1Chapter1StateofSubstances1

Gas1-1TheIdealGasEquationofState1-2Dalton’sLawofPartialPressures1-3TheKinetic-MolecularTheory

1-4RealGases2Liquid2-1EvaporationofLiquids2-2VaporPressure,C-Cequation2-3BoilingPointofLiquid3Solid24Plasma(等離子體)等離子體即指其中離子所帶的正、負電量是相等的[地球上只能在實驗條件下產生]氘氣，D2→D2++e－自然界中大量存在，宇宙中絕大多數（大于99%）的物質是以等離子狀態存在的，地球電離層、極光、閃電。35Superhidensity(超高密度態)Atveryhighpressures(greaterthan200atm),somegaseousmixturesconsistofmorethanonephase.Eg.heliumandxenon在高壓下物質的結構會產生很大的變化例1：絕緣→導體，半導→導→超導例2：104Pa下，95℃的會凝固成冰（熱冰）例3：106Pa時，H2(l.)可導電，并具有穩定的電導率41

Gas1-1TheIdealGasEquationofState(1)IdealGasItisanidealmodel:Agaswhichhasquantitybutnovolume,withoutinteractions,withoutlosingkineticenergywhencollideswitheachother.具有質量的幾何點，只有位置而不占有體積，分子間無相互引力，發生碰撞沒有動能損失.Underhightemperatureandlowpressure(T>0℃；P~severalatmospherepressures，P→0)Thedistanceamongmoleculesaremuchbiggerthanthemoleculesize,whichmeansthatcomparedwiththegasvolume,themoleculevolumeisverytiny.Interactionsamongmoleculescanbeneglected.5(2)TheIdealGasEquationofStateBoyle'slawV=constantB/P(T,nconstant)Charles'slawV=constantC

×T(P,nconstant)Avogadro'slawV=constantA

×n(T,Pconstant)

V=aconstant(Tn/P)

PV=nRT

6PV=nRT

P---PaV---m3n---molT---K(Kelvin)R--gasconstantR=PV/nT

=(1atm)(22.4141L/(1mol)(273.15K)=0.082atm·L/mol·K

=8.314J/mol?K7CalculateρandM：PV=nRT=mRT/Mρ=m/V=PVM/RTV=PM/RT

M=ρRT/P8Example:It’sfoundthat0.896gofapuregaseouscompoundcontainingonlyNandOoccupies0.524Latapressureof0.973×105Paandatemperatureof28.0℃.Whatarethemolecularweightandmolecularformulaofthegas?Solution：n=m/M=PV/RT∴M=mRT/PV=0.896×8.314×301/(0.973×105×0.524×10-3)=43.98g/mol∴ThemoleculeisN2O.91-2Dalton’sLawofPartialPressurespartialpressure:thepressureofeachgasinamixture.Ptotal=P1+P2+…=∑Pi

∵P1V=n1RTP2V=n2RT…PiV=niRTPtotalV=(P1+P2+…+Pi)V=(n1+n2+…+ni)RT=ntotalRT∴Pi/Ptotal=ni/ntotal=XiPi=Ptotal·Xi

Xi:molarfraction（摩爾分數）10Example:Whenamixtureofpotassiumchlorateandmanganesedioxidewasheatedtodecompose,itsquantitydecreased0.480gandanoxygenof0.377dm3wasobtainedbydrainingwatermethod(排水集氣法)。Thetemperatureis294Kandpressureis9.96×104Pa.Pleasecalculatethemolecularweightofoxygen.(Andthesaturatedvaporpressureis2.48×103Pa.)Solutions：

MnO2,△2KClO3(s.)→2KCl(s.)+3O2↑MO2=mO2/nO2

Ptotal=PH2O+PO2

∴PO2=Ptotal－PH2O=9.96×104－2.48×103=9.71×104(Pa)nO2=PO2·Vtotal/RT=9.71×104×0.377×10－3/(8.314×294)=0.0150(mol)MO2=mO2/nO2=0.480/0.0150=32.0(g/mol)

11Example:AsampleofPCl5(g.)weighing2.69gwasplacedina1.0Lflaskandcompletelyvaporizedattemperatureof250℃.Thetotalpressureobservedatthistemperaturewas1.00atm.ThepossibilityexiststhatsomeofthePCl5mayhavedissociatedaccordingtotheequationPCl5(g.)=PCl3(g.)+Cl2(g.)WhatmustbethefinalpartialpressuresofPCl5,PCl3andCl2undersuchexperimentalconditions?Solutions：nPCl5=2.69/MPCl5=2.69/208=0.0129(mol)P=nRT/V=0.0129×8.314×523/10－3=5.609×104(Pa)SinceP<1.00atm，somedissociationofPCl5musthaveoccurred.

12

PCl5(g.)=PCl3(g.)

