Question

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

• A. $CH_4$
• B. $C_2H_6$
• C. $CO_2$
• D. $Xe$

Answer 1

Answer: (C)

We know that
$P V=n R T$
or $P V =\frac{w}{m} R T $
or $m =\frac{w}{V} \frac{R T}{P}$
or $M=d \frac{R T}{P}$
$d =1.964 g / dm ^{3}=1.964 \times 10^{-3} \,g / cc $
$P =76\, cm =1 \,atm$
$R =0.0812\, L \,atm K ^{-1} mol ^{-1} $
$=82.1 \,cc \,atm K ^{-1} mol ^{-1}$
$T =273 K $
$m =\frac{1.964 \times 10^{-3} \times 82.1 \times 273}{1}=44$
The molecular weight of $CO _{2}$ is 44 .
So, the gas is $CO _{2}$