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State and Path Variables, Functions

If the densit...

Question

If the density of a certain gas at $30^{o} C$ and $768 t o r r$ is $1.35 k g / m^{3}$ , the density at STP would be:

A

1.48 k g / m^{3}

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B

1.58 k g / m^{3}

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C

1.25 k g / m^{3}

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D

1.4 k g / m^{3}

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Solution

The correct option is A $1.48 k g / m^{3}$
From Ideal gas law,

$P M = d R T$

$P_{1} = 768 t o r r$
$T_{1} = 30^{0} C = 303 K$
$d_{1} = 1.35 k g / m^{3}$

At STP,
$T_{2} = 273 K$
$P_{2} = 760 t o r r$

$\frac{P_{1}}{P_{2}} = \frac{d_{1} T_{1}}{d_{2} T_{2}}$

$\frac{768}{760} = \frac{1.35 \times 303}{d_{2} \times 273}$

$d_{2} = 1.48 k g / m^{3}$

Hence, option A is correct.

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