Lesson 7-4

Dalton's Law

     The total pressure in a container is the sum of the partial pressures of all the gases in the container.   That may sound like common sense to you, but that is Dalton's Law of partial pressures.  As simple as it may sound, it is one of the most useful of the gas laws in real life.  A common method of gas collection in the laboratory involves displacing water from a bottle, so that you know when the bottle is full of an invisible gas.   The gas that is left in the bottle will not be pure, it will be a mixture that contains a certain amount of water vapor.  To find the pressure of the dry gas alone, we need to subtract out the pressure of the water vapor.  This is one way that Dalton's law of partial pressure can be used.  In this form, the formula that we use looks like this:

P_{dry gas} = P_total - P_{water vapor}
Where P = Pressure

     In order to solve the problem in a real-life situation, you need a reference table that shows the pressure of water vapor at various temperatures.  Your textbook probably has such a table, but for convenience, I have provided one below.  There will be a link at the bottom of the page where you can print a table out to use on exams.

Now we will demonstrate how one problem of this type would be solved.

Example 1.  A sample of hydrogen gas is collected over water at 14.0 ^oC.  The pressure of the resultant mixture is 113.0 kPa.  What is the pressure that is exerted by the dry hydrogen alone?

Solving:

Write the formula you will need:             P_{dry gas} = P_total - P_{water vapor}

Look up the vapor pressure of water at 14.0 ^oC on table 18-4a:  1.6 kPa

List what is known and unknown:

P_{dry gas} = ?

P_total = 113.0 kPa

P_{water vapor} = 1.6 kPa

Substitute and solve:                  P_{dry gas} = P_total - P_{water vapor}

                                          P_{dry gas} = 113.0 kPa - 1.6 kPa

                                                     P_{dry gas} = 111.4 kPa

     Another way that you will be will use this gas law is to simply determine the partial pressure of another gas, other than water vapor, in a mixture.  These types of problems are very easy, and it would be best to look at the formula below:

P_total = P₁ + P₂ + . . . P_n

Where P₁, P₂, and P_n are the partial pressures of the gases involved.

     Below is an example of how this formula would be used:

Example 2.  A mixture of oxygen, hydrogen and nitrogen gases exerts a total pressure of 278 kPa.  If the partial pressures of the oxygen and the hydrogen are 112 kPa and 101 kPa respectively, what would be the partial pressure exerted by the nitrogen.

P_total = P₁ + P₂ + . . . P_n

                                                                      278 kPa = 112 kPa + 101 kPa + P_nitrogen

                                                                      P_nitrogen = 278 kPa - (112 kPa + 101 kPa)

                                                                      P_nitrogen = 65 kPa

Now, practice what you have learned with the links below.

Please forward all questions, comments and criticisms to Gregory L. Curran.
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Last Modified February 07, 2008