# In the container. This law also assumes that

In this lesson, you will learn how gases behave when they are mixed together and how to use Dalton’s law of partial pressures to calculate partial and total pressures of gases. You will also learn how to use this information to explain how to find the partial pressure of a gas collected over water.

## Gas Mixtures

It was a hot and humid day on Ideal Island, the place where all gases behave ideally. Remember, ideal gases move rapidly and randomly, they are not attracted to each other, and they have elastic collisions, meaning when they collide there is no loss in energy. Johnny Dalton and his family are vacationing on the island, and it happens to be one of the most humid days Johnny has experienced. This gets him thinking about humidity and the particles in the air.As you may know, air is a mixture of several different gases: about 78% of it is nitrogen, 20% is oxygen, one percent is argon and the remaining is a combination of water vapor, carbon dioxide and other gases.

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On more humid days, like today on the island, the amount of water vapor would exceed one percent and may even reach as high as four percent. Johnny Dalton decided to spend his day experimenting with different mixtures of gases, and while he was experimenting, he observed many different interesting features of gas mixtures.

## Partial Pressure of a Gas

One of his most important observations was that in a mixture of gases, each gas behaved independently of the other gases – meaning that if he had a container of five nitrogen molecules causing the pressure of the container to be five mmHg and he added four oxygen molecules to this same container, the pressure would increase to nine mmHg. Now, if he removed the original nitrogen molecules, the pressure would decreases back down to four mmHg. This showed him that each gas particle is going to fly around and hit the walls of the container, causing the pressure on its own; it wasn’t going to interfere with the other gas particles flying around. So, the more gas particles you have in a container, the higher the pressure in that container, and the less particles you have in a container, the lower the pressure.

If these two gases are mixed, each gas is going to exert its own pressure, or partial pressure, combining to create a total pressure in the container.

## Dalton’s Law of Partial Pressures

This phenomenon was so significant that it was named after Dalton. It became known as Dalton’s Law of Partial Pressures , and it simply states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. We can also look at this law in equation form.Going back to the previous mixture example, the partial pressure of the nitrogen was five mmHg, and the partial pressure of the oxygen was four mmHg.

The total pressure of the mixture was nine mmHg. This law can be used with any number of gas components, but it assumes that each gas behaves ideally and independently. Remember that ideal gases have no intermolecular forces, so they don’t affect each other, which means that each individual gas particle has an equal chance of hitting the wall and causing pressure, and the total pressure is a result of all of the collisions the particles have with the walls of the container. This law also assumes that the gases in the mixture won’t react with each other.We can use this equation to find the pressure of each separate gas in the atmosphere. Say the total atmospheric pressure on the island is 760 mmHg (this is the likely pressure of the atmosphere at sea level).

The pressure of each individual gas in the atmosphere would need to total 760 mmHg. If 78% of the atmosphere is nitrogen, then around 593 mmHg (78% of 760) would be pressure exerted due to the nitrogen. 152 mmHg of pressure would be due to the oxygen (that’s 20% of 760), and the rest of the pressure (15 mmHg) would come from the other gases in the atmosphere.

## Collecting a Gas over Water

Johnny decided to use his new knowledge of the additive properties of partial pressures in one final experiment.

One of Johnny’s favorite chemical reactions is the one between baking soda and vinegar. The combination produces a lot of carbon dioxide gas, which causes it to make bubbles and foam up! Johnny decided that this time he wants to keep the carbon dioxide that’s produced. Often in a chemistry lab, gas is collected over water (using water displacement).

Johnny started by combining the baking soda and vinegar in a test tube. It instantly began producing carbon dioxide.

If he were to put a cork on this test tube, it would produce so much carbon dioxide and cause so much pressure that the test tube may explode! He didn’t want that, so he used a stopper with a hole at the top for a hose to fit in. On the other end of the hose, the carbon dioxide started coming out. He put the hose in an inverted test tube filled with water, and eventually the carbon dioxide that was being created bubbled up and took the place of the water.

All he had left in the gas-collection test tube was carbon dioxide. Or did he?One aspect of this situation that takes place is the evaporation of the water into the gas-collection test tube. Some of it evaporates and goes off into the environment, and some of it evaporates into the test tube that is now filled with the newly created carbon dioxide. So, what you have in the test tube is your newly created carbon dioxide and some evaporated water (both of them are gases).

But, how much water vapor is in there? Well, that depends on the temperature of the water. Cold water doesn’t evaporate very quickly because the particles are moving so slow, and warm water does evaporate quickly because the particles are moving faster. So, the warmer the water, the faster the particles are moving, the more water vapor will be in the test tube and the less carbon dioxide you will have collected.Where Dalton’s Law enters the picture is when you add the two gases in the test tube (the carbon dioxide and the water vapor).

Provided the water level is even on the inside and outside of the test tube, the total pressure in the tube (which consists of the carbon dioxide and the water vapor) should be equal to the atmospheric pressure on the outside of the test tube.

## Sample Problem

Suppose you are collecting some oxygen using water displacement. The atmospheric pressure that day in the laboratory is 745 mmHg.

The water you are using is 25 degrees Celsius, which means that the pressure of the water vapor would be 24 mmHg. This water temperature and water vapor pressure relationship can be found using a reference table. Given all of this information, what is the pressure of the oxygen you collected? To solve this problem, we would need to set up an equation like this:

The pressure of the atmosphere outside of the test tube is equal to the partial pressure of the oxygen plus the partial pressure of the water vapor. Solving for the partial pressure of the oxygen, we would get 721 mmHg. What this means is that you didn’t really just collect oxygen.

In fact, about 3.2% of the gas particles were water vapor! That was found out by taking 24 mmHg (which is your oxygen pressure) and dividing that by the total pressure of 745 mmHg.

## Lesson Summary

Now this hot and humid day on the island should make a little more sense: the warmer the water surrounding the island, the faster the water particles are moving and the more of that water will evaporate. This will increase the partial pressure of the water vapor in the air surrounding the island because there will be more water vapor hitting things causing pressure! Because most gases behave independently, each gas in a container is going to contribute to its own pressure in that container, and the sum of all the individual pressures of each gas will equal the total pressure in that container.

This is called Dalton’s Law of Partial Pressures and it applies to all mixtures of ideal gases.

## Learning Outcome

At the end of this lesson, you should be able to define Dalton’s Law of Partial Pressures and apply it to a scientific problem involving water vapor.

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