If the air in a container contains 92.94% oxygen, what is the partial pressure of oxygen in the container if the total pressure 28.84 atm?

1. Break Down the Problem

To find the partial pressure of oxygen in the container, we will use Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. The partial pressure can be calculated using the formula:

$P_{O_2} = \text{Total Pressure} \times \frac{\text{Percentage of } O_2}{100}$

2. Relevant Concepts

• Partial Pressure Formula: $P_{i} = P \times \frac{n_i}{n_{total}}$
• Given:
  • Total Pressure $P = 28.84 \, \text{atm}$
  • Percentage of $O_2 = 92.94\%$

3. Analysis and Detail

Now we apply the formula:

$P_{O_2} = 28.84 \, \text{atm} \times \frac{92.94}{100}$

Calculating this step-by-step:

1. Convert the percentage to a decimal: $\frac{92.94}{100} = 0.9294$
2. Calculate the partial pressure of oxygen:

$P_{O_2} = 28.84 \, \text{atm} \times 0.9294$ $P_{O_2} \approx 26.85 \, \text{atm}$

4. Verify and Summarize

The calculation has been carried out according to the partial pressure formula and verified. The partial pressure of oxygen in the container is approximately $26.85 \, \text{atm}$.

Final Answer

The partial pressure of oxygen in the container is approximately 26.85 atm.