Assume that air is 21% oxygen and 79% nitrogen by volume. If the barometer pressure is 740 mm, the partial pressure of oxygen is closest to which one of the following ?

Options

A. 155 mm
B. 310 mm
C. 580 mm
D. 740 mm

Explanation

To find the partial pressure of oxygen in the air, we can use Dalton's Law of Partial Pressures. Here’s a step-by-step solution:

### Step 1: Understand the Composition of Air
Air is composed of 21% oxygen (O₂) and 79% nitrogen (N₂) by volume.

### Step 2: Identify Total Pressure
The total pressure of the air is given as 740 mm of mercury (mmHg).

### Step 3: Calculate the Mole Fraction of Oxygen
The mole fraction (X) of a component in a mixture is calculated as:
\[ X_{O_2} = \frac{\text{Volume of } O_2}{\text{Total Volume}} \]
In this case:
\[ X_{O_2} = \frac{21}{21 + 79} = \frac{21}{100} = 0.21 \]

### Step 4: Apply Dalton's Law of Partial Pressures
According to Dalton's Law, the partial pressure of a gas in a mixture can be calculated as:
\[ P_{O_2} = X_{O_2} \times P_{total} \]
Where:
- \( P_{O_2} \) is the partial pressure of oxygen.
- \( P_{total} \) is the total pressure (740 mmHg).

### Step 5: Calculate the Partial Pressure of Oxygen
Now, substituting the values:
\[ P_{O_2} = 0.21 \times 740 \, \text{mmHg} \]
Calculating this gives:
\[ P_{O_2} = 155.4 \, \text{mmHg} \]
Rounding this to the closest whole number, we get:
\[ P_{O_2} \approx 155 \, \text{mmHg} \]

### Conclusion
The partial pressure of oxygen is closest to **155 mmHg**.

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