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 Nm^(-2)`
C. `8 xx 10^(4) Nm^(-2)`
D. `0.25` atm

Explanation

To find the partial pressure of dioxygen (O₂) in a 1:4 mixture of dihydrogen (H₂) and dioxygen, we can follow these steps:

### Step 1: Understand the Molar Ratio
The mixture is given in a ratio of 1:4, which means:
- Moles of H₂ = 1
- Moles of O₂ = 4

### Step 2: Calculate Total Moles
To find the total number of moles in the mixture:
\[ \text{Total moles} = \text{Moles of H₂} + \text{Moles of O₂} = 1 + 4 = 5 \]

### Step 3: Calculate the Mole Fraction of Dioxygen
The mole fraction (χ) of dioxygen (O₂) can be calculated using the formula:
\[ \chi_{O₂} = \frac{\text{Moles of O₂}}{\text{Total moles}} = \frac{4}{5} = 0.8 \]

### Step 4: Use Dalton's Law of Partial Pressures
According to Dalton's Law, the partial pressure of a gas in a mixture is given by:
\[ P_{O₂} = \chi_{O₂} \times P_{\text{total}} \]
Where \( P_{\text{total}} \) is the total pressure of the mixture, which is given as 1 atm.

### Step 5: Calculate the Partial Pressure of Dioxygen
Now substituting the values into the equation:
\[ P_{O₂} = 0.8 \times 1 \, \text{atm} = 0.8 \, \text{atm} \]

### Final Answer
The partial pressure of dioxygen (O₂) is:
\[ P_{O₂} = 0.8 \, \text{atm} \]