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 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 Mixture Ratio
The mixture ratio of dihydrogen (H₂) to dioxygen (O₂) is given as 1:4. This means for every 1 mole of H₂, there are 4 moles of O₂.

### Step 2: Determine the Total Moles
Let's assume we have:
- 1 mole of H₂
- 4 moles of O₂

Thus, the total number of moles (n_total) in the mixture is:
\[ n_{\text{total}} = n_{\text{H}_2} + n_{\text{O}_2} = 1 + 4 = 5 \text{ moles} \]

### Step 3: Calculate the Mole Fraction of Dioxygen
The mole fraction (X) of dioxygen (O₂) can be calculated using the formula:
\[ X_{\text{O}_2} = \frac{n_{\text{O}_2}}{n_{\text{total}}} \]
Substituting the values:
\[ X_{\text{O}_2} = \frac{4}{5} = 0.8 \]

### Step 4: Use the Total Pressure to Find Partial Pressure
The partial pressure (P) of dioxygen can be calculated using Dalton's Law of Partial Pressures:
\[ P_{\text{O}_2} = X_{\text{O}_2} \times P_{\text{total}} \]
Where \( P_{\text{total}} \) is the total pressure, which is given as 1 atmosphere. Substituting the values:
\[ P_{\text{O}_2} = 0.8 \times 1 \text{ atm} = 0.8 \text{ atm} \]

### Step 5: Convert to Newton per Meter Square
To convert the pressure from atmospheres to Newtons per meter square (N/m²), we use the conversion factor:
1 atm = \( 1.013 \times 10^5 \) N/m².
Thus,
\[ P_{\text{O}_2} = 0.8 \text{ atm} \times 1.013 \times 10^5 \text{ N/m}^2 \]
\[ P_{\text{O}_2} = 0.8 \times 1.013 \times 10^5 = 8.104 \times 10^4 \text{ N/m}^2 \]

### Final Result
The partial pressure of dioxygen is approximately:
\[ P_{\text{O}_2} \approx 8 \times 10^4 \text{ N/m}^2 \]