3-化學(xué)平衡、離子對(duì)與絡(luò)合省公開課金獎(jiǎng)全國賽課一等獎(jiǎng)微課獲獎(jiǎng)?wù)n件

水文地球化學(xué)主講：郭清海中國地質(zhì)大學(xué)（武漢）環(huán)境學(xué)院一門關(guān)于地下水科學(xué)1/55化學(xué)平衡、離子對(duì)與絡(luò)合Chemicalequilibrium,IonPairingandComplexing2/55水是極性分子，是一個(gè)溶解能力很強(qiáng)溶劑它與包氣帶及含水層中巖石(土)接觸時(shí)，必定會(huì)發(fā)生溶解-沉淀反應(yīng)、氧化還原作用、界面反應(yīng)作用，這些反應(yīng)是控制地下水化學(xué)成份形成和演變主要作用。發(fā)生在地下水系統(tǒng)中水-巖相互作用普通為可逆反應(yīng)可逆反應(yīng)進(jìn)程符合化學(xué)平衡原理，能夠用質(zhì)量作用定律描述。第一節(jié)化學(xué)平衡3/55質(zhì)量作用定律化學(xué)反應(yīng)驅(qū)動(dòng)力與反應(yīng)物和生成物濃度相對(duì)大小關(guān)系相關(guān)發(fā)生在地下環(huán)境水-巖相互作用一樣受到質(zhì)量作用定律控制4/55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。地下水是一個(gè)真實(shí)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，包含相互碰撞及靜電引力作用。作用結(jié)果是，化學(xué)反應(yīng)相對(duì)減緩，一部分離子在反應(yīng)中不起作用了。所以，假如依然用水中各組分實(shí)測(cè)濃度進(jìn)行化學(xué)計(jì)算，就會(huì)產(chǎn)生一定程度偏差。為了確保計(jì)算準(zhǔn)確程度，就必須對(duì)水中組分實(shí)測(cè)濃度加以校正，校正后濃度稱為校正濃度，也就是活度。質(zhì)量作用定律中，濃度是以活度表示?；疃仁钦鎸?shí)濃度（實(shí)測(cè)濃度）函數(shù)，普通情況下，活度小于實(shí)測(cè)濃度。5/55理想溶液與活度A、理想溶液活度與實(shí)測(cè)濃度函數(shù)表示式為：a=γm

式中m為實(shí)測(cè)濃度（mol/L）；

γ為活度系數(shù)，其單位是實(shí)測(cè)濃度倒數(shù)（L/mol），a為活度，無量綱。不過，在實(shí)際應(yīng)用中，a和m單位相同，均為mol/L，

γ為無量綱系數(shù)?；疃认禂?shù)隨水中溶解固體（即礦化度）增加而減小，普通都小于1。當(dāng)水中溶解固體（TDS）很低時(shí)，r趨近于1，活度趨近于實(shí)測(cè)濃度。分子（包含水分子）和不帶電離子正確活度系數(shù)為1。在化學(xué)平衡計(jì)算中，要求固體和純液體活度為1。6/55B、活度系數(shù)公式在水文地球化學(xué)研究中，應(yīng)用最普遍活度系數(shù)計(jì)算公式是迪拜-休克爾（Debye-Huckel）方程：式中：r為活度系數(shù)；Z為離子電荷數(shù)；I為離子強(qiáng)度（mol/L）；A和B為取決于水介電常數(shù)、密度和溫度常數(shù)；a是與離子水化半徑相關(guān)常數(shù)。當(dāng)I＜0.1時(shí)，該方程準(zhǔn)確性很高離子強(qiáng)度I計(jì)算公式：式中：I為離子強(qiáng)度（mol/L）；Zi為i離子電荷數(shù)；mi為i離子濃度（mol/L）。7/55對(duì)于TDS高（I大于0.1mol/L）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(kuò)大迪拜-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a值與迪拜-休克爾方程式中a值不一樣。方程應(yīng)用范圍是I＜0.5mol/L。B、活度系數(shù)公式8/55在溫度一定時(shí)，K為常數(shù)，固體BaSO4“活度”為1，所以：[Ba2+][SO42-]=Ksp

