Question

If the density of a certain gas at ${30}^{\circ }{\text{C and 768 torr is 1.35 kgm}}^{-3}$ then its density at STP will be:

• A. $1.48{\text{kgm}}^{-3}$
• B. $0.125{\text{kgm}}^{-3}$
• C. $2.48{\text{kgm}}^{-3}$
• D. $1.80{\text{kgm}}^{-3}$

Answer 1

The correct option is A $1.48{\text{kgm}}^{-3}$

$\because d=\frac{PM}{RT}$
$\therefore$ for the same gas at two different pressures and temperatures, $\frac{d_1}{d_2}=\frac{P_1}{P_2}\times \frac{T_2}{T_1}$
$d_1=1.35{\text{kg m}}^{-3},P_1=768\text{torr},T_1=303\text{K}$
$d_2=?{\text{kg m}}^{-3},P_2=760\text{torr},T_2=273\text{K}\left(P_2\text{and}{T}_2\text{at STP}\right)$
$\therefore \frac{1.35}{d_2}=\frac{768}{760}\times \frac{273}{303}\Rightarrow d_2=1.48{\text{kgm}}^{-3}$