A mixture of hydrogen and oxygen at one bar pressue contains `20%` by weight of hydrogen . Partial pressure of hydrogen will be

Options

A. `0.2 ba r`
B. `0.4 ba r`
C. `0.6 ba r`
D. `0.8 ba r`

Explanation

To find the partial pressure of hydrogen in a mixture of hydrogen and oxygen at a total pressure of 1 bar, we can follow these steps:

### Step 1: Determine the total weight of the mixture
Given that the mixture contains 20% by weight of hydrogen, we can assume a total weight of the mixture. For simplicity, let's assume the total weight of the mixture is 100 grams.

### Step 2: Calculate the weight of hydrogen and oxygen
From the total weight of 100 grams:
- Weight of hydrogen (H₂) = 20% of 100 grams = 20 grams
- Weight of oxygen (O₂) = 100 grams - 20 grams = 80 grams

### Step 3: Calculate the number of moles of hydrogen and oxygen
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molar mass}} \]
- Molar mass of hydrogen (H₂) = 2 g/mol
- Molar mass of oxygen (O₂) = 32 g/mol

Calculating the moles:
- Moles of hydrogen (H₂) = \(\frac{20 \text{ grams}}{2 \text{ g/mol}} = 10 \text{ moles}\)
- Moles of oxygen (O₂) = \(\frac{80 \text{ grams}}{32 \text{ g/mol}} = 2.5 \text{ moles}\)

### Step 4: Calculate the total number of moles in the mixture
Total moles = Moles of H₂ + Moles of O₂
\[ \text{Total moles} = 10 + 2.5 = 12.5 \text{ moles} \]

### Step 5: Calculate the mole fraction of hydrogen
The mole fraction (X) of hydrogen is given by:
\[ X_{H2} = \frac{\text{Moles of H₂}}{\text{Total moles}} = \frac{10}{12.5} = 0.8 \]

### Step 6: Calculate the partial pressure of hydrogen
Using Dalton's Law of Partial Pressures, the partial pressure of hydrogen (P_{H2}) can be calculated as:
\[ P_{H2} = X_{H2} \times P_{total} \]
Where \(P_{total} = 1 \text{ bar}\):
\[ P_{H2} = 0.8 \times 1 \text{ bar} = 0.8 \text{ bar} \]

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

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