Ideal 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.
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.
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 = nnitrogen + noxygen
This expression for n can be substituted into the ideal gas law to
yield
P V = ( nnitrogen + noxygen ) 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 of the
ideal gas law into two terms, one for nitrogen and one for oxygen.
P = nnitrogen R T/V + noxygen R T/V
P = Pnitrogen + Poxygen
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. Pnitrogen is the
partial pressure of the nitrogen and Poxygen
is the partial
pressure of oxygen.
Pnitrogen = nnitrogen R T/V
Poxygen = noxygen R T/V
Conceptually
Pnitrogen is the contribution nitrogen molecules make to the
pressure and Poxygen 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 the same two-bulb apparatus employed in a previous exercise. The left bulb is filled with nitrogen gas (artificially colored blue) and the right bulb is filled with oxygen gas (artificially colored red). The volumes of the two bulbs are provided and manometers are provided to measure the pressure inside each bulb.
When the stopcock is open, the nitrogen will expand into the right bulb and the oxygen into the left bulb to produce a uniform mixture.
Each time you press the "New Conditions" button, the experiment will be reset with new volumes and initial pressures for the two 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?
Practice the calculations until you are able to solve the problem consistently.
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© 2000 David N. Blauch