Question

A mixture of hydrogen and oxygen has volume $500{\text{cm}}^3,$ temperature $300\text{K},$ pressure $400\text{kPa}$ and mass $0.76\text{g}.$ The ratio of masses of oxygen to hydrogen will be

• A. $16:3$
• B. $3:16$
• C. $8:3$
• D. $3:8$

Answer 1

The correct option is A $16:3$

Let $n_o$ be number of moles of oxygen and $n_h$ be number of moles of hydrogen
Mass of one mole of hydrogen is $2\text{g}$
Mass of one mole of oxygen is $32\text{g}$
Given total mass of mixture is $0.76\text{g}$
$32n_o+2n_h=0.76$
$16n_o+n_h=\mathrm{0.38....}\left(i\right)$
From ideal gas equation
$PV=(n_o+n_h)RT$
$n_o+n_h=\frac{PV}{RT}=\frac{400\times {10}^3\times 500\times {10}^{-6}}{\frac{25}{3}\times 300}=0.08$
$n_o+n_h=\mathrm{0.08...}\left(ii\right)$

Subtracting equations $\left(ii\right)\&\left(i\right)$

$15n_o=0.3\Rightarrow n_o=0.02$

$n_h=0.08-n_o=0.06$

Ratio of mass of oxygen to mass of hydrogen is $\frac{32n_o}{2n_h}=\frac{32\times 0.02}{2\times 0.06}=\frac{16}{3}$

Option $d$ is correct