beer lambert定律文档格式.docx

1、一. Lambert-Beer 定律光吸收基本定律“ Lambert-Beer 定律 ” 是说明物质对单色光吸收的强弱与吸光物质的浓度（c）和 液层厚度 （b）间的关系的定律，是光吸收的基本定律，是紫外-可见光度法定量的基础。Lambert定律 吸收与液层厚度 （b）间的关系Beer 定律 吸收与物质的浓度（c）间的关系“ Lambert-Beer 定律 ”可简述如下：当一束平行的单色光通过含有均匀的吸光物质的吸收池（或气体、固体）时，光的一部分被溶液吸收，一部分透过溶液，一部分被吸收池表面反射；设：入射光强度为 Io，吸收光强度为Ia，透过光强度为It，反射光强度为Ir，则它们之间的关系应为

2、： Io = Ia + It + Ir （4）若 吸收池的质量和厚度都相同，则 Ir 基本不变，在具体测定操作时 Ir 的影响可互相抵消（与吸光物质的 c及 b 无关）上式可简化为： Io= Ia + It （5）实验证明：当一束强度为 I0 的单色光通过浓度为 c、液层厚度为 b 的溶液时，一部分光被溶液中的吸光物质吸收后透过光的强度为 It ，则 它们之间的关系为：称为透光率，用 T % 表示。称为 吸光度，用 A 表示则 A = -lgT = K b c （7） 此即 Lambert-Beer 定律 数学表达式。L-B 定律 可表述为：当一束平行的单色光通过溶液时，溶液的吸光度 （A）

3、与溶液的浓度 （C） 和厚度 （b） 的乘积成正比。它是分光光度法定量分析的依据。二. 吸光度的加和性设 某一波长（ ）的辐射通过几个相同厚度的不同溶液c1，c2. cn，其透射光强度分别为 I1， I2. In，根据吸光度定义：这一吸光体系的总吸光度为而 各溶液的吸光度分别为：吸光度的和为：即 几个（同厚度）溶液的吸光度等于各分层吸光度之和。如果溶液中同时含有 n 中吸光物质，只要各组分之间无相互作用（不因共存而改变本身的吸光特性），则：A = K1C1 b1 + K2C2 b2 + KnCn bn = A1 + A2+ + An （10）应用：进行光度分析时，试剂或溶剂有吸收，则可由所测的

4、总吸光度 A 中扣除，即 以试剂或溶剂为空白的依据； 测定多组分混合物； 校正干扰。三. 吸光系数Lambert-Beer 定律中的比例系数“K ”的物理意义是：吸光物质在单位浓度、单位厚度时的吸光度。一定条件（T、 及溶剂）下， K 是物质的特征常数，是定性的依据。K 在标准曲线上为斜率，是定量的依据。常有两种表示方法：1. 摩尔吸光系数（ ）：当 c用 mol/L 、b 用 cm 为单位时，用摩尔吸光系数 表示，单位为 L/molcm A = c （11） 与 b及 c 无关。 一般不超过 105 数量级，通常： 104 为强吸收； 104 为中强吸收。吸收系数不可能直接用 1 mol/L

5、 浓度的吸光物质测量，一般是由较稀溶液的吸光系数换算得到。2. 吸光系数 当 c 用 g /L ，b 用 cm 为单位时，K 用吸光系数 a 表示，单位为 L/g A = a （12） 与 a 之间的关系为： = M a（13） 通常多用于研究分子结构a 多用于测定含量。四. 引起偏离 Lambert-Beer 定律的因素根据 L-B 定律，A与c的关系应是一条通过原点的直线，称为“标准曲线”。但事实上往往容易发生偏离直线的现象而引起误差，尤其是在高浓度时。导致偏离L-B定律的因素主要有：1. 吸收定律本身的局限性事实上， L-B 定律是一个有限的定律，只有在稀溶液中才能成立。由于在高浓度时（

6、通常 C 0.01mol/L），吸收质点之间的平均距离缩小到一定程度，邻近质点彼此的电荷分布都会相互受到影响，此影响能改变它们对特定辐射的吸收能力，相互影响程度取决于C，因此，此现象可导致 A与 C 线性关系发生偏差。此外，（ n 为折射率）只有当 c 0.01mol/L（低浓度）时，n 基本不变，才能用 代替 真 。2. 化学因素 溶液中的溶质可因 c 的改变而有离解、缔合、配位以及与溶剂间的作用等原因而发生偏离 L-B 定律的现象。例：在水溶液中，Cr（）的两种离子存在如下平衡Cr2O42- + H2O 2CrO42- + 2H+Cr2O42- 、CrO42- 有不同的 A 值，溶液的 A

7、 值是二种离子的 A 之和。但由于随着浓度的改变（稀释）或改变溶液的 pH 值， Cr2O42- /CrO42- 会发生变化，使C总与 A总 的关系偏离直线。消除方法：控制条件。3. 仪器因素（非单色光的影响）L-B 定律的重要前提是“单色光”，即 只有一种波长的光；实际上，真正的单色光却难以得到。由于吸光物质对不同 的光的吸收能力不同（ 不同），就导致对的偏离。“单色光”仅是一种理想情况，即使用棱镜或光栅等所得到的“单色光”实际上是有一定波长范围的光谱带，“单色光”的纯度与狭逢宽度有关，狭缝越窄，他所包含的波长范围也越窄。4. 其它光学因素（1）散射和反射：浑浊溶液由于散射光和反射光而偏离

