3-化學平衡、離子對與絡合

1、水文地球化學,主講：郭清海,中國地質大學（武漢）環(huán)境學院,一門關于地下水的科學,化學平衡、離子對與絡合Chemical equilibrium, Ion Pairing and Complexing,水是極性分子，是一種溶解能力很強的溶劑它與包氣帶及含水層中的巖石(土)接觸時，必定會發(fā)生溶解-沉淀反應、氧化還原作用、界面反應作用，這些反應是控制地下水化學成分形成和演變的重要作用。發(fā)生在地下水系統(tǒng)中的水-巖相互作用一般為可逆反應可

2、逆反應的進程符合化學平衡原理，可以用質量作用定律描述。,第一節(jié) 化學平衡,質量作用定律化學反應的驅動力與反應物和生成物的濃度相對大小關系相關發(fā)生在地下環(huán)境的水-巖相互作用同樣受到質量作用定律的控制,,理想溶液與活度,A、理想溶液,理想溶液：溶液中離子之間或分子之間沒有相互作用。地下水是一種真實溶液，不是理想溶液；水中離子（或分子之間）存在各種相互作用，包括相互碰撞及靜電引力作用。作用的結果是，化學反應相對減緩，一部分離子

3、在反應中不起作用了。因此，如果仍然用水中各組分的實測濃度進行化學計算，就會產生一定程度的偏差。為了保證計算的精確程度，就必須對水中組分的實測濃度加以校正，校正后的濃度稱為校正濃度，也就是活度。質量作用定律中，濃度是以活度表示的。活度是真實濃度（實測濃度）的函數(shù)，一般情況下，活度小于實測濃度。,理想溶液與活度,A、理想溶液,活度與實測濃度的函數(shù)表示式為：a = γm式中m為實測濃度（mol/L）； γ為活度系數(shù)，其單位是實測濃度

4、的倒數(shù)（L/mol），a為活度，無量綱。但是，在實際應用中，a和m的單位相同，均為mol/L， γ為無量綱的系數(shù)?；疃认禂?shù)隨水中溶解固體（即礦化度）增加而減小，一般都小于1。當水中溶解固體（TDS）很低時，r趨近于1，活度趨近于實測濃度。分子（包括水分子）和不帶電的離子對的活度系數(shù)為1。在化學平衡計算中，規(guī)定固體和純液體的活度為1。,B、活度系數(shù)公式,在水文地球化學研究中，應用最普遍的活度系數(shù)計算公式是迪拜-休克爾（Debye-H

5、uckel）方程：式中：r為活度系數(shù)；Z為離子的電荷數(shù)；I為離子強度（mol/L）；A和B為取決于水的介電常數(shù)、密度和溫度的常數(shù)；a是與離子水化半徑有關的常數(shù)。當I ＜ 0.1時，該方程精確性很高離子強度I的計算公式：式中：I為離子強度（mol/L）；Zi為i離子的電荷數(shù)；mi為i離子的濃度（mol/L）。,對于TDS高（ I大于0.1 mol/L ）的咸地下水、污水來說，迪拜-休克爾方程就不適用了。為此，戴維斯提出了擴大

6、的迪拜-休克爾方程，也稱為戴維斯（Davies）方程：與迪拜-休克爾方程相比，它增加了校正參數(shù)b，且式中的a值與迪拜-休克爾方程式中的a值不同。方程的應用范圍是I＜0.5 mol/L。,B、活度系數(shù)公式,在溫度一定時，K為常數(shù)，固體BaSO4的“活度”為1，所以：[Ba2+][SO42-] = Ksp Ksp稱為溶度積常數(shù)（Solubility Product Constant）。Ksp隨溫度而改變，例如Ba

