CHEMISTRY

GAS LAWS

CHEMISTRY
BOYLE'S LAW :

Boyle's Law states: If the temperature of a gas sample is kept constant, the volume of the sample will vary inversely as the pressure varies. This statement means that, if the pressure increases, the volume will decrease. If the pressure decreases, the volume will increase. This law can be expressed as an equation that relates the initial volume (V₁) and the initial pressure (P₁) to the final volume (V₂) and the final pressure (P₂). At constant temperature,

V1 V2

=

P2 P1

Rearranging this equation gives:

V1P1

=

V2P2

or

V2

=

V1

X

P1 P2

Boyle's Law is illustrated in Figure 9.8 which shows a sample of gas enclosed in a container with a movable piston. The container is kept at a constant temperature and subjected to a regularly increasing amount of pressure. When the piston is stationary, the pressure it exerts on the gas sample is equal to the pressure the gas exerts on it. When the pressure on the piston is doubled, it moves downward until the pressure exerted by the gas equals the pressure exerted by the piston. At this point the volume of the gas is halved. If the pressure on the piston is again doubled, the volume of gas decreases to one-fourth its original volume.

FIGURE 9.8 Boyle's Law: At constant temperature, the volume of a gas sample is inversely proportional to the pressure. The curve is a graph based on the data listed in the figure.

At the molecular level, the pressure of a gas depends on the number of collisions its molecules have with the walls of the container. If the pressure on the piston is doubled, the volume of the gas decreases by one-half. The gas molecules, now confined in a smaller volume, collide with the walls of the container twice as often and their pressure once again equals that of the piston.
How does Boyle's Law relate to the kinetic molecular theory? The first postulate of the theory states that a gas sample occupies a relatively enormous empty space containing molecules of negligible volume. Changing the pressure on the sample changes only the volume of that empty space - not the volume of the molecules.

Example: A sample of gas has a volume of 6.20 L at 20°C and 0.980 atm pressure. What is its volume at the same temperature and at a pressure of 1.11 atm? 1. Tabulate the data Initial Conditions Final Conditions volume V1 = 6.20 L V2 = ? pressure P1 = 0.980 atm P2 = 1.11 atm 2. Check the pressure unit. If they are different, use a conversion factor to make them the same. (Pressure conversion factors are found in the previous section.) 3. Substitute in the Boyle's Law Equation: 4. Check that your answer is reasonable. The pressure has increased the volume should decrease. The calculated final olume is less than the initial volume, as predicted.

CHARLES' LAW :

Charles' Law states: If the pressure of a gas sample is kept constant, the volume of the sample will vary directly with the temperature in Kelvin (Figure 9.9). As the temperature increases, so will the volume; if the temperature decreases, the volume will decrease. This relationship can be expressed by an equation relating the initial volume (V₁) and initial temperature (T₁ measured in K) to the final volume (V₂) and final temperature (T₂ measured in K). At constant pressure,

V1 V2

=

T1 T2

Rearranging this equation gives:

V2

=

V1

X

T2 T1

or

V2 T2

=

V1 T1

FIGURE 9.9 Charles' Law: At constant pressure, the volume of a gas sample is directly proportional to the temperature in degrees Kelvin.