States of Matter 1 Question 74
74. An evacuated glass vessel weighs $50.0 \mathrm{~g}$ when empty $148.0 \mathrm{~g}$ when filled with a liquid of density $0.98 \mathrm{~g} \mathrm{~mL}^{-1}$ and $50.5 \mathrm{~g}$ when filled with an ideal gas at $760 \mathrm{~mm} \mathrm{Hg}$ at $300 \mathrm{~K}$. Determine the molar mass of the gas.
(1998, 3M)
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Answer:
Correct Answer: 74. $\left(2.46 \mathrm{~m}^{3}\right)$
Solution:
- Mass of liquid $=148-50=98 \mathrm{~g}$
$\Rightarrow$ Volume of liquid $=\frac{98}{0.98}=100 \mathrm{~mL}=$ volume of flask
mass of gas $=50.5-50=0.50 \mathrm{~g}$
Now applying ideal gas equation : $p V=\left(\frac{w}{M}\right) R T$
$\Rightarrow \quad M=\frac{w R T}{p V}=\frac{0.5 \times 0.082 \times 300}{1 \times 0.1}=123 \mathrm{~g} \mathrm{~mol}^{-1}$
