Dalton’s Law Mixtures of Gases

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.

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.

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: P total = P 1 + P 2 + P

Application For example,In dry air we have: 78.09% N % O 2 The partial pressure of N 2 is - (0.7808)(101.3 kPa) = kPa The partial pressure of O 2 is - (0.2095)(101.3 kPa) = kPa

Application For dry air in general: GasVolume (%)Partial Pressure (kPa) Nitrogen Oxygen Argon Carbon Dioxide0.03 Total

Example 1 A gas mixture containing oxygen, nitrogen, and carbon dioxide has P O 2 = 20.1 kPa, P N 2 = 18.3 kPa, and P CO 2 = 34.4 kPa. What is P total ? P total = P 1 + P 2 + P 3 P total = P O 2 + P N 2 + P CO 2 P total = 20.1 kPa kPa kPa P total = 72.8 kPa

Example 2 A gas mixture containing oxygen, nitrogen, and argon has a total pressure of 50.2 kPa. If P O 2 = 20.1 kPa and P N 2 = 18.3 kPa what is P Ar ? P total = P 1 + P 2 + P 3 P total = P O 2 + P N 2 + P Ar P Ar = 50.2 kPa kPa kPa P total = 11.8 kPa P Ar = P total - P O 2 - P N 2

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. 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 and water vapor. 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. Water Vapor Pressure

A typical water vapor pressure table looks like this: Water Vapor Pressure T (°C)P (mm Hg)P (kPa)T (°C)P (mm Hg)P (kPa)

P atmosphere = P water + P gas P gas = P atmosphere - P water Water Vapor Pressure

Example 3 Hydrogen gas is collected over water at a temperature of 23.0°C with an atmospheric pressure of mm Hg. What is the partial pressure of the hydrogen gas in the collection tube. P atmosphere = P hydrogen + P water P hydrogen = P atmosphere - P water P hydrogen = mm Hg mm Hg P total = mm Hg P atmosphere = mm Hg P water = 21.1 mm Hg (from table)

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: P total = P 1 + P 2 + P