Question

some n₂ gas is mixed with some o₂ gas, and the sketch below shows a representative sample of the mixture. the total pressure of the mixture is measured, and found to be 600. torr. calculate the mole fraction and partial pressure of each gas in this mixture. round your answers to 3 significant digits. you may assume each gas behaves as an ideal gas.

Explanation:

Step1: Count the number of molecules

From the sketch, count the number of \( \text{N}_2 \) (blue) and \( \text{O}_2 \) (red) molecules. Let's assume: Number of \( \text{N}_2 \) molecules (\( n_{\text{N}_2} \)) = 2, Number of \( \text{O}_2 \) molecules (\( n_{\text{O}_2} \)) = 16. Total number of molecules (\( n_{\text{total}} \)) = \( 2 + 16 = 18 \).

Step2: Calculate mole fractions

Mole fraction of \( \text{N}_2 \) (\( X_{\text{N}_2} \)) = \( \frac{n_{\text{N}_2}}{n_{\text{total}}} = \frac{2}{18} \approx 0.111 \)
Mole fraction of \( \text{O}_2 \) (\( X_{\text{O}_2} \)) = \( \frac{n_{\text{O}_2}}{n_{\text{total}}} = \frac{16}{18} \approx 0.889 \)

Step3: Calculate partial pressures

Partial pressure of a gas (\( P_i \)) = \( X_i \times P_{\text{total}} \), where \( P_{\text{total}} = 600 \) torr.
Partial pressure of \( \text{N}_2 \) (\( P_{\text{N}_2} \)) = \( 0.111 \times 600 \approx 66.7 \) torr
Partial pressure of \( \text{O}_2 \) (\( P_{\text{O}_2} \)) = \( 0.889 \times 600 \approx 533 \) torr (or more accurately, \( \frac{16}{18} \times 600 = \frac{9600}{18} \approx 533 \) torr, \( \frac{2}{18} \times 600 = \frac{1200}{18} \approx 66.7 \) torr)

Answer:

• Mole fraction of \( \text{N}_2 \): \( \approx 0.111 \), Mole fraction of \( \text{O}_2 \): \( \approx 0.889 \)
• Partial pressure of \( \text{N}_2 \): \( \approx 66.7 \) torr, Partial pressure of \( \text{O}_2 \): \( \approx 533 \) torr

(Note: If the actual count from the sketch is different, adjust the numbers. For example, if \( \text{N}_2 \) is 2 and \( \text{O}_2 \) is 16 as per typical similar problems, the above calculations hold. If the sketch has different counts, recalculate accordingly.)