2 CHEMISTRY 100 Dr. Jimmy Hwang Sections 5 and 7 Tu & Th 9:30a. m CHEMISTRY 100 Dr. Jimmy Hwang Sections 5 and 7 Tu & Th 9:30a.m.-10:45a.m.Textbook: Zumdahl, Introductory Chemistry, 5th EditionOffice Hours: by appointmentExt (voic )
4 Overview In Chapter 12, our goals are for the students to: 1. Learn about atmospheric pressure and how barometers work.2. Learn the various units of pressure.3. Understand the law that relates the pressure and volume of a gas and use it in calculations.4. Learn about absolute zero.5. Learn about the law relating the volume and temperature of a sample of gas at a constant number of moles and pressure and use it in calculations.6. Understand the law relating the volume and number of moles of a a sample of gas at constant temperature and pressure and use it in calculations.7. Understand the ideal gas law and use it in calculations.
5 Overview In Chapter 12, our goals are for the students to: Understand the relationship between the partial and total pressures of a gas mixture and use it in calculations.Understand the relationship between laws and models (theories).Understand the basic postulates of the kinetic molecular theory.Understand the term temperature.Learn how the kinetic molecular theory explains the gas laws.Understand the molar volume of an ideal gas.Learn the definition of STP.Do stoichiometric calculations involving gases.
6 Gases Chapter 12Become familiar with the definition and measurement of gas pressureLearn the gas laws: Boyle’s law, Charle’s law, and Avogadro’s lawThe ideal gas lawLearn Dalton’s law of partial pressuresReview of Laws and ModelsStudy the kinetic molecular theory of gasesStudy the implications of the kinetic theory of gasesLook at gas stoichiometry
7 Properties of Gases Expand to completely fill their container Take the Shape of their containerLow Densitymuch less than solid or liquid stateCompressibleMixtures of gases are always homogeneousFluid2
8 Physical Characteristics of Gases Gases assume the volume and shape of their containers.Gases are the most compressible state of matter.Gases will mix evenly and completely when confined to the same container.Gases have much lower densities than liquids and solids.Exerts pressure on its surroundings.
9 The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a large metal can (a) and then turning off the heat and sealing the can.
10 As the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple.
11 Force Pressure = Area Pressure can be measured by a Barometer → Units of Pressure1 pascal (Pa) = 1 N/m21 torr = 1 mm Hg1 atm 760 torr1 atm 101,325 Pa760 torr 101,325 Pa
16 Boyle’s Law P a 1/V Constant temperature P x V = constant Constant amount of gasP x V = constantP1 x V1 = P2 x V2
17 Pressure and Volume: Boyle’s Law Pressure is inversely proportional to Volumeconstant T and amount of gasgraph P vs V is curvegraph P vs 1/V is straight lineas P increases, V decreases by the same factorP x V = constantP1 x V1 = P2 x V27
18 Boyle’s Law* Pressure Volume = Constant (T = constant) P1V1 = P2V2 (T = constant)V 1/P (T = constant)(*Holds precisely only at very low pressures.)
