Question

$2.9$ g of gas at $95{}^{\circ }C$ occupied the same volume as 0.184 g of dihydrogen at $17{}^{\circ }C$ at the same pressure. What is the molar mass of the gas?

Answer 1

Let M be the molar mass of the gas.
The number of moles of the gas, $n=\frac{2.9}{M}$.
The volume of the gas is $V=\frac{nRT}{P}$.
$V=\frac{2.9R\times 368}{MP}$
The number of moles of dihydrogen are $n^{\prime }=\frac{0.184}{2}=0.092$
The volume of dihydrogen gas is $=\frac{0.092\times R\times 290}{P}$.
At same pressure P, the volume of gas is equal to volume of dihydrogen.
$0.092R\times 290=\frac{2.9R\times 368}{M}$
$M=\frac{2.9\times 368}{0.092\times 290}=40$
Thus, the molar mass of the gas is $40g/mol$.