Mole Fraction and the Ideal Gas Law: Worked Examples

📚 Quick Study Guide

• ⚛️ Mole Fraction: The ratio of the number of moles of a component in a mixture to the total number of moles of all components in the mixture. Formula: $X_i = \frac{n_i}{n_{total}}$ where $X_i$ is the mole fraction of component i, $n_i$ is the number of moles of component i, and $n_{total}$ is the total number of moles in the mixture.
• 🌡️ Ideal Gas Law: An equation of state that describes the behavior of ideal gases. Formula: $PV = nRT$, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
• ⚖️ Partial Pressure: The pressure exerted by a single gas in a mixture of gases. Dalton's Law of Partial Pressures: The total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases: $P_{total} = P_1 + P_2 + P_3 + ...$
• 🧪 Relating Mole Fraction and Partial Pressure: The partial pressure of a gas in a mixture is equal to the mole fraction of that gas multiplied by the total pressure: $P_i = X_i * P_{total}$
• 🔢 Units: Ensure consistent units are used. R (ideal gas constant) often uses L atm / (mol K), so pressure should be in atm, volume in liters, and temperature in Kelvin.

🧪 Practice Quiz

1. What is the mole fraction of nitrogen in a mixture containing 2 moles of nitrogen and 6 moles of oxygen?
   1. 0.25
   2. 0.33
   3. 0.67
   4. 0.75
2. A container holds 4 moles of hydrogen, 3 moles of oxygen, and 1 mole of helium. What is the mole fraction of oxygen?
   1. 0.25
   2. 0.375
   3. 0.50
   4. 0.75
3. If the total pressure of a gas mixture is 3 atm and the mole fraction of gas A is 0.4, what is the partial pressure of gas A?
   1. 0.4 atm
   2. 0.8 atm
   3. 1.2 atm
   4. 2.6 atm
4. Using the ideal gas law, if you have 2 moles of a gas at a pressure of 5 atm and a volume of 10 L, what is the temperature (in Kelvin)? (R = 0.0821 L atm / (mol K))
   1. 100 K
   2. 200 K
   3. 305 K
   4. 400 K
5. A mixture contains 1 mole of gas X and 3 moles of gas Y. If the total pressure is 8 atm, what is the partial pressure of gas Y?
   1. 2 atm
   2. 4 atm
   3. 6 atm
   4. 8 atm
6. What volume will 0.5 moles of an ideal gas occupy at standard temperature and pressure (STP: 1 atm and 273 K)? (R = 0.0821 L atm / (mol K))
   1. 5.6 L
   2. 11.2 L
   3. 22.4 L
   4. 44.8 L
7. A container has 0.2 moles of CO2, 0.3 moles of N2, and 0.5 moles of H2. The total pressure is 2 atm. What is the partial pressure of N2?
   1. 0.4 atm
   2. 0.6 atm
   3. 0.8 atm
   4. 1.0 atm