With your lab partner, use the following scenarios as a guide to come up with the four properties of gases. Bicycle tires seem more flat in the winter than in the summer. A can of soda explodes if left in the hot sun. You blow air into a balloon and it gets bigger.

Gases can be described using the following four variables: Properties of Gases Gases can be described using the following four variables: V = volume of the gas (liters, L) P = pressure (atmospheres, atm) T = temperature (Kelvin, K) n = amount (moles, mol) UNITS

Tell me about: solids liquids gases

Solids: Students stay in place (no foot moving) and wiggle and jiggle and twist. Liquids: Feet can take baby steps in any direction while their upper bodies are still wiggling and jiggling. Gases: Have students cross their hands across their chests. Students move in a straight line as fast as they can until they hit a surface or another students and then they bounce off or reflect off in another direction until they hit something else.

Reflect In your notes: write your observations of the behavior of the three states of matter and explain how they behave differently. 

Postulates of the KMT Gases Consist of tiny particles (atoms or molecules) The actual volume of gas particles is negligible. Particles are far apart. The volume of a gas is effectively the volume the particles occupy, not their particle volume.

3. Particles are in constant, random,. straight line motion 3. Particles are in constant, random, straight line motion. Collisions with walls of their container generate pressure. 4. Gas particles do not attract or repel. Perfectly elastic collisions. 5. The average kinetic energy is directly proportional to the Kelvin temperature of the gas.

Kinetic Molecular Theory (KMT) of Gases KMT is a model to explain the behavior of gaseous particles and is based on extensive observations of the behavior of gases. If a gas follows all the postulates of the the KMT it is said to be an ideal gas.

The Kinetic Molecular Theory In a perfectly elastic collision, the kinetic energy of each molecule might change, but the total kinetic energy stays the same. Collisions between particles are elastic.

Pressure One gas molecule exerts a tiny force against the side of a balloon.

Pressure When you have a huge number of gas molecules colliding against the sides of a balloon, the force adds up. Force spread out over the inner surface of the balloon is pressure.

Kinetic Molecular Theory Particles in an ideal gas… have no volume. have elastic collisions. are in constant, random, straight-line motion. don’t attract or repel each other. have an avg. KE directly related to Kelvin temperature. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Kinetic Molecular Theory Postulates Evidence 1. Gases are tiny molecules in mostly empty space. The compressibility of gases. 2. There are no attractive forces between molecules. Gases do not clump. 3. The molecules move in constant, rapid, random, straight-line motion. Gases mix rapidly. 4. The molecules collide classically with container walls and one another. Gases exert pressure that does not diminish over time. 5. The average kinetic energy of the molecules is proportional to the Kelvin temperature of the sample. Charles’ Law The kinetic molecular theory of gases explains the laws that describe the behavior of gases and it was developed during the nineteenth century by Boltzmann, Clausius, and Maxwell Kinetic molecular theory of gases provides a molecular explanation for the observations that led to the development of the ideal gas law The kinetic molecular theory of gases is based on the following postulates: 1. A gas is composed of a large number of particles called molecules (whether monatomic or polyatomic) that are in constant random motion. 2. Because the distance between gas molecules is much greater than the size of the molecules, the volume of the molecules is negligible. 3. Intermolecular interactions, whether repulsive or attractive, are so weak that they are also negligible. 4. Gas molecules collide with one another and with the walls of the container, but collisions are perfectly elastic; they do not change the average kinetic energy of the molecules. 5. The average kinetic energy of the molecules of any gas depends on only the temperature, and at a given temperature, all gaseous molecules have exactly the same average kinetic energy. Postulates 1 and 4 state that molecules are in constant motion and collide frequently with the walls of their container and are an explanation for pressure 1. Anything that increases the frequency with which the molecules strike the walls or increases the momentum of the gas molecules increases the pressure. 2. Anything that decreases that frequency or the momentum of the molecules decreases the pressure. • Postulates 2 and 3 state that all gaseous particles behave identically, regardless of the chemical nature of their component molecules — this is the essence of the ideal gas law. • Postulate 2 explains how to compress a gas — simply decrease the distance between the gas molecules.

Atmospheric Pressure As you move upward through the atmosphere, the density decreases. This is because most air molecules are held close to Earth’s surface by gravity. As the density decreases, there are fewer molecules colliding with surfaces; hence, less pressure.

Real Gases Particles in a REAL gas… Gas behavior is most ideal… have their own volume attract each other Gas behavior is most ideal… at low pressures at high temperatures in nonpolar atoms/molecules Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Deviations from Ideality Some gas particles do repel each other so volume is greater than predicted. Some gas particles do attract each other so volume is reduced more than expected. Gas particles do have a volume so volume cannot be reduced beyond a certain point.

Answer the following in your notes: What do you suppose is between the dots (which represent air molecules)? If you put a drinking straw in water, place your finger over the opening, and lift the straw out of the water, some water stays in the straw. Explain.

Answer in your notebook: Look at the “Barometer” up front. How does it work? Why is the water not moving? How did the balloon in flask happen? How did I do this?

Gas Laws Do Now  What is pressure? Explain what happened to the can?

Convert 687 torrs into atmospheres. If temperature is constant, what happens to volume (V) as pressure (P) increases? What if P decreases? 1 torr = 1mm Hg 1 atm = 760 mm Hg 1 atm= 101.325 KPa

ANSWERS P V P V F A Pressure (P) is force per unit area 687 torr x 1 atm = 0.904 atm 760 torr If T is constant… as P increases, V decreases! as P decreases, V increases! P V P V

General Properties of Gases There is a lot of “free” space in a gas. Gases can be expanded infinitely. Gases fill containers uniformly and completely. Gases diffuse and mix rapidly.

Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related to Hg density column height

Pressure Column height measures Pressure of atmosphere 1 standard atmosphere (atm) * = 760 mm Hg (or torr) * = 29.92 inches Hg * = 14.7 pounds/in2 (psi) *HD only = 101.3 kPa (SI unit is PASCAL) * HD only = about 34 feet of water!

Pressure Conversions 475 mm Hg x = 0.625 atm 29.4 psi x A. What is 475 mm Hg expressed in atm? 1 atm 760 mm Hg B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 14.7 psi 475 mm Hg x = 0.625 atm 29.4 psi x = 1.52 x 103 mm Hg

Pressure Conversions A. What is 2 atm expressed in torr? B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

Inverse and Direct Proportions B

INVERSE PROPORTIONS As one variable goes up, the other goes down! Produces a curved graph… P V T constant AWESOME!!

A. Boyle’s Law P V PV = k

A. Boyle’s Law The pressure and volume of a gas are inversely related at constant mass & temp P V PV = k

P may change and V may change, but their product stays the same! Boyle's Law P1 x V1 = P2 x V2 P may change and V may change, but their product stays the same! Multiplying the two variables equals a constant.

P1V1=P2V2 Boyle’s Law V2 = P1V1 = P2 V2 = 0.947 atm (.15L) = 0.987 atm A gas filled syringe has a volume of 150mL and a starting pressure of 0.947atm. If the pressure is increased to 0.987 atm what is the new volume? Given: P1= 0.947 atm V1= 150mL= 0.15L P2= 0.987 atm V2 = ???? V2 = P1V1 = P2 V2 = 0.947 atm (.15L) = 0.987 atm

Problem: A deep sea diver is working at a depth where the pressure is 3.0 atmospheres. He is breathing out air bubbles. The volume of each air bubble is 2 cm3. At the surface the pressure is 1 atmosphere. What is the volume of each bubble when it reaches the surface?

Boyle In a thermonuclear device,the pressure of the 0.50 L of gas within the bomb casing reaches 4.0x106atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion?

P1V1 = P2V2 V2 = P1V1 . V2 = (4.0 x 106 atm)(0.50 L) . V2 = 2.0 x 106 L Boyle

Directly Proportional Ex: Charles’ Law (V as a function of T) T (K) V (mL) 50 100 200 150 300 400 250 500 600 350 700 800 450 900 1000 550 1100 1200 650 1300 1400

Temperature and Volume

DIRECT PROPORTIONS T As one variable goes up, so does the other! V Produces a straight line graph… Dividing the one variable by the other equals a constant. V1 V2 T1 T2 = YES!!!

Charles’s Law: V and T For two conditions, Charles’s law is written V1 = V2 (P and n constant) T1 T2 Rearranging Charles’s law to solve for V2 gives T2 x V1 = V2 x T2 T1 T2 V2 = V1 x T2 T1

Learning Check Solve Charles’s law expression for T2. V1 = V2 T1 T2

Solution Solve Charles’s law expression for T2. V1 = V2 T1 T2 Cross multiply to give: V1T2 = V2T1 Solve for T2 by dividing through by V1: V1T2 = V2T1 so T2 = T1 x V2 V1 V1 V1

Calculations Using Charles’s Law A balloon has a volume of 785 mL at 21 °C. If the temperature drops to 0 °C, what is the new volume of the balloon (P constant)?

Calculations Using Charles’s Law A balloon has a volume of 785 mL at 21 °C. If the temperature drops to 0 °C, what is the new volume of the balloon (P constant)? Conditions 1 Conditions 2 Know Predict V1 = 785 mL V2 = ? V decreases T1 = 21 °C T2 = 0 °C = 294 K = 273 K T decreases Be sure to use the Kelvin (K) temperature in gas calculations.

Calculations Using Charles’s Law (continued) STEP 2 Solve Charles’s law for V2: V1 = V2 T1 T2 V2 = V1 T2 T1 Temperature factor decreases T STEP 3 Set up calculation with data: V2 = 785 mL( 273 K ) = 729 mL 294 K

Learning Check A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)? 1) 443 °C 2) 170 °C 3) –82 °C

Practice problem V2 = 2.45 L (325K) = 273 K V1 V2 T1 T2 = V2 V2 T1 T2 The volume of a balloon is 2.45 L when at a temperature of 273 K. What happens to the volume when the temperature is raised to 325K? Given: V1= 2.45L T1= 273 K V2= ? T2 = 325 K V1 V2 T1 T2 = V2 V2 T1 T2 = V2 = 2.45 L (325K) = 273 K

Avogadro’s Law: V1 V2 n1 n2 =

Practice problem V1= 59.5 L n1= 2.55 mol V2= ??? n2 = 7.83 mol V1 V2 Answer = _______ L V1 V2 n1 n2 =

Gay-Lussac’s Law P 1 P 2 _ _ _ _ = _ _ _ _ _ T 1 T 2

Pressure depends on Temp Today’s temp: 35°F Today’s temp: 85°F Pressure Gauge Pressure Gauge

Practice problem A bike tire has a pressure of 0.987 atm at a temperature of 25°C and a new pressure of 0.795 atm.

Demo: Gay-Lussac’s Law Egg in a bottle & Balloon in flask

Gay-Lussac A sample of neon is at 89oC and 123 kPa. If the pressure changes to 145 kPa and the volume remains constant, find the new temperature, in K.

P1 = P2 T2 = T1P2 T1 T2 P1 . T2 = (362K) (145 kPa) . T2 = 427 K Gay-Lussac