山大《医学基础化学》双语课件10Titrimetry

1、Inorganic chemistryOrganic chemistryPhysical chemistryAnalytical chemistryChemistry 分析方法的分类分析任务定性分析 qualitative定量分析 quantitative结构分析 structural分析对象无机分析 inorganic有机分析 organic方法原理化学分析 chemical仪器分析 instrumental微量分析 micro试 样 用 量常量分析 macro半微量分析 semi-micro超微量分析 ultra-micro 分析目的例行分析 routine仲裁分析 arbitral1 分

2、析任务定性分析（qualitative analysis）： 鉴定物质由哪些元素、原子团或化合物组成定量分析(quantitative analysis)： 测定物质中有关成分的含量结构分析(structural analysis)： 研究物质的分子结构或晶体结构2 试样用量 方法试样质量试液体积常量分析半微量分析微量分析超微量分析0.1g0.010.1g0.110mg10mL110mL0.011mL 1%）、 微量组分（0.01%1%）、 痕量组分（ 0.01%） 3 分析目的例行分析（Routine analysis） ： 一般化验室日常生产中的分 析，也称常规分析仲裁分析（Arbitra

3、l analysis） ： 对分析结果有争议，要求权威部门用指定的方法、准确测定，进行裁判原分析结果是否正确，也称裁判分析。仲裁分析对分析方法和分析结果准确度要求高。Quantitative analysis(定量分析) Gravimetric analysisChemical analysis Volumetric analysis SpectrometryInstrumental analysis Chromatographic method Electrochemical analysis Volumetric analysis (volumetry, titrimetry)Acid-b

4、ase titration (neutralization titration) Oxidation-reduction titration Coordination titration (EDTA titration) Precipitation titration10-1 General Principles of titration10-2 Acid-Base Titration10-3 EDTA Titration10-4 Analytical Error and Significant FiguresA titration is a standard laboratory metho

5、d of chemical analysis which can be used to determine the concentration of a unknown reactant.In a titration two reagents are mixed, one with a known concentration and one with an unknown concentration. There is some way to indicate when the two reagents have reacted essentially completely, and at t

6、he end of the titration the unknown solutions concentration can be calculated. General Principles of titration Titration consists of adding carefully metered volumes of the solution of known concentration to the other solution of unknown concentration to reach an end-point. Typically, one reagent is

7、 a solution and is added from a buret. This solution is called the titrant or standard solution. The solution from the buret is added to a conical flask that contains either a measured volume of a solution or a weighed quantity of solid that has been dissolved. The buret has graduations that are use

8、d to read the volume of titrant added to the conical flask.Titration: Titrant (standard solution) Analyte (sample) Stoichiometric point Indicator Error of titration End point of titrationAnalyte(sample) in conical flaskindicatorTitrant in burettitration : fill buret remove bubble fill pipette(、) tit

9、ration titration The requirement of a titration are as follows:1. The reaction should be stoichiometric. 2. The reaction should be rapid. 3. There should be no side reactions, and the reaction should be specific. 4. There should be a marked change in some property of the solution when the reaction i

10、s complete. 5. The point at which the reaction is observed to be complete is called the end point. 6. The reaction should be quantitative. Operation system in titrametric analysis1. Prepare the standard solution2.standardization of the standard solution3.determine the content of the sampleStandard S

11、olution Standard solution The concentration of a standard solution must be known within the limits of accuracy necessary in the actual analysis for which it is being used. Significant figure Four figures are necessaryPrepare the standard solution1. Direct method: used primary standard substance Na2C

12、O3 standard solution 2. Indirect method: NaOH standard solution HCl standard solution2.间接配制法（标定法） 先配成一种接近所需浓度的溶液， 然后用基准物质（或用已经用基准物质标定过的另一标准溶液）来标定它的准确浓度。这种操作过程叫做“标定”。间接法配制标准溶液。Standardization of standard solution HCl by Na2CO3 , NaOH by HCl2.标定： 准确称取基准准物，溶解后滴定。1.配制溶液： 配制成近似所需浓度的溶液。 3.确定浓度 由基准物质的质量或标准

13、溶液的 浓度以及所取试液的体积计算之。 primary standard substance A primary standard substance should fulfill these requirements: 1. It should be 100.00% pure 2. It should be stable to drying temperatures 3. It should be readily available. 4. it should have a high formula weight.(large mole weight) 5. Reaction quickly