+Cl2(g.)

t=00.012900te0.0129－nnnPV=ntotalRT∴ntotal=PV/RT=1.013×105×1×10-3/(8.314×523)=0.0233=0.0129+n∴n=nPCl3=nCl2=0.0104molPPCl3=Ptotal×nPCl3/ntotal=1.013×105×0.0104/0.0233=0.4520×105(Pa)PCl2=PPCl3PPCl5=1.013×105×(0.0129－0.0104)/0.0233=0.1087×105(Pa)13Whenthetemperatureandpressureisconstant,thetotalvolumeofamixtureofgasesisequaltothesumofthepartialvolumesofthegasesinthemixture.Vtotal=V1+V2+…Xi=Vi/VtotalProof：

PV1=n1RTPV2=n2RTPVi=niRTP(V1+V2+…+Vi)=(n1+n2+…+ni)RTPVtotal=ntotalRT∴Vi/Vtotal=ni/ntotal=Xi14Severalquestionsconcerninggasmoleculesmovement:Howtomove?TherelationsamonguandP、V、n、TThedistributionofuIfu>100m/s,whywecannotsmelltheodorofH2Sinstantly?151-3TheKinetic-MolecularTheory

----AModelforGasBehavior(1)SupposeGasiscomposedofmolecules.Moleculesareinconstantmotion,inarandomway.0~lightspeed3×108m/sAlldirectionsSpeedchangesrapidlyMoleculesdon’taffecteachotherexceptelasticcollision.16（2）TheKinetic-MolecularTheorySupposingthatthereareNgasmoleculeswhoseweightisminacubelmonanedge，1/3moveupanddown,1/3movebackandforth,and1/3moverightandleft.今考慮一個分子，速度為u1左右運動,該分子每撞壁一次動量改變的絕對值為2mu1,△t=2l/u1

單位時間內動量的變化就是力

F=2mu1/△t=mu12/l17N1+N2+N3+…=N/3速度平方的均數

18rootmeansquarespeed(根均方速率)19玻爾茲曼常數k=R/N0=1.38×10-23J/KMeaningoftemperature：T∝EvEv∝TAtcertaintemperature,theaveragekineticenergyisthesame.20(3)ApplicationsDeducePartialPressureLawandDiffusionLawCalculatethespeedofmolecule21DiffusionLawIn1831GrahamdiscoveredthatifTandPisconstant,

M=ρRT/P

∵EA=EB2223Example:Calculatetheroot-mean-squarespeedofH2Smoleculeat298K.Solution:24Table.Theroot-mean-squarespeedofsomemoleculesat298K

MoleculeSpeed(m/s)H21930He1360H2O642O2482H2S468Ar431CO2411Xe23825(4)speeddistribution——speeddistributionfunction

就大量分子而言，一定條件下、T一定，每個分子的u隨時不斷地改變，完全是偶然的、隨機的。求單個分子的速率不僅沒有意義，而且不可能，速率分布遵循統計規律。我們可以求出u→u+△u內分子數△Nu：△Nu∝N·△u△Nu還與u有關.例：10～20m/s,410～420m/s，△u=10m/s；關系復雜，不是簡單的正比例關系。用一個由u表示的函數f(u)來表示。

△N=Nf(u)△uf(u)=△N/(N△u)物義：分布在速率u附近單位速率間隔內的分子數占總分子數的比率(百分數).26Themostprobablespeed最可幾速率AveragespeedTheroot-mean-squarespeedF(u)2728explanations：①u=0oru→∞，little；whiletherearemanymoleculeswhosespeedsuareinmiddle②Theareaunderthecurveis1③u→u+△u之間的陰影面積表示速率為u→u+△u的分子數占總分子數的分數29Figure1.2Distributionofmolecularspeeds30④Atthesametemperature，thespeeddistributionofdifferentgasesO2,N2,H2O,H231(5)Energydistribution（whichissimilartospeeddistribution)321-4RealGases

(1)compressibilityfactorPV/nRT

333435(2)VanderWalls(范德華方程)

1873年，荷蘭Vanderwalls分析引起偏差的兩個原因：實際氣體分子自身體積，使分子可以活動的空間減小，V－nb分子間作用力，使得分子不能全力以赴的碰撞器壁內層分子對碰撞器壁分子的引力和內部分子的密度成正比，也和碰撞的外層分子的密度成正比P內∝(n/V)2，即P內

=a(n/V)2修正：(P+an2/V2)(V－nb)=nRT

實際氣體碰撞氣體所產生的壓力<理想氣體碰撞氣體所產生的壓力36（3）liquefraction（液化作用）Experimentsshow：①T↓Eg.N2bp.=-196℃②T↓andP↑，criticalconstant(臨界常數)Tc：加壓下使氣體液化的一定TPc：在Tc時所需的最低PVc：在Tc、Pc時1mol氣體所占的VLowTcindicatesthegasisdifficulttobeliquefied,whichhassomerelationshipwithmolecularstructure.37Non-polarmolecules,suchasHe、H2、N2、O2，interactionsamongmoleculesareverysmall,thustheyaredifficulttobeliquefied.Eg.N2Tc=126K（-147℃）,Pc=3.39×106Pa≈30atmCO2Tc=304.1K（31℃）,Pc=7.39×106Pa≈70atm38當氣態物質處于Tc、Pc和Vc時，氣、液T>Tc氣相T=Tc兩者無別，不夠穩定的特殊狀態。（液態）T<Tc氣、液共存392Liquid2-1EvaporationofLiquids(1)vaporpressure

referstothepressureofliquidvaporformedbyevaporationofliquidinaclosedcontainer.與其本身的液體同在一處的氣體，其壓力叫蒸氣壓。40(2)Saturatedvaporpressure

Themaximumpressureofaliquidvaporformedbyevaporationoftheliquidinaclosedcontainerdependsonlyonthetemperatureoftheliquid.當V蒸=V凝時，動態平衡，此時的蒸氣叫飽和蒸氣，所產生的壓強只與液體本身及T有關，與液面上方空間的V、液體的量無關。41Et2O,Acetone,EtOH,H2O42同一液體，T↑，Ni↑（Ek大的），逸出的分子數↑，P↑同一溫度下，液體分子間作用力強，分子難以逸出，蒸氣壓P就小。eg.作用力H2O>C2H5OH>CH3COCH3>(C2H5)2O∴同一溫度321K時P：H2O<C2H5OH<CH3CO