7、SO4的溶度積，298K時Ksp=1.08×10-10；323K時Ksp=1.98×10-10?？芍狟aSO4的Ksp隨溫度的升高而稍增大。,溶度積常數(shù),溶度積常數(shù)：即難溶鹽的平衡常數(shù)以BaSO4的溶解與沉淀過程為例說明BaSO4 = Ba2+ + SO42-,離子活度積（IAP）和飽和指數(shù)（SI）,離子活度積（IAP）為水溶液中組成某難溶鹽類的陰、陽離子含量之乘積（并不特指反應達到平衡的時刻）與溶度積和離子

8、活度積有關的概念——飽和指數(shù)：SI = IAP/Ksp一般為：SI ＝ lg (IAP/Ksp )用SI可判斷反應方向與進程SI 0時，水溶液過飽和SI = 0時，水溶液處于溶解平衡狀態(tài),仍以BaSO4的溶解與沉淀過程為例說明： BaSO4（固）== Ba2+ + SO42-SI 0時， BaSO4的沉淀速度大于溶解速度，BaSO4溶液處于過飽和狀態(tài)；SI = 0時， BaSO4的沉淀速度等于溶解

9、速度，溶解過程和沉淀過程達到平衡，溶液為飽和溶液。,以SI值判斷礦物的溶解是比較可靠的而用SI值判斷礦物沉淀可能不甚可靠因為有些礦物，特別是白云石和許多硅酸鹽礦物，盡管SI值為比較大的正值，處于過飽和狀態(tài)時，也可能不產生沉淀。例如，雖然海水與白云石處于過飽和狀態(tài)，但無沉淀的趨勢。產生這種情況的化學機理比較復雜，與化學動力學等有很大的關系。一般來說，根據(jù)SI值判斷水與巖石、礦物的反應狀態(tài)，對于地下淡水來說，還是很有用的,飽和指數(shù)的

10、應用,溶度積常數(shù)和溶解度,溶解度：在給定的溫度和壓力下，溶液中某溶解物達到溶解平衡時的總量嚴格說來，物質的溶解度只有大小之分，沒有在水中絕對不溶解的物質。習慣上把溶解度小于0.01g/100g水的物質叫做 “難溶物”,溶度積常數(shù)值可用來估計和比較難溶電解質的溶解度大?。篈B型化合物：AB(固) ＝ A+ + B-平衡時：[A+] = [B-] = S ；Ksp= [A+][B-] = S2AB2或A2B型化合物：AB2(固) ＝

11、 A2+ + 2B- Ksp = [A2+][B-]2 = S·(2S)2 = 4S3AB3型化合物：AB3(固) ＝A3+ + 3B- Ksp = [A3+][B-]3 = 27s4由上述關系可知，相同類型的難溶電解質（例如同是AB型或AB2型）相比，溶度積越小的，溶解度（以摩爾濃度表示）也越小。,溶解度（以S表示；單位：mol/L）和溶度積的定量關系,仍以BaSO4為例加以說明如果在飽和BaSO4溶液中加KNO3

12、，KNO3就完全電離為K+和NO3-離子，結果使溶液中的離子總數(shù)目增加，由于SO42-和Ba2+被眾多的異號離子（K+、NO3-）所包圍，其活動性有所降低。這樣，Ba2+和SO42-有效濃度降低，促使下面的溶解平衡被打破，并向右移動：BaSO4（固）== Ba2++SO4結果為BaSO4的溶解度增加，直至上述溶解反應達到平衡為止，這時Ksp值變大了。這種因加入強電解質而使物質溶解度增大的效應也叫做鹽效應。如果加入的可溶性強電解質的

13、濃度很小，例如溶液的離子強度值＜10-3 mol/L，則可以不考慮鹽效應對難溶性強電解質Ksp值的影響。,鹽效應,一種礦物溶解于水中，如水溶液中已有或加入了某種離子與該礦物溶解后產生的離子相同，則礦物的溶解度將降低。仍以BaSO4為例加以說明：如果在飽和BaSO4溶液中加BaCl2，Ba2+的濃度將上升。這樣，Ba2+和SO42-的離子積將大于活度積，促使下面的溶解-沉淀平衡被打破，并向左移動：BaSO4（固）== Ba2++SO

