Question

The pressure in a vessel that contained pure oxygen dropped from $2000$ torr to $1500$ torr in $40$min as the oxygen leaked through a small hole into a vacuum. When the same vessel was filled with another gas, the pressure dropped from $2000$ torr to $1500$ torr in $80$ min. What is the molecular weight of the second gas?

Answer 1

The pressure drop = 2000-1500 = 500 torr

Gas is oxygen having molar mass = 16g

In second case, pressure drop = 2000-1500 = 500torr

Rate of diffusions are inversely proportional to molar masses

$\frac{R_{d_1}}{R_{d_2}}=\sqrt{\frac{M_2}{M_1}}$

$\frac{500}{500}=\sqrt{\frac{M_2}{16}}$

Squaring both sides and calculating we get

M2 = 16g