2ObjectivesUnderstand the definition of pressure. Use the definition to predict and measure pressure experimentallyDescribe experiments that show relationships between pressure, temperature, volume, and moles of a gas sampleUse empirical gas laws to predict how change in one of the properties of a gas will affect the remaining properties.Use empirical gas laws to estimate gas densities and molecular masses.Use volume-to-mole relationships obtained using the empirical gas laws to solve stoichiometry problems involving gases.
3Objectives6. Understand the concept of partial pressure in mixtures of gases.7. Use the ideal kinetic-molecular model to explain the empirical gas laws.8. List deficiencies in the ideal gas mode3el that will cause real gases to deviate from behaviors predicted by the empirical gas laws. Explain how the model can be modified to account for these deficiencies.
5Definition of GasGas: large collection of particles moving at random throughout a volume that is primarily empty space. Have relatively large amount of energy.Gas pressure: due to collisions of randomly moving particles with the walls of the container.Force/unit area
6Definition of Gases STP: 0°C, and 1 atmosphere pressure Elements that exist as gases at STP: hydrogen, nitrogen, oxygen, fluorine, chlorine and Noble GasesIonic compounds are all solidsMolecular compounds - depends on the intermolecular forces. Most are liquids and solids. Some are gaseous
7Properties of Gases Assume the volume and shape of their container CompressibleMix evenly and completely when confined to the same containerLower densities than liquids and solidsAllotropes: O2 ↔O3
8Kinetic Molecular Theory of Gases Tiny particles in continuous motion ( the hotter the gas, the faster the molecules are moving) with negligible volume compared to volume of container.Molecules are far apart from each otherDo not attract or repel each other (?).All collisions are elastic (gas does not lose energy when left alone).The energy is proportional to Kelvin temperature. At a given temperature all gases have the same average KE.
9Properties of Gases Observation Hypothesis Gases are easy to expand Gases are easy to compressGases have densities that are 1/1000 of solid or liquid densitiesGases completely fill their containersHot gases leak through holes faster than cold gases
10Properties of Gases Observation Hypothesis Gases are easy to expand Gas molecules do not strongly attract each otherGases are easy to compressGas molecules don’t strongly repel each otherGases have densities that are 1/1000 of solid or liquid densitiesMolecules are much farther apart in gases than in liquids and solidsHot gases leak through holes faster than cold gasesGas molecules are in constant motion
11Atmospheric PressureIntensive or Extensive Property?
12PressurePressure is due to collisions between gas molecules and the walls of the container. Magnitude determined by: force of collisions and frequency.Pressure: force per unit area: P =F/AStandard temperature: 0ºC = KStandard pressure: 1 atm in US; 1 bar elsewhere
13Pressure Unit Symbol Conversions Pascal Pa 1 Pa = 1 N/m2 Psi lb/in2 AtmosphereAtm1 atm = Pa = 14.7 lb/in2Bar1 bar = PaTorr760 torr = 1 atmMillimeter mercurymm Hg1 mm Hg = 1 torr
14Pressure: ExamplesHow much pressure does an elephant with a mass of 2000 kg and total footprint area of 5000 cm2 exert on the ground?Estimate the total footprint area of a tyrannosaur weighing kg. Assume it exerts the same pressure on its feet that the elephant does.
15Pressure Measuring pressure: Strategy: Relate pressure to fluid column heightsYou can’t draw water higher than 34 feet by suction alone. Why?Hypothesis: atmospheric pressure supports the fluid columnDevelop the equation
17Pressure: BarometerBarometer measures atmospheric pressure as a mercury column height.
18Pressure: Open-Manometer Manometer measures gas pressure as a difference in mercury column heights.Two types: closed manometeropen manometer
19Measuring Gas Pressure Closed-manometer : the arm not connected to the gas sample is closed to the atmosphere and is under vacuum.Explain how you can read the gas pressure in the bulb.
20Pressure: Examples3. Calculate the difference in pressure between the top and the bottom of a vessel exactly 76 cm deep filled at 25 ºC with a) water; b) mercury (d = 13.6 g/cm3)(7.43 x 103 Pa;100.9 x 103 Pa)4. How high a column of air would be necessary to cause the barometer to read 76 cm of mercury, if the atmosphere were of uniform density 1.2 kg/m3?dHg = kg/m3 (8.6 km)5. A Canadian weather report gives the atmospheric pressure as kPa. What is the pressure in atmospheres? Torr? Mm Hg?
