A mixture of hydrogen and oxygen at `1` bar pressure contains `20%` of hydrogen by weight. Calculate the partial pressure of hydrogen.

Explanation

To solve the problem of calculating the partial pressure of hydrogen in a mixture of hydrogen and oxygen at 1 bar pressure with 20% hydrogen by weight, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the weight of the components in the mixture**:
- Since the mixture contains 20% hydrogen by weight, if we consider a total weight of 100 grams of the mixture, then:
- Weight of hydrogen = 20 grams
- Weight of oxygen = 100 grams - 20 grams = 80 grams

2. **Calculate the number of moles of hydrogen and oxygen**:
- The number of moles of hydrogen (H₂) can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molecular weight}} \]
- Molecular weight of hydrogen (H₂) = 2 g/mol
- Number of moles of hydrogen = \(\frac{20 \text{ g}}{2 \text{ g/mol}} = 10 \text{ moles}\)

- The number of moles of oxygen (O₂) can be calculated similarly:
- Molecular weight of oxygen (O₂) = 32 g/mol
- Number of moles of oxygen = \(\frac{80 \text{ g}}{32 \text{ g/mol}} = 2.5 \text{ moles}\)

3. **Calculate the total number of moles in the mixture**:
- Total moles = Moles of hydrogen + Moles of oxygen
- Total moles = \(10 + 2.5 = 12.5 \text{ moles}\)

4. **Calculate the mole fraction of hydrogen**:
- Mole fraction of hydrogen (X_H₂) is given by:
\[ X_{H_2} = \frac{\text{Moles of hydrogen}}{\text{Total moles}} = \frac{10}{12.5} = 0.8 \]

5. **Calculate the partial pressure of hydrogen**:
- The partial pressure of hydrogen (P_H₂) can be calculated using Dalton's Law of Partial Pressures:
\[ P_{H_2} = X_{H_2} \times P_{\text{total}} \]
- Given that the total pressure (P_total) is 1 bar:
\[ P_{H_2} = 0.8 \times 1 \text{ bar} = 0.8 \text{ bar} \]

### Final Answer:
The partial pressure of hydrogen in the mixture is **0.8 bar**.