Kinetic Theory and the Behavior of GASES

Kinetic Theory Most substances commonly exist in one state of matter: solid, liquid, or gas Kinetic Theory: states that the tiny particles in all forms of matter are in constant motion Kinetic energy: energy of motion

Nature of Solids Do the particles in a solid move? YES! The particles of a solid move, but not with enough kinetic energy to break forces and flow!!!! Melting Point: the temperature at which a solid turns into a liquid Particle kinetic energy (temperature) increase enough to FLOW!

Crystal Structure and Unit Cells Crystal: the atoms/ions/molecules are arranged in regular repeating patterns Think of a salt crystal. No matter how small you break it, it will still be a cube. IT IS A CUBE AT THE IONIC LEVEL Allotropes: two or more different molecular forms of the same element -CARBON: diamond and graphite! Amorphous Solid: lacks an ordered internal structure -rubber, plastic, glass

Nature of Liquids Particles of a liquid are moving, but with less energy than particles of a gas. They are moving more slowly! Intermolecular forces! Particles of a liquid are attracted to one another This is why a liquid FLOWS but has definite volume!

Evaporation Vaporization: the conversion of a liquid to a gas or vapor Evaporation: when this conversion occurs at the surface of a liquid that is NOT boiling Vapor pressure: force due to the gas above a liquid in a closed container What happens to vapor pressure as you increase temperature?

Boiling Point Boiling Point: the temperature at which the vapor pressure of the liquid is just equal to the external pressure What will happen to the boiling point of a substance as you increase altitude? WHY?

Kinetic Theory and Gases 1. A gas is composed of particles that are considered to be small, hard spheres. These spheres have insignificant volume and are far apart from one another 2. The particles in a gas move rapidly in constant random motion 3. All collisions are perfectly elastic Total kinetic energy remains constant

Gas Pressure Gas pressure is the force exerted by a gas per unit surface area of the object Vacuum: Space with no particles and no pressure Atmospheric Pressure: results from colission of air molecules with objects Less air pressure as elevation increases. WHY? Barometer: device used to measure atmospheric pressure SI unit of pressure is the pascal (Pa). Also use mm HG and atm

Kinetic Energy and Kelvin Scale The Kelvin temperature scale reflects the relationship between temperature and average kinetic energy. Temperature goes up? Energy goes up Temperature goes down? Energy goes down. Energy flows from high to low Soooo, what is happening to a glass of water when you put ice in it?

Absolute Zero Absolute zero is equal to 0 K At this temperature, the motion of all particles THEORETICALLY stop Why theoretically?

CONVERSIONS! 0 degrees Celsius = 273 K So….. Celsius = K - 273 Kelvin = Celsius + 273 STP: Standard Temperature and Pressure Temperature = 0 degrees Celsius, 273 K Pressure = 1 atm, 101.3 kPa, 760 mmHg, 14.7 psi

Changes of STATE Phase Diagram: gives the conditions of temperature and pressure at which a substance exists as a solid, liquid, or gas Melting/freezing, boiling evaporating/condensing Triple point: all three phases exist together at equilibrium Once you reach 100 degrees Celsius and water boils, the temperature will stay at 100 degrees Celsius until all the liquid is in the vapor state. WHY????

Let’s review the kinetic theory and GASES 1. A gas is composed of particles that are considered to be small, hard spheres. These spheres have insignificant volume and are far apart from one another 2. The particles in a gas move rapidly in constant random motion 3. All collisions are perfectly elastic Total kinetic energy remains constant

Compressibility: a measure of how much the volume of matter decreases under pressure It is assumed that no attractive forces exist between gas particles. WHY???? Gas particles are moving too rapidly with too much kinetic energy. Collisions are COMPLETELY ELASTIC!

Variables that describe a gas 1. Pressure (P): units = pascals or kilopascals 2. Volume (V): units = liters 3. Temperature (T): units = kelvins 4. number of moles (n): unit = moles Why is temperature in kelvin????

