5.4
Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions
Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each gas in…
The pressure of a pure gas is the sum of molecular collisions between its particles and surrounding surfaces. A gas sample with fewer particles in a given volume exerts a lower pressure than a sample with more particles in the same volume.
But what is the pressure of a mixture of different gases? For a multicomponent gas mixture, the pressure is the sum of collisions from all gas molecules.
It is assumed that each component in the mixture exerts its own pressure that is independent of the other gases present. The pressure from any individual component is called its partial pressure.
The total pressure of the ideal gas mixture equals the sum of the partial pressures of its components. This observation is Dalton's law of partial pressures.
By applying the ideal gas law, the partial pressures of the individual gas components are substituted with measurable variables.
Since the gases in the mixture occupy the same volume and are at the same temperature, the equation can be simplified.
The sum of the moles of the individual components equals the total number of moles of all gas components, ntotal. Therefore, the total pressure of the gas mixture is equal to ntotal multiplied by the constant RT over V.
The number of moles of a component divided by the total moles in the mixture is the mole fraction.
Rearranging the mole fraction for total moles, and substituting ntotal in Dalton’s law of partial pressures yields expressions for the total pressure. Rearranging again, the partial pressure of a gas in a mixture is the product of its mole fraction and the total pressure of the mixture.
So, in a gas mixture, the partial pressure of any component, i, is equal to the mole fraction of i multiplied by the total pressure.
As an example calculation, suppose a container filled with two gases, helium, and argon, is 40% by volume argon. This implies that the mole fraction of argon is 0.4. If the total pressure is 4 atm, what is the partial pressure of helium?
Using the equation for the partial pressure of a gas, the partial pressure of argon is equal to its mole fraction multiplied by the total pressure. Thus, 0.4 times 4 atm gives the partial pressure of argon as 1.6 atm.
Since the sum of partial pressures equals the total pressure, the equation can be rearranged so that the partial pressure of argon can be subtracted from the total pressure. Thus, the partial pressure of helium is 2.4 atm.
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Q1: What is partial pressure in a gas mixture?
Partial pressure is the pressure exerted by an individual gas component in a mixture, as if that gas occupied the container alone. Each gas in a mixture exerts its own pressure independently of other gases present, assuming no chemical reactions occur. The partial pressure depends on the number of molecular collisions from that specific gas component with container surfaces.
Q2: How does Dalton's law of partial pressures work?
Dalton's law states that the total pressure of a gas mixture equals the sum of the partial pressures of all component gases. Since each gas occupies the same volume and temperature, their individual pressures add together without interference. This principle applies to ideal gas mixtures where gases do not chemically interact.
Q3: What is mole fraction and how does it relate to partial pressure?
Mole fraction is the ratio of a component's moles to the total moles in a mixture. The partial pressure of any gas equals its mole fraction multiplied by the total pressure of the mixture. This relationship allows you to calculate individual gas pressures when you know the composition and total pressure.
Q4: How do you calculate partial pressure from mole fraction?
Use the equation: partial pressure of component i equals its mole fraction times the total pressure. For example, if argon comprises 40% of a mixture (mole fraction 0.4) at 4 atm total pressure, argon's partial pressure is 0.4 × 4 atm = 1.6 atm. The remaining pressure belongs to other components.
Q5: Why does each gas in a mixture exert independent pressure?
Gas molecules are far apart and rarely collide with each other. Each gas component contributes pressure through its own molecular collisions with container walls, independent of other gases present. This independence holds true for ideal gases that do not chemically react, making pressure additive in mixtures.
Q6: How does the ideal gas law apply to gas mixtures?
The ideal gas law can be applied to each component separately or to the entire mixture. For a mixture, total pressure equals the total moles of all gases times RT divided by volume. Since all components occupy the same volume and temperature, the total pressure depends only on the combined number of moles present.
Q7: What determines the total pressure of a gas mixture at constant temperature and volume?
At constant temperature and volume, total pressure is determined solely by the total number of moles of gas present. Adding more gas molecules increases collisions with container walls, raising pressure proportionally. The identity of the gases does not matter, only their combined quantity.