化學課件】chapter 5 chemical equilibrium

1、O返回 Chemical EquilibriumO返回5.1 The conditions of chemical equilibrium and affinity of chemical reaction 5.2 The equilibrium constant of a reaction and isothermal equation 5.3 Heterogeneous chemical equilibrium 5.4 Determination of equilibrium constants 5.5 The standard Gibbs function of formationO返回

2、5.8 Coupling reaction5.7 Chemical equilibrium of simultaneous reaction5.6 The response of reactions to the conditionsExpress mathematically how the equilibrium constant depends on the temperature, and derive and use the vant Hoff equation.O返回 We have seen that the natural direction of all change at

3、constant temperature and pressure is towards minimum Gibbs function. The idea is entirely general, and in this chapter we use it as a basis for the discussion of chemical transformations.O返回Is the natural tendency for the mixture A+B to go to the mixture C+D, or the opposite? This can be answered by

4、 calculating the Gibbs function of each mixture.If the sum of the Gibbs functions of A+B is higher than that of C+D, then the reaction has a tendency to roll from left to right.O返回Suppose a reaction：DEFGdefg BBddnBBddnBased on extent of reaction：BBB0Or:O返回BBBddddnpVTSG,BBBBBBdddT pGn （）BB(dd )nAt co

5、nst. T and P，,BBB() (a) TpG ：1 molrm,BBB (b) TpG（）O返回 ,Brm,B() , ()T pBT pGG 或 rm,()0T pGThe reaction spontaneously proceeds from left to right.rm,()0T pGThe reaction spontaneously proceeds from right to left.rm,()0T pGThe reaction is at equilibrium.Use to determine:O返回0)(,pTGFrom left to right0)(,p

6、TGFrom right to left0)(,pTGAt equilibriumPTG,is the slope of G with recpect to the extent of reaction .O返回O返回O返回 1922年，比利時熱力學專家德唐德（De donder）首先引進了化學反應親和勢的概念。他定義化學親和勢A為： def ,BBB ()T pGA mr-GA或 A是狀態(tài)函數(shù)，體系的強度性質(zhì)。用A判斷化學反應的方向具有“勢”的性質(zhì)，即：A0 反應正向進行 A0 反應逆向進行A=0 反應達平衡O返回The simplest assumption is to suppose t

7、hat the species are perfect gases, in which case their chemical potentials are determined by their partial pressures:ABmrabGaAAbBBPPRTaPPRTblnlnO返回mrGaAbBABPPPPRTab/lnaAbBmrPPPPRTG/ln0 - Reaction proceeds - Reaction is at equilibriumO返回BBB,mr)(pTGBBBBBB( )lnfTRTp $BBB( , )( )lnfT pTRTp$rmBBB( )( )GT

8、T $Brm,rmBB()( )lnT pfGGTRTp $ is the standard molar Gibbs function of the reactionrm( )GT$fB is the fugacity of BSubstituting this expression, givesO返回ghGHrmdeDrEm(/) (/)( )ln(/) (/)fpfpGTRTfpfpG $rm( )lnfGTRTQ $DEGHdegh Reaction:Where Q is the reaction quotient.O返回When the reaction is at equilibri

9、um， 0mr GghGHrmdeDE(/) (/)ln(/)(/(fpfpRTfpfTpG $lnfRTK $ is the thermodynamic equilibrium constant.fK$ It should be noticed that vides a way of measuring the standard Gibbs functions of reactions.O返回Use the vant Hoff equation：rmlnlnffGRTKRTQ $rmlnlnppGRTKRTQ $For pg reaction:rm0ppKQG$ from lef

10、t to rightrm0ppKQG$from right to leftrm0ppKQG$at equilibrium.O返回Subscript m denoting the extent of reaction is unity i.e. 1 mol .rm( )G T$fK$rm( )lnfGTRTK $rm,2rm,12GG$2,2,1()ffKK$Example：HI(g)2g)(Ig)(H22HI(g)g)(Ig)(H221221（1）（2）is referred toO返回Distinguish the thermodynamic equilibrium constant fro

11、m pressure and composition equilibrium constants. Example：DEGHdeghBHGBdBDEghpeppKppp pK1. Pressure equilibrium constantwhen0BpK(Dimension is unity)O返回BHGBBDEghxdexxKxxxBBpKKpxxK2.mole fraction equilibrium constantA pg obeys Dolton partial pressure law，BBpxp O返回BHGBBDEghcdeccKcccBB)(RTKKpccK3Concentr

12、ation equilibrium constant pg，cRTpO返回BBBaKa ，BBBcac$BB()acrKKKc$aK 4Activity equilibrium constantO返回aAbBmrPPPPRTKG/ln)298(KRT lnaAbBPPPPK/)(abaAbBPPP)()(abPPK)()()()(abaAbBPRTCRTC)()(abaAbBRTPCC)()(abCRTPK)(/abaAbBRTCPCCCCO返回32CaCO (s)CaO(s)CO (g)2(CO )/pKpp$is dissociation pressure )CO(2p) s (CaCO3

