Gas Pressure and Partial Pressures

Partial Pressures and Total Pressure

  • If you have multiple gases in a mixture, the total pressure is the sum of the partial pressures of each gas.
    • Example: Half an atmosphere of nitrogen and half an atmosphere of oxygen equals one atmosphere of pressure.
    • P{total} = P{N2} + P{O_2}

Practice Problem: Mixture of Gases

  • Given:
    • A mixture of oxygen, carbon dioxide, and nitrogen.
    • Total pressure: P_{total} = 0.97 atm
    • Partial pressure of carbon dioxide: P{CO2} = 0.70 atm
    • Partial pressure of nitrogen: P{N2} = 0.12 atm
  • Goal: Find the partial pressure of oxygen (P{O2}).
  • Formula:
    • P{total} = P{O2} + P{CO2} + P{N_2}
  • Substitute the values:
    • 0.97 = P{O2} + 0.70 + 0.12
  • Solve for P{O2}:
    • P{O2} = 0.97 - 0.70 - 0.12 = 0.15 atm

Irrelevant Information

  • The volume of the chamber (e.g., 12 liters) might be given to confuse you; it's not needed for these types of calculations where you're only adding pressures.

Adding Pressures with Significant Figures

  • Example problem:
    • Gas 1: 0.5 atm
    • Gas 2: 5.5 atm
    • Total pressure: 0.5 + 5.5 = 6.0 atm
  • Rule for Addition/Subtraction with Sig Figs:
    • The result should have the same number of decimal places as the number with the fewest decimal places.
    • In this case, 0.5 has one decimal place, so the answer should also have one decimal place.

Collecting Gas Over Water

  • Process:
    • A gas is produced by a reaction and bubbled through water into a container.
    • The gas displaces the water until the pressure inside the container equals the atmospheric pressure outside.
  • Total Pressure:
    • The total pressure inside the container is the sum of the partial pressure of the collected gas and the vapor pressure of water.
    • P{total} = P{gas} + P{H2O}

Water Vapor Pressure

  • Water vapor pressure depends on temperature.
    • Warmer water results in more water vapor.
  • Using a Water Vapor Pressure Table:
    • A table provides the vapor pressure of water at different temperatures.
    • Example: At 13 degrees Celsius, the vapor pressure of water is 11.2 mmHg.

Example Problem: Collecting Carbon Dioxide Over Water

  • Given:
    • Carbon dioxide is collected over water at 13 degrees Celsius.
    • The total pressure (barometric pressure) is 758 mmHg.
  • Goal: Find the partial pressure of carbon dioxide (P{CO2}).
  • Steps:
    1. Find the water vapor pressure at 13 degrees Celsius from the table: P{H2O} = 11.2 mmHg.
    2. Use the formula: P{total} = P{CO2} + P{H_2O}
    3. Substitute the values: 758 = P{CO2} + 11.2
    4. Solve for P{CO2}: P{CO2} = 758 - 11.2 = 746.8 mmHg.
    5. Round to the nearest whole number due to the ones place of 758: P{CO2} = 747 mmHg.

Conversions

  • If the barometric pressure is given in a unit other than mmHg (e.g., kPa or atmospheres), convert it to mmHg before solving the problem.