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Ideal Gas Equation

Density of a ...

Question

Density of a gas is found to be $5.46 g / d m^{3}$ at $27^{\circ} C$ at 2 bar pressure. What will be its density at STP?

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Solution

Given,
$d_{1} = 5.46 g / d m^{3}$
$p_{1} = 2 b a r$
$T_{1} = 27^{\circ} C = (27 + 273) K = 300 K$
$P_{2} = 1 b a r$
$T_{2} = 273 K$
$d_{2} = ?$
The density $(d_{2})$ of the gas at STP can be calculated using the equation,
$d = \frac{M . p}{R T}$
therefore $\frac{d_{1}}{d_{2}} = \frac{\frac{M p_{1}}{R T_{1}}}{\frac{M p_{2}}{R T_{2}}}$
$\Rightarrow \frac{d_{1}}{d_{2}} = \frac{p_{1} T_{2}}{p_{2} T_{1}}$
$\Rightarrow d_{2} = \frac{p_{2} T_{1} d_{1}}{p_{1} T_{2}}$
= $\frac{1 \times 300 \times 5.46}{2 \times 273}$
$= 3 g d m^{- 3}$
Hence, the density of the gas at STP will be $3 g d m^{- 3}$

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Density of a gas is found to be 5.46 g/dm³ at 27 °C at 2 bar pressure. What will be its density at STP?

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