3Section 5.1- Pressure Force per unit area (P = force/area). Gas molecules fill container.Molecules move around and hit sides.Collisions are the force.Container is the area.Measured with a barometer.
4How Does A Barometer Work? Vacuum760 mm HgThe pressure of the atmosphere at sea level will cause the column of mercury to rise to 760 mm Hg.1 atm = 760 mm HgPressure of atmosphere pushes on HgAs a result, Hg rises up into the glass tubeWhen atmospheric pressure changes, so does the level of Hg because they are always equal (but opposite) in pressure.*Hg stops rising when it’s equal to atmospheric pressure
5Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals = kPa*The first two are provided on the AP equation sheet. No need to memorize the third- I assume you’ll be given that if you need to use it.
6THE GAS LAWS OF BOYLE, CHARLES, AND AVOGADRO Section 5.2THE GAS LAWS OF BOYLE, CHARLES, AND AVOGADRO
7About the Laws…You should be aware of the following laws, however we will not focus heavily on them as they can be derived from the ideal gas law.After briefly going through each of the following laws, we will see how to derive each from the ideal gas law.
8Boyle’s LawPressure and volume are inversely related at constant temperature.P1V1 = P2V2As one goes up, the other goes down.Ex: if P increases (at constant T), V must go downFurther studies show that Boyle’s Law is only true at very low PThis will be discussed more in 5.8Gases that obey these laws are called ideal gases.For the same gas at constant temp, k does not change. Therefore we can say that the product of any pressure and volume for that gas at that temperature is equal to the product of some other pressure and volume for that gas.
9Charles’s Law As one goes up/down, so does the other. Volume of a gas varies directly with the temperature at constant pressure.V V2T T2As one goes up/down, so does the other.=
10Avogadro's LawAt constant temperature and pressure, the volume of gas is directly related to the number of moles.V V2n n2As one goes up/down, so does the other.=
11Gay- Lussac LawAt constant volume, pressure and temperature are directly related.P P2T T2As one goes up/down, so does the other.=
12Combined Gas LawCombination of Boyle’s Law, Charles’ Law, and Gay-Lussac Law.Moles of gas remain constant.P1V P2V2T T2=
13Summary Boyle’s: P1V1 = P2V2 Charles’: V1/T1 = V2/T2 Avogadro’s: V1/n1 = V2/n2Gay-Lussac: P1/T1 = P2/T2Combined: P1V1/T1 = P2V2/T2That’s a lot of laws! Or we can just use the Ideal Gas Law!
14Combined Gas Law Cont.Ex: A 2.3L sample of gas has a pressure of 1.2atm at 200.K. If the pressure is raised to 1.4atm and the temperature is increased to 300.K, what is the volume of the gas?V2 = P1V1T2T1P2V2 = 3.0 L
15PracticeEx: A 12.2L sample of gas has 0.50mol of O2 at 1atm and 25°C. How many moles of O2 would occupy 19.4L at the same temperature and pressure?Solution: V1/n1 = V2/n2(12.2L)/(0.50mol) = (19.4L)/(n2)n2 =0.80mol*In other words, 0.80mol of O2 would be required to fill 19.4L in order to keep the same pressure as 0.50mol of O2 in 12.2L.
16AP Practice QuestionA sample of argon gas is sealed in a container. The volume of the container is doubled. If the pressure remains constant, what must happen to the temperature?It doesn’t change.It is halved.It is doubled.It is squared.Can solve this two ways- (1) By remembering Charles’ Law (2) Using the Ideal Gas Law. Here we will use Charles’ Law.
17Demonstration Warm-Up! Observe the demonstration.Keep in mind the properties of gases we have discussed so far: P, V, T, and n.Think about these properties before and after imploding the can. Why do you think the can was crushed?As temperature decreases, so does the pressure and volume.Remind you of a law we looked at?
20Ideal Gas LawPV = nRTAt standard temperature and pressure (STP): V = 22.4L at 1atm, 0ºC, and n = 1mol. These conditions were used to determine R (ideal gas constant):R = L atm/mol K= J/mol K= L torr/mol KTells you about a gas NOW.The other laws tell you about a gas when it changes.KNOW THIS!Choose R value according to units of P
21Ideal Gas Law Cont.Looking back at the possible values for R, you will notice that all units for temperature are in K.When using the ideal gas law for calculations, convert all temperatures to K!Recall conversion: K = °C (provided on AP equation sheet)
22Ideal Gas Law Derivation Practice May be asked to prove one of the laws discussed before!Strategy: get all constants in the ideal gas law on one side and changing variables on the other.We will go several of these in class.
23AP Practice QuestionA 1.15mol sample of carbon monoxide gas has a temperature of 27°C and a pressure of 0.300atm. If the temperature is lowered to 17°C at constant volume, what is the new pressure? a) 0.290atm c) 0.206atm b) 0.519atm d) 0.338atm
24Ideal Gas Law- Why ‘Ideal’? Ideal gases are hypothetical substances.Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature.They do not behave exactly according to this law, but they behave closely enough.Law provides good estimates of gas behavior under these conditions.Unless told otherwise, assume ideal gas behavior and use the ideal gas law.
