Gas Mixtures and Partial Pressure
So far we have only been dealing with pure gases. How do we apply the gas laws to mixtures of two or more gases?
Daltons Law of Partial Pressures ® The total pressure of a mixture of gases equals the sum of the pressures that each gas would exert if it were alone.
Mathematically Daltons Law of Partial Pressures can be written as:
Ptot = P1 + P2 + P3 +
This property greatly simplifies our life (actually it probably doesnt simplify your life that much, but it makes working the homework, quiz and exam problems a lot easier).
When we apply the ideal gas law to mixtures of gases each component gas will have its own P and n, but all of the component gases will have the same T and V.
What is the total pressure exerted by a mixture of 2.00 g of H2 (MW = 2.016 g/mol), 8.00 g of N2 (MW = 28.01 g/mol) and 12.0 g of Ar (AW = 39.95 g/mol) at 273 K in a 10.0 L vessel?
First we need to calculate the number of moles of each gas:
2.00 g H2 ´ [1 mol/2.016 g] = 0.992 mol
8.00 g N2 ´ [1 mol/28.01 g] = 0.286 mol
12.0 g Ar ´ [1 mol/39.95 g] = 0.300 mol
Now we can calculate the partial pressure of each gas:
P(H2) = nRT/V = [(0.992)(0.08206)(273)]/(10.0) = 2.22 atm
P(N2) = nRT/V = [(0.286)(0.08206)(273)]/(10.0) = 0.641 atm
P(Ar) = nRT/V = [(0.300)(0.08206)(273)]/(10.0) = 0.672 atm
We can now use the law of partial pressures to calculate the total pressure:
Ptot = P(H2) + P(N2) + P(Ar) = 2.22 + 0.641 + 0.672 = 3.53 atm
A somewhat shorter approach to the same answer would have been to total the number of moles before applying the ideal gas law:
ntot = n(H2) + n(N2) + n(Ar) = 0.922 + 0.286 + 0.300 = 1.578 mol
Ptot = nRT/V = [(1.578)(0.08206)(273)]/(10.0) = 3.53 atm
Another way we can use Daltons Law of Partial Pressures is to calculate the partial pressure of any gas in a mixture if we know the total pressure and the number of moles of each gas (and vice versa).
P1/Ptot = n1/ntot
If a gas which is 5 mol% H2 and 95 mol% N2 is present in a container at 200 atm, what is the partial pressure of each gas?
P(H2) = PtotnH2/ntot = [(200 atm)(0.05ntot)]/( ntot) = 10 atm
P(N2) = PtotnN2/ntot = [(200 atm)(0.95ntot)]/( ntot) = 190 atm