13、Consider a reactionEquilibrium between ideal gas and pure condensed phases: If the substances taking part in the chemical equilibrium is of more than one phase, O返回S(g)H)g(NHHS(s)NH234example：S)H()NH(23ppp32(NH )(H S)ppppKp$214(/)p p$It is said earlier that chemical potentials of condensed phases ar

14、e insensitive to the pressure change, unless the pressure is very large.O返回G concentrates our attention on the system, and lets us avoid having to think explicitly about the entropy of the surroundings. In an isothermal change G can be related to the enthalpy and entropy changes of the system by BGG

15、mfBmrO返回rmlnaGRTK $rmexp(/)aKGRT$ Using rGm , calculate the thermodynamic equilibrium constant:O返回22rm(1) C(s)O (g)CO (g)(1)G$122rm2(2) CO(g)O (g)CO (g) (2)G$12rm2(3) C(s)O (g)CO(g)(3)G$rmrmrm(3)(1)(2)GGG $(1)(3)(2)pppKKK$(1) - (2) 得（3） 2. 計算實驗不易測定的平衡常數(shù)例如，求 的平衡常數(shù)122C(s)O (g)CO(g)O返回3近似估計反應的可能性rmrmln

16、pGGRTQ $只能用 判斷反應的方向。但是，當 的絕對值很大時，基本上決定了 的值，所以可以用來近似地估計反應的可能性。0,mrf)(wpTGrmG$mrGO返回fmG$（B,T）Define the Gibbs function of reaction and calculate it from tables of Gibbs function of formation.Calculate the equilibrium constants for reactions on the basis of the Gibbs function information given in Table

17、 X.X.O返回fmG$rmBfmB(B)GG$rmG$ At T(1)mrmrSTHdTCKHmpTKrmr,298)298()198(298,TKmprmrTdTCKSTO返回If the equilibrium constant is known at a temperature T*, its value at another temperature T can be found as follows. In each caseRTTGTKmr)()(lnRTTGTKmr)()(lnO返回Subtracting these relates the two equilibrium con

18、stants:RTTGRTTGTKTKmrmr)()()()(lnNow write G = H - T S, and make the approximation that neither H nor S changes significantly over the temperature range of interest:O返回RTSRTTHRTSRTTHTKTKmrmrmrmr)()()()()()(lnTTRTHmr11)()()(lnTKTKThe last equation is very remarkable because it predicts the shift in e

19、quilibrium when the temperature is changed; all we need to known is the standard molar enthalpy of reaction.O返回2)(THTTGmrpmrfmrKRTGlnfmrKRTGlnpfTKR)ln(2lnRTHdTKdmrfO返回The infinitesimal expression of vant Hoff relationrm2dlndpKHTRT$對吸熱反應，升高溫度，增加，對正反應有利。rm0H$pK$對放熱反應，升高溫度，降低，對正反應不利。pK$rm0H$O返回If we as

20、sure that does not depend on the temperature this equation integrates to rmH$2rm121()11ln()( )ppKTHRTTKT$CRTHKmrflnO返回當理想氣體用濃度表示時，因為 ，可以得到pcRTrm2dlndcKUTRT$2rm121()11ln()( )ccKTURTTKT$這個公式在氣體反應動力學中有用處。O返回Provides a way of measuring the enthalpy of a reaction without using a calorimeter, but in pract

21、ice it is inaccurate.Equilibrium compositions are measured over a range of temperatures (at constant pressure), and lnK is plotted against 1/T. It follows from eq.that the slope is -Hm/R.O返回 Le chatelier原理，增加壓力，反應向體積減小的方向進行。這里可以用壓力對平衡常數(shù)的影響從本質(zhì)上對原理加以說明。BBB()ppKp $BppyBB)(Bppky)()ln(lnlnlnppkKBByTpK)ln

22、(Typk)ln(pB= 0O返回Typk)ln(pB00BaA=bB0abab O返回 對于分子數(shù)增加的反應，加入水氣或氮氣，會使反應物轉(zhuǎn)化率提高，使產(chǎn)物的含量增加。)ln(lnlnlnppkKBByBBBByBBBnnykBnknpTnpTnknK,)ln()ln(0nBO返回 在一個反應體系中，如果同時發(fā)生幾個反應，當?shù)竭_平衡態(tài)時，這種情況稱為同時平衡。 在處理同時平衡的問題時，要考慮每個物質(zhì)的數(shù)量在各個反應中的變化，并在各個平衡方程式中同一物質(zhì)的數(shù)量應保持一致。O返回例題：600 K時， 與 發(fā)生反應生成，繼而又生成，同時存在兩個平衡：3CH Cl(g)2H O(g)3CH OH32(