21The Gas Laws: State of Gas PropertySymbolUnitProperty TypePressurePatm, torr, PaIntensiveVolumeVL, cm3ExtensiveTemperatureTKMolesnmolextensive
22The Gas Laws: State of Gas Any equation that relates P, V, T, and n for a material is called an equation of state.Experiment shows PV = nRT is an approximate equation of state for gases.R is the gas law constantDetermined by measuring P, V, T, n and computing R = PV/nTValue depends on units chosen for P, V, TNotice: 1 Joule = 1 N m = 1(Pa) (m3)
23The Gas LawsGas laws deal with the MACROSCOPIC view of gases and we try to explain the macroscopic properties by examining the microscopic behaviors (many molecule behaviors)
25Boyle’s Law: Experiment Relate volume to pressure when everything else is constant. Experiment: trapped air bubble at 298 KVolume, mLPressure, torrPV )mL torr)10.0760.020.0379.630.0253.240.0191.0Graphs?
26Boyle’s Law: Experiment Relate volume to pressure when everything else is constant. Experiment: trapped air bubble at 298 KVolume, mLPressure, torrPV (mL torr)10.0760.07.60 x 10320.0379.67.59 x 10330.0253.240.0191.07.64 x 103Graphs?
27Boyle’s Law: Volume/Pressure Relationship At constant n, and T, the volume of a gas decreases proportionately as its pressure increases. If the pressure is doubled, the volume is halved.
28Boyle’s Law: Volume/Pressure Relationship What happens to the volume of the gas as the pressure increases? Mathematical Relationship?
29Plot of Boyle’s LawV versus PV versus 1/PType of Graphs?
30Boyle’s Law MOLECULAR VIEW Boyle’s Law – the volume of a fixed amount of gas at constant temperature and constant number of moles is inversely proportional to the gas pressure.MOLECULAR VIEW
31Boyle’s Law MOLECULAR VIEW: Boyle’s Law – the volume of a fixed amount of gas at constant temperature and constant number of moles is inversely proportional to the gas pressure.MOLECULAR VIEW:Confining molecules to a smaller space increases the number (frequency) of collisions, and so increases the pressure
32Charles' Law (V/T Relationships) Relate volume to temperature, everything else is constant. Experiment: He bubble trapped at 1 atm.V, mLT, ºCT, (K)V/T, mL/K40.00.0273.244.025.0298.047.750.0323.251.375.0348.255.3100.0373.280.0546.3
33Charles' Law (V/T Relationships) Relate volume to temperature, everything else is constant. Experiment: He bubble trapped at 1 atm.V, mLT, ºCT, (K)V/T, mL/K40.00.0273.20.14644.025.0298.00.14847.750.0323.251.375.0348.20.14755.3100.0373.280.0546.3
34Charles’ Law: Volume/Temperature Relationships At constant n and P, the volume of a gas increases proportionately as its absolute temperature increases, If the absolute temperature doubles, the volume is doubled.K = ºC
35Charles’ LawA plot of V versus T for a gas sample. What type of graph? Equation?
37Charles' LawKinetic Interpretation of Charles's Law? Why higher pressure? Equation?Frequency and force of collision…
38Charles’ Law MOLECULAR VIEW The volume of the gas is directly proportional to its Kelvin temperature, when everything else is constant.MOLECULAR VIEW
39Charles’ Law MOLECULAR VIEW The volume of the gas is directly proportional to its Kelvin temperature, when everything else is constant.MOLECULAR VIEWRaising temperature increases the number of collisions and force of collisions (KE increases) with container wall. If the walls are flexible, they will be pushed back and the gas expands.
