Question

The density of a gas is 1.964 g dm${}^{-3}$ at 273 K and 76 cm. Hg. The gas is:

• A. $C{H}_4$
• B. $C_2{H}_6$
• C. $C{O}_2$
• D. $Xe$

Answer 1

The correct option is C $C{O}_2$

$pV=nRT$ or $pV=\frac{w}{M}RT$ or $M=\frac{w}{V}\frac{RT}{p}$ or $M=d\frac{RT}{p}$

Here, $d=1.964g/dm$${}^3$ $=1.964\times {10}^{-3}g/cc$

P = 76 cm = 760 mm Hg = 1 atm

R = 0.0821 L atm K${}^{-1}$ mol${}^{-1}$

$=82.1ccatm{K}^{-1}mo{l}^{-1}$

$T=273K$

$\therefore M=\frac{1.964\times {10}^{-3}\times 82.1\times 273}{1}=44$

The molecular weight of $C{O}_2$ is 44.

So, the gas is $C{O}_2$.