23、CH ) O32333 22(1) CH Cl(g)H O(g)CH OH(g)HCl(g)(2) 2CH OH(g)(CH ) O(g)H O(g)已知在該溫度下， 。今以等量的 和開始，求 的平衡轉(zhuǎn)化率。,1,20.00154,10.6ppKK$3CH Cl2H O3CH ClO返回解：設(shè)開始時 和 的量為1.0，到達平衡時，生成HCl的量為x， 生成 的量為y，則在平衡時各物的量為：3CH Cl2H O32(CH ) O323(1) CH Cl(g)H O(g)CH OH(g)HCl(g)112xyxxyx3322(2) 2CH OH(g)(CH ) O(g)H O(g) -2 1- x

24、yxyyO返回因為兩個反應的 都等于零，所以pxKK$BB,1,22(2 )0.00154(1)(1)(1)10.6(2 )ppxy xKxxyyxyKxy $將兩個方程聯(lián)立，解得 。 的轉(zhuǎn)化率為0.048或4.8 。0.048, 0.009xy3CH ClO返回 It can be seen quite often that certain reactions are not spontaneous i.e. G 0. But if the same reactions are coupled to other reactions, which are spontaneous, the or

25、iginal reactions become feasible. This can only be possible if the total free energy change I.e., sum of the free energies of the second and the original reaction is negative.O返回例如：在298.15 K時：-12242rm,1 (1) TiO (s)2Cl (g)TiCl (l)O (g) 161.94 kJ mol G$反應(1)、(2)耦合，使反應(3)得以順利進行。-122rm,2(2) C(s)O (g)CO

26、(g) 394.38 kJ molG $-1rm2242,3 (3) TiO (s)C(s)2Cl (g)TiCl (l)CO (g) 232.44 kJ mol G 則$O返回The standard Gibbs free energy for the forward reaction is related to the equilibrium constant by the expression: The H can be obtained from the variation of lnK with temperature:The S is then calculable as O返回1

27、 的估算rm( )GT$r(298.15 K)T rrrmrmrmrmrmrrmrmr( )( )( )( )()d( )()dTpTTpTGTHTTSTHTHTCTCSTSTTT $當 不大，或不要作精確計算時，設(shè) ，則：pC0pCrmrmrrmr( )()() GTHTTSTabT $這里實際上設(shè)焓和熵變化值與溫度無關(guān)，從298.15 K的表值求出任意溫度時的 值。rmG$O返回For an equilibrium between a liquid A and a gas A (the vaporization and condensation of A):)()(glAAAt P ,T;

28、lglgmrG)ln(PPRTAggplgPgg)ln(PPRTAO返回2估計反應的有利溫度rmrmrm( )( )( )GTHTTST $ 通常焓變與熵變在化學反應中的符號是相同的。要使反應順利進行，則 越小越好。rm( )GT$rmrm(1) ( )0, ( )0HTST$提高溫度對反應有利。rmrm(2) ( )0, ( )0HTST$降低溫度對反應有利。The endO返回JACOBUS HENRICUS VANT HOFF (1852-1911) Dutch physical chemist,received the first Nobel Prize in chemistry in

29、 1901 for “the discovery of the laws of chemical dynamics and of osmotic pressure.” Vant Hoff was one of the early developers of the laws of chemical kinetics,developing mehtods for determining the order of a reaction;he deduced the relation between temperature and the equilbrium constant of a chemi

30、cal reaction. O返回In 1874, vant Hoff (and also J.A. Le Bel, independently) proposed what must be considered one of the most important ideas in the history of chemistry, namely the tetrahedral carbon bond. Vant Hoff carried Pasteurs ideas on asymmetry to the molecular level , and asymmetry required bo

31、nds tetrahedrally distributed about a central carbon atom. Structural organic chemistry was born.O返回JOHN DALTON (1766-1844)English chemist, physicist, and meteorologist, is considered by many to be the “father of the atomic theory of matter,although grandfather is perhaps a more he suffered. In 1803

32、, he published his paper “Absorption of Gases by Water and Other Liquids,” in which he presented what is now known as Daltons law of partial pressures. O返回He was led to his theory of atomism by his studies of gases. In one of his papers published in 1805, he said, “Why does not water admit its bulk

33、of every kind of gas alike?The circumstance depends on the weight and number of the ultimate particles of the several gases.” John Dalton was led to the atom by reflecting that different gases had different values of the Henrys law constant.忿鏅獉酆奌殼貫蚇洉垢驁匧鉻嘧靿螒翌堪椐姬椸卝炊淪浂鯰霄輢鏹箆摯熙丄庳榠浝鋌鉉傜瞰啷疰棊澗搡竽粵耒坎馪鸞倬幰騡澈蘋鎯蒪氙

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