Question

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

• A. $3.0{\text{g dm}}^{-3}$
• B. $5.0{\text{g dm}}^{-3}$
• C. $6.0{\text{g dm}}^{-3}$
• D. $10.82{\text{g dm}}^{-3}$

Answer 1

The correct option is A $3.0{\text{g dm}}^{-3}$

As We Know,
$P=\frac{n}{V}RT=\frac{m}{V}\times \frac{RT}{M}=\frac{dRT}{M}$,
Because $\frac{m}{V}=d\left(\text{density}\right)$
or $d=\frac{PM}{RT}ord\propto \frac{P}{T}$
$\Rightarrow \frac{d_1}{d_2}=\frac{P_1}{P_2}\times \frac{T_2}{T_1}or{d}_2=\frac{d_1\times P_2\times T_1}{P_1\times T_2}$
$\Rightarrow d_2=\frac{5.46\times 1\times 300}{2\times 273}=3.0{\text{g dm}}^{-3}$
Hence, correct option is (a).