25AP Practice QuestionA sample of aluminum metal is added to HCl. How many grams of aluminum metal must be added to an excess of HCl to produce 33.6L of hydrogen gas at STP?18.0g35.0g27.0g4.50g
26Section 3 HomeworkComplete the gas laws worksheet AND #33, 40, 43, 52 on pg
28Gases and Stoichiometry Reactions involve moles of substances.Recall that at STP (0ºC and 1 atm) 1mol of any gas occupies 22.4 L.At STP this can be a conversion factor: 1mol/22.4L or 22.4L/1molIf not at STP, use the ideal gas law to calculate moles or volume of a substance.
29Can double check using ideal gas law Section 4 ExampleQuicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume of carbon dioxide produced at STP if 152g of calcium carbonate are completely decomposed.CaCO3 CaO + CO2Convert to moles: 152g x 1mol = 1.52mol100.09g CaCO31:1 mole ratio of CaCO3 to CO mol CO2Use STP conditions & stoichiometry:At STP 1mol = 22.4L1.52mol x (22.4L/1mol) = 34.1L CO2Can double check using ideal gas law
30Gas Density and Molar Mass Recall: D = m/VLet mmolar stand for molar massmmolar = m/n so n = m/mmolarPV = nRT solve for n: n= PV/RTThus m/mmolar = PV/RTSolve for mmolar: mmolar = mRT/VPReplace m/V with D: mmolar = DRT/PIf density, temperature, and pressure are known, molar mass can be found.
31AP Practice QuestionDetermine the formula for a gaseous silane (SinH2n+2) if it’s density is 5.47g/L at 0ºC and 1.00atm.*There are several ways to solve!SiH4Si2H6Si3H8Si4H10
33DALTON’S LAW OF PARTIAL PRESSURES Section 5.5DALTON’S LAW OF PARTIAL PRESSURES
34Dalton’s Law of Partial Pressures The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.Total pressure = sum of partial pressures.Ptot = P1 + P2 + PP1, P2, P3 are individual gasesFrom the ideal gas law: PTotal = (nTotal)RTV
35Partial Pressures Cont. What does Dalton’s Law tell us about ideal gases?Total # of gas particles, not their identities, is important.V of individual gas particles doesn’t affect the total P.Forces between gas particles doesn’t affect the total P.If these were important, the different identities of gas particles would affect the total P differently.
36CH4(g) + 2O2(g) CO2(g) + 2H2O(g) AP Practice QuestionA gaseous mixture at 25°C contained 1mol CH4 and 2mol O2, and P = 2atm. The gases underwent the following reaction:CH4(g) + 2O2(g) CO2(g) + 2H2O(g)What is the P in the container after the reaction goes to completion and the T is allowed to return to 25°C?1atm2atm3atm4atm
37AP Practice QuestionA sealed, rigid container is filled with three identical gases: A, B, and C. The partial pressure of each gas is known as well as T and V. What additional information is needed to find the masses of the gases in the container?a) average distance travelled between molecular collisionsb) the intermolecular forcesc) the molar masses of the gasesd) the total pressure
38The mole fraction Ratio of moles of a substance to the total moles. symbol is Greek letter chi cc1 = n1 = P1ntot PtotMole fractions have no units!
39AP Practice QuestionA reaction makes a mixture of CO2, CO, and H2O. The gaseous products contained 0.60mol CO2, 0.30mol CO, and 0.10mol H2O. If the total P is 0.80atm, what is the partial P of CO?0.24atm0.34atm0.080atm0.13atm
40Vapor Pressure Water evaporates! When water evaporates, the resulting water vapor has a pressure.Vapor pressure changes with T- must be looked up.Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure.Vapor pressure must be given.
41AP Practice QuestionA sample of methane gas was collected over water at 35°C. The sample had a total pressure of 756mm Hg. Determine the partial pressure of methane gas in the sample. (Vapor pressure of water at 35°C is 41mm Hg.)760mm Hg41mm Hg715mm Hg797mm Hg
43Collapsing Can Demo Watch the demonstration. Why did the can collapse? -The heat vaporized the water, which in turn increased P and pushed air out of the can.-When the can was inverted the water vapor quickly cooled. This caused a quick drop in P (created a partial vacuum because essentially no air was left to maintain P).-The atmospheric P outside of the can was much greater than P inside of the can, which allowed the can to be crushed.
44THE KINETIC MOLECULAR THEORY OF GASES Section 5.6THE KINETIC MOLECULAR THEORY OF GASES
45Kinetic Molecular Theory (KMT)- Explains Behavior & Properties of Gases Gases are made up of molecules or atoms.V of particles can be ignored (very small in comparison to distance b/t particles).Particles constantly move and collide with each other and the walls of the container. Collisions with the walls of the container cause P of the gas.Particles don’t attract or repel each other; when they collide, it’s elastic (no KE is lost- it’s transferred).The average KE is proportional to the Kelvin T.