40Charles’ LawAssume that you have a sample of gas at 350 K in a sealed container, as represented in (a). Which of the drawings (b) – (d) represents the gas after the temperature is lowered from 350 K to 150 K
41Gay Lussac’s Law Molecular View; The pressure of the gas is directly proportional to its Kelvin temperature, when everything else is constant.Molecular View;
42Gay Lussac’s Law Molecular View; The pressure of the gas is directly proportional to its Kelvin temperature, when everything else is constant.Molecular View;Raising the temperature increases the number of collisions and the kinetic energy of the molecules. More collisions with greater energy (force) means higher pressure.
46Avogadro’s Law: Relates n to Volume At constant T and P, the volume of a gas is directly proportional to moles of gas. Molar volume is almost independent of the type of gas.Samples of two gases with the same V, P, T contain the same number of molecules.MOLECULAR VIEW
47Avogadro’s Law: Relates n to Volume At constant T and P, the volume of a gas is directly proportional to moles of gas. Molar volume is almost independent of the type of gas.Samples of two gases with the same V, P, T contain the same number of molecules (moles).MOLECULAR VIEWType of gas does not influence distance between molecules too much.
48Avogadro’s Law: Example 6 Show the approximate level of the movable piston in drawings (a) and (b) after the indicated changes have been made to the initial gas sample.
50Example 7Show the approximate level of the movable piston in drawings (a), (b), and (c ) after the indicated changes.
51Gas Laws: Examples8. A balloon indoors, where the temperature is 27.0 ºC, has a volume of 2.00 L. What will be its volume outdoors, where the temperature is ºC? (Assume no change in pressure)[ 1.67 L]9. A sample of nitrogen occupies a volume of 2.50 L at -120 ºC and 1.00 atm. Pressure. To which of the following approximate temperatures should the gas be heated in order to double its volume while maintaining a constant pressure?-240 ºC ºC ºC ºC[30.0 ºC]
52Gas Laws: Examples10. Calculate the volume occupied by 4.11 g of methane gas at STP.[5.74 x 103L]11. What is the mass of propane, C3H8, in a 50.0 L container of the gas at STP?
53Ideal Gas LawPV = nRTGas Constant R = (L atm)/(mol K)
54Examples12. Sulfur hexafluoride, SF6 is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel container of volume 5.43 L at 69.5 ºC (9.42 atm)13. Calculate the volume (in liters) occupied by 7.40 g of CO2 at STP ( 3.77 L)
55Gas Laws: Examples14. A gas initially at 4.0 L, 1.2 atm, and 66 º undergoes a change so that its final volume an temperature become 1.7 L and º C. What is its final pressure? Assume the number of moles remains unchanged.15. A certain container holds 6.00 g of CO2 at ºC and 100. kPa pressure. How many grams of CO2 will it hold at 30.0 ºC and the same pressure?
57Gas Density and Molar Mass Purple M&M Do Red TooOrMichael Mo do the right thing
58Density and Molar Mass: Examples 16. Calculate the density of methane gas, CH4, in grams per liter, at 25 ºC and atm.[0.641 g CH4/L]17. Under what pressure must O2(g) be maintained at 25 ºC to have density of 1.50 g/L?[1.15 atm]18. The density of a gaseous organic compound is 3.38 g/L at 40.0 ºC and 1.97 atm. What is its molar mass?[44.1 g/mol]19. A gaseous compound is 78.14% boron, 21.86% hydrogen. At 27.0 º C, 74.3 mL of the gas exerted a pressure of 1.12 atm. If the mass of the gas was g, what is its molecular formula? [B2H6]
59Stoichiometry Involving Gases Use regular Stoichiometry techniques, except thatfor non STP conditions, and 22.4 L/mole for STPconditions.
60Stoichiometry: The Law of Combining Volumes Involving Gases When gases measured at the same temperature and pressure are allowed to react, the volumes of gaseous reactants and products are in small whole-number ratios.
61Stoichiometry: The Law of Combining Volumes Involving Gases (Avogadro’s Explanation) When the gases are measured at the same temperature and pressure, each of the identical flasks contains the same number of molecules.