14、4結果為BaSO4的溶解度減小，直至上述沉淀反應達到平衡為止。這種因加入相同的離子而使物質溶解度減小的效應也叫做同離子效應。如水溶液中同時存在同離子效應與鹽效應，前者對溶解度的影響要大得多。,同離子效應,熱力學體系的性質、狀態(tài),體系和環(huán)境在熱力學中，被研究的對象稱為熱力學體系，簡稱體系體系以外、與體系有關聯(lián)的其他物體稱為環(huán)境或外界一杯水、一個地質露頭、一個地下水系統(tǒng)都可作為一個體系封閉體系與環(huán)境之間只有能量交換而無物質交換

15、的體系開放體系與環(huán)境之間既有能量交換又有物質交換的體系孤立體系與環(huán)境之間能量交換和物質交換兩者全無的體系,在獲取化學反應的平衡常數(shù)時所用到的化學熱力學知識,當體系的各種性質具有確定的數(shù)值時，就稱該體系處于一定的狀態(tài)。如果這些性質中的一個或多個發(fā)生了變化，就意味著體系的狀態(tài)發(fā)生了變化。也就是說，熱力學中用體系的性質來確定或描述體系的狀態(tài)的和狀態(tài)的變化。反之，如體系的狀態(tài)確定了，體系的一切性質也就完全確定了。由于決定體系狀態(tài)

16、的這些性質同體系的狀態(tài)之間有著這樣的依從關系，所以又把體系的這些性質稱狀態(tài)性質或狀態(tài)函數(shù)。體系的溫度、壓力、體積、密度、電位、折光率、粘度、自由能……等等，都是狀態(tài)函數(shù)。,狀態(tài)和狀態(tài)函數(shù),體系到達某一狀態(tài)后，若不再隨時間改變，則稱體系處于熱力學平衡狀態(tài)，簡稱平衡狀態(tài)。處于平衡狀態(tài)時，體系的各種性質不隨時間改變，都具有確定的值。但從微觀來看，分子、原子、電子等仍處于不停的運動之中。所以，平衡是動態(tài)的。平衡必須在一定的條件下才能

17、保持，所以它又是相對的和暫時的。,平衡狀態(tài),化學反應體系處于平衡狀態(tài)的三個條件,力學平衡條件 體系處于平衡狀態(tài)時，體系的壓力必須不隨時間改變，體系內各部分的壓力必須處處相等若器壁不是剛性的，除了體系內部的壓力必須處處均勻外，還必須使體系的壓力與外界(環(huán)境)的壓力保持相等熱平衡條件 體系處于平衡狀態(tài)時必須保持自身的溫度不變，體系內部的溫度亦必須處處均勻。若體系與環(huán)境之間未隔以絕熱壁，還應使體系與環(huán)境的溫度相等,化學平衡條件 體

18、系處于平衡狀態(tài)時還必須滿足化學平衡條件。滿足化學平衡條件的體系，在其內部應無化學反應發(fā)生，或雖有化學反應發(fā)生，但其正、逆反應進行的速度相等判斷化學反應是否已達平衡，可每隔一段時間從體系中取樣分析，若歷次測定的濃度不變，就說明體系已到達了平衡狀態(tài)。熱力學體系常用溫度、壓力和物質化學組成(濃度)這三種狀態(tài)參數(shù)來表述，當這三種狀態(tài)參數(shù)都保持固定不變時，該體系達到熱力學平衡狀態(tài)，一旦在外界作用下使某一狀態(tài)參數(shù)發(fā)生改變，平衡就遭破壞。熱力學

19、常用“標準狀態(tài)”一詞，是指溫度為298.15K(25℃)、壓力為一巴的狀態(tài)。,化學反應體系處于平衡狀態(tài)的三個條件,焓是系統(tǒng)狀態(tài)函數(shù)，它指一種化學反應向環(huán)境提供的熱量總值，以符號H表示，ΔH指一種反應的焓變化。在標準狀態(tài)下，最穩(wěn)定的單質生成1摩爾純物質時的焓變化，稱為標準生成焓，以ΔHf表示例如：水的ΔHf ＝ 285.8 kJ/mo1，就是說，在標準狀態(tài)下，l mol H2和l/2 mol O2生成1 mol H2O時所生成的熱量為