19 As pressure increases, the volume of SO2 decrease (at const. T)P1V1P2V2 =
20 Gas Pressure Pressure = total force applied to a certain area larger force = larger pressuresmaller area = larger pressureGas pressure caused by gas molecules colliding with container or surfaceMore forceful collisions or more frequent collisions mean higher gas pressure3
21 Air Pressure Constantly present when air present Decreases with altitudeless airVaries with weather conditionsMeasured using a barometerColumn of mercury supported by air pressureLonger mercury column supported = higher pressureForce of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury4
23 Measuring Pressure of a Trapped Gas Use a manometerOpen-end manometerif gas end lower than open end, Pgas = Pair + diff. in height of Hgif gas end higher than open end, Pgas = Pair – diff. in height of Hg5
25 Units of Gas Pressure atmosphere (atm) height of a column of mercury (mm Hg, in Hg)torrPascal (Pa)pounds per square inch (psi, lbs./in2)1.000 atm = mm Hg = in Hg = torr = 101,325 Pa = kPa = psi6
26 Summary: Boyle’s Law Pressure is inversely proportional to Volume constant T and amount of gasgraph P vs V is curvegraph P vs 1/V is straight lineas P increases, V decreases by the same factorP x V = constantP1 x V1 = P2 x V27
27 Boyle’s Law P a 1/V Constant temperature P x V = constant Constant amount of gasP x V = constantP1 x V1 = P2 x V2
28 Example 12.2 What is the new volume if a 1.5 L sample of freon-12 at 56 torr is compressed to 150 torr?Write down the given amountsP1 = 56 torr P2 = 150 torrV1 = 1.5 L. V2 = ? LConvert values of like quantities to the same unitsboth Pressure already in torrvalue of V2 will come out in L8
29 Example 12.2 (continued) What is the new volume if a 1.5 L sample of freon-12 at 56 torr is compressed to 150 torr?Choose the correct Gas LawSince we are looking at the relationship between pressure and volume we use Boyle’s LawP1 x V1 = P2 x V2Solve the equation for the unknown variable9
30 Example 12.2 (continued) What is the new volume if a 1.5 L sample of freon-12 at 56 torr is compressed to 150 torr?Plug in the known values and calculate the unknownP1 = 56 torr P2 = 150 torrV1 = 1.5 L. V2 = ? L10
31 Absolute ZeroTheoretical temperature at which a gas would have zero volume and no pressurecalculated by extrapolation0 K = °C = -459 °FKelvin T = Celsius TNever attainablethough we’ve gotten real close!All gas law problems use Kelvin temperature scale!11
32 Charle’s Law: Volume-Temperature Relationship (n and P const.) As T increasesV increases
33 Figure 12.7: Plots of V (L) versus T (°C) for several gases.
34 Figure 12. 8: Plots of V versus T as in Figure 12 Figure 12.8: Plots of V versus T as in Figure 12.7, except that here the Kelvin scale is used for temperature.
35 Volume and Temperature: Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.V = bT (n and P = constant)b = a proportionality constant
37 Summary: Charles’ Law Volume is directly proportional to Temperature constant P and amount of gasgraph of V vs T is straight lineas T increases, V also increasesV = constant x Tif T measured in KelvinV1 = V2T T212
38 (Calculating Volume using Charle’s Law). A 2 (Calculating Volume using Charle’s Law). A 2.0-L sample of air is collected at 298 K and then cooled to 278 K. The pressure is held constant at 1.0 atm. Calculate the volume of the air at 278 K. Does the volume increase or decrease?V1 = 2.0 LV2 = ?T1 = 298 KT2 = 278 KT2 x V1T1278 K x 2.0 L278 K=V2 == 1.9 LThe volume gets smaller when the temperature decreases.
39 V1/T1 = V2/T2 V1 = 2.58 L V2 = ? T1 = 15 °C = 15+273 = 288 K (Calculating Volume using Charle’s Law). A sample of gas at 15 C (at 1 atm) has a volume of 2.58 L. The temperature is then raised to 38 C (at 1 atm). Calculate the new volume. Does the volume of the gas increase or decrease?V1/T1 = V2/T2V1 = 2.58 LV2 = ?T1 = 15 °C == 288 KT2 = 38 °C == 311 KT2 x V1T1311 K x 2.58 L288 K=V2 == 2.79 LThe volume gets smaller when the temperature decreases.
40 V1/T1 = V2/T2 V1 = 2.1 L V2 = 2.3 L T1 = 298 K T2 = ? V2 x T1 V1 (Calculating Temperature using Charle’s Law). A balloon is filled with helium, and its volume is 2.1 L at 298 K. The balloon will burst if its volume exceeds 2.3 L. At what temperature would you expect the balloon to burst?V1/T1 = V2/T2V1 = 2.1 LV2 = 2.3 LT1 = 298 KT2 = ?V2 x T1V12.3 L x 298 K2.1 L=T2 == 362 K
41 Volume and Moles: Avogadro’s Law Volume directly proportional to the number of gas moleculesV = constant x n (moles)Constant P and TMore gas molecules = larger volumeCount number of gas molecules by molesOne mole of any ideal gas occupies L at standard conditions - molar volumeEqual volumes of gases contain equal numbers of moleculesIt doesn’t matter what the gas is!13
42 Avogadro’s Law V a number of moles (n) V = constant x n V1/n1 = V2/n2 Constant temperatureConstant pressureV = constant x nV1/n1 = V2/n2
43 Figure 12.9: The relationship between volume V and number of moles n (at constant T and P) . As the number of moles is increased from 1 to 2 (a to b), the volume doubles. When the number of moles is tripled (c), the volume is also tripled.