Factors affecting Gas Pressure Why does a balloon pop? Think of some ways that you could make a balloon pop. Sketch what is happening at the molecular level when a balloon pops

How can you make a balloon pop? 1. Add more gas If you increase the number of particles, the number of collisions increase = increase in pressure 2. Decrease the volume (squish it) The more a gas in compressed, the greater the pressure it exerts inside of the container 3.Raise the Temperature! Since temperature is a measure of kinetic energy, raising the temperature means a rise in kinetic energy = rise in number of collisions = higher pressure

SOOOOOO Number of moles of gas go up? Pressure goes up Volume goes down? Pressure goes up Temperature goes up? Pressure goes up # mole to pressure = direct relationship Volume to pressure = inverse relationship Temperature to pressure = direct relationship

THE GAS LAWS!!! Pressure to Volume = BOYLE’S LAW we already know that as volume goes down, pressure goes up. This is an inverse relationship (think opposite) Boyle’s law: for a given mass of a gas at constant temperature, the volume of the gas varies inversely with the pressure VOLUME GOES UP, PRESSURE GOES DOWN

Boyle’s Law Equation Why constant temperature? Why constant number of moles? So only one variable is considered at a time. P1 x V1 = P2 x V2 Since temperature is a constant, and number of moles is a constant, we can look at just temperature and pressure. Just identify the variables you know and solve for the unknown!

Let’s Try it! 1. A high altitude balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the balloon rises to a pressure that is only 25.0 kPa. Assume that temperature remains a constant. What do you know? V1 = 30.0 L, P1 = 103 kPa, P2 = 25.0 kPa What do you want to know? The ending volume, V2 Boyle’s law states = P1 x V1 = P2 x V2 Fill in the knowns and solve for the unknown!

More Practice! The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if temperature remains constant? 1.What do you know? 2. What do you want to know? 3. Plug it into the equation and solve!

A gas with a volume of 4.00 L at a pressure of 205 kPa is allowed to expand to a volume of 12.0 L. What is the pressure in the container f the temperature remains constant?

Review Boyle’s law= relates volume and pressure P1 x V1 = P2 x V2 Pressure goes up? Volume goes down Units: volume is generally liters (L), pressure is generally kilopascals (kPa) or atmospheres (atm) Why do temperature and number of moles have to be constant????

You try it! 1. If a gas at 25.0 °C occupies 3.60 liters at a pressure of 1.00 atm, what will be its volume at a pressure of 2.50 atm? 2. A gas occupies 1.56 L at 1.00 atm. What will be the volume of this gas if the pressure becomes 3.00 atm? 3. A gas occupies 11.2 liters at 0.860 atm. What is the pressure if the volume becomes 15.0 L? 4. A gas occupies 4.31 liters at a pressure of 0.755 atm. Determine the volume if the pressure is increased to 1.25 atm. 5. 635 mL of a gas is at a pressure of 8.00 atm. What is the volume of the gas at standard pressure (STP)?

Challenge! 6. Chlorine gas occupies a volume of 1.2 liters at 720 torr pressure. What volume will it occupy at 1.0 atm pressure? 7. Fluorine gas exerts a pressure of 200 kPa. When the pressure is changed to 1.50 atm, its volume is 250 mL. What was the original volume? 8. A sample of gas has a volume of 12.0 L and a pressure of 1.00 atm. If the pressure of gas is increased to 1000 mm Hg, what is the new volume of the gas? 9. A container of oxygen has a volume of 30.0 mL and a pressure of 500,000 Pa. If the pressure of the oxygen gas is reduced to 28 psi and the temperature is kept constant, what is the new volume of the oxygen gas? 10. Ammonia gas occupies a volume of 450. mL at a pressure of 720. atm. What volume will it occupy at standard pressure (STP)? 11. A 40.0 L tank of ammonia has a pressure of 1000 mmHg. Calculate the volume of the ammonia if its pressure is changed to 500 torr while its temperature remains constant.   Pressure Conversions: 1 atm = 101.3 kPa = 101,325 Pa = 760 mm Hg = 760 torr = 14.7 lb/in2 (psi)

