Question

At $0^{\circ }C$, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Answer 1

Density (d) of the substance at temperature (T) can be given by the expression,
$d=\frac{Mp}{RT}$
Now, density of oxide $\left(d_1\right)$ is given by,
$d_1=\frac{M_1{p}_1}{RT}$
Where, $M_1$ and $p_1$ are the mass and pressure of the oxide respectively.
Density of dinitrogen gas $\left(d_2\right)$ is given by,
$d_2=\frac{M_2{p}_2}{RT}$
Where, $M_2$ and $p_2$ are the mass and pressure of the oxide respectively.
According to the given question,
$d_1=d_2\therefore M_2{p}_1=M_2{p}_2$
Given
$p_1=2bar{p}_2=5bar$
Molecular mass of nitrogen, $M_2=28g/mol$
Now, $M_1=\frac{M_2{p}_2}{p_1}=\frac{28\times 5}{2}=70g/mol$
Hence, the molecular mass of the oxide is 70 g/mol.