Partial Pressure and Mole Fraction: Worked Examples

📚 Quick Study Guide

• ⚛️ Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases: $P_{total} = P_1 + P_2 + P_3 + ...$
• ⚗️ The partial pressure of a gas is the pressure that the gas would exert if it occupied the same volume alone: $P_i = X_i * P_{total}$, where $P_i$ is the partial pressure of gas 'i'.
• ⚗️ Mole fraction ($X_i$) is the ratio of the number of moles of one component to the total number of moles of all components in the mixture: $X_i = \frac{n_i}{n_{total}}$
• 🌡️ Remember to use consistent units for pressure (e.g., atm, kPa, mmHg) and ensure temperatures are in Kelvin for gas law calculations: $K = °C + 273.15$.
• 💡 When calculating mole fractions, make sure to find the total number of moles first.

Practice Quiz

1. Question 1: A container holds 2 moles of nitrogen gas and 3 moles of oxygen gas. If the total pressure is 5 atm, what is the partial pressure of nitrogen?
   1. 2 atm
   2. 3 atm
   3. 2.5 atm
   4. 5 atm
2. Question 2: A gas mixture contains 40g of Argon (Ar) and 4g of Helium (He). If the total pressure is 10 atm, what is the partial pressure of Helium? (Molar mass of Ar = 40 g/mol, He = 4 g/mol)
   1. 1 atm
   2. 5 atm
   3. 9 atm
   4. 2 atm
3. Question 3: The partial pressure of oxygen in a container is 200 mmHg, and the total pressure is 760 mmHg. What is the mole fraction of oxygen?
   1. 0.263
   2. 0.560
   3. 0.737
   4. 0.200
4. Question 4: A flask contains 1 mole of $N_2$, 2 moles of $O_2$, and 3 moles of $H_2$. If the total pressure is 12 atm, what is the partial pressure of $O_2$?
   1. 2 atm
   2. 4 atm
   3. 6 atm
   4. 12 atm
5. Question 5: In a mixture of gases, the partial pressure of $CO_2$ is 0.5 atm and the mole fraction is 0.25. What is the total pressure of the mixture?
   1. 0.125 atm
   2. 1 atm
   3. 2 atm
   4. 4 atm
6. Question 6: A container holds equal masses of Helium (He) and Neon (Ne). The total pressure in the container is 6 atm. What is the approximate partial pressure of Neon? (Molar mass of He = 4 g/mol, Ne = 20 g/mol)
   1. 1 atm
   2. 2 atm
   3. 5 atm
   4. 3 atm
7. Question 7: If the mole fraction of a gas in a mixture is 0.4 and the total pressure is 3 atm, what is the partial pressure of the gas?
   1. 0.4 atm
   2. 0.6 atm
   3. 1.2 atm
   4. 3 atm