Charles’ Law Charles’ law relates temperature and volume. The volume of a fixed mass of gas is directly proportional to it’s kelvin temperature if pressure is kept the same. Temperature goes up? Volume goes up! Think of a helium balloon. What happens if you leave it in your trunk over night? V1/T1 = V2/T2

Let’s try it! A balloon inflated in a room 24 degrees Celsius has a volume of 4.00 L. The balloon is heated to 58 degrees Celsius. What is the new volume if pressure remains constant? V1= 4.00 L T1= 24 degrees Celsius V2= ? T2= 58 degrees Celsius V1/T1 = V2/T2 4.00L/ 24 degrees C = ?/ 58 degrees C

You try it! 1. If a sample of gas occupies 6.80 L at 325 degrees Celsius, what will be its volume at 25 degrees Celsius if the pressure does not change? 2. Exactly 5.00L of air at -50.0 degrees Celsius is warmed to 100.0 degrees Celsius. What is the new volume if pressure remains constant?

Gay-Lussac’s Law This law relates temperature and pressure Gay-Lussac’s law states that the pressure of a gas is directly proportional to the kelvin temperature scale. Temperature goes up? Pressure goes up! P1/T1 = P2/T2 YOU MUST CONVER TO KELVIN!!! K = C + 273

Let’s try it! The Gas left in a used aerosol can is at a pressure of 103 kPa at 25 degrees Celsius. If this can is thrown into a fire, what is the pressure when its temperature reaches 928 degrees Celsius? Hint: CONVERT TO KELVIN FIRST!!!! P1= 103 kPa T1= (25 +273) = 298 K P2= ? T2= (928 + 273) = 1201 K P1/T1 = P2/T2 103 kPa/ 298 K = ?/1201 K P2= 415 kPa

You Try It! The pressure in a car tire is 198 kPa at 27 degrees Celsius. At the end of a 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. Why do you need to check your tire’s air pressure when it gets cold?

(P1 x V1)/T1 = (P2 x V2)/T2 The Combined Gas Law We can express all of these relationships in a single equation! (P1 x V1)/T1 = (P2 x V2)/T2

Let’s Try It! The volume of a gas-filled balloon is 30.0L at 40 degrees Celsius and 153 kPa pressure. What volume will the balloon have at STP? STP = 273 K and 101.2 kPa V1= 30.0 L T1= (40 + 273) 313 K P1= 153 kPa V2= ? T2= 273 K P2= 101.3 kPa

You Try It! A gas at 155 kPa and 25 degrees Celsius occupies a container with an initial volume of 1.00L. By changing the volume, the pressure of the gas increases to 605 kPa as the temperature is raised to 125 degrees Celsius. What is the new volume? HINT: CONVERT TO KELVIN!

And another one! A 5.00 L air sample at a temperature of -50 degrees Celsius has a pressure of 107 kPa. What will be the new pressure if the temperature is raised to 102 degrees Celsius and the volume expands to 7.00 L? HINT: CONVERT TO KELVIN!!!!

Let’s Review so far!!! Combined Gas Law Boyle’s Law: Pressure-Volume (P1 x V1)/T1 = (P2 x V2)/T2 Boyle’s Law: Pressure-Volume Inverse relationship P1 x V1 = P2 x V2 Charles’s Law: Temperature-Volume Direct Relationship V1/T1 = V2/T2 Gay-Lussac’s Law: Temperature-Pressure P1/T1 = P2/T2

Ok, Ok, Don’t hate me, BUT… All of these laws make MAJOR assumptions about the behavior of gases. These assumptions are not always correct in the real world. DRY ICE! So we need to make mention to these assumptions. These equations/relationships only work if gases behave in an IDEAL WAY (do exactly what they are supposed to do)