Ksp稱為溶度積常數(shù)（SolubilityProductConstant）。Ksp隨溫度而改變，比如BaSO4溶度積，298K時(shí)Ksp=1.08×10-10；323K時(shí)Ksp=1.98×10-10。可知BaSO4Ksp隨溫度升高而稍增大。

溶度積常數(shù)

溶度積常數(shù)：即難溶鹽平衡常數(shù)以BaSO4溶解與沉淀過程為例說明BaSO4=Ba2++

SO42-9/55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陰、陽離子含量之乘積（并不特指反應(yīng)到達(dá)平衡時(shí)刻）與溶度積和離子活度積相關(guān)概念——飽和指數(shù)：SI=IAP/Ksp普通為：SI＝lg(IAP/Ksp)用SI可判斷反應(yīng)方向與進(jìn)程SI<0時(shí)，水溶液不飽和SI>0時(shí)，水溶液過飽和SI=0時(shí)，水溶液處于溶解平衡狀態(tài)10/55仍以BaSO4溶解與沉淀過程為例說明：

BaSO4（固）==Ba2++SO42-SI<0時(shí)，BaSO4溶解速度大于沉淀速度，溶液處于未飽和狀態(tài)；SI>0時(shí)，BaSO4沉淀速度大于溶解速度，BaSO4溶液處于過飽和狀態(tài)；SI=0時(shí)，BaSO4沉淀速度等于溶解速度，溶解過程和沉淀過程到達(dá)平衡，溶液為飽和溶液。11/55以SI值判斷礦物溶解是比較可靠而用SI值判斷礦物沉淀可能不甚可靠因?yàn)橛行┑V物，尤其是白云石和許多硅酸鹽礦物，盡管SI值為比較大正值，處于過飽和狀態(tài)時(shí)，也可能不產(chǎn)生沉淀。比如，即使海水與白云石處于過飽和狀態(tài)，但無沉淀趨勢(shì)。產(chǎn)生這種情況化學(xué)機(jī)理比較復(fù)雜，與化學(xué)動(dòng)力學(xué)等有很大關(guān)系。普通來說，依據(jù)SI值判斷水與巖石、礦物反應(yīng)狀態(tài)，對(duì)于地下淡水來說，還是很有用飽和指數(shù)應(yīng)用12/55溶度積常數(shù)和溶解度

溶解度：在給定溫度和壓力下，溶液中某溶解物到達(dá)溶解平衡時(shí)總量嚴(yán)格說來，物質(zhì)溶解度只有大小之分，沒有在水中絕對(duì)不溶解物質(zhì)。習(xí)慣上把溶解度小于0.01g/100g水物質(zhì)叫做“難溶物”13/55溶度積常數(shù)值可用來預(yù)計(jì)和比較難溶電解質(zhì)溶解度大小：AB型化合物：AB(固)＝A++B-平衡時(shí)：[A+]=[B-]=S；Ksp=[A+][B-]=S2AB2或A2B型化合物：AB2(固)＝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(guān)系可知，相同類型難溶電解質(zhì)（比如同是AB型或AB2型）相比，溶度積越小，溶解度（以摩爾濃度表示）也越小。

