A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen . What would be the partial pressure of dihydrogen in bar ?

Options

A. `0.8`
B. `1.8`
C. `2.8`
D. 3

Explanation

To find the partial pressure of dihydrogen (H₂) in a mixture with dioxygen (O₂) at a total pressure of 1 bar, we can follow these steps:

### Step 1: Understand the given data
We know that the mixture contains 20% by weight of dihydrogen (H₂). This means that in a total of 100 grams of the mixture, 20 grams are dihydrogen and 80 grams are dioxygen.

### Step 2: Calculate the number of moles of each gas
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

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

- For dioxygen (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
\[ \text{Total moles} = \text{Moles of H₂} + \text{Moles of O₂} = 10 + 2.5 = 12.5 \text{ moles} \]

### Step 4: Calculate the mole fraction of dihydrogen
The mole fraction (X) of a component in a mixture is given by:
\[ X = \frac{\text{Number of moles of the component}}{\text{Total number of moles}} \]

For dihydrogen:
\[ X_{H₂} = \frac{10 \text{ moles}}{12.5 \text{ moles}} = \frac{10}{12.5} = 0.8 \]

### Step 5: Calculate the partial pressure of dihydrogen
The partial pressure (P) of a gas in a mixture can be calculated using Dalton's Law:
\[ P_{H₂} = X_{H₂} \times P_{\text{total}} \]

Given that the total pressure \(P_{\text{total}} = 1 \text{ bar}\):
\[ P_{H₂} = 0.8 \times 1 \text{ bar} = 0.8 \text{ bar} \]

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

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