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States of Matter — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryStates of Matter3 Marks
Question
An evacuated vessel weights 50 g when empty, 144 g when filled with liquid of density $0.47 \mathrm{~g} \mathrm{~mL}^{-1}$ and 50.5 g when filled with ideal gas at 760 mm Hg and 300 K . Calculate molar mass of ideal gas. $\left[R=0.08212\right.$ atom $\left.\mathrm{K}^{-1} \mathrm{~mol}^{-1}\right]$
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Answer

Mass of liquid filling the vessel = 144g - 50g = 94g
Volume of liquid = Volume of vessel
$= \frac{\text{Mass of liquid }}{\text{density of liquid}} = \frac{94}{0.47\text{g mL}^{-1}}$
$\text{V = 200mL = 0.2L, T = 300K,}\\\text{P = 760mm = 1atm}$
$\text{Mass of gas = 50.5g} - \text{50.0g = 0.5g, M = ?}$
$\text{R} = 0.0821 \text{L atm} \text{K}^{-1} \text{mol}^{-1}$
$\text{pV} = \frac{\text{m}}{\text{M}} \times \text{RT}$
$1\times 0.2 = \frac{0.5}{\text{M}}\times 0.0821 \times 300$
$\text{M}= \frac{24.63 \times 10}{2 \times 2} = \frac{246.3}{4}$
$= 61.575 \text{g} \text{ mol}^{-1}$

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