A candle is burnt in a beaker until it extinguishes itself. A sample of gaseous mixture in the beaker contains `6.08 xx 10^(20)` molecules of `N_(2), 0.76 xx 10^(20)` molecules of `O_(2)`, and `0.50 xx 10^(20)` molecules of `CO_(2)`. The total pressure is 734 mm of Hg. The partial pressure of `O_(2)` would be

Options

A. 760.0 mm of Hg
B. 76.0 mm of Hg
C. 7.6 mm of Hg
D. 0.76 mm of Hg

Explanation

To find the partial pressure of \( O_2 \) in the gaseous mixture, we can follow these steps:

### Step 1: Identify the given values
- Number of molecules of \( N_2 = 6.08 \times 10^{20} \)
- Number of molecules of \( O_2 = 0.76 \times 10^{20} \)
- Number of molecules of \( CO_2 = 0.50 \times 10^{20} \)
- Total pressure \( P_T = 734 \, \text{mmHg} \)

### Step 2: Calculate the total number of molecules
To find the total number of molecules in the mixture, we add the number of molecules of all components:
\[ \text{Total molecules} = N_2 + O_2 + CO_2 = 6.08 \times 10^{20} + 0.76 \times 10^{20} + 0.50 \times 10^{20} \]
\[ = 6.08 + 0.76 + 0.50 = 7.34 \times 10^{20} \]

### Step 3: Calculate the mole fraction of \( O_2 \)
The mole fraction \( \chi_{O_2} \) of \( O_2 \) is given by:
\[ \chi_{O_2} = \frac{\text{Number of molecules of } O_2}{\text{Total number of molecules}} = \frac{0.76 \times 10^{20}}{7.34 \times 10^{20}} \]
\[ = \frac{0.76}{7.34} \]

### Step 4: Calculate the partial pressure of \( O_2 \)
Using Dalton's Law of Partial Pressures, the partial pressure \( P_{O_2} \) can be calculated as:
\[ P_{O_2} = P_T \times \chi_{O_2} \]
Substituting the values we have:
\[ P_{O_2} = 734 \times \frac{0.76}{7.34} \]

### Step 5: Perform the calculations
First, calculate the mole fraction:
\[ \chi_{O_2} = \frac{0.76}{7.34} \approx 0.103 \]
Now, substitute this back into the equation for partial pressure:
\[ P_{O_2} = 734 \times 0.103 \approx 75.6 \, \text{mmHg} \]
Rounding this value gives us:
\[ P_{O_2} \approx 76 \, \text{mmHg} \]

### Final Answer
The partial pressure of \( O_2 \) is approximately \( 76 \, \text{mmHg} \).

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