1、Physical ChemistryThe Properties of GasesDefinition of Physical ChemistryPhysical chemistry stands in the same relation to the subdivisions of chemistry in which philosophy stands toward all the sciences.Its main object is to unify thought within the science of chemistry;therefore,it might well be n
2、amed,the“philosophy of chemistry”-S.L.Bigelow,1912The Properties of GasesEquations of StateBulk Variables Volume-m3 Pressure-Pa Temperature-K Composition-molesVolume length3 units m3 or cm3 liter=1000 cm3 molar volume Vm=V/n1 m1 m1 mPressure Force/Area units Pascal=Newton/m2=Joule/m3 atmosphere=1013
3、25 Pa bar=100000 Pa mm Hg torrhTemperature thermometryT Volume only for an ideal gas or real gases in the low pressure limit Composition moles:niS ni=n mole fraction:xiS xi=1 partial pressure:piS pi=pEquations of State P,V,T,and n are not independent.Any three will determine the fourth.An equation o
4、f state is an equation that relates P,V,T,and n for a given substance.Gases have the simplest equations of state.The simplest equation of state is the ideal gas law,pV=nRTIdeal Gas Law p=pressure V=volume n=moles T=temperature R=universal gas contant=0.08206 L-atm/mol-KnRTpV Partial Pressure pA=part
5、ial pressure of gas A V=total volume nA=moles of gas A T=temperature R=universal gas contant=0.08206 L-atm/mol-KRTnVpAADaltons Law The total pressure is the sum of all the partial pressure.pVnRTnVRTVRTnpJJJJJJIdeal Gas Model Molecules may be treated as point masses relative to the volume of the syst
6、em.Molecular collisions are elastic,i.e.kinetic energy is conserved.Intermolecular forces of attraction and repulsion have negligible on the molecular motion.Compressibility The compressibility of a gas is defined by If the gas behaves ideally,then Z=1 at all pressures and temperatures.For real gase
7、s,however,Z varies with pressure,and deviates from its ideal valueRTpVZmArgon Compressibility 273 K 0.00.51.01.52.02.502004006008001000pressure(atm)ZZ=pVm/RTattractiverepulsiveIntermolecular Forces-3-2-1012341.52.02.53.03.54.0distanceEnergyattractiverepulsiveTaylor Series0220221=(0)f and=(0)f where)
8、0(f+)0(f +)0f(=)f(xxdxfddxdfxxxTaylor Series Example 32321x-112(0)f12)(f1(0)f11(x)f1f(0)11f(x)xxxxxxxConvergence of(1-x)-1x1+x1+x+x21+x+x2+x3(1-x)-10.01 1.0101.0101.0101.0100.10 1.1001.1101.1111.1110.20 1.2001.2401.2481.2500.30 1.3001.3901.4171.429Virial ExpansionZ pZB pC ppVRTB pC pBCm()()0122where
9、 second virial coefficientthird virial coefficienttcoefficien virial third=tcoefficien virialsecond=where/1)/1()/1()0()/1(22CBVCVBRTpVVCVBZVZmmmmmmVirial ExpansionRelation of p and 1/V Expansions22RTBCCRTBBSecond Virial Coefficients B 100 K 273 K 373 K 600 K He 11.4 12.0 11.3 10.4 Ar-187.0-21.7-4.2
10、11.9 N2-160.0-10.5 6.2 21.7 O2-197.5-22.0-3.7 12.9 CO2 -149.7-72.2-12.4 cm3/moleVirial Expansion Advantages fits gas data as accurately as desired.uses the ideal gas law as a base.Disadvantages infinite number of terms.virial coefficients are temperature dependent.van der Waals Equationpa VVbnRTVVbp
11、pa Vmmm effmeffm/,22repulsionattractionvan der Waals EquationpRTVbaVmm2van der Waals constants a(dm6 atm mole-1)b(dm mole-1)He 0.034 0.0237 Ar 1.345 0.0322 N2 1.390 0.0391 O2 1.360 0.0318 CO2 3.592 0.0427 Successive ApproximationVRTpaVbmm2“Solve”the van der Waals equation for V.Use an intial estimat
12、e to evaluate the right hand side.Use this calculated value of V as a better estimate.Repeat till converged.Ideal Gas Isotherms0501001502000.01.02.03.04.05.0100K4000K2000K1000K500KVm/Lp/atmvan der Waals Isotherms-Ar-100-500501001502000.000.100.200.300.40Vm/Lp/atm100K150K200K500KCritical Constants pc
13、 (atm)Vm,c (cm3)Tc (K)He 2.26 57.76 5.2 Ar 48.00 75.25 150.7 N2 33.54 90.10 126.3 O2 50.14 78.00 154.8 CO2 72.85 94.0 304.2 Inflection Points-500050010001500-10-50510 xy y y(x)Inflection PointsAt the inflection point x and 0dydxd ydxx xx x000022Carbon Dioxide Critical Isotherm01002003004005006000.00.10.20.30.4Ideal GasReal Gas304 KVm/Lp/atmvan der Waals Inflection PointdpdVRTVbaVd pdVRTVbaVVbpabmmmmmmm cc()()/,232234220260327solution:and 11112222VbVbVbVpRTVba RTVbVmmmmmmm/van der Waals Virial Expansion