20、285.8kJ焓可作為化學反應熱效應的指標，化學反應的熱效應是指反應前后生成物和反應物標準生成焓的差值，熱力學上稱這個差值為反應的標準焓變化，以ΔHr表示。其計算方法如下：ΔHr＝ΣΔHf (生成物)—ΣΔHf (反應物) ΔHr為正值，屬吸熱反應； ΔHr為負值，屬放熱反應,焓,CaCO3溶解： CaCO3 ＝ Ca2+ + CO32-ΔHr＝ΔHCa +ΔHCO3 -ΔHCaCO3 ＝(-54

21、2.83) + (-677.1) - (-1207.4) ＝ -12.53kJ/molCaCO3沉淀：Ca 2+ + CO32- ＝ CaCO3ΔHr＝ ΔHCaCO3 -ΔHCa -ΔHCO3 ＝ (-1207.4) - (-542.83) - (-677.1) ＝ 12.53kJ/mol,CaCO3的溶解和沉淀反應,上述計算說明，CaCO3溶解，ΔHr為負值，屬放熱反應；CaCO3沉淀，ΔHr為正值，屬吸熱

22、反應。,熱力學中的一個狀態(tài)函數(shù)，也稱為吉布斯自由能。在熱力學中，自由能的含義是指一個反應在恒溫恒壓下所能做的最大有用功，以符號“G”表示。ΔG是指一個反應的自由能變化。在標準狀態(tài)下，最穩(wěn)定的單質生成1摩爾純物質時的自由能變化，稱為“標準生成自由能”，以“ΔGf”表示。在標準狀態(tài)下，某一反應自由能變化稱為“反應的標準自由能變化”，以“ΔGr”表示，其計算方法為ΔGr＝ΔGf (生成物) - ΔGf (反應物) 化學反應中的驅動力，一

23、般用自由能變化來代表。在恒溫恒壓條件下自由能判據(jù)為：,自由能,2、自由能與化學平衡,根據(jù)化學熱力學原理，可推導出反應的標準自由能變化與平衡常數(shù)的關系式：ΔGr = -RTlnK式中ΔGr為反應的標準自由能變化（kJ/mol）；R為氣體常數(shù)（0.008314kJ/mol）；T為絕對溫度；K為平衡常數(shù)在標準狀態(tài)下，T ＝ 298.15K (T ＝ 25℃ + 273.15)，將R和T值代入上式，并轉換為以10為底的對數(shù)，則Lg K

24、＝ - 0.175ΔGr (kJ/mol) 只要從文獻中能查到反應中所有組分的ΔGf值，即可算得標準狀態(tài)下的ΔGr，進而求得平衡常數(shù)K,范特霍夫式,用于求取標準狀態(tài)以外的情況下的K值原因：反應的自由能變化隨溫度和壓力的不同變化明顯；但反應的標準焓變化與溫度和壓力關系不大；地殼淺部幾百米內，流體壓力對平衡常數(shù)K的影響極小，可忽略不計；因此，對該范圍內的水文地球化學反應，平衡常數(shù)只與反應的溫度有關，可通過反應的標準焓變化求得。,已

25、知白云石在標準狀態(tài)下的溶度積常數(shù)為10-17，試求白云石在5℃下的溶度積常數(shù)。范特霍夫式： R = 0.008314kJ/mol,課堂作業(yè)2：,,Very soon after the publication of the Debye-Hückel theory, it was realized that the theory did not fit experimental measurements of activ

26、ity coefficients for many electrolytes, especially ones with constituent ions of a valence of two or more.Bjerrum, in 1926, postulated the formation of ion pairs in solution to account for these deviations. For example,