溶解度（以S表示；單位：mol/L）和溶度積定量關(guān)系14/55仍以BaSO4為例加以說明假如在飽和BaSO4溶液中加KNO3，KNO3就完全電離為K+和NO3-離子，結(jié)果使溶液中離子總數(shù)目增加，因?yàn)镾O42-和Ba2+被眾多異號(hào)離子（K+、NO3-）所包圍，其活動(dòng)性有所降低。這么，Ba2+和SO42-有效濃度降低，促使下面溶解平衡被打破，并向右移動(dòng)：BaSO4（固）==Ba2++SO4結(jié)果為BaSO4溶解度增加，直至上述溶解反應(yīng)到達(dá)平衡為止，這時(shí)Ksp值變大了。這種因加入強(qiáng)電解質(zhì)而使物質(zhì)溶解度增大效應(yīng)也叫做鹽效應(yīng)。假如加入可溶性強(qiáng)電解質(zhì)濃度很小，比如溶液離子強(qiáng)度值＜10-3mol/L，則能夠不考慮鹽效應(yīng)對(duì)難溶性強(qiáng)電解質(zhì)Ksp值影響。鹽效應(yīng)15/55一個(gè)礦物溶解于水中，如水溶液中已經(jīng)有或加入了某種離子與該礦物溶解后產(chǎn)生離子相同，則礦物溶解度將降低。仍以BaSO4為例加以說明：假如在飽和BaSO4溶液中加BaCl2，Ba2+濃度將上升。這么，Ba2+和SO42-離子積將大于活度積，促使下面溶解-沉淀平衡被打破，并向左移動(dòng)：BaSO4（固）==Ba2++SO4結(jié)果為BaSO4溶解度減小，直至上述沉淀反應(yīng)到達(dá)平衡為止。這種因加入相同離子而使物質(zhì)溶解度減小效應(yīng)也叫做同離子效應(yīng)。如水溶液中同時(shí)存在同離子效應(yīng)與鹽效應(yīng)，前者對(duì)溶解度影響要大得多。同離子效應(yīng)16/55熱力學(xué)體系性質(zhì)、狀態(tài)體系和環(huán)境在熱力學(xué)中，被研究對(duì)象稱為熱力學(xué)體系，簡稱體系體系以外、與體系相關(guān)聯(lián)其它物體稱為環(huán)境或外界一杯水、一個(gè)地質(zhì)露頭、一個(gè)地下水系統(tǒng)都可作為一個(gè)體系封閉體系與環(huán)境之間只有能量交換而無物質(zhì)交換體系開放體系與環(huán)境之間現(xiàn)有能量交換又有物質(zhì)交換體系孤立體系與環(huán)境之間能量交換和物質(zhì)交換二者全無體系在獲取化學(xué)反應(yīng)平衡常數(shù)時(shí)所用到化學(xué)熱力學(xué)知識(shí)17/55當(dāng)體系各種性質(zhì)含有確定數(shù)值時(shí)，就稱該體系處于一定狀態(tài)。假如這些性質(zhì)中一個(gè)或多個(gè)發(fā)生了改變，就意味著體系狀態(tài)發(fā)生了改變。也就是說，熱力學(xué)中用體系性質(zhì)來確定或描述體系狀態(tài)和狀態(tài)改變。反之，如體系狀態(tài)確定了，體系一切性質(zhì)也就完全確定了。因?yàn)闆Q定體系狀態(tài)這些性質(zhì)同體系狀態(tài)之間有著這么依從關(guān)系，所以又把體系這些性質(zhì)稱狀態(tài)性質(zhì)或狀態(tài)函數(shù)。體系溫度、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)18/55體系抵達(dá)某一狀態(tài)后，若不再隨時(shí)間改變，則稱體系處于熱力學(xué)平衡狀態(tài)，簡稱平衡狀態(tài)。處于平衡狀態(tài)時(shí)，體系各種性質(zhì)不隨時(shí)間改變，都含有確定值。但從微觀來看，分子、原子、電子等仍處于不停運(yùn)動(dòng)之中。所以，平衡是動(dòng)態(tài)。平衡必須在一定條件下才能保持，所以它又是相正確和暫時(shí)。平衡狀態(tài)19/55化學(xué)反應(yīng)體系處于平衡狀態(tài)三個(gè)條件力學(xué)平衡條件

體系處于平衡狀態(tài)時(shí)，體系壓力必須不隨時(shí)間改變，體系內(nèi)各部分壓力必須處處相等若器壁不是剛性，除了體系內(nèi)部壓力必須處處均勻外，還必須使體系壓力與外界(環(huán)境)壓力保持相等熱平衡條件

體系處于平衡狀態(tài)時(shí)必須保持本身溫度不變，體系內(nèi)部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(yīng)使體系與環(huán)境溫度相等20/55化學(xué)平衡條件

