Air contains 23 % oxygen and 77 % nitrogen by weight. The percentage of `O_(2)` by volume is

Options

A. 28.1
B. 20.7
C. 21.8
D. 23

Answer

To find the percentage of \( O_2 \) by volume in air, we can follow these steps:

### Step 1: Determine the mass of each gas in a sample
Assume we have a 100 g sample of air. According to the problem, air contains:
- 23% Oxygen (O2) by weight
- 77% Nitrogen (N2) by weight

Thus, in a 100 g sample:
- Mass of \( O_2 = 23 \, \text{g} \)
- Mass of \( N_2 = 77 \, \text{g} \)

### Step 2: Calculate the number of moles of each gas
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

- Molar mass of \( O_2 \) = 32 g/mol
- Molar mass of \( N_2 \) = 28 g/mol

Calculating the moles:
- Moles of \( O_2 = \frac{23 \, \text{g}}{32 \, \text{g/mol}} = 0.71875 \, \text{mol} \approx 0.71 \, \text{mol} \)
- Moles of \( N_2 = \frac{77 \, \text{g}}{28 \, \text{g/mol}} = 2.75 \, \text{mol} \)

### Step 3: Calculate the total number of moles
Now, we can find the total number of moles of the gases:
\[ \text{Total moles} = \text{Moles of } O_2 + \text{Moles of } N_2 = 0.71 + 2.75 = 3.46 \, \text{mol} \]

### Step 4: Calculate the percentage of \( O_2 \) by volume
The percentage of \( O_2 \) by volume can be calculated using the formula:
\[ \text{Percentage of } O_2 = \left( \frac{\text{Moles of } O_2}{\text{Total moles}} \right) \times 100 \]

Substituting the values:
\[ \text{Percentage of } O_2 = \left( \frac{0.71}{3.46} \right) \times 100 \approx 20.7\% \]

### Final Answer
The percentage of \( O_2 \) by volume in air is approximately **20.7%**.

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