14、 titre Determine the content of the sample毫升标准溶液(A)相当于被测物(B)的质量。 表示为 TB/A = gmL-1 或 %mL-T (Fe /K2Cr2O7) = 0.005260gmL-1，表示 1 mL K2Cr2O7标准溶液相当于0.005260g Fe，即1 mLK2Cr2O7标准溶液恰好能与0.005260g Fe2+反应 .若滴定消耗21.45mL K2Cr2O7标准溶液，试样中含Fe量为多少？0.005260gmL-121.45mL = 0.1128g10-2 Acid-Base titration 1 Titration of a

15、 Strong Acid with a Strong Base the chemical reaction is the neutralization H3O+(aq) + OH- (aq) 2H2O(l) titrant: 0.1000 mol/L NaOH (in buret) titrate: 0.1000 mol/L HCl 20.00ml (in conical flask). Initially, V =0.00ml NaOH added H3O+= 0.1000mol/L pH = 1.00pH = 2.28 . V=18.00ml NaOH mol/L added mmoles

16、 acid left unreacted=2.000-1.800 =0.2000 volume solution =20.00+18.00=38.00ml . V=19.80ml NaOH mol/L added mmoles acid left unreacted = 2.000-1.9800 = 0.02000 volume solution = 20.00+19.80 = 39.80mlpH = 3.30. V=19.98ml NaOH mol/L added mmoles acid left unreacted = 2.000 - 1.9800 =0.02000 volume solu

17、tion = 20.00+19.98 = 39.98mlpH = 4.3. V=20.00ml NaOH mol/L added It is arrived at the equivalence point, the point in this titration: H3O+ = OH- H30+ = 1.0010-7 (mol/L) pH = 7.00. V=20.02ml NaOH mol/L added after the equivalence point mmoles base unreacted = 2.002-2.000 = 0.02000 volume solution = 2

18、0.00+20.02 = 40.02ml pOH = 4.30 pH =14-4.3=9.7.V=20.20ml NaOH mol/L added pOH = 3.30 pH =14-3.3=10.7 .V=22.00ml NaOH mol/L added pOH = 2.32 pH =14-2.32 =11.68.V=40.00ml NaOH mol/L added pOH = 1.5 pH =14-1.5=12.51020Titration jump Figure 10-1: A titration curve for the titration of a strong acid by a

19、 strong base. The magnitude of the titration jump will depend on both the concentration of the acid and the concentration of the base. Usually, the concentration of standard solution should be 0.10000.5000mol/Lcurve1. 100ml 0.1 mol/L HCl versus 0.1mol/L NaOHcurve2. 100ml 0.01 mol/L HCl versus 0.01mo

20、l/L NaOHcurve3. 100ml 0.001 mol/L HCl versus 0.001mol/L NaOH Titration curves at different concentrationtitration jump p4.39.7 5.45.38.7 3.4 3 6.37.7 1.4 突跃范围与酸碱浓度的关系 溶液的浓度愈稀，滴定突跃范围愈窄；若酸碱浓度低于104 mo1L1时，没有明显的滴定突跃。酸碱溶液的浓度高时，滴定突跃范围就宽。但每滴溶液中所含的酸碱溶液的量增多，在计量点附近多加或少加半滴（0.02ml）标准溶液而引起的误差较大。 所以在分析工作中，通常采用0.1

21、0.5 mo1L1的酸碱标准溶液。 2、Titration of a Weak Acid with a Strong Base titrant: 0.1000mol/L NaOH (in buret)titrate: 0.1000mol/L HAc 20.00ml (in conical flask). 2-1. V =0.00ml NaOH HAc + H2O Ac- + H3O+ 2-2. Less than the equivalent volume of NaOH has been added HAc(aq) + OH-(aq) = H2O(l) + Ac-(aq) 1). V = 1

22、8.00ml of 0.1000mol/LNaOH has been added 2).V = 19.98ml of 0.1000mol/LNaOH has been added: 3. V =20.00ml The equivalent volume of NaOH has been added Ac- + H2O = HAc + OH- at equivalence point: at equivalence point pOH = 5.27 pH = pKw pOH =14-5.27 = 8.734 V=20.02ml More than the equivalent volume of

23、 NaOH has been added . pOH = 4.30 pH = pKw-pOH =14.00-4.30 = 9.70Figure10-2: A titration curve for the titration of a weak acid by a strong base. titration jump 7.759.7 p 1.9512Figure10-2: A titration curve for the titration of a weak acid by a strong base. the titration curve with the acid dissocia

24、tion constant of HA. Figure: Calculated curves showing the titration of 0.1000mol/LNaOH with 0.02mol/LHA . As the acid becomes weaker, the change in slope at the equivalence point becomes less abrupt.浓度相同 强度不同的弱酸： Ka愈大，酸性愈强，突跃范围愈大；反之亦然。 实验表明，弱酸 c Ka10-8 条件下，能够准确被滴定。 作为判断弱酸能否被滴定的依据。If Ka 9), there is

25、 no titration jump, so the weak acid can not be titrate by strong basethe requirement of a weak acid can be titrated: accuracyTitration of a Weak Acid with a Strong Base (中文书 p246)Detection of the end point: indicatorAn acid-base indicator is itself an weak acid or weak base that is highly colored.

