2 Pressure Barometer – first pressure measuring device Torricelli, 1643 A glass tube filled with mercury, inverted into a dish of mercury.At sea level, height of mercury in the tube is 760 mmWhy does the Hg stay in the tube, defying gravity?
3 Air PressureWhy does a barometer measure lower air pressure when a storm is approaching?Lower air pressure means the weight of air being pulled toward the earth is lowerAir is being pulled UP, so air is rushing into a low (wind)Air pressure is also lower at higher elevationAt 9600 ft, air pressure is only 560 mmLess air pushing down on earth’s surface
4 ManometerThe principle of a manometer measurement depends on the fact that given the same fluid, pressure is the same at equal heights.Pgas= Patm – h OR Pgas= Patm + hManometer is a substitute for a Barometer and both measure mm HgMm Hg =Torr
5 Pressure Standard Atmosphere = 760 torr = 760 mm Hg Pressure = Force/areaSI units of measureForce = NewtonsArea = m2SI unit of measure for pressure is Pascal (Pa)1 Standard atmosphere – 101,325 Pa
6 Gas Laws Boyles Law Charles Law Guy-Lussac’s Law (Not used much) Avogadro’s LawIdeal Gas LawAll Lead To:Gas Stoichiometry
7 Boyles Law Boyle studied pressure and volume PV = k Variation: Temperature constantAmount of gas constantVariation:V=k/PP=k/VBoyles Law is also frequently written and used as:P1V1 = P2V2
8 Charles Law Studied relationship between pressure and temperature Determined that plots of volume vs. temperature are linearV = bTConstant pressureConstant amount of gasNOTE: gas cannot have a negative volume, so temperature cannot be negative. Thus we MUST use Kelvin scale for temperature at all times.More on this laterVariations:V/T=b
9 Charles Law Charles Law is also frequently written and used as: V1/T1 = V2/T2
10 Avogadro’s LawPostulated that equal volumes of gases at the same temperature and pressure contain the same number of ‘particles’.Avogadro’s LawV = ana = proportionality constantN = number of moles of gasVariations:V/n = a (constant)
11 Combined Gas Law Assumes constant amount of gas PV/T = k Or P1V1/T1 = P2V2/T2
12 Ideal Gas Law Boyles Law: V = k/P (constant T & n) Charles Law: V = bT (constant P & n)Avogadro’s Law: V=an (constant P & T)Combined: V = R(Tn/P)Or PV=nRTR is universal gas constant ( L*Atm/mole*K)MAKE SURE ALL TEMPS ARE IN KELVINThis is the IDEAL GAS LAWReal gasses behave somewhat differently
13 Gas StoichiometryMolar volume of a gas = L at standard temperature and pressureSTP (standard temperature and pressure)0ºC (273K)1 atm (760 torr or 760 mm HgUsing gas density:Density = mass/volumePV=nRT P = nRT/V
14 Gas Stoichiometry Using Density Density = mass/volumePV=nRT P = nRT/Vn = mass/molar mass =m/molar massP = (m/molar mass)RT/VP = mRT/V(molar mass)m/V = density (d)P = dRT/molar massMolar mass = dRT/P
15 Dalton’s Law of Partial Pressures Applies to GassesFor a mixture of gasses in a container, the total pressure is the sum of the pressures that each gas will exert if it were alonePTOTAL = P1 + P2 + P3+…..PTOTAL = n1RT/V + n2RT/V + n3RT/V….Equals (n1 + n2 + n3 + …)RT/VEquals NtotalRT/V
16 Collecting Gas Over Water Whenever you collect gas over water, water vapor is present:Water molecules escape from surface of waterPressure due to water, depends on temperature, and is the vapor pressure of water.Total pressure of gas collected is Pressure of gas + pressure of water vapor
17 Kinetic Molecular Theory A theory summarizes observed behaviorA model allows you to use theories to predict behaviorAlso can be viewed as a way of understanding, a way of thinking, a mental constructKMT is a model based on gas laws
18 Kinetic Molecular Theory Particles are so small compared to distances between the particles that the volume of the particles can be assumed to be negligible (zero).The particles are in constant motion. Collisions of the particles with the walls of the container are the cause of pressure exerted by the gas.The particles are assumed to exert no forces on each other; they are assumed to neither attract nor repel each other.The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.