62Examples (Stoichiometry) 20. How many liters of O2(g) are consumed for every 10.0 L of CO2(g) produced in the combustion of liquid pentane, C5H12, if each gas is measured at STP?[16.0 L O2]21. Given the reactionC6H12O6(s) + O2(g) → 6CO2(g) + 6H2O(g),calculate the volume of CO2 produced at 37.0 ºC and 1.00 atm when 5.60 g of glucose is used up in the reaction [4.75 L]22. A 2.14 L- sample of hydrogen chloride gas at 2.61 atm and 28.0 ºC is completely dissolved in 668 mL of water to form hydrochloric acid solution. Calculate the molarity of the acid solution [0.338M]
63Dalton’s Law of Partial Pressure Assume that you have a mixture of He (4 amu) and Xe ( 131 amu) at 300 K. Which of the drawings best represents the mixture (blue= He; green = Xe)?
64Dalton’s Law of Partial Pressure What is the partial pressure of each gas – red, yellow, and green – if the total pressure inside the following container is 600 mm Hg?2. What is the volume of each gas inside the container, if the total volume of this vessel is 1.0 L?
66Dalton’s Law of Partial Pressures Mole fraction: moles of component per mole of mixtureAvogadro’s Law: mole fraction = volume fraction for ideal gasExamples:2 L of He gas is mixed withy 3 L of Ne gas. What is the mole fraction of each component?Air is approximately 79% N2 and 21 %O2 by mass. What is the mole fraction of O2 in the air?
67Dalton’s Law of Partial Pressures Partial Pressure – the pressure of an individual gas component in a mixture: PAExamples:One mole of air contains 0.79 moles of nitrogen and 0.21moles of oxygen. Compute the partial pressure of these gases at a total pressure of 1.0 atm atm and at a total pressure of 3.0 atm (about the pressure experienced by a diver under 66 ft of seawater).What is the mole fraction of water in the headspace of a soda bottle, if the gas is at 2.0 atm and 25 ºC is torr?
68Dalton’s Law of Partial Pressures Ptotal = P1 + P2 + P3 +……. PnP1 = x1PT
69Dalton’s Law of Partial Pressures Dalton’s Law: The total pressure of a mixture of gases is just the sum of the pressures that each gas would exert if it were present alone.MOLECULAR VIEWMolecules of a gas do not attract or repel each other. The distances between particles are very large, therefore each particular gas occupies the entire container and adds its pressure to the total pressure in the container.
70Dalton’s Law: Examples 23. A mixture containing mol He, mol of Ne, and mol of Ar is confined in a 7.00 L vessel at 25 ºC.A) Calculate the partial pressure of each of the gasses in the mixture.B) Calculate the total pressure of the mixture.[P of He 1.88 atm; P of Ne 1.10 atm; P of Ar atm; P total 3.34 atm]24. The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen?[7.87 x 10-1]
71Dalton’s Laws: Examples 25. What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm? [4.13 atm]26. Ca(s) + H2O(l) →Ca(OH)2 + H2(g)H2(g) was collected over water. The volume of gas at 30.0 ºC and P= 988 mm Hg is 641 mL. What is the mass (in grams) of the H2 gas obtained? The pressure of water at 30.0 ºC is mm Hg.[ g]Dalton’s Law
72Dalton’s Laws: Additional Problems 27. A gaseous mixture made from 6.00 g of oxygen and 9.00 g of methane is placed in a 15.0 – L vessel at 0.00°C What is the partial pressure of each gas, and what is the total pressure in the vessel?[0.281 atm O2; CH4; atm total]28. A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent of CO2, 18.0 mol percent O2; and 80.5 mol percent of Ar. (a) calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 120 –L space at 295 K, how many moles of O2 are needed?[PO2 = 134 torr; nO2 = mol]
73Dalton’s law of Partial Pressure 29. The apparatus shown consists of three bulbs connected by stopcocks. What is the pressure inside the system when the stopcocks are opened? Assume that the lines connecting the bulbs have zero volume and that the temperature remains constants.[PCO2 = atm; PH2 = atm; P Ar = atm; PT = atm]
74When these valves are opened, what is the partial pressure Example 304.00 LCH43.50 LO21.50 LN22.70 atm.58 atm.752 atmWhen these valves are opened, what is the partial pressureof each gas and the total pressure in the assembly?[P of CH4 = 1.2 atm; P of N2 = atm;P of O2 = atm; P total : add all the pressures]
75Kinetic Molecular Theory of Gases Gas particles are in continuous motion ( the hotter the gas, the faster the molecules are moving) with negligible volume compared to volume of container.Molecules are far apart from each otherDo not attract or repulse each other (?).All collisions are elastic (gas does not lose energy when left alone).The energy is proportional to Kelvin temperature. At a given temperature all gases have the same average KE.