12.4 Ideal Gas Law If we continue our assumptions about the behavior of gases, we can write another equation that factors in the number of moles of gas present. Ideal Gas Law: Relates pressure, volume, number of moles, and temperature of a gas P x V = n x R x T R = ideal gas constant = 8.31 (L x kPa)/(K x mol)

Ideal Gas Law and Kinetic Theory What is the kinetic theory (again)? The definition of the kinetic theory that we use assumes all gases are IDEAL gases. Still valid because real gases behave as ideal gases in many scenarios.

Let’s Practice You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2.00 x 104 kPa at 28 degrees Celsius. How many moles of nitrogen gas does the cylinder contain? 1. CONVERT TO KELVINS!!!! (28 degrees Celsius = 301 K) 2. V = 20.0L P= 2.00 x 104 kPa T = 301 K R= 8.31 (L x kPa)/(K x mol) 3. Plug and Chug! PV = nRT 2.00 x 104 kPa x 20.0 L = n x 8.31 (L x kPa)/(K x mol) x 301 K n = 1.60 x 102 mol nitrogen gas

You Try It! 1. When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain? 2. What pressure will be exerted by 0.450 mol of a gas at 25 degrees Celsius if it is contained in a 0.650 L vessel?

But wait, there’s more! Now that you can find the MOLES of a gas, you can use mole conversions to express the quantity of gas in other ways! 1 mol= 6.02 x 1023 atoms/molecules Mass of 1 mole = PERIODIC TABLE!

Let’s Try It! A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 42 degrees Celsius. How many KILOGRAMS of methane does this natural gas deposit contain? 1. CONVERT TO KELVIN! (42+273= 315K) 2. Identify Knowns V= 2.24 x 106 L P= 1.50 x 103 kPa T = 315 K R= 8.31 (L x kPa)/(K x mol) PV = nRT n= 1.28 x 106 mol CH4

NOT DONE YET! Ok, now you have moles of methane, but the problem asks for KILOGRAMS OF METHANE! We don’t have a conversion to go directly to kilograms, but we can convert to grams! PERIODIC TABLE!!!!! Molar mass of CH4 (from periodic table) = 16g 1.28 x 106 mol CH4 x 16 g CH4/1 mol CH4= 2.05 x 107 g CH4 1 kg = 1000 g 2.05 x 107 g CH4 x 1 kg/1000g = 2.05 x 104 kg CH4

You Try It! 1. A child has a lung capacity of 2.20 L. How many grams of air do her lung hold at a pressure of 102 kPa and a normal body temperature of 37 degrees Celsius. (assume the molar mass of air: a mixture of gases: is 29 g/mol)

More Practice What volume will 12.0 g of oxygen gas occupy at 25 degrees Celsius and a pressure of 52.7 kPa?

Gas Molecules: Mixtures and Movements Avogadro’s Hypothesis: equal volumes of gases at the same temperature and pressure contain equal numbers of particles. Consider this for a second: What Avogadro was suggesting is that the same number of objects would be present regardless of the object. Does this make sense on a macro scale? WHY does it work for gases??? 1 mole of gas occupies 22.4 L at STP

Dalton’s Law Dalton’s Law of Partial Pressures: at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases. Ptotal = P1 + P2 + P3…

Let’s try it! Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (PO2) at 101.3 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

Graham’s Law Diffusion: tendency of molecules to move towards areas of lower concentration until the concentration is uniform throughout Effusion: the process in which a gas escapes escapes through a tiny hole in the container. Graham’s law of effusion: the rate of effusion of a gas is inversely proportionate to the square root of the gas’s molar mass. THIS IS ALSO TRUE FOR DIFFUSION!!! If two bodies have different masses but the same kinetic energy, the lighter body travels FASTER!