5 Gases: Macroscopic Observation Gases fill the container into which they are placedGases are compressibleGases mix completely and evenly when confined to the same containerGases have much lower densities than solids or liquids (g/L)
6 Gases: Molecular ViewFill space evenly and completely: randomly, fast moving particlesLow density and compressibility: large distances between particlesIdealized assumptionsGas particles have no volumeGas particles have no interaction, so identity of gas particle is inconsequential
7 Gases: Historical View Molecular basisKinetic energy of molecules much greater than intermolecular forcesHistorical studies precede the atomFirst we will look at non-molecular properties
9 Pressure Velocity = distance / time (m/s) Acceleration = change in velocity / time (m/s2)Force = mass x acceleration (kg m/s2 = N)Pressure is the force of the gas pressing on a given area P = F/A (N/m2 = Pa)Ability to cut with a knife doesn’t depend simply on amount of force
11 Pressure Pressure = Force/Area Force = mass * acceleration Acceleration = g = pull of gravitymass = r*V = r*h*A where r=density of Hg, h= height of Hg, A = cross-sectional area of columnForce = r*h*A*gPressure=(r*h*A*g)/A = r*h*gP height and densityIf the density of mercury is 13.6g/ml, what is the height of a column of water under vacuum at atmospheric pressure? (76 cm =2.5 ft)
17 Boyle’s Law P 1/V , when one sample is kept at constant temperature Acts as an “Ideal Gas”
18 Ideal GasPressure is inversely proportional to volume at a range of constant temperatures and sample sizesk changes value at different temperatures, but is constant…well, almost constantAlso notice that identity of gas matters little, and all approach same ideal (all data from 1 mol samples at 0 oC)
19 Ideal Gas Molecular perspective Assumptions Good assumptions? Molecules occupy no spaceMolecules do not interact with each otherGood assumptions?
20 Test your Understanding When you blow up your tire, you increase the pressure and volume simultaneously. According to Boyle, pressure and volume are inversely proportional. What gives?
21 Charles’s Law Jacque Charles (1746-1823) Solo balloon flight At constant pressure, volume increases linearly with temperatureWrite Law
22 Charles’s Law (1783)V TT in KelvinK = oC + 273Absolute zero
23 Pressure and Temperature Draw Pressure as a function of Temperature at constant volume
24 Avagadro’s Law (1811) In light of Dalton’s Atomic Theory (1808) Based on Gay-LussacLaw of combining volumes
25 Avogadro’s LawAt constant P and T, the volume of a gas is proportional to the amount of gasmolar volume Vm = V/nV nLittle known historical fact: Junior High nickname happened to be “The Mole”
26 Combined Ideal Gas Law V proportional to 1/P V proportional to T V proportional to n𝑉=𝑅 𝑛𝑇 𝑃PV = nRT
27 Problem Types If three variables known, calculate fourth Some conditions change—how does it affect others?StoichiometryDetermine a molar mass
28 Molar Volume Molar Volume = Vm Vm at STP = 22.41 L/mol Defined as the volume taken up per mole of gasVm at STP = L/molStandard Pressure is 1 atmWhat is standard temperature in Celcius?
29 Strategy/Sketch: Answer: 7.0 x 102 oC A flask that can withstand an internal pressure of 2500 torr, but no more, is filled with a gas at 21.0 oC and 758 torr and heated. At what temperature will it burst?Strategy/Sketch:Answer: 7.0 x 102 oC
30 Change in State of Ideal Gas If the stopcock is opened, the total pressure is atm. What was the original pressure of the red bulb? Strategy: Logic Check:2.00L Ar at 360 torr1.00 L Ar unknown pressureAssumption Check: According to ideal gas, would the total pressure change if the right bulb were filled with 1 L of carbon dioxide?Answer: x 103 torr
31 Gas Density 𝑃𝑉=𝑛𝑅𝑇 𝑃𝑉 𝑚 = 𝑛𝑅𝑇 𝑚 where m = mass in grams 𝑚 𝑉 = density in grams/Liter𝑚 𝑛 = molar mass in g/mol𝑃 𝜌 = 𝑅𝑇 𝑀 where ρ = density & M = molar mass
32 Experimental Importance 𝑃 𝜌 = 𝑅𝑇 𝑀If you had a sample of an unknown gas, what could you measure experimentally? What could you determine about the gas?
33 Dalton’s Law of Partial Pressures Extension of ideal gas assumptionsFor a mixture of two gases A and B, the total pressure, PT, is PT = PA + PB“Partial Pressure”Since two gases by definition are at same V and T, 𝑛 𝑎 𝑛 𝑏 = 𝑃 𝑎 𝑃 𝑏Useful case: 𝑛 𝑎 𝑛 𝑡𝑜𝑡𝑎𝑙 = 𝑃 𝑎 𝑃 𝑡𝑜𝑡𝑎𝑙An example of early utility of Dalton’s atomic theory
34 Mole FractionMole fraction (χ) is the number of moles of one component of a mixture divided by the total moles in the mixture: 𝑛 𝑎 𝑛 𝑡𝑜𝑡𝑎𝑙χ A + χ B + χ C = 1The partial pressure of any gas, A, in a mixture is given by: PA = χ A ( PT )
36 Collecting a Gas Over Water Gases collected by water displacement are a mixture of the gas and water vapor.All liquids have a certain amount in the gas phase. This is known as the Vapor Pressure of the liquid. It is temperature dependent.PT = Pgas + PH2O
39 Kinetic Molecular Theory Describes gases at the molecular level1. Gases consist of small particles separated by large distances (assume no volume.)2. Constant, random motion. Collisions with wall cause pressure3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE).4. KE T, average kinetic energy only changes when temperature changes.
47 The meaning of Temperature 𝑃𝑉 𝑛 = 2 3 (KE)ave and 𝑃𝑉 𝑛 = RTKEave = 3 2 RT where R = J/mol KKelvin temperature is measurable quantity that is directly proportional to the random motion (kinetic energy) of the particles
52 “Typical” Velocities at 298 K in m/s These gases are at the same temperature, so they have the same __________ but they have different average velocities because they have different _________________.
53 Three ways to describe a “typical velocity” Most probableAverageRMS
54 Determination of RMS velocity KEave = 3 2 RT = Na 1 2 𝑚 𝑢 2𝑢 2 = 3𝑅𝑇 𝑚 𝑁 𝑎Root mean square velocity
57 Gas Motion on a Molecular Level EffusionDiffusion
58 Diffusion and Effusion Diffusion – mixing due to motionEffusion – passage of a gas through a small hole into an evacuated spaceRatio of effusion or diffusion rates depends on relative velocities of gases𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 1 𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 2 = 3𝑅𝑇/𝑚1 3𝑅𝑇/𝑚2 = 𝑚2 𝑚1
60 Real Gases: Check Assumptions 1. Gases consist of small particles separated by large distances (assume no volume.)2. Constant, random motion. Collisions with wall cause pressure3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE).4. KE T, average kinetic energy only changes when temperature changes.
61 Assumptions that FailGases have no contribution to volume. Is this assumption equally valid at all states?
62 Assumptions that FailGases velocity is unaffected by attraction to other particles.