26、The color of the ionized form is markedly different from that of the un-ionized form.These substances are usually composed of highly conjugated organic constituentsAssume the indicator is a weak acid HIn H+ + In-Base colorAcid color甲基橙此式说明：当选择的指示剂一定，pKHIn一定，溶液的pH值决定指示剂 的比值，使其在不同酸度的溶液中显示不同的颜色。 (red)

27、(yellow)The ratio of the concentration of the two form: 1) Un-ionized form 2) Ionized formIndicators require a transition range变色范围: Indicators require a transition range: change two pH unitsDuring this transition the observed color is a mixture of the two colorsThe indicator changes colore over a p

28、H range， generally only one color is observed pH=pKHIn (transition point 变色点of indicator )溴甲酚绿溴百里酚兰溴酚兰麝香草酚兰茜草黄8.0Choosing an indicator The pKHIn of the indicator should be close to the pH of the equivalence point. we seek an indicator whose transition range overlaps the steepest part of the titratio

29、n jump as closely as possible. Some colors are easier to see than others8.0201.指示剂的用量： 在不影响终点颜色观察的前提下，少加为宜； 使其在终点时的颜色变化便于观察。 2.温度： 引起指示剂解离常数的变化，变色范围因此而改变。影响酸碱指示剂变色范围的因素少加: 颜色冲淡，肉眼难以分辨和观察。多加: 不易产生颜色突变，会迟钝。 （本身消耗部分滴定剂， 带来误差）。 混合指示剂（缩小变色范围的方法） 利用颜色的互补作用使颜色变化敏锐，易观察。如混合指示剂甲基紫+溴甲酚绿1.pH 指示剂惰性染料（色不随pH变）2.两种

30、不同变色范围的pH指示剂范围窄了pH4.0 pH5.6 pH4.2 pH6.3 黄 蓝 红 紫 红 绿 溴甲酚绿 甲基紫 pH5 5.210-3 Coordination Titrations Complexometric titration (coordination titration or EDTA titration): A titration based on formation of a complex ion is called . Chelating agent: An organic agent that has two or more groups capable of c

31、omplexing with a metal ion is called a chelating agent. Chelate: the complex formed is called a chelate. Ligand: the chelating agent is called the ligand.EDTA: Ethylenediaminetetraacetic acid (EDTA)is by far the most widely used chelator in analytical chemistry. HOOCCH2 CH2COOH H+NCH2CH2N+H HOOCCH2

32、CH2COOH Hexaprotic system H6Y2+ Ionization of EDTA H6Y2+ H5Y+ + H+ Ka1 = 1.3610-1 H5Y+ H4Y + H+ Ka2 = 2.510-2 H4Y H3Y- + H+ Ka3 = 1.010-2 H3Y- H2Y2- + H+ Ka4 = 2.1610-3 H2Y2- HY3- + H+ Ka5 = 6.9210-7 HY3- Y4- + H+ Ka6 = 5.5210-11Acid-Base properties pK1=0.0 pK2=1.5 pK3=2.0 pK4=2.66 pK5=6.16 pK6=10.2

33、4 各型体浓度取决于溶液pH值: pH 1 强酸性溶液 H6Y2+ pH 2.676.16 主要H2Y2- pH 10.26碱性溶液 Y4-Characteristics of EDTA complexes 1) It forms strong 1:1complexes with most metal ions. 2) Metal complexes is easy to dissolve. 3) Stability. octahedral compoundHNCMOMn+Y4- MYn-4离子lgKf离子lgKf离子lgKf离子lgKfLi+2.79Eu3+17.35Fe2+14.32Cd2

34、+16.46Na+1.66Tb3+17.67Fe3+25.10Hg2+21.70Ba2+9.30Dy3+18.30Co2+16.31Al3+16.30Mg2+8.70Yb3+19.57Co3+36.00Sn2+22.11Ca2+10.69Ti3+21.30Ni2+18.62Pb2+18.08Sr2+8.73Cr3+23.40Cu2+18.80Bi3+27.94La3+15.50MoO2 + 28.00Ag+7.32Th4+23.20Sm3+17.14Mn2+13.87Zn2+16.50U()25.80表 EDTA配合物的lg Kf（I= 0.1, 2025）主反应： M + Y = MY Kf

