Question

An evacuated glass vessel weighs $50.0\text{g}$ when it is empty and $148.0\text{g}$ when it is filled with a liquid having a density of $0.98{\text{g/mL}}^{-1}$ and $50.5\text{g}$ when it is filled with an ideal gas at $760\text{mm}Hg$ and $300\text{K}$. Determine the molecular weight of the gas (round off to the nearest possible integer).

Answer 1

Mass of the liquid in the glass vessel $=148-50=98\text{g}$
Volume of the liquid$=\frac{\text{mass}}{\text{density}}=\frac{98}{0.98}=100\text{mL}$
Similarly, mass of the gas $=50.5-50=0.5\text{g}$
Since, the volume of the liquid is 100 $mL$, it means that the volume of the glass vessel is 100 mL
On applying the ideal gas equation, we have,
$PV=\frac{w}{M}RT$
where, w = weight of the gas
M = molecular weight of the gas
P = 760 $mmHg$ = 1 atm
Substituting the values,
$\frac{760}{760}\times \frac{100}{1000}=\frac{0.5}{M}\times 0.0821\times 300$
On solving, the molecular weight of the gas M =123 $g/mol$