體系處于平衡狀態(tài)時(shí)還必須滿足化學(xué)平衡條件。滿足化學(xué)平衡條件體系，在其內(nèi)部應(yīng)無化學(xué)反應(yīng)發(fā)生，或雖有化學(xué)反應(yīng)發(fā)生，但其正、逆反應(yīng)進(jìn)行速度相等判斷化學(xué)反應(yīng)是否已達(dá)平衡，可每隔一段時(shí)間從體系中取樣分析，若歷次測(cè)定濃度不變，就說明體系已抵達(dá)了平衡狀態(tài)。熱力學(xué)體系慣用溫度、壓力和物質(zhì)化學(xué)組成(濃度)這三種狀態(tài)參數(shù)來表述，當(dāng)這三種狀態(tài)參數(shù)都保持固定不變時(shí)，該體系抵達(dá)熱力學(xué)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(xué)慣用“標(biāo)準(zhǔn)狀態(tài)”一詞，是指溫度為298.15K(25℃)、壓力為一巴狀態(tài)?；瘜W(xué)反應(yīng)體系處于平衡狀態(tài)三個(gè)條件21/55焓是系統(tǒng)狀態(tài)函數(shù)，它指一個(gè)化學(xué)反應(yīng)向環(huán)境提供熱量總值，以符號(hào)H表示，ΔH指一個(gè)反應(yīng)焓改變。在標(biāo)準(zhǔn)狀態(tài)下，最穩(wěn)定單質(zhì)生成1摩爾純物質(zhì)時(shí)焓改變，稱為標(biāo)準(zhǔn)生成焓，以ΔHf表示比如：水ΔHf＝285.8kJ/mo1，就是說，在標(biāo)準(zhǔn)狀態(tài)下，lmolH2和l/2molO2生成1molH2O時(shí)所生成熱量為285.8kJ焓可作為化學(xué)反應(yīng)熱效應(yīng)指標(biāo)，化學(xué)反應(yīng)熱效應(yīng)是指反應(yīng)前后生成物和反應(yīng)物標(biāo)準(zhǔn)生成焓差值，熱力學(xué)上稱這個(gè)差值為反應(yīng)標(biāo)準(zhǔn)焓改變，以ΔHr表示。其計(jì)算方法以下：ΔHr＝ΣΔHf(生成物)—ΣΔHf(反應(yīng)物)ΔHr為正值，屬吸熱反應(yīng)；ΔHr為負(fù)值，屬放熱反應(yīng)焓22/55CaCO3溶解：CaCO3＝Ca2++CO32-ΔHr＝ΔHCa+ΔHCO3-ΔHCaCO3

＝(-542.83)+(-677.1)-(-1207.4)＝-12.53kJ/molCaCO3沉淀：Ca2++CO32-＝CaCO3ΔHr＝ΔHCaCO3

-ΔHCa-ΔHCO3

＝(-1207.4)-(-542.83)-(-677.1)＝12.53kJ/molCaCO3溶解和沉淀反應(yīng)上述計(jì)算說明，CaCO3溶解，ΔHr為負(fù)值，屬放熱反應(yīng)；CaCO3沉淀，ΔHr為正值，屬吸熱反應(yīng)。23/55熱力學(xué)中一個(gè)狀態(tài)函數(shù)，也稱為吉布斯自由能。在熱力學(xué)中，自由能含義是指一個(gè)反應(yīng)在恒溫恒壓下所能做最大有用功，以符號(hào)“G”表示。ΔG是指一個(gè)反應(yīng)自由能改變。在標(biāo)準(zhǔn)狀態(tài)下，最穩(wěn)定單質(zhì)生成1摩爾純物質(zhì)時(shí)自由能改變，稱為“標(biāo)準(zhǔn)生成自由能”，以“ΔGf”表示。在標(biāo)準(zhǔn)狀態(tài)下，某一反應(yīng)自由能改變稱為“反應(yīng)標(biāo)準(zhǔn)自由能改變”，以“ΔGr”表示，其計(jì)算方法為ΔGr＝ΔGf(生成物)-ΔGf(反應(yīng)物)

