A mixture of hydrogen and oxygen contains $$40\%$$ hydrogen by mass when the pressure is $$2.2 \text{ bar}$$. The partial pressure of hydrogen is ______ bar.

We need to find the partial pressure of hydrogen in the mixture.

The mixture contains $$40\%$$ hydrogen by mass.

Let the total mass of the mixture be $$100 \text{ g}$$.

Mass of $$H_2 = 40 \text{ g}$$

Mass of $$O_2 = 100 - 40 = 60 \text{ g}$$

Molar mass of $$H_2 = 2 \text{ g/mol}$$

Molar mass of $$O_2 = 32 \text{ g/mol}$$

$$n_{H_2} = \frac{40}{2} = 20 \text{ mol}$$

$$n_{O_2} = \frac{60}{32} = 1.875 \text{ mol}$$

Total moles = $$20 + 1.875 = 21.875 \text{ mol}$$

$$\chi_{H_2} = \frac{n_{H_2}}{n_{\text{total}}} = \frac{20}{21.875}$$

Using Dalton's law of partial pressures:

$$p_{H_2} = \chi_{H_2} \times P_{\text{total}}$$

$$= \frac{20}{21.875} \times 2.2$$

$$= \frac{20 \times 2.2}{21.875}$$

$$= \frac{44}{21.875}$$

$$= 2.0114 \approx 2 \text{ bar}$$

Hence, the partial pressure of hydrogen is 2 bar.