Behavior of Gas Molecules KINETIC MOLECULAR THEORY and the ABCs of Gas Laws

Essential Question How do gases behave? How do things like pressure, temperature and volume affect gases? Can we perform gas stoichiometry?

Launch activity Take 5 minutes and fill in your chart: What are some key characteristics of solids, liquids and gases in regards to spacing, potential of movement, and filling a container?

Launch Activity Use these questions to help you: In which phase is there the least spacing? In which phase is there the most potential for movement? Which phase(s) do(es) not have a definite shape?

Launch activity Solid Liquid Gases Spacing Potential for movement Filling a container

Behavior of gases How would you describe the behavior of gases? How do they differ from solids and liquids? How do the molecules interact with each other? What happens if you keep filling a balloon?

Kinetic Molecular Theory In 1860, Two scientists developed the Kinetic Molecular Theory to explain the behavior of gases and the relationship among pressure, volume, temperature and number of particles in a gas sample. The theory describes particle size, motion and energy.

Kinetic Molecular Theory It is called “kinetic” because the word kinetic means “to move”. Objects in motion have kinetic energy! Quick check – what is potential energy mean then?

Kinetic Molecular Theory po·ten·tial en·er·gy Noun the energy possessed by virtue of position relative to others, stresses within itself, electric charge, and other factors.

Particle Size Gases consist of small particles separated by empty space The volume of the particles is so small in comparison to the empty space, we say… The volume or size of the individual particles is negligible or equal to zero All content by HST Educational Innovations © 2012. All rights reserved. Use of this material is invited with proper attribution to the source.

Particle Motion Gas particles are in constant, random motion. Gas particles move in straight line (linear) motion until they collide with the boundary or with other gas particles Collision between gas particles are elastic meaning no energy is lost. Particles are assumed to NOT attract or repel each other

Kinetic Energy = ½ (mass) (velocity)2 Particle Energy Since all of the molecules are in linear motion, and therefore have a velocity, they possess kinetic energy as defined by the following equation: Kinetic Energy = ½ (mass) (velocity)2 KE = ½ mv2 Temperature is simply a measure of the average kinetic energy of the particles in a sample.

Behavior of gases In describing the behavior of gases, we talk about Temperature Volume Pressure Before we can learn to solve Gas Law problems, we must investigate these new three vocabulary words

TEMPERATURE Two scales to measure temperature: Celsius: Kelvin: 0°C - temperature at which water freezes 100°C - temperature at which water turns to gas Kelvin: O K - Absolute Zero where all motion stops! 273 K - temperature at which water freezes 373 K - temperature at which water turns to gas

TEMPERATURE CONVERSION From Celsius → Kelvin Add 273 degrees 40ºC + 273 = 313K From Kelvin → Celsius Subtract 273 degrees 248 K - 273 = - 25ºC For gas law problems, we MUST use Kelvin in our calculations!

VOLUME Volume is defined as the space that matter occupies. The base unit for volume is the liter 1 liter (L) = 1000 milliliters (mL) 1 milliliter (mL) = 1 cubic centimeter (cm3) All content by HST Educational Innovations © 2012. All rights reserved. Use of this material is invited with proper attribution to the source.

PRESSURE Pressure is defined as the amount of force applied to an area of matter: Force Pressure = ---------- Area Gas particles apply force on the container as particles collide with the boundary The SI unit for pressure is the pascal (Pa) named after Blaise Pascal (1623-1662) a French mathematician and philosopher.

Pressure There are many traditional units for pressure: Newton per meter squared (N/m2) Pressure per square inch (psi) – used for your tires! Millimeters of mercury (mmHg) – from barometers Torr – defined as the same as mmHg Bar – often used in pressure gauges Atmospheres (atm) Since there are so many units, we need to CONVERT

Pressure Conversions Important pressure conversions When doing these problems, be sure to be consistent with your pressure units! 1 atm = 101.3kPa 1 atm = 760 mmHg 1 atm = 760 torr 1 kPa = 0.009869 atm 1 kPa = 7.501 mmHg 1 kPa = 7.501 torr

STANDARD TEMPERATURES & PRESSURES (STP) All content by HST Educational Innovations © 2012. All rights reserved. Use of this material is invited with proper attribution to the source.

Let’s practice The pressure atop the world’s highest mountain, Mt Everest is usually about 33.6 kPa. Convert this pressure to atmospheres. How does this compare to the pressure at sea level? 0.33 atm Sea level is 1.0 atm

Let’s practice The atmospheric pressure in Denver, Colorado is usually about 84 kPa. What is this pressure in atm and torr units? 0.83 atm 630.21 torr

Check for understanding Work with a partner on completing: Let’s practice problems

The Gas Laws

Demo #1 Demo: Take a syringe and depress it to see how it feels. Now hold your finger over the end and depress again. What happens? What relationship can we draw between pressure and volume?

Demo #1 Now add a baby marshmallow to the syringe. Place the syringe at the farthest out positon. Cover with a cap or your finger and push the syringe in as far as you can. What happens to the marshmallow? Release your finger or the cap. What happens to the marshmallow? Now try it the opposite way!

Cartesian Diver Demo A small amount of air is placed inside a pipette and sealed and placed inside the water bottle. Squeezing the bottle (increases/decreases) the pressure inside the bottle. As a result, the volume of air (increases/decreases) sending the diver down! (Density = mass/volume)

Gas Law Relationships What was the relationship between Pressure Volume This is called Boyles Law In order to do this experiment, what did we not change – or hold constant?

