A sealed glass container contains 0.80 moles co2 and 0.35 moles n exerting a total pressure of 774 torr. Calculate the mole fraction and partial pressure of each gas
The correct answer and explanation is:
To solve this problem, we need to calculate:
- The mole fraction of each gas
- The partial pressure of each gas
Step 1: Find total number of moles
ntotal=nCO2+nN=0.80+0.35=1.15 molesn_{\text{total}} = n_{\text{CO}_2} + n_{\text{N}} = 0.80 + 0.35 = 1.15 \text{ moles}
Step 2: Mole fractions
The mole fraction of a gas is calculated as: Xgas=ngasntotalX_{\text{gas}} = \frac{n_{\text{gas}}}{n_{\text{total}}}
Mole fraction of CO₂: XCO2=0.801.15≈0.6957X_{\text{CO}_2} = \frac{0.80}{1.15} \approx 0.6957
Mole fraction of N: XN=0.351.15≈0.3043X_{\text{N}} = \frac{0.35}{1.15} \approx 0.3043
Check: 0.6957+0.3043=1.0000.6957 + 0.3043 = 1.000
Step 3: Partial pressures
The partial pressure of each gas is: Pgas=Xgas×PtotalP_{\text{gas}} = X_{\text{gas}} \times P_{\text{total}}
Partial pressure of CO₂: PCO2=0.6957×774≈538.4 torrP_{\text{CO}_2} = 0.6957 \times 774 \approx 538.4 \text{ torr}
Partial pressure of N: PN=0.3043×774≈235.6 torrP_{\text{N}} = 0.3043 \times 774 \approx 235.6 \text{ torr}
Check: 538.4+235.6=774 torr538.4 + 235.6 = 774 \text{ torr}
Final Answers:
- Mole fraction of CO₂: 0.6957
- Mole fraction of N: 0.3043
- Partial pressure of CO₂: 538.4 torr
- Partial pressure of N: 235.6 torr
Explanation (300 words):
Gases in a mixture contribute to the total pressure in proportion to the amount of substance present, measured in moles. This principle is known as Dalton’s Law of Partial Pressures. The law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component gas.
Mole fraction is the ratio of the number of moles of one component to the total number of moles in the mixture. It is a dimensionless number that shows what fraction of the total mixture each gas represents.
In this case, we started by calculating the total moles of gas in the container. The mixture contained 0.80 moles of carbon dioxide and 0.35 moles of nitrogen, adding up to 1.15 moles in total. Using this, we found the mole fraction of each gas by dividing its moles by the total.
Once the mole fractions were known, we used them to calculate the partial pressure of each gas by multiplying the mole fraction by the total pressure. The sum of the partial pressures equaled the total pressure, confirming the correctness of the calculation.
This approach helps understand how gases behave in mixtures, such as in the air or chemical reactions in closed systems. It is widely applied in chemistry, biology, and environmental science, especially when dealing with respiration, gas exchange, or industrial processes.