure state.
Hence, $P_{A} = P_{A}^{o} X_{A}$ ......(1)
According to Dalton law of partial pressures, the partial pressure of a component of a gas is equal to the product of the total pressure and mole fraction of the gas in gaseous state.
$P_{A} = P_{T} Y_{A}$ ......(2)
Combining equations (1) and (2) we get $P_{A}^{o} X_{A} = P_{T} Y_{A}$
But $P_{A}^{o} > P_{T}$
Hence, $X_{A} < Y_{A}$

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