Boyle’s Law Examines the behavior of gas under the condition of constant temperature As the volume containing gas particles is reduced, the particles are forced closer together. Can be written as: P1V1 = P2V2 1 stands for initial conditions 2 stands for final conditions

Boyle’s Law is an Inverse Relationship As Pressure ↑, Volume ↓ As Pressure ↓, Volume ↑ Boyle’s Law is an Inverse Relationship

Problems Let’s try some problems. Before solving each problem, predict if your value will increase or decrease. Then solve. Check your answer to see if it agrees with your prediction!

Boyles Law problems The gas in a 600 mL balloon has a pressure of 1.20 atm. If the temperature remains constant, what will be the pressure of the gas in the balloon when it is compressed to 400 mL? 1.8 atm

Boyles Law problems 2. An oxygen container has a volume of 48 mL and a pressure of 420 kPa. What is the volume of this gas when the pressure is 105 kPa? 192 ml

Boyles Law problems 3. A tank of compressed CO2 has a pressure of 850 psi and a volume of 150 mL. What is the volume of this gas when the pressure is 45 psi? 2,833 ml

Demo #2 Balloon and the Flask (or Hot Air Ballooning) Place 10 mLs. or so of water in an Erlenmeyer flask. Stretch an un-inflated balloon over the mouth of the flask (250 mL. flask). Place the flask on hot plate What happens to the balloon? Why?

Demo #2 Now, put the flask in a beaker of ice and let it cool. Now what does the balloon do? Why?

Gas Law relationships What was the relationship between Temperature Volume This is called Charles’ Law In order to do this experiment, what did we not change – or hold constant?

Charles’ Law Examines the behavior of gas under the condition of constant pressure As the volume containing gas particles is reduced, the particles must move slower to exert the same force over a smaller surface area. or As temperature is decreased, the particles would exert less force on the available surface area. In order to restore the pressure lost through this process, the surface area has to be reduced to compensate.

Temperature must be in KELVINS! Charles’ Law is a Direct Relationship V1 V2 -------- = --------- T1 T2 Temperature must be in KELVINS! Charles’ Law is a Direct Relationship

Charles Law problems A 240 mL sample of argon gas at 270 K is cooled until the volume is 180 mL. What is the new temperature? 202.5 K

Charles Law problems 2. A container of oxygen with a volume of 60 L is heated from 300 K to 400 K. What is the new volume? 80 L

Charles Law problems 3. When a piston with a volume of 35 mL is heated from 25ºC to 323ºC it expands. Assuming the pressure on the piston remains the same, determine the new volume of the cylinder. 70 mL

Demo #3 Fill a shallow dish with water (colored blue) Place two candles in the dish with water Cover with large beaker Look at the level of the water before and after the candles go out?

Gas Law Relationships What was the relationship between Temperature Pressure This is called Gay-Lussac’s Law In order to do this experiment, what did we not change – or hold constant?

Gay-Lussac’s Law Examines the behavior of gas under the condition of constant volume. An increase in temperature increase the collision frequency and energy, thus increasing pressure.

Gay Lussac’s Law -------- = --------- T1 T2 P1 P2 -------- = --------- T1 T2 Temperature must be in KELVINS Gay Lussac’s Law is a Direct Relationship

Gay Lussac’s problems Determine the pressure change when a constant volume of gas at 1.00 atm is heated from 20.0 °C to 30.0 °C. 1.03 atm

Gay Lussac’s problems 2. A gas has a pressure of 0.370 atm at 50.0 °C. What is the pressure at standard temperature? 0.31 atm

Gay Lussac’s problems 3. A gas has a pressure of 699.0 mm Hg at 40.0 °C. What is the temperature at standard pressure? 340 K

Teeter Totter Is there a way we can easily remember all of these relationships?

Demo #4 Demo: Boil water inside a soda can; invert into a ice bath. What happens? What laws are we seeing in action?

Demo #4 According to Charles’ Law, as temperature inside the can rapidly decreases, the volume this air will proportionally reduce in volume. According to Boyle’s Law, the water pressure on the outside wall of the can will assist the trapped air in reducing its volume by increasing the pressure and crushing the can. Together, the laws are “combined”!

COMBINED GAS LAW Combines all three gas laws and allows us to solve for changing conditions.

Combined Gas Law problems A canister containing air has a volume of 85 cm3 and a pressure of 1.45 atm when the temperature is 310 K. What is the pressure when the volume is increased to 180 cm3 and the temperature is reduced to 280K? 0.62 atm

Combined Gas Law problems 2. Air is transferred from a 75 L tank where the pressure is 125 psi and the temperature is 288 K to a tire with a volume of 6.1 L and a pressure of 25 psi. What is the new temperature? 4.69 K

Combined Gas Law problems 3. A helium balloon at 28ºC has a volume of 1.8 L and a pressure of 102 kPa. What is the volume of the balloon when is rises into the atmosphere where the pressure is 85 kPa and the temperature is 4ºC? 1.99 L

Wrap it up with a video http://ed.ted.com/lessons/1207-1-a-bennet-brianh264 (2:49) If that doesn’t work: https://www.youtube.com/watch?v=BY9VGS2eXas

Let’s practice Work on 1. Properties of Gases Questions 2. Mixed up Gas Law problems For each problem – identify the gas law, predict if the unknown value will increase or decrease, and then solve.