Gas Laws: Dalton's Law of Partial Pressures

Concepts

One of the important predictions made by Avogadro is that the identity of a gas is unimportant in determining the P-V-T properties of the gas. This behavior means that a gas mixture behaves in exactly the same fashion as a pure gas. (Indeed, early scientists such as Robert Boyle studying the properties of gases performed experiments using gas mixtures, most notably air, rather than pure gases.)

The Ideal Gas Law

P V   =   n R T

predicts how the pressure, volume, and temperature of a gas depend upon the number of moles of the gas. The number of moles, n, is the total moles of all the gas-phase species.

Air, for example, is composed primarily of nitrogen and oxygen. In a given sample of air, the total number of moles is can be approximated as

n   =   n_nitrogen   +   n_oxygen

This expression for n can be substituted into the Ideal Gas Law to give

P V   =   ( n_nitrogen   +   n_oxygen ) R T

All molecules in the gas have access to the entire volume of the system, thus V is the same for both nitrogen and oxygen. Similarly, both compounds experience the same temperature. One can therefore split this expression for the Ideal Gas Law into two terms, one for nitrogen and one for oxygen.

P   =   n_nitrogen R T / V   +   n_oxygen R T / V

P   =   P_nitrogen   +   P_oxygen

The above equation is called Dalton's Law of Partial Pressure, and it states that the pressure of a gas mixture is the sum of the partial pressures of the individual components of the gas mixture.
P_nitrogen is the partial pressure of nitrogen and P_oxygen is the partial pressure of oxygen.

P_nitrogen   =   n_nitrogen R T / V

P_oxygen   =   n_oxygen R T / V

You'll notice that the equations for the partial pressures are really just the Ideal Gas Law, but the moles of the individual component (nitrogen or oxygen) are used instead of the total moles. Conceptually P_nitrogen is the contribution nitrogen molecules make to the pressure and P_oxygen is the contribution oxygen molecules make.

Exercise

Objective

• Employ Boyle's Law and Dalton's Law of Partial Pressures to predict the pressure of a gas mixture.

This exercise involves two bulbs connected by a tube with a stopcock. In this virtual experiment, the left bulb is filled with pure nitrogen gas (artificially colored blue) and the right bulb is filled with pure oxygen gas (artificially colored red). The stopcock is initially closed to prevent the gases from mixing. The volumes of the two bulbs are indicated and manometers are provided to measure the pressure inside each bulb. Pressing the "New Conditions" button resets the experiment with new volumes and new initial pressures for the two pure gases.

When the stopcock is opened, the nitrogen will expand into the right bulb and the oxygen into the left bulb to produce a gas mixture that uniformly fills both bulbs.

Use Boyle's Law to calculate the partial pressure of nitrogen and the partial pressure of oxygen in the final gas mixture. Use these partial pressures and Dalton's Law to calculate the pressure for the gas mixture.

Open the stopcock and measure the final pressure. Was your calculation accurate?