the pressure of a `1 : 4` mixture of dihydrogen and dioxygen enclosed in a vessel is one atmosphere. What would be the partial pressure of dioxygen ?

Options

A. `0.8 xx 10^(5)` atm
B. `0.008 N m^(-2)`
C. ` 8 xx 10^(4) N m^(-2)`
D. 0.25 atm

Explanation

To find the partial pressure of dioxygen in a 1:4 mixture of dihydrogen and dioxygen with a total pressure of 1 atmosphere, we can follow these steps:

### Step 1: Understand the Mole Ratio
The ratio of dihydrogen (H₂) to dioxygen (O₂) is given as 1:4. This means for every 1 mole of dihydrogen, there are 4 moles of dioxygen.

### Step 2: Determine the Number of Moles
Assuming we have 1 mole of dihydrogen, we can calculate the moles of dioxygen:
- Moles of H₂ = 1
- Moles of O₂ = 4

### Step 3: Calculate Total Moles
Now, we can find the total number of moles in the mixture:
- Total moles = Moles of H₂ + Moles of O₂ = 1 + 4 = 5 moles

### Step 4: Calculate the Mole Fraction of Dioxygen
The mole fraction of dioxygen (O₂) can be calculated using the formula:
\[ \text{Mole Fraction of O₂} = \frac{\text{Moles of O₂}}{\text{Total Moles}} = \frac{4}{5} \]

### Step 5: Use Dalton's Law of Partial Pressures
According to Dalton's Law, the partial pressure of a gas in a mixture is given by:
\[ \text{Partial Pressure of O₂} = \text{Mole Fraction of O₂} \times \text{Total Pressure} \]
Substituting the values we have:
\[ \text{Partial Pressure of O₂} = \left(\frac{4}{5}\right) \times 1 \text{ atm} = 0.8 \text{ atm} \]

### Step 6: Convert to Other Units (if necessary)
The partial pressure can also be expressed in different units. For example:
\[ 0.8 \text{ atm} = 0.8 \times 10^5 \text{ N/m}^2 = 8 \times 10^4 \text{ N/m}^2 \]

### Final Answer
The partial pressure of dioxygen (O₂) is **0.8 atm** or **8 × 10^4 N/m²**.

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