27、 for a divalent cation A and a divalent anion B in solution, he suggested that a reaction of the form:takes place that would be described by an equilibrium constant expression:,Ion Pairing and Complexing: Introduction

28、,He reasoned that the formation of the ion pair AX0 would account for the observed lower values for measured activity coefficient values as compared to predicted values. Association of ions into pairs seems reasonable be

29、cause two ions of opposite charge in solution exert an attractive force for each other in solution.Although ion pairing does occur in aqueous solution and contributes in a major way to the breakdown in the Debye-Hü

30、ckel equation, the extent of ion pairing in water is much lower compared to most other solvents. This is principally due to the very high dielectric constant of water.,Ion Pairing and Complexing: Introduction,In terms of

31、 the behavior of ions in solution, a solvent of high dielectric constant tends to prevent ions of opposite charge from pairing up compared to a one of low dielectric constant.Because of its high dielectric constant, wat

32、er is very effective at keeping ions apart in solution. Nevertheless, ion pairing still occurs in aqueous solutions.,Ion Pairing and Complexing: Introduction,If a strictly electrostatic model of interion attraction is ap

33、plied, the tendency of an ion to attract an ion of opposite charge in solution would increase with the field strength of the ion, i.e. its charge/surface area ratio. Thus higher-charged cations should ion pair to a great

34、er extent with a given anion than lower-charged cations.For a suite of cations of the same charge, the smallest would most likely pair with a given anion. But what radius is selected to make such a comparison — the cati

35、on’s crystallographic ionic radius or its hydrated radius?,Factors influencing the degree of ion association,To answer this, a distinction must be made between outer sphere and inner sphere ion pairs or alternatively, so

36、lvent-separated vs contact ion pairs.,Factors influencing the degree of ion association,The ions in outer sphere ion pairs remain separated by solvent molecules in solution. So it is their hydrated radii that dictate the

37、ir effective field strengths and consequently their probability to form ion pairs. The bicarbonate ion pairs with alkali earth metal cations are examples of this type of behavior.Examine the following dissociation const

38、ants for these ion pairs, i.e., for the reaction:,Factors influencing the degree of ion association,Ba2+ is more effective at pairing with HCO3? in solution than any of the other alkali earth metal ions because it has th

39、e smallest hydrated radius. On the other hand, if the dissociation constants of these same metal ions with respect to hydroxide ion pair formation are examined, the exact opposite trend is found.,Factors influencing the

40、degree of ion association,Dissociation constants for bicarbonate ion pairs at 25 oC,Dissociation constants for hydroxide ion pairs at 25 oC,Remembering that these hydroxide ‘ion pairs’ are really just the first hydrolysi

41、s products of the metal ions, the paired hydroxide ion is merely a water molecule in direct contact with the metal ion that has had one of its hydrogen ions ejected into the bulk solution.Thus, because of the direct con

42、tact, the likelihood for hydroxide ion pairing is dictated by the crystallographic radius of the cation, not the hydrated radius.It is not just hydroxide ions, however, that exhibit a tendency for inner sphere associati

43、on with metal cations. Many other anions do this as well. Inner sphere ion association is generally referred to as complexing rather than ion pairing.,Factors influencing the degree of ion association,Sometimes, more com

44、plicated trends of ion pair dissociation constants are observed for a related group of cations with a single anion. Examine the following list of dissociation constants for the alkali metal sulfate ion pairs.The values

45、go through a maximum with increasing crystallographic radius. This indicates a tendency towards a more inner sphere type of ion association going down the periodic table from Li+ to Cs+ ion.,Factors influencing the degre

46、e of ion association,Some of the important ion pairs in natural waters are given in the table below along with their dissociation constants at 25 oC.Dissociation constants for ion pairs or complexes important in natura

47、l waters at 25 oC,Factors influencing the degree of ion association,Notes:Cl? does not complex appreciably with any alkali or alkali earth metal cation. Cl? does complex, however, with transition and actinide metal cati