44 Ideal Gas LawBy combing the proportionality constants from the gas laws we can write a general equationR is called the gas constantThe value of R depends on the units of P and VGenerally use R = when P in atm and V in LUse the ideal gas law when have gas at one conditionMost gases obey this law when pressure is low (at or below 1 atm) and temperature is high (above 0°C)If a gas changes some conditions, the unchanging conditions drop out of the equationPV = nRT14
45 Ideal Gas Law 1 Boyle’s law: V a (at constant n and T) P Charles’ law: V a T (at constant n and P)Avogadro’s law: V a n (at constant P and T)V anTPA single equation has been derived which relates to amount, temperature, and pressure. Relation between variables:R is the gas constant,can be calculated from expt.V = constant x = RnTPPV = nRT
46 Ideal Gas Law PV = nRT R = proportionality constant = L atm molP = pressure in atm; 1 atm = kPa; atm = 760 mmHgV = volume in litersn = amount in molesT = temperature in Kelvin (TK = tºC + 273)Holds closely at P < 1 atm
48 What is the volume (in liters) occupied by 49.8 g of HCl at 1.00 atm? T = 0 °C = 273 KP = 1 atmPV = nRTn = 49.8 g x1 mol HCl36.45 g HCl= 1.37 molV =nRTPL•atm1.37 mol x x 273 Kmol•KV =1 atmV = 30.6 L
49 Example 12.8 Using the Ideal Gas Law in Calculations Question: A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0 °C and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. (Assume that the gas behaves ideally.)Answer: mol
50 Example 12.8 Using the Ideal Gas Law Calculations Involving Conversion of Units Question: What volume is occupied by mol of carbon dioxide at 25 ºC and 371 torr ?Answer: L
51 Example 12.11. Calculating Volume Changes Using the Ideal Gas Law Question: A sample of diborane gas, B2H6, a substance that bursts into flames when exposed to air, has a pressure of atm at a temperature of –15 ºC and a volume of 3.48 L. If conditions are changed so that the temperature is 36 ºC and the pressure is atm, what will be the new volume of the sample? Hint: Calculate V2 from the combined gas law:Answer: 3.07L
52 Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures each gas would exert independentlyPartial pressures is the pressure a gas in a mixture would exert if it were alone in the containerPtotal = Pgas A + Pgas B + …Particularly useful for determining the pressure a dry gas would have after it is collected over waterPair = Pwet gas = Pdry gas + Pwater vaporPwater vapor depends on the temperature, look up in table16
53 Partial Pressures The partial pressure of each gas in a mixture can be calculated using the Ideal Gas Law17
54 Figure 12.10: When two gases are present, the total pressure is the sum of the partial pressures of the gases.
55 Dalton’s Law of Partial Pressures For a mixture of gases in a container,PTotal = P1 + P2 + P
56 Figure 12.11: The total pressure of a mixture of gases depends on the number of moles of gas particles (atoms or molecules) present, not on the identities of the particles.
57 Experimental setup for Example 12.13 Bottle full of oxygen gas and water vapor2KClO3 (s) KCl (s) + 3O2 (g)PT = PO + PH O2
58 Using Dalton’s Law of Partial Pressures using Fig. 12.12 Question: A sample of solid potassium chlorate, KClO3, was heated in a test tube (see Figure 12.12) and decomposed according to the reactionKClO3 (s) 2 KCl (s) + 3 O2(g)The oxygen produced was collected by displacement of water at 22 ºC. The resulting mixture of O2 and H2O vapor had a total pressure of 754 torr and a volume of L. Calculate the partial pressure of O2 in the gas collected and the number of moles of O2 present. The vapor pressure of water at 22 ºC is 21 torr.Ans: P(O2) = atm and n(O2) = 2.59 10-2 mol
59 Example using Dalton’s Law of Partial Pressure Not all pollution is due to human activity. Natural sources, including volcanoes, also contribute to air pollution. A scientist tries to generate a mixture of gases similar to those found in a volcano by introducing 15.0 g of water vapor, 3.5 g of SO2 and 1.0 g of CO2 into a 40.0L vessel held at 120 ºC. Calculate the partial pressure of each gas and the total pressure. Ans.: PH2O = atm, PSO2 = atm, PCO2 = atm; Ptot = atm.
