### Dalton's Law of Partial Pressures

This law was discovered by John Dalton in 1801.

For any pure gas (let's use helium), PV = nRT holds true. Therefore, P is directly proportional to n if V and T remain constant. As n goes up, so would P. Or the reverse.

Suppose you were to double the moles of helium gas present. What would happen?

However, suppose the new quantity of gas added was a DIFFERENT gas. Suppose that, instead of helium, you added neon.

What would happen to the pressure?

Answer: the pressure doubles, same as before.

Dalton's Law immediately follows from this example since each gas is causing 50% of the pressure. Summing their two pressures gives the total pressure.

Written as an equation, it looks like this:

PHe + PNe = Ptotal

Dalton's Law of Partial Pressures: each gas in a mixture creates pressure as if the other gases were not present. The total pressure is the sum of the pressures created by the gases in the mixture.

Ptotal = P1 + P2 + P3 + .... + Pn

Where n is the total number of gases in the mixture.

The only necessity is that the two gases do not interact in some chemical fashion, such as reacting with each other.

The pressure each gas exerts in mixture is called its partial pressure.

The most common use of Dalton's Law seen in high school is with water vapor.

A common method of collecting gas during an experiment is by trapping it "over water." An inverted bottle filled with water sits in a water bath. A tube from the reaction vessel conducts the gas into the bottle where it bubbles to the top and displaces water, which runs out the mouth of the bottle into the water bath.

However, there is an unavoidable problem. The gas saturates with water vapor and now the total pressure inside the bottle is the sum of two pressures - the gas itself and the added water vapor.

WE DO NOT WANT THE WATER VAPOR PRESSURE.

So we get rid of it by subtraction.

This means we must get the water vapor pressure from somewhere.

We get it from a table because the water vapor pressure depends only on the temperature, NOT how big the container is or the pressure of the other gas. Usually the textbook will have an abbreviated table with more complete tables in reference manuals like "The Handbook of Chemistry and Physics." So finally, here is the example problem: 0.750 L of a gas is collected over water at 23.0°C with a total pressure of 99.75 kPa. What is the pressure of the dry gas? Look up the vapor pressure data here.

The ChemTeam will leave you to work this one out!

Another common concept that crops up in a Dalton's Law context is mole fraction.

Suppose you had equal moles of two different gases in a mixture. Then the mole fraction for each would be 0.50.

The mole fraction for each gas is simply the moles of that gas divided by the total moles in the mixture.

Seems simple enough. How does it relate to Dalton's Law?

Answer: the mole fraction also gives the fraction of the total pressue each gas contributes. So if the mole fraction for a gas was 0.50, then it would contribute 50% of the total pressure. If the mole fraction of a gas was 0.15, then its partial pressure would be 0.15 times the total pressure.

The reverse is also true. If you divided the partial pressure of a gas by the total pressure, you would get the mole fraction for that gas. (I hope you know enough by now that the two pressures would have to be in the same units!)

By the way, mole fractions are unitless numbers. The mole (or pressure) units cancel out.