Exactly 1.0 mole of oxygen gas and 7.0 moles of nitrogen gas are in a container. The total gas pressure is 5.7 atm. What is the partial pressure of nitrogen in atm?
The correct answer and explanation is:
Correct Answer:
The partial pressure of nitrogen gas (N₂) is 5.0 atm.
Explanation (300 words):
To calculate the partial pressure of a gas in a mixture, we use Dalton’s Law of Partial Pressures, which states:
Total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas.
Mathematically: Ptotal=PO2+PN2P_{\text{total}} = P_{O_2} + P_{N_2}
Each gas’s partial pressure is proportional to the number of moles it contributes, and is given by: Pgas=(ngasntotal)×PtotalP_{\text{gas}} = \left( \frac{n_{\text{gas}}}{n_{\text{total}}} \right) \times P_{\text{total}}
Step-by-step solution:
- Given:
- Moles of oxygen gas (O2O_2) = 1.0 mol
- Moles of nitrogen gas (N2N_2) = 7.0 mol
- Total pressure = 5.7 atm
- Calculate total moles of gas:
ntotal=nO2+nN2=1.0+7.0=8.0 moln_{\text{total}} = n_{O_2} + n_{N_2} = 1.0 + 7.0 = 8.0 \text{ mol}
- Find the mole fraction of nitrogen:
χN2=nN2ntotal=7.08.0=0.875\chi_{N_2} = \frac{n_{N_2}}{n_{\text{total}}} = \frac{7.0}{8.0} = 0.875
- Calculate the partial pressure of nitrogen:
PN2=χN2×Ptotal=0.875×5.7=4.9875≈5.0 atmP_{N_2} = \chi_{N_2} \times P_{\text{total}} = 0.875 \times 5.7 = 4.9875 \approx \boxed{5.0 \text{ atm}}
Conclusion:
The partial pressure of a gas in a mixture depends on its relative mole fraction. Since nitrogen contributes 7 out of the 8 total moles, it dominates the mixture and exerts a larger share of the pressure. Using the mole fraction and total pressure, we determine nitrogen’s partial pressure is approximately 5.0 atm.