60 Laws and Models: A Review Aim: To understand the relationship between laws and models (theories). The laws are the ideal gas laws, and the model (theory) we want to look at is the Kinetic Molecular Theory of Gases.
61 Real GasesDeviate at least slightly from the ideal gas law because of two factors:Gas molecules attract one anotherGas molecules occupy a finite volume.Both of these factors are neglected in the ideal gas law. Both increase in importance when the molecules are close together (high P, low T).This means that at high pressures and/or low temperatures, the properties of gases deviate significantly from the predictions of the ideal gas equation. An ideal gas is really a hypothetical substance. At low pressures and/or high temperatures, real gases approach the behavior expected for an ideal gas.
62 Real GasesMust correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
63 Kinetic - Molecular Theory The properties of solids, liquids and gases can be explained based on the speed of the molecules and the attractive forces between moleculesIn solids, the molecules have no translational freedom, they are held in place by strong attractive forcesMay only vibrate18
64 Kinetic - Molecular Theory In liquids, the molecules have some translational freedom, but not enough to escape their attraction for neighboring moleculesThey can slide past one another, rotate as well as vibrateIn gases, the molecules have “complete” freedom from each other, they have enough energy to overcome “all” attractive forcesKinetic energy depends only on the temperature19
65 Describing a Gas using KM theory Gases are composed of tiny particlesThe particles are small compared to the average space between themAssume the molecules do not have volumeMolecules constantly and rapidly moving in a straight line until they bump into each other or the wallAverage kinetic energy proportional to the temperatureResults in gas pressureAssumed that the gas molecules attraction for each other is negligible20
66 Postulates of the Kinetic - Molecular Theory of Gases Gases consist of tiny particles (atoms or molecules).These particles are so small, compared with the distances between them, that the volume (size) of the individual particles can be assumed to be negligible (zero).The particles are in constant random motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas.The particles are assumed not to attract or to repel each other.The average kinetic energy of the gas particle is directly proportional to the Kelvin temperature of the gas.18
67 Basic equation of the kinetic-molecular theory for the Pgas This equation can be rearranged to give, for NA molecules,The Kelvin temperature (T) of a gas is directly proportional to the average translational energy of its molecules.
68 The Meaning of Temperature per moleculeper moleThe Kelvin temperature (T) of a gas is directly proportional to the average translational energy of its molecules.New meaning of temperature: The zero temperature is the temperature at which translational molecular motion should cease.
69 Gas Properties Explained Gases have indefinite shape and volume because the freedom of the molecules allows them to move and fill the container they’re inGases are compressible and have low density because of the large spaces between the molecules21
70 The Meaning of Temperature The Kelvin temperature (T) of a gas is directly proportionalto the average translational energy of its molecules.Temperature is a measure of the average kinetic energy of the molecules in a sampleNot all molecules have same kinetic energyKinetic energy is directly proportional to the Kelvin Temperatureaverage speed of molecules increases as the temperature increase (actually as T).22
71 Root Mean Square Velocity Derivation: The root mean square velocity can be derived by equating the kinetic energy of the molecule to be equal to the thermal energy, i.e.½ m u2 = 3/2 kT.
