Question

An evacuated glass vessel weighs $50 \,g$ when empty, $144.0\, g$ when filled with a liquid of density $0.47 \,g \,ml^{-1}$ and $50.5\, g$ when filled with an ideal gas at $760 \,mm \,Hg$ at $300\, K$. The molar mass of the ideal gas is: ($R= 0.0821\, L$ atm. $K^{-1} \,mol^{-1}$)

• A. $61.575$
• B. $130.98$
• C. $123.75$
• D. $47.87$

Answer 1

Answer: (A)

$61.575$

Answer 2

Weight of empty glass vessel = $50\, g$
Weight of glass vessel filled with liquid = $144.0\, g$
$\therefore$ Weight of liquid $=144-50=94\, g$
Density of liquid $=0.47\, gmL ^{-1}$
$\therefore$ Volume of liquid $=\frac{94}{0.47}=200\, mL =0.2\, L$
Mass of glass vessel filled with gas $=50.5\, g$
$\therefore$ Mass of gas $(m)=50.5-50=0.5\, g$
By using ideal gas equation,
$pV =\frac{ m }{ W } RT$
where, $p =760\, mm,\, Hg =1\, atm$,
$V= 0.2\,L\, T =300\,K$
and $R =0.0821\, L$ atm $K ^{-1} mol ^{-1}$
$\therefore$ Molar mass $( M )=\frac{ mRT }{ pV }$
$=\frac{0.5 \times 0.0821 \times 300}{1 \times 0.2}$
$=61.575\, g\, mol ^{-1}$