A candle is burnt in a beaker until extinguishers itseft. A sample of gaseous mixutre in the beaker contains `6.08 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: Calculate the total number of moles of gas in the mixture
We have the number of molecules of \( O_2 \) and \( CO_2 \). We need to find the total number of moles, which includes \( O_2 \), \( CO_2 \), and \( N_2 \) (which we will assume is present in the mixture).

Given:
- Number of molecules of \( O_2 = 6.08 \times 10^{20} \)
- Number of molecules of \( CO_2 = 0.50 \times 10^{20} \)
- Number of molecules of \( N_2 = 0.76 \times 10^{20} \) (assumed from the transcript)

### Step 2: Calculate the total number of molecules
\[ \text{Total molecules} = \text{molecules of } O_2 + \text{molecules of } CO_2 + \text{molecules of } N_2 \]
\[ = 6.08 \times 10^{20} + 0.50 \times 10^{20} + 0.76 \times 10^{20} \]
\[ = (6.08 + 0.50 + 0.76) \times 10^{20} = 7.34 \times 10^{20} \]

### Step 3: Calculate the mole fraction of \( O_2 \)
The mole fraction of \( O_2 \) is given by:
\[ \text{Mole fraction of } O_2 = \frac{\text{moles of } O_2}{\text{total moles}} \]
\[ = \frac{6.08 \times 10^{20}}{7.34 \times 10^{20}} = \frac{6.08}{7.34} \]

### Step 4: Calculate the partial pressure of \( O_2 \)
Using Dalton's Law of Partial Pressures, the partial pressure of \( O_2 \) can be calculated as:
\[ P_{O_2} = P_{\text{total}} \times \text{Mole fraction of } O_2 \]
Given that \( P_{\text{total}} = 734 \, \text{mm Hg} \):
\[ P_{O_2} = 734 \, \text{mm Hg} \times \frac{6.08}{7.34} \]

### Step 5: Calculate the numerical value
Calculating the above expression:
\[ P_{O_2} = 734 \times \frac{6.08}{7.34} = 734 \times 0.828 = 608 \, \text{mm Hg} \]

### Final Answer
The partial pressure of \( O_2 \) is \( 608 \, \text{mm Hg} \).

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