72 Pressure and Temperature As the temperature of a gas increases, the average speed of the molecules increasesthe molecules hit the sides of the container with more force (on average)the molecules hit the sides of the container more frequentlythe net result is an increase in pressureGay-Lussac’s Law states that for a fixed amount of gas (fixed number of moles) at a fixed volume, the pressure is proportional to the temperature.Gay-Lussac’s Law:23
73 Volume and Temperature In a rigid container, according to KM theory, raising the temperature increases the pressureFor a cylinder with a piston, the pressure outside and inside stay the sameTo keep the pressure from rising, the piston moves out increasing the volume of the cylinderas volume increases, pressure decreasesTherefore KM theory predicts that the volume of a gas will increase as we raise its temperature at a constant pressure. This agrees with experimental observation (as summarized by Charle’s law).24
74 Kinetic Molecular Theory of Gases A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points that is, they possess mass but have negligible volume (V zero).Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic.Gas molecules exert neither attractive nor repulsive forces on one another.The average kinetic energy of the molecules is proportional to the absolute temperature of the gas in K. Any two gases at the same temperature will have the same average kinetic energy.
75 Kinetic Molecular Theory of Gases Gases consist of atoms or molecules in continuous, random motion.Collisions between gas particles are elastic.V gas particles << V containerAttractive forces between particles 0).The average kinetic energy of the molecules is proportional to the absolute temperature; Etrans = c TAt a given temperature, all gases have the same average translational kinetic energy. In other words, c is a universal constant (for all gases).Etrans = ½ m u2 = c T where m = mass molecule, u = avg. speed, T = temp. in K, and c is a constant which has the same value for all gases.
76 Kinetic theory of gases and … Compressibility of Gases :Boyle’s LawP a collision rate with wallCollision rate a number density (Average collision rate with the walls.htm)Number density a 1/VP a 1/VCharles’ LawCollision rate a average kinetic energy of gas moleculesAverage kinetic energy a TP a T
77 Kinetic theory of gases and … Avogadro’s LawP a collision rate with wallCollision rate a number densityNumber density a nP a nDalton’s Law of Partial PressuresMolecules do not attract or repel one anotherP exerted by one type of molecule is unaffected by the presence of another gasPtotal = S Pi
78 Gas StoichiometryUse the general algorithms discussed previously to convert masses or solution amounts to molesUse gas laws to convert amounts of gas to molesor vice versa25
80 C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l) Gas StoichiometryWhat is the volume of CO2 produced at 37ºC and 1.00 atm when 5.60 g of glucose are used up in the reaction:C6H12O6 (s) + 6O2 (g) CO2 (g) + 6H2O (l)g C6H12O mol C6H12O mol CO V CO21 mol C6H12O6180 g C6H12O6x6 mol CO21 mol C6H12O6x5.60 g C6H12O6= mol CO20.187 mol x x KL•atmmol•K1.00 atm=nRTPV == 4.76 L
81 PV = nRT PV (1 atm)(22.42L) R = = nT (1 mol)(273.15 K) The conditions 0 ºC and 1 atm are called standard temperature and pressure (STP).Experiments show that at STP, 1 mole of an ideal gas occupies L.PV = nRTR =PVnT=(1 atm)(22.42L)(1 mol)( K)R = L • atm / (mol • K)
82 What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0C = KP = 1 atmPV = nRTn = 49.8 g x1 mol HCl36.45 g HCl= 1.37 molV =nRTPV =1 atm1.37 mol x x KL•atmmol•KV = 30.6 L
83 Example A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present?STP: T = 0 0C = 273 K,P = 1 atmPV = nRTAt STP, 1 mole of an ideal gas occupies L. Using Avogadro’s Law, V/n = constn =PVRT1.00 atm x 1.75 Ln =L • atmmol • KX 273KTwo methods to solve this problem: 1. By using Ideal Gas Law or2. By using Avogadro’s Law.V = 7.81 x 10-2 mol
84 Example 12.17. Gas Stoichiometry: Reactions Involving Gases at STP Quicklime, CaO, is produced by heating calcium carbonate, CaCO3. Calculate the volume of CO2 produced at STP from the decomposition of 152 g of CaCO3 according to the reactionCaCO3 (s) CaO (s) + CO2 (g)Answer: This is a gas stoichiometry problem. First calculate the number of moles of CO2 from the balanced chemical equation. Then use Avogadro’s Law to calculate the volume of CO2 gas produced at STP. Remember mol = 22.4 L (STP)