48、ons — elements such as Fe, Mn, Cd, Pb, Cu and Zn.Temperature data on ion pair and complex dissociation constants are often scarce.Dissociation constant data for carbonate complexes with transition metals and actinides

49、are also scarce.,Factors influencing the degree of ion association,The principal difference between an ion pair and a complex is that the constituent ions of an ion pair are solvent-separated in solution whereas the cons

50、tituent ions of a complex are in direct contact or coordinated to each other. Strong covalent bonding often exists between the constituent ions of a complex whereas in an ion pair the bonding is largely electrostatic.As

51、 a result of this distinction, many of the properties of these species are different. However, it is often not possible to make a clear cut distinction between what is a complex and what is an ion pair. A complete gradat

52、ion exists from one endmember to the other in solution.,Distinction between Ion Pairs and Complexes,Confining the discussion to endmembers, the kinetics of complex formation are slow compared to ion pair formation. Where

53、as reaction times to form an ion pair or to dissociate it are measured on the order of millionths of a second, complex reactions can require much longer time to attain equilibrium.For an anion (the ligand in a complex)

54、to complex with a cation, it has to replace one of the water molecules directly coordinated to the cation. Depending upon how effectively this water molecule is bonded to the cation, the reaction may proceed slowly requi

55、ring many minutes or even many hours to reach equilibrium.,Distinction between Ion Pairs and Complexes,For example, the half-life for the exchange of a H2O molecule within the first hydration sheath of Cr3+ ion is 40 h —

56、 unusually long compared to other trivalent metal cations.Consequently, the attainment of equilibrium between Cr3+ and the chromium amine complex CrNH33+ upon addition of ammonia to a Cr3+-containing solution will requi

57、re at least several days.,Distinction between Ion Pairs and Complexes,The effect of temperature on the stability of ion pairs and complexes is also different.An increase in temperature generally results in increased ion

58、 pair formation, but complexes are often destabilized with an increase in temperature.This reflects a strong exothermic character to the enthalpy for the dissociation reaction of the ion pair in solution as opposed to

59、 an often endothermic character to the enthalpy of reaction for complex dissociation.,Distinction between Ion Pairs and Complexes,The enthalpy for the reaction:is related to the variation of the equilibrium constant

60、 with temperature through the Van’t Hoff equation:For ion pair dissociation, ΔHR is negative and K for the dissociation reaction decreases with increasing temperature, i.e., greater formation of AX0 at higher temperat

61、ure. The reverse is often found for complexes.,Distinction between Ion Pairs and Complexes,Some enthalpy and entropy changes for ion pair and complex dissociation reactions are given in the accompanying table.,Distinctio

62、n between Ion Pairs and Complexes,Dissociation reaction enthalpy and entropy changes for various ion pairs and complexes at 25 oC,This tendency for greater ion pair formation with temperature and less complex formation c

63、an be rationalized conceptually in the following manner.Complexes can be thought of as ions tightly bonded to each other. Increased thermal vibrations at higher temperatures tend to break the ions apart.By contrast, io

64、n pairs are held together by electrostatic forces that develop as ions of opposite charge approach each other in solution. With an increase in temperature, more close encounters of ions of opposite charge occur and the p

65、robability for the formation of ion pairs increases.,Distinction between Ion Pairs and Complexes,The thermodynamic reason for the often positive enthalpies for the dissociation reactions of complexes is that much greater

66、 energy (heat) is required to break apart the tightly bonded constituent ions of the complex compared to the ion pair.Without this component of heat, the enthalpy of a complex or ion pair dissociation reaction would be

67、negative (or exothermic) because as the constituent ions break apart, some water molecules from solution are added to the hydration sheaths of the ions and much of their rotational and vibrational energy is released.,Dis

68、tinction between Ion Pairs and Complexes,One feature of complex formation is that multiple species may form between a cation and ligand. Ligand ions may replace one, two, three or more water molecules of the cation’s hyd