Question

An evacuated glass vessel weighs 50 g when empty, 148 g when filled with a liquid of density 0.98 g/ml and 50.5 g when filled with an ideal gas at 760 mm Hg at 300K. Determine the molecular weight of the gas.

Answer 1

Given,  

Weight of the evacuated glass vessel = 50 g

Weight of liquid = 148 g; Liquid of density = 0.98 g/ml

When filled with ideal gas its weight is 50.5 g with gas at 760 mm Hg at 300 K

Actual weight of the liquid = 148 - 50 = 98 g

Liquid volume $= \frac { 98 }{ 0.8 }$ = 100 ml  

The vessel volume = vessel of 100 ml contain “ideal gas” at pressure and temperature of 760 mm Hg and 300 K respectively.

Weight of ideal gas = 50.5 - 50 = 0.5 g

Using, PV = nRT  

We Know that, $V=\frac { w }{ m }$

So, $PV=\frac { w }{ m } RT$

$\frac { 760 }{ 760 } \quad \times \quad \frac { 100 }{ 1000 } \quad =\quad \frac { 0.5 }{ m } \quad \times \quad 0.082\quad \times \quad 300\quad \left[ n\quad =\quad \frac { 0.5 }{ m } \right]$

(We know that pressure of ideal gas is 760mm Hg. Given pressure is also 760 mm Hg. So 760/760 = P = 1)  

Therefore, the “molecular weight” of gas (m) = 123 g/mol