化學(xué)反應(yīng)中驅(qū)動(dòng)力，普通用自由能改變來代表。在恒溫恒壓條件下自由能判據(jù)為：自由能24/552、自由能與化學(xué)平衡依據(jù)化學(xué)熱力學(xué)原理，可推導(dǎo)出反應(yīng)標(biāo)準(zhǔn)自由能改變與平衡常數(shù)關(guān)系式：ΔGr=-RTlnK式中ΔGr為反應(yīng)標(biāo)準(zhǔn)自由能改變（kJ/mol）；R為氣體常數(shù)（0.008314kJ/mol）；T為絕對(duì)溫度；K為平衡常數(shù)在標(biāo)準(zhǔn)狀態(tài)下，T＝298.15K(T＝25℃+273.15)，將R和T值代入上式，并轉(zhuǎn)換為以10為底對(duì)數(shù)，則LgK＝-0.175ΔGr(kJ/mol)只要從文件中能查到反應(yīng)中全部組分ΔGf值，即可算得標(biāo)準(zhǔn)狀態(tài)下ΔGr，進(jìn)而求得平衡常數(shù)K25/55范特霍夫式用于求取標(biāo)準(zhǔn)狀態(tài)以外情況下K值原因：反應(yīng)自由能改變隨溫度和壓力不一樣改變顯著；但反應(yīng)標(biāo)準(zhǔn)焓改變與溫度和壓力關(guān)系不大；地殼淺部幾百米內(nèi)，流體壓力對(duì)平衡常數(shù)K影響極小，可忽略不計(jì)；所以，對(duì)該范圍內(nèi)水文地球化學(xué)反應(yīng)，平衡常數(shù)只與反應(yīng)溫度相關(guān)，可經(jīng)過反應(yīng)標(biāo)準(zhǔn)焓改變求得。26/55已知白云石在標(biāo)準(zhǔn)狀態(tài)下溶度積常數(shù)為10-17，試求白云石在5℃下溶度積常數(shù)。范特霍夫式：R=0.008314kJ/mol課堂作業(yè)2：27/55VerysoonafterthepublicationoftheDebye-Hückeltheory,itwasrealizedthatthetheorydidnotfitexperimentalmeasurementsofactivitycoefficientsformanyelectrolytes,especiallyoneswithconstituentionsofavalenceoftwoormore.Bjerrum,in1926,postulatedtheformationofionpairsinsolutiontoaccountforthesedeviations.Forexample,foradivalentcationAandadivalentanionBinsolution,hesuggestedthatareactionoftheform:takesplacethatwouldbedescribedbyanequilibriumconstantexpression:IonPairingandComplexing:Introduction28/55HereasonedthattheformationoftheionpairAX0wouldaccountfortheobservedlowervaluesformeasuredactivitycoefficientvaluesascomparedtopredictedvalues.Associationofionsintopairsseemsreasonablebecausetwoionsofoppositechargeinsolutionexertanattractiveforceforeachotherinsolution.AlthoughionpairingdoesoccurinaqueoussolutionandcontributesinamajorwaytothebreakdownintheDebye-Hückelequation,theextentofionpairinginwaterismuchlowercomparedtomostothersolvents.Thisisprincipallyduetotheveryhighdielectricconstantofwater.IonPairingandComplexing:Introduction29/55Intermsofthebehaviorofionsinsolution,asolventofhighdielectricconstanttendstopreventionsofoppositechargefrompairingupcomparedtoaoneoflowdielectricconstant.Becauseofitshighdielectricconstant,waterisveryeffectiveatkeepingionsapartinsolution.Nevertheless,ionpairingstilloccursinaqueoussolutions.IonPairingandComplexing:Introduction30/55Ifastrictlyelectrostaticmodelofinterionattractionisapplied,thetendencyofaniontoattractanionofoppositechargeinsolutionwouldincreasewiththefieldstrengthoftheion,i.e.itscharge/surfacearearatio.Thushigher-chargedcationsshouldionpairtoagreaterextentwithagivenanionthanlower-chargedcations.Forasuiteofcationsofthesamecharge,thesmallestwouldmostlikelypairwithagivenanion.Butwhatradiusisselectedtomakesuchacomparison—thecation’scrystallographicionicradiusoritshydratedradius?Factorsinfluencingthedegreeofionassociation31/55Toanswerthis,adistinctionmustbemadebetweenoutersphereandinnersphereionpairsoralternatively,solvent-separatedvscontactionpairs.Factorsinfluencingthedegreeofionassociation32/55Theionsinoutersphereionpairsremainseparatedbysolventmoleculesinsolution.Soitistheirhydratedradiithatdictatetheireffectivefieldstrengthsandconsequentlytheirprobabilitytoformionpairs.Thebicarbonateionpairswithalkaliearthmetalcationsareexamplesofthistypeofbehavior.Examinethefollowingdissociationconstantsfortheseionpairs,i.e.,forthereaction:Factorsinfluencingthedegreeofionassociation33/55Ba2+ismoreeffectiveatpairingwithHCO3?insolutionthananyoftheotheralkaliearthmetalionsbecauseithasthesmallesthydratedradius.Ontheotherhand,ifthedissociationconstantsofthesesamemetalionswithrespecttohydroxideionpairformationareexamined,theexactoppositetrendisfound.FactorsinfluencingthedegreeofionassociationDissociationconstantsforbicarbonateionpairsat25oCDissociationconstantsforhydroxideionpairsat25oC34/55Rememberingthatthesehydroxide‘ionpairs’arereallyjustthefirsthydrolysisproductsofthemetalions,thepairedhydroxideionismerelyawatermoleculeindirectcontactwiththemetalionthathashadoneofitshydrogenionsejectedintothebulksolution.Thus,becauseofthedirectcontact,thelikelihoodforhydroxideionpairingisdictatedbythecrystallographicradiusofthecation,notthehydratedradius.Itisnotjusthydroxideions,however,thatexhibitatendencyforinnersphereassociationwithmetalcations.Manyotheranionsdothisaswell.Innersphereionassociationisgenerallyreferredtoascomplexingratherthanionpairing.Factorsinfluencingthedegreeofionassociation35/55Sometimes,morecomplicatedtrendsofionpairdissociationconstantsareobservedforarelatedgroupofcationswithasingleanion.Examinethefollowinglistofdissociationconstantsforthealkalimetalsulfateionpairs.Thevaluesgothroughamaximumwithincreasingcrystallographicradius.ThisindicatesatendencytowardsamoreinnerspheretypeofionassociationgoingdowntheperiodictablefromLi+toCs+ion.Factorsinfluencingthedegreeofionassociation36/55Someoftheimportantionpairsinnaturalwatersaregiveninthetablebelowalongwiththeirdissociationconstantsat25oC.Dissociationconstantsforionpairsorcomplexesimportantinnaturalwatersat25oCFactorsinfluencingthedegreeofionassociation37/55Notes:Cl?doesnotcomplexappreciablywithanyalkalioralkaliearthmetalcation.Cl?doescomplex,however,withtransitionandactinidemetalcations—elementssuchasFe,Mn,Cd,Pb,CuandZn.Temperaturedataonionpairandcomplexdissociationconstantsareoftenscarce.Dissociationconstantdataforcarbonatecomplexeswithtransitionmetalsandactinidesarealsoscarce.Factorsinfluencingthedegreeofionassociation38/55Theprincipaldifferencebetweenanionpairandacomplexisthattheconstituentionsofanionpairaresolvent-separatedinsolutionwhereastheconstituentionsofacomplexareindirectcontactorcoordinatedtoeachother.Strongcovalentbondingoftenexistsbetweentheconstituentionsofacomplexwhereasinanionpairthebondingislargelyelectrostatic.Asaresultofthisdistinction,manyofthepropertiesofthesespeciesaredifferent.However,itisoftennotpossibletomakeaclearcutdistinctionbetweenwhatisacomplexandwhatisanionpair.Acompletegradationexistsfromoneendmembertotheotherinsolution.DistinctionbetweenIonPairsandComplexes39/55Confiningthediscussiontoendmembers,thekineticsofcomplexformationareslowcomparedtoionpairformation.Whereasreactiontimestoformanionpairortodissociateitaremeasuredontheorderofmillionthsofasecond,complexreactionscanrequiremuchlongertimetoattainequilibrium.Forananion(theligandinacomplex)tocomplexwithacation,ithastoreplaceoneofthewatermoleculesdirectlycoordinatedtothecation.Dependinguponhoweffectivelythiswatermoleculeisbondedtothecation,thereactionmayproceedslowlyrequiringmanyminutesorevenmanyhourstoreachequilibrium.DistinctionbetweenIonPairsandComplexes40/55Forexample,thehalf-lifefortheexchangeofaH2OmoleculewithinthefirsthydrationsheathofCr3+ionis40h—unusuallylongcomparedtoothertrivalentmetalcations.Consequently,theattainmentofequilibriumbetweenCr3+andthechromiumaminecomplexCrNH33+uponadditionofammoniatoaCr3+-containingsolutionwillrequireatleastseveraldays.DistinctionbetweenIonPairsandComplexes41/55Theeffectoftemperatureonthestabilityofionpairsandcomplexesisalsodifferent.Anincreaseintemperaturegenerallyresultsinincreasedionpairformation,butcomplexesareoftendestabilizedwithanincreaseintemperature.Thisreflectsastrongexothermiccharactertotheenthalpyforthedissociationreactionoftheionpairinsolutionasopposedtoanoftenendothermiccharactertotheenthalpyofreactionforcomplexdissociation.DistinctionbetweenIonPairsandComplexes42/55Theenthalpyforthereaction:isrelatedtothevariationoftheequilibriumconstantwithtemperaturethroughtheVan’tHoffequation:Forionpairdissociation,ΔHRisnegativeandKforthedissociationreactiondecreaseswithincreasingtemperature,i.e.,greaterformationofAX0athighertemperature.Thereverseisoftenfoundforcomplexes.DistinctionbetweenIonPairsandComplexes43/55Someenthalpyandentropychangesforionpairandcomplexdissociationreactionsaregivenintheaccompanyingtable.DistinctionbetweenIonPairsandComplexesDissociationreactionenthalpyandentropychangesforvariousionpairsandcomplexesat25oC44/55Thistendencyforgreaterionpairformationwithtemperatureandlesscomplexformationcanberationalizedconceptuallyinthefollowingmanner.Complexescanbethoughtofasionstightlybondedtoeachother.Increasedthermalvibrationsathighertemperaturestendtobreaktheionsapart.Bycontrast,ionpairsareheldtogetherbyelectrostaticforcesthatdevelopasionsofoppositechargeapproacheachotherinsolution.Withanincreaseintemperature,morecloseencountersofionsofoppositechargeoccurandtheprobabilityfortheformationofionpairsincreases.DistinctionbetweenIonPairsandComplexes45/55Thethermodynamicreasonfortheoftenpositiveenthalpiesforthedissociationreactionsofcomplexesisthatmuchgreaterenergy(heat)isrequiredtobreakapartthetightlybondedconstituentionsofthecomplexcomparedtotheionpair.Withoutthiscomponentofheat,theenthalpyofacomplexorionpairdissociationreactionwouldbenegative(orexothermic)becauseastheconstituentionsbreakapart,somewatermoleculesfromsolutionareaddedtothehydrationsheathsoftheionsandmuchoftheirrotationalandvibrationalenergyisreleased.DistinctionbetweenIonPairsandComplexes46/55Onefeatureofcomplexformationisthatmultiplespeciesmayformbetweenacationandligand.Ligandionsmayreplaceone,two,threeormorewatermoleculesofthecation’shydrationsheath.Thisisnotthecaseforionpairformation.Expressedasstepwiseformationconstants,suchsequentialligandcomplexationreactionswouldbewrittenas:Stepwisecomplexformation47/55Anotherwayofexpressingsequentialcomplexformationisbyoverallreactions.InsteadofusingKitorefertotheequilibriumconstantforthesereactions,theconventionistousethetermβi.Therelationbetweenthetwosetsofreactionconstantsis:Or:Stepwisecomplexformation48/55logKivaluesforsequentialmetal-ligandcomplexreactionsgenerallydecreaseinvaluewhereasthevaluesforlogβiincrease.Theexpressionsforcadmiumcyanidecomplexformation,forexample,aregiveninthefollowingtable.Stepwisecomplexformation49/55Distributiondiagramscanbeconstructedforsequentialcomplexformationinmuchthesamewayastheyaredrawnforsequentialhydrolysisproducts.Examinethefollowingdistributiondiagramforcadmiumcyanidecomplexes.Stepwisecomplexformation50/55Metalionsandligandscanbeclassifiedaseithersoftorhardonthebasisoftheirelectronconfigurations.Softionsusuallyhavelowpositivechargeorhighnegativecharge;largeradii;higheratomicnumbers;andincompleteelectronshellconfigurations.Hardionstendtohavehighpositivechargeorlownegativecharge;smallradii;loweratomicnumbers;andcompleteorhalf-filledelectronshellconfiguration