76Properties of Gases Observation Hypothesis Gases are easy to expand Gas molecules do not strongly attract each otherGases are compressibleParticles have small volumes compared to continer. Lots of empty spaceGases are easy to compressGas molecules don’t strongly repel each otherGases have densities that are 1/1000 of solid or liquid densitiesMolecules are much farther apart in gases than in liquids and solidsHot gases leak through holes faster than cold gasesGas molecules are in constant motion
77Properties of Gases Observation Hypothesis Gases undergo elastic collisions: when gas is left alone at constnat temperature, it does not liquefy or vaporize (no energy exchange)Gas molecules are like billiard balls – do not stick to each other (do not attract, do not repel)Hot gases leak through holes faster than cold gasesGas molecules are in constant motion
78Kinetic Molecular Theory of Gases Ideal gas limitations:Gases can be liquefied if cooled enough.Real gas molecules do attract one another to some extent otherwise the particles would not condense to form a liquid.
79Maxwell Distribution Curves Average Kinetic Energy at a given temperature is constant for a gas sampleBut, the speeds of the molecules vary(during to collisions with each other and with the walls of the container)Physics: momentum is conserved(playing pool)
81Gas Laws: Maxwell’s Distribution Curves Molecules in a gas move at different speeds.The Maxwell Distribution Curves show how many molecules are moving at a particular speed.The distribution shifts to higher speeds at higher temperatures.377 m/s900 m/scompare1500 m/s
82MKT of Gases: Equations KE = ½ m(urms)2Average KE = (3/2) RTMaxwell equation for the root mean square velocity:Urms =The Urms is not the same as the mean (average ) speed. The difference is small.
83Average Molecular speed Average molecular kinetic energy depends only on temperature for ideal gases.Therefore:Higher temperature = higher root-mean- square speed (RMS), rmsHigher molecular weight (molar mass) = lower urms speed (same temperature)
84Average Root Mean Square: Examples 31. Calculate the Urms speed, urms, of an N2 molecule at 25ºC.(5.15 x 102 m/s)32. Calculate the urms speed of helium atoms 25ºC (1.36 x 103 m/s)33. Calculate the Urms speed of chlorine atoms at 25ºC (323 m/s)
86Diffusion and Effusion (a) Diffusion: mixing of gas molecules by random motion under conditions where molecular collisions occur.(Ib) Effusion: the escape of a gas through a pinhole without molecular collisions
87Diffusion and Effusion HCl and NH3: What will happen?
88Graham’s Law of Diffusion Under the same conditions of temperature and pressure, the rate of diffusion of gas molecules are inversely proportional to the square root of their molecular masses.
89Graham’s Law of Diffusion 34. It has taken 192 seconds for 1.4 L of an unknown gas to effuse through a porous wall and 84 seconds for the same volume of N2 gas to effuse at the same temperature and pressure. What is the molar mass of the unknown gas? (146 g/mol)35. In a given period of time, 0.21 moles of a gas of MM = 26 gmol-1 effuses. How many moles of HCN would effuse in the same period of time?36. Calculate and compare the urms of Nitrogen gas at 35oC and 299K.
90Real GasesProblems with the Kinetic Molecular Theory of "Ideal" Gases:1. Gas particles have volume (they are not point masses). The volume becomes important under certain conditions.2. When gas particles are close to each other, they attract each other.
91PV = nRT equation when rearranged: For 1 mole of gas:PV = nRT equation when rearranged:Plot of (PV)/(RT) for1 mole of gasThe value for the equation is not always equal to 1Corrections to the Ideal Gas Equation is needed
92Factors that Affect Ideality Deviation from ideal behavior as a function of temperature for nitrogen gas:
93Factors that Affect Ideality of Gases Interactions between the molecules (intermolecular forces): important at low temperatures and small free volumeActual volumes of the molecules: important at high pressures and small free volume.Free volume: the space in the container that is not occupied by the molecules.
