A mixture of hydrogen and oxygen has volume $2000 {cm}^{3}$ , temperature $300 K$ , pressure $100 kPa$ and mass $0.76 g$ . The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant $R = 8.3 J K^{- 1} {mol}^{- 1}$ ]

Question

A mixture of hydrogen and oxygen has volume $2000 {cm}^{3}$ , temperature $300 K$ , pressure $100 kPa$ and mass $0.76 g$ . The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be

[Take gas constant $R = 8.3 J K^{- 1} {mol}^{- 1}$ ]

TestHub · Accepted Answer

From the ideal gas equation, total number of moles in the mixture are,

$n = \frac{P V}{R T} = \frac{2 \times 10^{- 3} \times 100 \times 10^{3} \times 3}{25 \times 300}$ $\Rightarrow n = \frac{2}{25} = 0.08$

If number of moles of oxygen are $n_{1}$ and of hydrogen are $n_{2}$

$n_{1} + n_{2} = n = 0.08 \dots (1)$

And total mass of the mixture

$n_{1} (32) + n_{2} (2) = 0.76 \dots (2)$

Solving the above equations,

$n_{1} = 0.02$ and $n_{2} = 0.06$

$\frac{n_{2}}{n_{1}} = 3$

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