The Behavior of Gases Kinetic Theory - “kinetic” = motion - kinetic energy – the energy an object has due to motion - kinetic theory – states that the tiny particles in all forms of matter are in constant motion

Basic Assumptions of the Kinetic Theory: 1. A gas is composed of particles (atoms or molecules). The particles are small, hard and have a lot of space between them. 2. The particles in gas move constantly in a constant random motion. Motion is a straight line until they collide with something that changes the direction.

3. All collisions are perfectly elastic. During collisions kinetic energy is transferred without loss from one particle to another, and total kinetic energy remains constant.

Gas Pressure Gas pressure is the force exerted by a gas per unit surface area of an object. No particles = no pressure = vacuum Barometer – used to measure gas pressure Pascal – metric unit of pressure Atmospheric pressure at sea level is kPa (kiloPascals) Increase in temp. = increase in kinetic energy = increase in pressure of gas in an enclosed volume

Factors Affecting Gas Pressure Amount of Gas: more gas particles = increased gas pressure: 2 X n = 2 X P (n = number of moles of gas P = pressure in kPa) Gas particles flow from areas of high numbers (high pressure) to areas of low numbers of particles

Volume: - reduced space (volume) = increased pressure: ½ V = 2 X P - increased space (volume) = reduced pressure: 2 X V = ½ P

Temperature: - increase in temperature = increase in pressure - decrease in temperature – decrease in pressure

Standard Pressure and Temperature Volume of gas varies as temp. and pressure change Volume of gas is determined at STP (standard temperature and pressure) standard temp. = 0o C 273 K standard pressure = kPa or 1 atmosphere 1 atm = 0o at the beach = 14 pounds of pressure per square inch on your body.

The Gas Laws! Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law

Boyle’s Law (1662) “For a given mass of gas at constant temperature, the volume of the gas varies inversely with the pressure.” Pressure = Volume Volume = Pressure P 1 X V 1 = P 2 X V 2

Example: A high altitude balloon contains 30.0 liters of helium at 103 kPa. What is the volume when the balloon rises to a volume where the pressure is only 25.0 kPa? (Assume that the temperature remains the same.) P 1 = 103 kPa V 1 = 30 L P 2 = 25.0 kPa V 2 = ? P 1 X V 1 = P 2 X V 2 V 2 =30.0 L X 103 kPa 25.0 kPa = 124 L V 2 = P 1 X V 1 P 2

Pressure conversions: On a daily basis, pressure is measured in psi – “pounds per square inch” 1 psi = kPa problems must be solved in kPa

Try these: The pressure on 2.5 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temperature remains constant? A gas with a volume of 4.0 L at a pressure of 30 psi is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant? (Convert to kPa to solve, then back to psi.)

Charles’ Law (1787) “The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.” Temperature = volume V 1 = V 2 T 1 T 2

Example: A balloon inflated in a room at 24 o C has a volume of 4.0 L. The balloon is then heated to a temperature of 58 o C. What is the new volume if the pressure remains constant? V 1 = 4.0 L T 1 = 24 o C T 2 = 58 o C V 2 = ?L Express the temp in kelvins: T 1 = 24 o C = 297 K T 2 = 58 o C = 331 K V 2 = V 1 X T 2 = 4.0L X 331 K = 4.46 L T K

Try These: If a sample of gas occupies 6.80 L at 325 o C, what will be its volume at 25 o C if the pressure does not change? Exactly 5.0 L of air at –50.0 o C is warmed to 100 o C. What is the new volume if the pressure remains the same?

Gay-Lussac’s Law “The pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.” temperature = pressure P 1 = P 2 T 1 T 2

Example: The gas in a used aerosol can is at a pressure of 103 kPa at 25 o C. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928 o C? P 1 = 103 kPa T 1 = 25 o C T 2 = 928 o C P 2 = ? kPa T 1 = 25 o C = 298 K T 2 = 928 o C = 1201 K P 2 = 103 kPa X 1201 K = 415 kPa 298 K

Try this one! The pressure in an automobile tire is 198 kPa at 27 o C. At the end of the trip on a hot sunny day, the pressure has risen to 225 kPa. What is the temperature of the air in the tire? (Assume that the volume has not changed.)

The Combined Gas Law The three gas laws can be combined: The other laws can be obtained by holding one quantity (P,V or T) constant: P 1 X V 1 = P 2 X V 2 T 1 T 2 P 1 X V 1 = P 2 X V 2 X T 1 T 2 (Temp. is constant) Equals Boyle’s Law!

Try These! A gas at 155 kPa and 25 o C occupies a container with an initial volume of 1.0 L. By changing the volume, the pressure of the gas increases to 605 kPa as the temperature is raised to 125 o C. What is the new volume? A 5.0 L air sample at a temperature of –50 o C has a pressure of 107 kPa. What will be the new pressure if the temperature is raised to 102 o C and the volume expands to 7.0 L?