19 Boyles Law If volume decreases, pressure increases. KMT says a decrease in volume means the particles will hit the wall more often
20 Pressure and Temperature Ideal Gas Law: Pressure is directly proportional to temperatureKMT: as temperature increases;Speeds of particles increasesParticles hit wall with greater forceParticles hit walls with greater frequencyResult: increased pressure
21 Charles LawIdeal Gas Law: at constant pressure, volume of gas is directly proportional to temperature KelvinKMT: When heated;Speed of molecules increasesHit walls with greater forceHit walls with greater frequencyOnly way to keep pressure constant is to increase volume
22 Avogadro’s LawIdeal Gas Law: Volume is directly proportional to number of particles presentConstant temperature & pressureKMT: If you add more particles to a container;Pressure would increaseOnly way to maintain pressure is to increase volume
23 Dalton’s LawDalton: Total pressure is the sum of the partial pressuresKMT: Assumes;all gas particles are independent of each otherVolumes of individual particles are unimportantIdentities of particles do not matter
24 Deriving Ideal Gas Law Apply particle physics to assumptions of KMT: Use definitions of velocity, momentum, force, pressureSee Appendix 2 for detailsKE = 1/2 mv2 where v is root mean squared speed.Total kinetic energy is KE = NA(1/2 mv2) where N is Avogadro's numberFinal derivation is: P = 2/3 (n NA(1/2 mv2) / V)
25 What is Temperature? KMT bases temperature on Kelvin Because it is based on average kinetic energy of the particlesRequires an absolute energy scaleHence: Kelvin
26 Problem:Calculate the average kinetic energy of the CH4 particles in a sample of CH4 gas at 273K and at 546K
27 Thursday Effusion and Graham’s Law Diffusion Real Gases and van der Waal’s equation.
28 Effusion & Diffusion Diffusion – the mixing of gases without agitation Effusion – passage of a gas through a tiny orifice (hole)
29 Effusion Graham’s Law of Effusion √M2 Rate of Effusion for gas 1 √M1 = M1 and M2 are molar masses for the gases.
30 Diffusion Diffusion takes a long time Even though molecules are travleing 450 and 660 m/sWhy?Tube is filled with airLots of collisions with air that don’t lead to a reactionDifficult to describe theoretically
31 NextReal GasesCorrections for pressureCorrections for volume
32 Real GasesIdeal gas behavior is best thought of as the behavior approached by real gases under certain conditions.Ideal gas behavior fails at:Low temperaturesHigh pressuresReal gases behave most like ideal gases at:High temperatureLow pressure
33 Real Gases Ideal gas assumption of volume is incorrect: Molecules always take up some space.Correct for volume by subtracting volume for the moleculesVREAL = VIDEAL-nbn is number of molesb is an empirical correction constantSo:P’ = nRT/(V-nb)
34 Real GasesBut we still have to correct for the fact that real gases DO have attraction forces.Effect is to make observed pressure POBS smaller than it normally would if there were no attractions:POBS = (P’ – correction factor)(nRT/(V-nb) – correction factorSize of correction factor depends on concentration of the gas molecules in particles per liter (n/V)Higher concentration, more likely particles are close enough to attract. Depends on square of number of particles because 2 particles have to get close enough.
35 Real GasesSo:POBS = P’ – s(n/V)2Inserting correction factors for both volume and attractions gives the equation:POBS = (nRT/(V-nb)) – a(v/V)2Pressure correction factorVolume of containerVolume correction factor
36 Van Der Waals EquationPOBS + a(n/V)2 x (V-nB) = nRT