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.
  • $P<em>{total} = P</em>{N<em>2} + P</em>{O_2}$

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: $P<em>{CO</em>2} = 0.70$ atm
  • Partial pressure of nitrogen: $P<em>{N</em>2} = 0.12$ atm
• Goal: Find the partial pressure of oxygen ($P<em>{O</em>2}$).
• Formula:
  • $P<em>{total} = P</em>{O<em>2} + P</em>{CO<em>2} + P</em>{N_2}$
• Substitute the values:
  • $0.97 = P<em>{O</em>2} + 0.70 + 0.12$
• Solve for $P<em>{O</em>2}$:
  • $P<em>{O</em>2} = 0.97 - 0.70 - 0.12 = 0.15$ 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.
  • $P<em>{total} = P</em>{gas} + P<em>{H</em>2O}$

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 ($P<em>{CO</em>2}$).
• Steps:
  1. Find the water vapor pressure at 13 degrees Celsius from the table: $P<em>{H</em>2O} = 11.2$ mmHg.
  2. Use the formula: $P<em>{total} = P</em>{CO<em>2} + P</em>{H_2O}$
  3. Substitute the values: $758 = P<em>{CO</em>2} + 11.2$
  4. Solve for $P<em>{CO</em>2}$: $P<em>{CO</em>2} = 758 - 11.2 = 746.8$ mmHg.
  5. Round to the nearest whole number due to the ones place of 758: $P<em>{CO</em>2} = 747$ 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.