Ch 12.6 Dalton’s Law of Partial Pressures
So far we have only been dealing with pure gases. How do we apply the gas laws to mixtures of two or more gases?
Dalton’s Law of Partial Pressuresstates that the total pressure of a mixture of gases equals the sum of the pressures that each gas would exert if it were alone.
Mathematically, Dalton’s Law of Partial Pressures can be written as:
Ptotal= P1+ P2+ P3+ …
Where the total pressure of a gas mixture equals the sum of the partial pressure for each gas present:
This property greatly simplifies our calculations.
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. Again, the pressure of each gas in a mixture is its partial pressure.
Assumptions:
All gas particles in a mixture are treated equally. Their individual atomic or molecular volumes are not significant.
There are no significant intermolecular attractions between gas particles (atoms or molecules) given the relatively large amount of space between them as compared to particles in a solid or a liquid substance.
Example:
What is the total pressure exerted by a mixture of 2.00 g of H2, 8.00 g of N2 and 12.0 g of Ar at 273 K in a 10.0 L vessel?
First we need to calculate the number of moles of each gas:
Now we can calculate the partial pressure of each gas:
Use the law of partial pressures to calculate the total pressure of the gas mixture:
Ptot= P(H2) + P(N2) + P(Ar) = 2.22 atm + 0.641 atm + 0.672 atm = 3.53 atm
A shorter approach to the total pressure of the gas mixture would have been to total the number of moles before applying the ideal gas law:
If the total pressure of a gas mixture is known, the partial pressure of each gas is simply the total pressure times the mole fraction for each gas. This also works with percentages of each gas present.
Partial pressure of a gas= Total pressure of gas mixture (mol gas/total moles)
Example:
If a gas mixture containing6.0 mol H2and 9.0 molN2is present in a container at 20.0 atm, what is the partial pressure of each gas?
Total moles present = 6.0 mol H2 + 9.0 mol N2 = 15.0 mol total
The mole fraction of H2 = 6.0 mol/15.0 mol = 0.40
The mole fraction of N2 = 9.0 mol/15.0 mol = 0.60
P(H2) = Ptotal x mole fraction H2 = Ptotal(nH2/ntotal)= 20.0 atm x (6.0 mol H2/15.0 mol total) = 8.0 atm
P(N2) = Ptotal x mole fraction N2 = Ptotal(nN2/ntotal)= 20.0 atm x (9.0 mol N2/15.0 mol total) = 12 atm