Dalton's Law of Partial Pressures Ken Rogers Miami Killian

Watch as we fill a large glass flask with two gases. Dalton’s Law is one of the simplest gas laws. It says, for a mixture of gases, the total pressure of the gases is the sum of each gases partial pressure. Or, more simply, Ptotal = P1 + P2 + P3 + . . . Watch as we fill a large glass flask with two gases.

1 5.3 atm 3.0 atm 2 6 3 5 4

Ptotal = P1 + P2 5.3 atm = 3.0 atm + P2 2.3 atm = P2 The pressure of the first gas was 3.0 atmospheres. The total pressure of both gases was 5.3 atmospheres. Substituting those pressures into the equation: Ptotal = P1 + P2 5.3 atm = 3.0 atm + P2 2.3 atm = P2 The pressure of the second gas must have been 2.3 atm.

The pressures were also proportional to the number of gas molecules. There were more molecules of the first gas, so its pressure was greater than the second gas.

Dalton’s law is used another way. Measuring the volume of a gas can be difficult. You just can’t pour a gas into a graduated cylinder to measure its volume, because the graduated cylinder is already filled with a gas. . . air. The solution is to fill the graduated cylinder with water and then add the gas.

Watch the simulation of a technique for measuring the volume of a gas. Only instead of using a graduated cylinder, we’ll be using a gas measuring tube. Watch the simulation of a technique for measuring the volume of a gas. We’ll be measuring a gas produced by the heating of KClO3. 2KClO3 (s) a 2KCl (s) + 3O2 (g)

gas measuring tube is filled with water and then stoppered A substance that produces a gas is placed in the test tube.

A hose connects the test tube to the gas measuring tube so that any gas produced, is transferred to the gas measuring tube.

The substance is heated, producing a gas which bubbles into the gas measuring tube.

If the water level inside had been higher, water would be added to the beaker until the water levels were the same and therefore the pressures the same. The gas measuring tube is raised to equalize the pressure. Because the water level inside the tube is lower than outside, the pressure is greater. The volume of the gas is then measured. . . . and the temperature of the water taken.

The only problem is, the gas we produced is not pure. Whenever a gas is collected a over water, some of the water evaporates and produces a second gas. . . water vapor. So we have a mixture of gases. This is where Dalton’s Law of Partial Pressures comes in.

The warmer the water, the more that evaporates. The total pressure of the 2 gases is the same as the outside (atmospheric) pressure. That’s why we equalized the pressures by raising the gas measuring tube. The pressure of the water vapor depends on the temperature of the water. The warmer the water, the more that evaporates. So you consult the Table of Water Vapor Pressures (from the back of your book).

Temperature (oC) Pressure (mm Hg) 0.0 4.6 5.0 6.5 10.0 9.2 15.0 12.8 20.0 17.5 25.0 23.8 30.0 31.8 35.0 42.2 40.0 55.3

Ptotal = PO2 + PH2O 755 mm Hg = PO2 + PH2O If the atmospheric pressure was 755 mm Hg that day, and the temperature of the water was 25oC, Ptotal = PO2 + PH2O 755 mm Hg = PO2 + PH2O

Temperature (oC) Pressure (mm Hg) 0.0 4.6 5.0 6.5 10.0 9.2 15.0 12.8 20.0 17.5 25.0 23.8 30.0 31.8 35.0 42.2 40.0 55.3

Ptotal = PO2 + PH2O 755 mm Hg = PO2 + PH2O 755 mm Hg = PO2 + 23.8 mm Hg 731.2 mm Hg = PO2

You can now use Boyle’s Law to figure out the volume of the dry gas at any pressure. P1 . V1 = P2 . V2 731.2 mm Hg . V1 = P2 . V2 Volume of gas in gas measuring tube Volume of gas at P2

For example if the volume of the gas was 250 mL at 25oC, and we wanted to know its volume at 755 mm Hg, P1 . V1 = P2 . V2 731.2 mm Hg . 250 mL = 755 mm Hg . V2 731.2 mm Hg . 250 mL = V2 755 mm Hg 242 mL = V2 So the water vapor must have been occupying 8 mL.