Question

We have two vessels of equal volume, one filled with hydrogen and the other with an equal mass of Hellum. The common temperature is ${27}^{\circ }C$.
If pressure of Hydrogen vessel is $2atm$, what is the pressure of Helium?

Answer 1

The equation of state for one mole of a gas is
$pV=RT=NkT$
Where $N$ is Avogadro's number (no. of molecules in one mole) and $k$ is Boltzmann's constant. If a gas has $n$ molecules, the equation of state will be
$pV=nkT$
For a given volume and a given temperature, we have
$p\propto n$.
Since $H_2$ and $He$ have the same volume and the same temperature $\left({27}^{\circ }C\right)$, we have
$\frac{p_H}{p_{He}}=\frac{n_H}{n_{He}}=\frac{2}{1}$
Here, $p_H=2atm.$
$\therefore p_{He}=1atm$.