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

Explanation

To calculate the partial pressure of hydrogen in a mixture of hydrogen and oxygen at 1 bar pressure, where the mixture contains 20% by weight of hydrogen, we can follow these steps:

### Step 1: Determine the weight of hydrogen and oxygen
Given that the mixture contains 20% by weight of hydrogen, we can assume a total weight of the gas mixture to be 100 grams for simplicity.

- Weight of hydrogen (H₂) = 20% of 100 g = 20 g
- Weight of oxygen (O₂) = 100 g - 20 g = 80 g

### Step 2: Calculate the number of moles of hydrogen and oxygen
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]

- Molar mass of hydrogen (H₂) = 2 g/mol
- Molar mass of oxygen (O₂) = 32 g/mol

Calculating the moles:
- Moles of hydrogen (H₂):
\[ \text{Moles of H₂} = \frac{20 \text{ g}}{2 \text{ g/mol}} = 10 \text{ moles} \]

- Moles of oxygen (O₂):
\[ \text{Moles of O₂} = \frac{80 \text{ g}}{32 \text{ g/mol}} = 2.5 \text{ moles} \]

### Step 3: Calculate the total number of moles in the mixture
Total moles in the mixture:
\[ \text{Total moles} = \text{Moles of H₂} + \text{Moles of O₂} = 10 + 2.5 = 12.5 \text{ moles} \]

### Step 4: Calculate the mole fraction of hydrogen
The mole fraction (X) of hydrogen is given by:
\[ X_{\text{H₂}} = \frac{\text{Moles of H₂}}{\text{Total moles}} = \frac{10}{12.5} \]

Calculating the mole fraction:
\[ X_{\text{H₂}} = 0.8 \]

### Step 5: Calculate the partial pressure of hydrogen
The partial pressure of hydrogen (P_H₂) can be calculated using the formula:
\[ P_{\text{H₂}} = X_{\text{H₂}} \times P_{\text{total}} \]
where \(P_{\text{total}} = 1 \text{ bar}\).

Calculating the partial pressure:
\[ P_{\text{H₂}} = 0.8 \times 1 \text{ bar} = 0.8 \text{ bar} \]

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

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