dalton’s law mixtures of gases. introduction from the kinetic theory of gases, at a given...

Dalton’s LawMixtures of Gases

IntroductionFrom 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.

IntroductionIf 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.

IntroductionThis 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 + ...

ApplicationFor 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

ApplicationFor dry air in general:

Gas Volume (%) Partial Pressure (kPa)

Nitrogen 78.09 79.11

Oxygen 20.95 21.22

Argon 0.93 0.95

Carbon Dioxide 0.03 0.03

Total 100.00 101.31

Example 1A 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

Example 2A 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 = 50.2 kPa - 20.1 kPa - 18.3 kPa

Ptotal = 11.8 kPa

PAr = Ptotal - PO2 - PN2

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)

20.0 17.5 2.34 22.5 20.4 2.7220.5 18.1 2.41 23.0 21.1 2.8121.0 18.6 2.49 23.5 21.7 2.9021.5 19.2 2.57 24.0 22.4 2.9822.0 19.8 2.64 24.5 23.1 3.10

Patmosphere = Pwater + Pgas

Pgas = Patmosphere - Pwater

Water Vapor Pressure

Example 3Hydrogen 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 = Phydrogen + Pwater

Phydrogen = Patmosphere - Pwater

Phydrogen = 754.2 mm Hg - 21.1 mm Hg

Ptotal = 733.1 mm Hg

Patmosphere = 754.2 mm HgPwater = 21.1 mm Hg (from table)

SummaryDalton’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 + ...