94Factors Affecting Ideality of Gases: low temperatures and small free volumes Distance between molecules is related to gas concentration:At high concentration (high P, low V):Molecules are closer (higher concentration) = stronger intermolecular attractions = deviation from idealityRepulsion make pressure higher than expected by decreasing free volumeAttractions make pressure lower than expected by breaking molecular collisions (plastic collisions)
95Effect of Intermolecular Attractions Orange molecules attract purple molecules.Therefore: purple molecule exert less force when it collides with the wall.No attractive forces = more force
96Real Gases: Effect of Pressure At high pressuresIntermolecular distances between molecules decreaseAttractive forces start to play a roleStickiness factorMeasured pressure is less than expectedCorrection for lower pressure
97Real Gases: Effect of Volume Volume should go to zero, but it does not.At low pressure, the gas occupies the entire container and its volume is insignificant compared to the volume of the container.At high pressure, the volume of a real gas is somewhat larger than the ideal value for an ideal gas as gas molecules take up space.
98Correction due to volume: (V – nb) V = volume of the containern = number of molesB = volume of a mole of particlesCorrection for volume
99Real Gases: Corrections Constant needed to correct intermolecular attractive forces (make it larger)Constant needed to correct for volume of individual gas molecules (make it smaller)The constants are characteristic properties of the substances: depend on the make-up and geometry of the substance
100Van der Waals Constants for Common Gases Compounda (L2-atm/mol2)b (L/mol)HeNe0.2107H20.2444Ar1.345O21.360N21.390CO1.485CH42.253CO23.592NH34.170
101Real Gases: Comparison Ideal gasReal gasObey PV=nRTAlwaysOnly at low pressuresMolecular volumeZeroSmall, but not zeroMolecular attractionSmallMolecular repulsionsmall
102Real Gases Large deviation form ideality: Large intermolecular attractive forces (IMF)Large Molar Mass (and subsequently volume)Real Conditions:high pressureslow volumesIdeal Conditions:Low pressures (atmospheric and up to ≈ 50 atmHigh temperatures
105Factors Affecting Ideality of Gases Tug-of-war between these two effects causes the following:Repulsion win at very high pressureAttractions win at moderate pressureNeither attractions nor repulsions are important at low pressure.
10622.41 L atm O2 CO2 PV P (at constant T) PV versus P at Constant T (1 mole of Gas)22.41 L atmO2CO2PVP (at constant T)
107V of a real gas > V of an ideal gas because V of gas molecules is significant when P is high. Ideal Gas Equation assumes that the individual gas molecules have no volume.
109Plots of Charles’ LawA plot of V versus T for a gas sample. What type of graph?
110Kinetic Molecular Theory of Gases 1. Gases are composed of tiny atoms or molecules (particles) whose size is negligible compared to the average distance between them. This means that the volume of the individual particles in a gas can be assumed to be negligible (close to zero).2. The particles move randomly in straight lines in all directions and at various speeds.3. The forces of attraction or repulsion between two particles in a gas are very weak or negligible (close to zero), except when they collide.4. When particles collide with one another, the collisions are elastic (no kinetic energy is lost). The collisions with the walls of the container create the gas pressure.5. The average kinetic energy of a molecule is proportional to the Kelvin temperature and all calculations should be carried out with temperatures converted to K.
111Notes: Kinetic Molecular Theory of Gases The observation that gases are compressible agrees with the assumption that gas particles have a small volume compared to the container.b. Elastic collisions agree with the observation that gases when left alone in a container do not seem to lose energy and do not spontaneously convert to the liquid.c. The assumptions have limitations. For example, gases can be liquefied if cooled enough. This means real gas molecules do attract one another to some extent otherwise the particles would never stick to one another in order to condense to form a liquid.
113Maxwell- Boltzmann Velocity (energy) Distribution Plot of Probability (fraction of molecules with given speed) versus root mean square velocity of the molecules.
114Maxwell Distribution Curve Variation in particle speeds for hydrogen gas at 273KurmsThe vertical line on the graph represents the root-mean-square-speed (urms).The root-mean-square-speed is the square root of the averages of the squares of the speeds of all the particles in a gas sample at a particular temperature.