Question

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

Answer 1

Given,
$d_1=5.46g/d{m}^3$
$p_1=2bar$
$T_1={27}^{\circ }C=(27+273)K=300K$
$P_2=1bar$
$T_2=273K$
$d_2=?$
The density $\left(d_2\right)$ of the gas at STP can be calculated using the equation,
$d=\frac{M.p}{RT}$
therefore $\frac{d_1}{d_2}=\frac{\frac{M{p}_1}{R{T}_1}}{\frac{M{p}_2}{R{T}_2}}$
$\Rightarrow \frac{d_1}{d_2}=\frac{p_1{T}_2}{p_2{T}_1}$
$\Rightarrow d_2=\frac{p_2{T}_1{d}_1}{p_1{T}_2}$
=$\frac{1\times 300\times 5.46}{2\times 273}$
$=3gd{m}^{-3}$
Hence, the density of the gas at STP will be $3gd{m}^{-3}$