Chemistry: Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures

Let's say that, for one reason or another, we're not happy with the regular air we've been breathing our entire lives. Instead of breathing that same old boring air that's floating around outside, we're interested in making "custom air" that fits our youthful, "extreme" personality.

To improve our air, we're going to fill our house with a supercharged air mixture of 40% oxygen by volume, 40% nitrogen by volume, and 20% helium by volume (because high squeaky voices are fun).

As it turns out, John Dalton was also interested in making his own special blend of custom air (Editor's note: This is yet another lie). He reasoned that the total pressure of the custom air in his house would be equal to the sum of the individual pressures of each gas inside the house. His reasoning has been immortalized as Dalton's Law of Partial Pressures, which states:

• P_tot = P₁ + P₂ + P₃ + …

P_tot is the total pressure of all the gases in the mixture, P₁ is the amount of pressure due to gas #1, P₂ is the amount of pressure due to gas #2, and so on. The pressures on the right side of the equation are referred to as partial pressures because they represent the pressure that each gas would exert under the same conditions of temperature and volume if the other gases weren't present.

As a result, if we decided to pump all of the air out of my house and insert a mixture of air containingbe exerted by that gas alone if all 0.300 atm of oxygen, 0.300 atm of nitrogen, and 0.150 atm of helium, the total pressure of the mixture of gases would be:

• P_tot = 0.300 atm + 0.300 atm + 0.150 atm
• P_tot = 0.750 atm

Because each of the individual gases in a mixture of gases is assumed to be an ideal gas, we can treat each of them independently. As a result, if we only know the number of grams or moles of each gas in the mixture, we can use any of the gas laws discussed earlier in this section to find the total pressure of the entire mixture of gases in a problem.

Example: Without doing any prior calculations to see if it's a good idea, I've placed 150 mol O₂, 250 mol N₂, and 75 mol He in my bedroom (which has a volume of 48,000 L and from which I previously removed all the air). If the temperature is 25º C, what is the overall gas pressure inside my bedroom?

Solution: Because each of the gases in this mixture is ideal gas, we can treat each one of them individually using the ideal gas law.

• The partial pressure of O₂:
  (P_oxygen)(48,000 L) = (150 mol)(0.08206 L atm/mol K)(298 K)
  P_oxygen = 0.076 atm
• The partial pressure of N₂:
  (P_nitrogen)(48,000 L) = (250 mol)(0.08206 L atm/mol K)(298 K)
  P_nitrogen = 0.13 atm
• The partial pressure of He:
  (P_helium)(48,000 L) = (75 mol)(0.08206 L atm/mol K)(298 K)
  P_helium = 0.038 atm

Using Dalton's Law, the total pressure of all the gases in this mixture is:

• P_tot = P_oxygen + P_nitrogen + P_helium
• P_tot = 0.076 atm + 0.13 atm + 0.038 atm
• P_tot = 0.24 atm.

This is roughly the same air pressure that exists at the top of Mt. Everest, which makes breathing difficult.