5 Steps to a 5 AP Chemistry

Pressure–Temperature Relationship: Gay-Lussac’s Law

Gay-Lussac’s lawdescribes the relationship between the pressure of a gas and its Kelvin

temperature if the volume and amount are held constant. Figure 8.5 represents the process

of heating a given amount of gas at a constant volume.

As the gas is heated, the particles move with greater kinetic energy, striking the inside

walls of the container more often and with greater force. This causes the pressure of the gas

to increase. The relationship between the Kelvin temperature and the pressure is a direct one:

P/T=kg or P 1 /T 1 =P 2 /T 2

Gases  107

cool heat

Room

Temperature

Figure 8.4 Volume–temperature relationship for gases.

heat

Figure 8.5 Pressure–temperature relationship for gases. As the temperature

increases, the gas particles have greater kinetic energy (longer arrows) and collisions

are more frequent and forceful.

Combined Gas Law

In the discussion of Boyle’s, Charles’s, and Gay-Lussac’s laws we held two of the four vari-

ables constant, changed the third, and looked at its effect on the fourth variable. If we keep

the number of moles of gas constant—that is, no gas can get in or out—then we can com-

bine these three gas laws into one, the combined gas law, which can be expressed as:

(P 1 V 1 )/T 1 =(P 2 V 2 )/T 2

Again, remember: In any gas law calculation, you must express the temperature in

kelvin.

In this equation there are six unknowns; given any five, you should be able to solve for

the sixth.

For example, suppose a 5.0-L bottle of gas with a pressure of 2.50 atm at 20°C is

heated to 80°C. We can calculate the new pressure using the combined gas law. Before we

start working mathematically, however, let’s do some reasoning. The volume of the bottle

hasn’t changed, and neither has the number of moles of gas inside. Only the temperature

KEY IDEA

KEY IDEA