Question

Pressure of 1 g of an ideal gas A at 27 ${}^{\circ }C$ is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses?

Answer 1

Let M and M' be the molar masses of ideal gases A and B respectively.
The number of moles of gas A and B are $\frac{1}{M}$ and $\frac{2}{M^{\prime }}$ respectively.
Let P and P' be the pressures of gases A and B respectively.
$P=2bar$
$P+P^{\prime }=3bar$
$P^{\prime }=3-2=1bar$
The ideal gas equations for two gases A and B are,
$PV=nRT$......(i)
$P^{\prime }V=n^{\prime }RT$......(ii)
Divide equation (i) by equation (ii).
$\frac{P}{P^{\prime }}=\frac{n}{n^{\prime }}=\frac{1\times M^{\prime }}{2\times M}=\frac{M^{\prime }}{2M}$

$\frac{M^{\prime }}{M}=2\frac{P}{P^{\prime }}=\frac{2\times 2}{1}=4$

$M^{\prime }=4M$