Question

$3.7\text{g}$ of a gas at $25{}^{\circ }\text{C}$ occupies the same volume as $0.184\text{g}$ of hydrogen at $17{}^{\circ }C$ and at the same pressure. What is the molar mass of the gas in grams (g)?

• A. 41.33
• B. 55.26
• C. 15.38
• D. 33.69

Answer 1

The correct option is A 41.33

For hydrogen,
$w=0.184\text{g};T=17+273=290\text{K};M=2$
We know that, $PV=\frac{w}{M}RT$
$=\frac{0.184}{2}\times R\times 290...\left(i\right)$
For the unknown gas,
$w=3.7\text{g};T=25+273=298\text{K};M=?$
$PV=\frac{3.7}{M}\times R\times 298...\left(ii\right)$
Equating both the equations as P and V are same :
$\frac{3.7}{M}\times R\times 298=\frac{0.184}{2}\times R\times 290$
or $M=\frac{3.7\times 298\times 2}{0.184\times 290}=41.33g$