A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen. Calculate the partial pressure of dihydrogen.

Options

A. 0.8 bar
B. 0.4 bar
C. 1.6 bar
D. 3.2 bar

Answer

To solve the problem of finding the partial pressure of dihydrogen (H₂) in a mixture with dioxygen (O₂) at a total pressure of 1 bar and with dihydrogen constituting 20% by weight, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Pressure and Weight Percentage**:
- Given: Total pressure (P_total) = 1 bar
- Weight percentage of dihydrogen (H₂) = 20%
- Therefore, weight percentage of dioxygen (O₂) = 100% - 20% = 80%

2. **Assume a Total Mass for the Mixture**:
- For simplicity, assume the total mass of the gas mixture is 100 grams.
- Thus, mass of H₂ = 20 grams and mass of O₂ = 80 grams.

3. **Calculate the Number of Moles**:
- Molar mass of H₂ = 2 g/mol
- Molar mass of O₂ = 32 g/mol
- Number of moles of H₂ = mass of H₂ / molar mass of H₂ = 20 g / 2 g/mol = 10 moles
- Number of moles of O₂ = mass of O₂ / molar mass of O₂ = 80 g / 32 g/mol = 2.5 moles

4. **Calculate the Mole Fraction of H₂**:
- Total moles = moles of H₂ + moles of O₂ = 10 + 2.5 = 12.5 moles
- Mole fraction of H₂ (X_H₂) = moles of H₂ / total moles = 10 / 12.5 = 0.8

5. **Calculate the Partial Pressure of H₂**:
- The partial pressure of a gas can be calculated using Dalton's Law of Partial Pressures:
- Partial pressure of H₂ (P_H₂) = P_total × X_H₂
- P_H₂ = 1 bar × 0.8 = 0.8 bar

### Final Answer:
The partial pressure of dihydrogen (H₂) in the mixture is **0.8 bar**.

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