46KMT Cont. Assumes gases are ideal. BUT no gases are truly ideal- they only approach ideal behavior (specifically nonpolar gases at low P and high T).In reality, gases DO have V (although small), and they CAN interact with each other.Even so, assuming ideal behavior gives us good enough answers about properties of gases.
47KMT #3 describes motion; let’s quantify it: urms = √(3RT/mmolar) urms is root mean square velocityR value used is 8.314J/molKmolar mass in kg/mol (b/c J = kgm2/s2)#5: KE per mole (average KE) = 3/2 RTRecall definition of T! Directly related!Units: J/molKE per molecule = ½ mv2 this is the only equation given on AP exam!- Units: JLarge! For H2 at 20°C = 2,000m/s
48Root Mean Square Velocity Example What is the root mean square velocity for the atoms in a sample of He gas at 25°C?Convert T to K: = 298KM = 4.00g/mol kg/molurms = 136m/s
49Range of velocitiesThe average distance a molecule travels between collisions with another gas particle is called the mean free path and is small (near 10-7)Results in a range of velocities.Temperature is an average. There are molecules of many speeds in the average.This is shown on a graph called a velocity distribution.
50Maxwell-Boltzmann Distribution Notice that with higher T, average velocities increase and so does the velocity range.273 K1273 K2273 Knumber of particlesMolecular Velocity
51AP Practice QuestionTwo balloons are at the same T and P. One contains 14g of nitrogen and the other contains 20.0g of argon. Which of the following is true?D of N2 > D of ArAverage speed of N2 > average speed of Ar moleculesAverage KE of N2 molecules > average KE of Ar moleculesV of N2 container < V Ar
52AP Practice QuestionIncreasing the T of an ideal gas from 50°C to 75°C at constant V will cause which of the following to increase for the gas?average molecular mass of the gasaverage distance between moleculesaverage speed of the moleculesdensity of the gas
54EFFUSION AND DIFFUSION Section 5.7EFFUSION AND DIFFUSION
55Effusion Passage of gas through a small hole, into a vacuum. Effusion rate = speed at which the gas is transferred into the vacuum.Graham’s Law - the relative rates of effusion are inversely proportional to the square roots of the molar masses of the gas particles.
56Diffusion The spreading of a gas through a room (mixing of gases). Slow considering molecules move at hundreds of meters per second.Slower movement is caused by collisions with other molecules in the air.Best estimate is Graham’s Law.Ratio is actually less.More complex analysis required.
59Real GasesReal molecules do take up space and they do interact with each other (especially polar molecules).Need to add correction factors to the ideal gas law to account for these.a = correction factor for pressureb = correction factor for volume
60Volume Correction P’ = nRT (V-nb) The actual volume free to move in is less because particles do take up some of the volume.More molecules will have more effect (taking up more space).Corrected volume V’ = V - nbb is a constant that differs for each gas.P’ = nRT (V-nb)
61a = proportionality constant Pressure CorrectionMolecules are attracted to each other- pressure on the container will be less than ideal gases.Size of correction factor depends on the # of molecules per liter (conc. of gas).More molecules = closer together and more likely to interact/attract.Since two molecules interact, the effect must be squared.()2Vna = proportionality constantPobserved= P’ - a
62( ) All Together Pobs= nRT - a n 2 V-nb V Called the Van der Waal’s equation if rearranged:Corrected Corrected Pressure VolumeNOT given on AP Equation sheet!
63Graphing Real GasesFor ideal gases PV/nRT should be 1 (since both are equal according to ideal gas law).Not seen for real gases.Notice the effect of T on ideal gas behavior.
64Graphing Real GasesDeviation from ideal behavior depends on identity of the gas too.Smaller, nonpolar gases exhibit more ideal behavior.
65Where Do Constants Come From? a and b are experimentally determined.Different for each gas.Bigger molecules have larger b.a depends on both size and polarity.Note: table of constants for some gases is on pg. 210 in the book.
66Graphing Real Gases Take a closer look at H2 on the graph. Most ideal behavior, so it has lowest ‘a’ value of the gases shown for Van der Waals equation.Lower a means less correction needed.Thus it must have weak intermolecular forces.Real gas behavior can tell us how big of a role intermolecular forces play in attraction between gas molecules.This is with respect to this graph only!! Larger a value = more correction needed = more intermolecular attraction = less ideal behavior.
67AP Practice QuestionThe true volume of a real gas is smaller than that calculated from the ideal gas equation. This occurs because the ideal gas equation does not consider which of the following?Attraction between moleculesShapes of moleculesVolume of moleculesMass of molecules
68AP Practice QuestionWhich of the following gases probably shows the greatest deviation from ideal gas behavior?HeO2SF4SiH4