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# Dalton's Law of Partial Pressures

## Introduction to calculating pressures of gas mixtures

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Dalton's Law of Partial Pressures

#### Is there oxygen available on Venus?

The atmosphere of Venus is markedly different from that of Earth. The gases in the Venusian atmosphere are 96.5% carbon dioxide and 3% nitrogen. The atmospheric pressure on Venus is roughly 92 times that of Earth, so the amount of nitrogen on Venus would contribute a pressure well over 2700 mm Hg. And there is no oxygen present, so we couldn’t breathe there. Not that we would want to go to Venus – the surface temperature is usually over 460°C.

### Dalton’s Law of Partial Pressures

Gas pressure results from collisions between gas particles and the inside walls of their container. If more gas is added to a rigid container, the gas pressure increases. The identities of the two gases do not matter. John Dalton, the English chemist who proposed the atomic theory, also studied mixtures of gases. He found that each gas in a mixture exerts a pressure independently of every other gas in the mixture. For example, our atmosphere is composed of about 78% nitrogen and 21% oxygen, with smaller amounts of several other gases making up the rest. Since nitrogen makes up 78% of the gas particles in a given sample of air, it exerts 78% of the pressure. If the overall atmospheric pressure is 1.00 atm, then the pressure of just the nitrogen in the air is 0.78 atm. The pressure of the oxygen in the air is 0.21 atm.

The partial pressure of a gas is the contribution that gas makes to the total pressure when the gas is part of a mixture. The partial pressure of a gas is indicated by a  $P$ with a subscript that is the symbol or formula of that gas. The partial pressure of nitrogen is represented by  $P_{N_2}$ . Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the component gases. Dalton’s law can be expressed with the following equation:

$P_{\text{total}}=P_1+P_2+P_3+\ldots$

The figure below shows two gases that are in separate, equal-sized containers at the same temperature and pressure. Each exerts a different pressure,  $P_1$ and $P_2$ , reflective of the number of particles in the container. On the right, the two gases are combined into the same container, with no volume change. The total pressure of the gas mixture is equal to the sum of the individual pressures. If  $P_1 = 300 \text{ mmHg}$ and $P_2 = 500 \text{ mmHg}$ , then $P_{\text{Total}}=800 \text{ mmHg}$ .

Dalton’s law says that the pressure of a gas mixture is equal to the partial pressures of the combining gases.

#### Summary

• The total pressure in a system is equal to the sums of the partial pressures of the gases present.

#### Practice

Review the concepts at the link below and work the sample problems:

#### Review

1. What is the foundation for Dalton’s law?
2. Argon makes up about 0.93% of our atmosphere. If the atmospheric pressure is 760 mm Hg, what is the pressure contributed by argon?
3. On a given day, the water vapor in the air is 2.5%. If the partial pressure of the vapor is 19.4 mm Hg, what is the atmospheric pressure?