Gas Laws

The Gas Laws Describe HOW gases behave. Can be predicted by the The Kinetic Theory

4 things In order to completely describe a gas you need to measure 4 things 1.Pressure 2.Temperature 3.Volume 4.Number of particles

Gas Pressure Pressure is defined as force per unit area. Gas particles exert pressure when they collide with the walls of their container. The SI unit of pressure is the pascal (Pa). However, there are several units of pressure –Pascal (Pa) –Kilopascal (KPa) –Atmosphere (atm)

1 atm 4 Liters As the pressure on a gas increases

2 atm 2 Liters …the volume decreases Pressure and volume are inversely related

Temperature Raising the temperature of a gas increases the pressure if the volume is held constant. The molecules hit the walls harder. The only way to increase the temperature at constant pressure is to increase the volume.

If you start with 1 liter of gas at 1 atm pressure and 300 K and heat it to 600 K one of 2 things happens 300 K

Either the volume will increase to 2 liters at 1 atm 300 K 600 K

300 K 600 K Or the pressure will increase to 2 atm. More collisions mean greater pressure

Changing the Size of the Container In a smaller container molecules have less room to move Hit the sides of the container more often As volume decreases pressure increases.

The effect of adding gas When we blow up a balloon we are adding gas molecules. Doubling the number of gas particles doubles the pressure More molecules means more collisions Fewer molecules means fewer collisions.

1 atm If you double the number of molecules…

…You double the pressure 2 atm

As you remove molecules from a container…….. 4 atm

….the pressure decreases 2 a tm

2

Avogadro’s Hypothesis Nitrogen, N 2 Hydrogen, H 2 Oxygen, O 2 1 mole of each gas has the same number of molecules at STP

Boyle’s Law At a constant temperature, pressure and volume are inversely related As one goes up the other goes down P 1 x V 1 = P 2 x V 2

A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume? Example P 1 = 1 atm V 1 = 25 L P 2 = 1.5 atm V 2 = ? (1 atm)(25 L)=(1.5 atm)(V 2 ) 16.7 L

A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to volume to 43 L? A sample of Helium gas is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L? Example

Charles’ Law The volume of a gas is directly proportional to the Kelvin temperature when the pressure is held constant

Example A sample of gas at 40.0 °C occupies a volume of 2.32 L. If the temperature is raised to 75.0 °C what will the new volume be? V 1 = 2.32 L T 1 = V 2 = ? T 2 = MUST CONVERT TEMP TO K!!!!!!! 2.58 L V1 = V2 T1 T L = V2 313K 348 K

Examples What is the pressure inside a L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? At what temperature will the can above have a pressure of 2.2 atm?

Combined Gas Law The Combined Gas Law Deals with the situation where only the number of molecules stays constant. P 1 x V 1 = P 2 x V 2 T 1 T 2

Example A gas at kPa and 30.0°C fills a flexible container to a volume of 2.00 L. If the temperature was raised to 80.0°C and the pressure was increased to kPa, what is the new volume?

Example P 1 V 1 = P 2 V 2 T 1 T 2 P 1 = kPa V 1 = 2.00 L T 1 = 30.0 °C = 303 K P 2 = kPa V 2 = ? T 2 = 80.0 °C = 353 K

Example P 1 V 1 = P 2 V 2 T 1 T 2 (110.0)(2.00L) = (440.0kPa)(V 2 ) 303K 353K V 2 = L

Dalton’s Law of Partial Pressures The total pressure inside a container is equal to the sum of the partial pressure due to each gas. The partial pressure of a gas is the contribution by that gas hitting the wall. P Total = P 1 + P 2 + P 3 + …

We can find out the pressure in the fourth container By adding up the pressure in the first 3 2 atm1 atm3 atm6 atm

Dalton’s Law of Partial Pressures A gas mixture contains H 2, He, Ne, and Ar. The total pressure of the mixture is 93.6 kPa. The partial pressures of He, Ne, and Ar are 15.4 kPa, 25.7 kPa, and 35.6 kPa respectively. What is the pressure exerted by H 2 ? P T = P H2 + P He + P Ne + P Ar P H2 = 16.9 kPa

Dalton’s Law of Partial Pressures A person using an oxygen mask is breathing air with 33% Oxygen. What is the partial pressure of the Oxygen when the air pressure in the mask is 110 kPa? 33% of 110 kPa 36 kPa

Diffusion & Effusion u Molecules moving from areas of high concentration to low concentration. u Perfume molecules spreading across the room. u Effusion - Gas escaping through a tiny hole in a container. u Both depend on the speed of the molecules

Bigger molecules move slower at the same temp. Bigger molecules effuse and diffuse slower Helium effuses and diffuses faster than air -escapes from balloon. Diffusion

Kinetic Molecular Theory Three main points to the kinetic theory of gases. Gases are made of small particles, which are spread very far apart from each other and behave independently of one another. Gas particles constantly move, randomly, yet in a straight line until acted upon by an outside force or barrier. All collisions are perfectly elastic which means that no energy is gained or lost during the collision.

Ideal Gases We are going to assume that gases behave ideally Does not really exist Assume particles have no volume Assume no attractive forces between molecules ONLY 2 ELEMENTS TO BEHAVE MOST LIKE AN IDEAL GAS ARE HYDROGEN AND HELIUM

Ideal Gases vs Real Gases Real Gases deviate from the Ideal Gases: 1)Volume of a gas is significant (22.4 L) 2)Gas particles can condense, so do have forces of attraction between particles Real gases differ when at low temp and high pressure