Question

Some potassium permanganate was heated in a test tube. After collecting one litre of oxygen at room temperature, it was found that the test tube had undergone a loss in mass of $1.32g$. If one litre of hydrogen under the same conditions of temperature and pressure has a mass of $0.0825g$.
Calculate the relative molecular mass of oxygen.

Answer 1

Let $P$ be the pressure and $V$ be the volume of oxygen gas and hydrogen gas.

Then,

For oxygen gas

$PV=\frac{1.32}{M}\times R\times 298$

where M is the relative molecular mass of oxygen gas

For hydrogen gas

$PV=\frac{0.0825}{2}\times R\times 298$

Now,

$\frac{1.32}{M}\times R\times 298=\frac{0.0825}{2}\times R\times 298$

$M=\frac{1.32\times 2}{0.0825}$

$M=32g$

Hence, relative molecular mass of oxygen gas is 32 gm