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Understanding Dalton’s Law of Partial Pressures in Gas Mixtures

Dalton's Law of Partial Pressures states that in a mixture of gases, the total pressure is the sum of the individual partial pressures. This principle arises from the kinetic theory of gases, which explains that gas pressure depends on the number of collisions between gas particles and the walls of their container. Each gas in a mixture contributes its own pressure, regardless of its identity. This is crucial in applications like collecting gases over water, where water vapor pressure must be accounted for.

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Understanding Dalton’s Law of Partial Pressures in Gas Mixtures

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  1. Dalton’s Law • Mixtures of Gases

  2. Introduction • From the kinetic theory of gases, at a given temperature and in a given volume • gas pressure depends only on the number of atoms colliding with the walls of the container • the more collisions, the higher the pressure • the fewer the collisions, the lower the pressure • Therefore, the larger the amount of gas in a container, the higher the pressure.

  3. Introduction • If we have a mixture of gases in our container • each different set of gas particles will contribute its own set of collisions • the identity of the individual gases is irrelevant. • This means that each gas will have its own pressure. • This pressure is called the partial pressure of the gas.

  4. Introduction • This was studied by Dalton who proposed the following law (Dalton’s Law of Partial Pressures): • “In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.” • We use the equation: • Ptotal = P1 + P2 + P3 + ...

  5. Application • For example,In dry air we have: • 78.09% N2 • 20.95% O2 • The partial pressure of N2 is - • (0.7808)(101.3 kPa) = 79.11 kPa • The partial pressure of O2 is - • (0.2095)(101.3 kPa) = 21.22 kPa

  6. Application • For dry air in general:

  7. Example 1 A gas mixture containing oxygen, nitrogen, and carbon dioxide has PO2 = 20.1 kPa, PN2 = 18.3 kPa, and PCO2 = 34.4 kPa. What is Ptotal? • Ptotal = P1 + P2 + P3 • Ptotal = PO2 + PN2 + PCO2 • Ptotal = 20.1 kPa + 18.3 kPa + 34.4 kPa • Ptotal = 72.8 kPa

  8. Example 2 A gas mixture containing oxygen, nitrogen, and argon has a total pressure of 50.2 kPa. If PO2 = 20.1 kPa and PN2 = 18.3 kPa what is PAr? • Ptotal = P1 + P2 + P3 • Ptotal = PO2 + PN2 + PAr • PAr = Ptotal - PO2 - PN2 • PAr = 50.2 kPa - 20.1 kPa - 18.3 kPa • Ptotal = 11.8 kPa

  9. Water Vapor Pressure • Most often in chemistry we use Dalton’s law of partial pressure when we collect gas over water. • When we generate a gas in a chemical reaction, we often want to capture that gas. • Usually, we bubble the gas from the reaction into a water filled collection tube.

  10. Water Vapor Pressure • We can measure the volume of the tube directly. • And (after some adjustment), we can assume the pressure in the collection tube is the same as atmospheric pressure. • But, the gas in the tube has the gas we want andwater vapor.

  11. Water Vapor Pressure • We can use Dalton’s law of partial pressures to subtract out the water vapor so we know just the pressure of the gas we collected. • We use a water vapor pressure data table to determine the partial pressure of water at any given temperature.

  12. Water Vapor Pressure • A typical water vapor pressure table looks like this:

  13. Water Vapor Pressure • Patmosphere = Pwater + Pgas • Pgas = Patmosphere - Pwater

  14. Example 3 Hydrogen gas is collected over water at a temperature of 23.0°C with an atmospheric pressure of 754.2 mm Hg. What is the partial pressure of the hydrogen gas in the collection tube. • Patmosphere = 754.2 mm Hg • Pwater = 21.1 mm Hg (from table) • Patmosphere = Phydrogen + Pwater • Phydrogen = Patmosphere - Pwater • Phydrogen = 754.2 mm Hg - 21.1 mm Hg • Ptotal = 733.1 mm Hg

  15. Summary • Dalton’s Law of Partial Pressures: • “In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.” • We use the equation: • Ptotal = P1 + P2 + P3 + ...

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