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Ideal Gas Equation

The density o...

Question

The density of a gas at $27^{\circ} C$ and 760 $m m$ pressure is 24. Calculate the temperature at which it will be 18, the pressure remaining constant.

V = 200.1 K

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V = 400.2 K

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V = 800.4 K

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None of these

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Solution

The correct option is B $V = 400.2 K$
Given
$d_{1} = 24$
$T_{1} = 27^{\circ} C$ or $300.15 K$
$P_{1} = 760 m m$ or $1 a t m$
$d_{2} = 18$
$T_{2} = ?$
$P_{2} = 760 m m$ or $1 a t m$
$W e k n o w d e n s i t y = \frac{P M}{R T}$
$∴ \frac{d_{1}}{d_{2}} = \frac{P_{1}}{T_{1}} \times \frac{T_{2}}{P_{2}} = \frac{T_{2}}{T_{1}} (∵ P_{1} = P_{2} = 1 a t m)$
$∴ T_{2} = \frac{d_{1}}{d_{2}} \times T_{1}$
or $T_{2} = \frac{24}{18} \times 300.15 = 400.2 K$

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