Question

Density of a gas is found to be $2.5g/d{m}^3$ at ${27}^0$C and $4$ atm pressure. The density of same gas (in$g/d{m}^3$) at STP will be:

• A. $0.69$
• B. $1.42$
• C. $0.63$
• D. $1.83$

Answer 1

The correct option is A $0.69$

$d=\frac{MP}{RT}$

$\Rightarrow \frac{d_1}{d_2}=\frac{P_1}{T_1}\times \frac{T_2}{P_2}$ for the same gas at different $T$ & $P$ $⟶\left(1\right)$

Initial conditions,

$d_1=2.5g/d{m}^3$, $T_1=27+273=300K$, $P_1=4atm$

At STP,

$d_2=?$, $T_2=273K$, $P_2=1atm$

$\therefore \left(1\right)\Rightarrow \frac{2.5}{d_2}=\frac{4}{300}\times \frac{273}{1}$

$\therefore d_2=\frac{2.5\times 300}{4\times 273}=0.686g/d{m}^3\simeq 0.69g/d{m}^3$