35、副反应： Y + H+ HY、H2Y、H6Y EDTA的酸效应 M + L ML、ML2、MLn 金属离子的配位效应 1 酸度的影响 EDTA的酸效应 由于酸度（H+）的影响导致EDTA的配位能力降低的现象。 则酸效应越强，EDTA的有效浓度越小，其配位能力越弱。 2.金属离子的配位效应 由于配位剂L的存在导致主反应能力降低的现象。 影响EDTA配合物稳定性的因素Figure (10-7) gives the minimum pH needed for titration of many metal ions. 配位滴定中酸度的控制EDTA的酸效应曲线问题：Mg2+ Zn2+ 混合滴定分别测定

36、含量？Mg2+ Zn2+Zn2+ 调节pH=4 滴定Mg2+ 调节pH=10 滴定2. 其它配位剂的影响金属离子的配位效应主反应： M + Y = MY Kf M + L ML、ML2、MLn 金属离子的配位效应 由于配位剂L的存在导致主反应能力降低的现象。Zn2+ Al3+ EDTAAl3+ + 6F- = AlF63-NH4F(掩蔽剂)问题: Zn2+ 滴定含量测定？ MLn的稳定性越高，配位效应越强 Kf ? 用EDTA： 滴定金属离子M， 当滴定到计量点附近时， 溶液pM值产生突跃。配位滴定曲线如EDTA滴定Ca2+， 通过计算过程中各点的pM值，绘制出一条曲线（右图）2040V 1金

37、属指示剂配合物与金属指示剂本身色差要大。 2指示剂与金属离子的显色反应要灵敏、迅速、可逆。 3金属指示剂配合物及金属指示剂本身要易溶。 4金属指示剂配合物的稳定性要适宜。A metal ion indicator is a compound whose color changes when it binds to a metal ion.Metal Ion Indicators金属指示剂应具备的条件:特点：(与酸碱指示剂比较) 金属离子指示剂通过M的变化确定终点 酸碱指示剂通过H+ 的变化确定终点Metal Ion Indicators Eriochrome Black T is a typi

38、cal indicator.It contains three ionizable protons, so we will represent it by H3In. -H+ -H+ H2In- HIn2- In3- pKa2=6.3 pKa3=11.6pH12 orangepH=810 blue铬黑T1) Before EDTA was added Mg2+ + HIn2- MgIn- + H+ (blue) (red)2) Among titration Mg2+ + HY3- MgY2- + H+ (colorless) (colorless)3) End point MgIn- + H

39、Y3- MgY2- + HIn2- (red) (colorless) (colorless) (blue) KMgY2 - KMgIn- This can be used for the titration of Mg2+ with EDTAOf couse, the metal indicator complex must be less stable than that of the metal-EDTA complex, or else the EDTA will not displace it from the metal.on the other hand, it must not

40、 be too weak,or the EDTA will stare replacing it at the beginning of the titration, and a diffuse end point will result. In general, the metal indicator complex should be 10 to 100 time less stable than the metal-titrant complex.Application of EDTA titration Determine overall hardness of waterHard w

41、ater and soft waterOverall hardness of water is amount of Ca2+ and Mg2+ in water. 1= 1mmol/L Ca2+ and Mg2+ Titrant : EDTA (Na2H2Y) pH = 8 10 (NH3-NH4Cl buffer) Indicator : EBTCaY2- MgY2- MgIn- CaIn- 1) Before EDTA was added (pH 10) Mg2+ + HIn2- MgIn- + H+ (blue) (red) 2) Among titration (pH =8 10) C

42、a2+ + HY3- CaY2- + H+ Mg2+ + HY3- MgY2- + H+ 3) End point (pH8) MgIn- + HY3- MgY2- + HIn2- (red) (colorless) (colorless) (blue)10-4 Analytical Error and Significant Figures定量分析中的误差: 受方法、仪器、试剂、操作人员等的多种因素的影响，分析过程中的测量误差是客观存在、不可避免的。 了解分析过程中误差产生的原因及其出现的规律，以便采取相应的措施减小误差，以提高分析结果的准确度。Systematic Error or Det

43、erminate Error: It can in principle be discovered and corrected. Errors of the method Operative errors Instrumental errors Reagent errorsAnalytical Error定量分析误差产生的原因1. 系统误差 由某种固定因素引起的误差，是在测量过程中重复出现、正负及大小可测，并具有单向性的误差。可通过其他方法验证而加以校正。分为： 方法误差 由所选择的方法本身决定，无法避免 操作误差 操作者本人所引起，可消除或减少 仪器及试剂误差 由仪器性能或试剂性质决定 个人

