Understanding Gas Behavior: Kinetic Theory & Gas Laws

Passing Gas Objectives: • correctly describe the 5 pts of kinetic molecular theory • for each law: • define • include math expressions • if appropriate generate a graph that illustrates • use math expressions to calculate gas law problems

Characteristics of Gases • Gases expand to fill a container • Gases form homogeneous mixtures with other gases • Gases can be easily compressed • Readily measured properties of gas are its temperature, volume, and pressure

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: • Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion. • These particles move in a straight line until they collide with another particle or the walls of the container. • These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space. • There is no force of attraction between gas particles or between the particles and the walls of the container.

5. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container. 6.The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

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 101.3 kPa (kiloPascals) • Increase in temp. = increase in kinetic energy = increase in pressure of gas in an enclosed volume

relationships • between number of particles, temperature, pressure, and volume • phenomena we experience daily

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

Volume: - reduced space (volume) = increased pressure:  V = - increased space (volume) = reduced pressure: V = P  P 

Temperature: -  temperature =  in pressure -  temperature =  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. = 0 ° C 273 K • standard pressure = 101.3 kPa or 1 atmosphere • 1 atm = 0° 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 P1 X V1 = P2 X V2

V2 =30.0 L X 103 kPa 25.0 kPa = 124 L 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.) V2 = P1 X V1 P2 P1 = 103 kPa V1 = 30 L P2 = 25.0 kPa P1 X V1 = P2 X V2 V2 = ?

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?

V1 = V2 T1 T2 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 • Temperature = volume

V2 = V1 X T2 = 4.0L X 331 K = 4.46 L T1 297 K Example: • A balloon inflated in a room at 24oC has a volume of 4.0 L. The balloon is then heated to a temperature of 58oC. What is the new volume if the pressure remains constant? V1 = 4.0 L T1 = 24oC T2 = 58oC V2 = ?L Express the temp in kelvins: T1 = 24oC + 273 = 297 K T2 = 58oC + 273 = 331 K

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

P1 = P2 T1 T2 Gay-Lussac’s Law • “The pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.” temperature = pressure temperature = pressure

P2 = 103 kPa X 1201 K = 415 kPa 298 K Example: • The gas in a used aerosol can is at a pressure of 103 kPa at 25oC. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928oC? T1 = 25oC + 273 = 298 K T2 = 928oC + 273 = 1201 K P1 = 103 kPa T1 = 25oC T2 = 928oC P2 = ? kPa

Try this one! • The pressure in an automobile tire is 198 kPa at 27oC. 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.)

P1 X V1 = P2 X V2 T1 T2 P1 X V1 = P2 X V2 X T1 T2 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: (Temp. is constant) Equals Boyle’s Law!

Try These! • A gas at 155 kPa and 25oC 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 125oC. What is the new volume? • A 5.0 L air sample at a temperature of –50oC has a pressure of 107 kPa. What will be the new pressure if the temperature is raised to 102oC and the volume expands to 7.0 L?

Understanding Gas Behavior: Kinetic Theory & Gas Laws