4.7: Dalton's Law of Partial Pressure
- Page ID
- 423639
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- Apply Dalton's Law of Partial Pressures.
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 \(1.00 \: \text{atm}\), then the pressure of just the nitrogen in the air is \(0.78 \: \text{atm}\). The pressure of the oxygen in the air is \(0.21 \: \text{atm}\).
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 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:
\[P_\text{total} = P_1 + P_2 + P_3 + \cdots \nonumber \]
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 \(P_1 = 300 \: \text{mm} \: \ce{Hg}\) and \(P_2 = 500 \: \text{mm} \: \ce{Hg}\), then \(P_\text{total} = 800 \: \text{mm} \: \ce{Hg}\).
A mixture of gases contains 0.305 atm Ar, 0.24 atm He, and 1.10 atm Xe. What is the total pressure?
Solution
Step 1: List the known quantities and plan the problem.
Known
- P Ar = 0.303 atm
- P He = 0.24 atm
- P Xe = 1.10 atm
Unknown
- P total
Step 2: Solve.
Since all of the pressures are in units of atm, we do not need to do any conversions before solving.
P total = P Ar + P He + P Xe = 0.303 atm + 0.24 atm + 1.10 atm = 1.64 atm
The answer is reported to two decimal places.
Summary
- Dalton's Law of Partial Pressures states that the total pressure in a system is equal to the sum of the partial pressures of the gases present.