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

(70) The density $(d)$ of a gas at a given temperature $(T)$ and pressure $(p)$ is given by the ideal gas equation: $d = \frac{Mp}{RT}$.
For the oxide,$d_1 = \frac{M_1 p_1}{RT}$.
For dinitrogen,$d_2 = \frac{M_2 p_2}{RT}$.
Given that $d_1 = d_2$ at the same temperature,we have:
$\frac{M_1 p_1}{RT} = \frac{M_2 p_2}{RT}$
$M_1 p_1 = M_2 p_2$
Given values:
$p_1 = 2 \ bar$
$p_2 = 5 \ bar$
$M_2 = 28 \ g/mol$ (for $N_2$)
Substituting the values:
$M_1 \times 2 = 28 \times 5$
$M_1 = \frac{140}{2} = 70 \ g/mol$.
The molecular mass of the oxide is $70 \ g/mol$.