44、误差 由分析人员的主观原因造成 Indeterminate Errors or Random Errors: which represent the experimental uncertainty that occurs in any measurement.纠正方法：“多次测量，取平均值” 以减少偶然误差。偶然误差又称不定误差或随机误差，由于一些难以察觉的或不可控制的随机因素导致的误差。系统误差与偶然误差之比较Accuracy And Precision Accuracy is the degree of agreement between the measured value and t

45、he true value.Precision is defined as the degree of agreement between replicate measurements of the same quantity. Ways of Expressing Accuracy 1. Absolute Errors (E)2. Relative Error (RE)准确度(accuracy)在一定测量精度的条件下分 析结果与真值的接近程度。常以绝对误差(E)和相对误差(RE)来表示。1. Absolute Errors (E):2. Relative Error (RE) The abs

46、olute error expressed as a percentage of the true value is the relative error. RE = E/T100% The difference between the true value (T) and the measured value (x)。 E = x T(测定值与真值之差)（绝对误差在真值中所占的百分率）例真值称得量绝对误差(x T)相对误差 (x T)体重62.5kg62.4kg0.1kg买白糖1kg0.9kg0.1kg抓中药0.2kg0.1kg0.1kg从表中的例子中你看出了什么问题T用相对误差比绝对误差表

47、示准确度结果要好Sample of Weigh by Analysis BalanceW1 =0.0021gW2=0.5432gAbsolute Errors (E)?E1= E2 0.0001RE = E/T100%RE1 =1 / 21100% RE1 RE2 =1 / 5432100% RE2 误差是相对真值而言的。而真值是客观存在的数值，我们是不知道的。T = ? 实际工作中如何获得真实值?_以测定多次的平均值来表示。 Absolute deviation (d)Relative deviation(Rd)Absolute average deviation (d )Relative

48、average deviation (Rd) 多次重复测定某一量时所得测量值的离散程度， 常以偏差来表示。精密度(precision)偏差的表示方法绝对偏差相对偏差 相对平均偏差（精密度）测定值与平均值之差 绝对偏差占平均值的百分率 平均偏差占平均值的百分率化学定量分析（常量分析）要求精密度在0.1% 0.3%之间。以平均偏差和相对偏差表示精密度比较简单。在一系列测定结果中，小偏差占多数，大偏差占少数，如果按总的测定次数计算算术平均值偏差，所得结果会偏小，大偏差得不到应有的反映。为了凸显较大偏差的影响引入标准偏差(standard deviation) 。n:为测定次数relation sta

49、ndard deviation(RSD)coefficient of variation（CV） 是标准偏差占平均值的百分数滴定分析为常量分析，相对平均偏差应小于0.2%举例：滴定管的读数误差为0.02mL。计算消耗滴定剂 2mL，20mL，和40mL 时的相对误差。解：当 V2mL 时， RE1 0.02/2.00 100% =1%； V20mL 时，RE2 0.02/20.0 100% =0.1% V40mL 时，RE30.02/40.0 100% = 0.05% 若要求滴定分析的相对误差在0.2以内，消耗滴定剂的体积应不小于多少毫升？分析： 若要保证整个滴定分析的相对误差在0.2以内，

50、读数时的相对误差必须在0.1以内。 V（E/ RE）1000.02/0.1%=20 ml 答：为使滴定分析的相对误差在0.2以内， 滴定剂的体积应不小于20ml。XXddd/XS39.8739.9440.1039.7439.9039.8839.905-0.035+0.035+0.195-0.165-0.005-0.0250.0771.920.117相对标准偏差 也称变异系数(CV)，其计算式为： CV =S / x 100%本例中 CV = 0.29%例:在分析某一样品中Cl含量为：39.87,39.94,40.10, 39.74,39.90,39.88，求各偏差值减免误差的途径1、选择合适的分析方法 容量分析的准确度高。仪器分析灵敏度高。2、减少测量误差 应减少每个测量环节的误差，天平称量应 取样0.2克以上，滴定剂体积应大于20毫升。3、增加平行测定次数，减小偶然误差 分析化学通常要求在3-5次。提高分析结果准确度的方法 1). 对照试验以标准样品代替试样进行的测定，以校正测定过程中的系统误差。 方法有标准样比对法或加入回收法(用标准样品、管理样、人工合成样等)、选择标准方法(主要是国家标准等)、相互校验(内检、外检等)。2). 空白试验不加试样但完全照测定方法进行操作的试验，消除由干扰杂质或溶剂对器皿腐蚀等所产生的系统误差