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Ideal Gas Equation

To an evacuat...

Question

To an evacuated vessel with movable piston under total pressure of $1 a t m, 0.1 m o l$ of $H e$ and $1.0 m o l$ of an unknown compound (vapour pressure = $0.68 a t m$ at $0^{\circ} C$ ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at $0^{\circ} C$ is close to (nearest integer)

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Solution

The external pressure or total pressure is $1 a t m$ and the vapour pressure of the compound is $0.68 a t m$ .
Let $n_{x}$ be the moles of unknown compound present in vapour form.
Now according to Dalton's law:
Partial pressure of gas $\propto$ mole fraction.
Partial pressure of gas $=$ mole fraction $\times$ Total pressure
$0.68 = \frac{n_{x}}{n_{x} + n_{H e}} \times 1 0.68 = \frac{n_{x}}{n_{x} + 0.1} n_{x} = 0.212 m o l$
Ideal gas equation :
$P V = n_{T} R T n_{T} = n_{H e} + n_{x} V = \frac{n_{T} R T}{P} V = \frac{(0.212 + 0.1) \times 0.0821 \times 273}{1} \approx 7 L$

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Ideal Gas Equation

Standard XII Chemistry

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