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Relationship between Vapor Density & Relative Molecular Mass

If Xm, Xp a...

Question

If $X_{m}, X_{p}$ and $X_{v}$ are mole fraction, pressure fraction and volume fraction respectively for a gaseous component in mixture. Select the correct relationship between them.

A

X_{m} = X_{p} = X_{v}

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B

X_{p} = \frac{1}{X_{v}}

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C

X_{m} = \frac{1}{X_{P}} = \frac{1}{X_{V}}

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D

X_{V} = \frac{1}{X_{p}} = \frac{1}{X_{m}}

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Solution

The correct option is A $X_{m} = X_{p} = X_{v}$
As we know,
$P_{A}^{'} = P_{T} \cdot X_{A}$
$∴ X_{A} = \frac{P_{A}^{'}}{P_{T}}$
i.e., Pressure fraction $=$ mole fraction
Also, from Amagat's law of partial volume total volume of a mixture of gas is equal to the sum of partial volume of the constituents gases, i.e.,
$V_{A}^{'} = V_{T} \cdot X_{A}$
$\frac{V_{A}^{'}}{V_{T}} = X_{A}$
i.e., volume fraction is equal to mole fraction.
So, pressure fraction $=$ mole fraction $=$ volume fraction

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