8、L-B（2）非平行光IntroductionMany compounds absorb ultraviolet （UV） or visible （Vis.） light. The diagram below shows a beam of monochromatic radiation of radiant power P0, directed at a sample solution. Absorption takes place and the beam of radiation leaving the sample has radiant power P.The amount of ra

9、diation absorbed may be measured in a number of ways: Transmittance, T = P / P0% Transmittance, %T = 100 T Absorbance, A=log10 P0 /Plog10 1/T log10 100%T2-log10 %TThe last equation, A = 2 - log10 %T , is worth remembering because it allows you to easily calculate absorbance from percentage transmitt

10、ance data.The relationship between absorbance and transmittance is illustrated in the following diagram:So, if all the light passes through a solution without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero,

11、 and absorption is infinite.The Beer-Lambert LawNow let us look at the Beer-Lambert law and explore its significance. This is important because people who use the law often dont understand it - even though the equation representing the law is so straightforward:A=ebcWhere A is absorbance （no units,

12、since A = log10 P0 / P ）e is the molar absorbtivity with units of L mol-1 cm-1b is the path length of the sample - that is, the path length of the cuvette in which the sample is contained. We will express this measurement in centimetres.c is the concentration of the compound in solution, expressed i

13、n mol L-1The reason why we prefer to express the law with this equation is because absorbance is directly proportional to the other parameters, as long as the law is obeyed. We are not going to deal with deviations from the law. Lets have a look at a few questions.Question : Why do we prefer to expr

14、ess the Beer-Lambert law using absorbance as a measure of the absorption rather than %T ?Answer : To begin, lets think about the equations.%T = 100 P/P0 = e -ebcNow, suppose we have a solution of copper sulphate （which appears blue because it has an absorption maximum at 600 nm）. We look at the way

15、in which the intensity of the light （radiant power） changes as it passes through the solution in a 1 cm cuvette. We will look at the reduction every 0.2 cm as shown in the diagram below. The Law says that the fraction of the light absorbed by each layer of solution is the same. For our illustration,

16、 we will suppose that this fraction is 0.5 for each 0.2 cm layer and calculate the following data:Path length / cm 0 0.2 0.4 0.6 0.8 1.0 %T 100 50 25 12.5 6.25 3.125 Absorbance 0.3 0.9 1.2 1.5 A = ebc tells us that absorbance depends on the total quantity of the absorbing compound in the light path

17、through the cuvette. If we plot absorbance against concentration, we get a straight line passing through the origin （0,0）.Note that the Law is not obeyed at high concentrations. This deviation from the Law is not dealt with here.The linear relationship between concentration and absorbance is both si

18、mple and straightforward, which is why we prefer to express the Beer-Lambert law using absorbance as a measure of the absorption rather than %T. What is the significance of the molar absorbtivity, e ? To begin we will rearrange the equation A = ebc :e = A / bcIn words, this relationship can be state

19、d as e is a measure of the amount of light absorbed per unit concentration.Molar absorbtivity is a constant for a particular substance, so if the concentration of the solution is halved so is the absorbance, which is exactly what you would expect.Let us take a compound with a very high value of mola

20、r absorbtivity, say 100,000 L mol-1 cm-1, which is in a solution in a 1 cm pathlength cuvette and gives an absorbance of 1.e = 1 / 1 cTherefore, c = 1 / 100,000 = 1 10-5 mol L-1Now let us take a compound with a very low value of e, say 20 L mol-1 cm-1 which is in solution in a 1 cm pathlength cuvett

21、e and gives an absorbance of 1.Therefore, c = 1 / 20 = 0.05 mol L-1The answer is now obvious - a compound with a high molar absorbtivity is very effective at absorbing light （of the appropriate wavelength）, and hence low concentrations of a compound with a high molar absorbtivity can be easily detec

22、ted. What is the molar absorbtivity of Cu2+ ions in an aqueous solution of CuSO4 ? It is either 20 or 100,000 L mol-1 cm-1 I am guessing that you think the higher value is correct, because copper sulphate solutions you have seen are usually a beautiful bright blue colour. However, the actual molar a

23、bsorbtivity value is 20 L mol-1 cm-1 ! The bright blue colour is seen because the concentration of the solution is very high.b-carotene is an organic compound found in vegatables and is responsible for the colour of carrots. It is found at exceedingly low concentrations. You may not be surprised to

24、learn that the molar absorbtivity of b-carotene is 100,000 L mol-1 cm-1 !Review your learningYou should now have a good understanding of the Beer-Lambert Law; the different ways in which we can report absorption, and how they relate to each other. You should also understand the importance of molar a

25、bsorbtivity, and how this affects the limit of detection of a particular compound.Beer-Lambert LawThe Beer-Lambert law （or Beers law） is the linear relationship between absorbance and concentration of an absorbing species. The general Beer-Lambert law is usually written as:A = a（lambda） * b * cwhere

26、 A is the measured absorbance, a（lambda） is a wavelength-dependent absorptivity coefficient, b is the path length, and c is the analyte concentration. When working in concentration units of molarity, the Beer-Lambert law is written as:A = epsilon * b * cwhere epsilon is the wavelength-dependent mola

27、r absorptivity coefficient with units of M-1 cm-1. InstrumentationExperimental measurements are usually made in terms of transmittance （T）, which is defined as:T = I / Iowhere I is the light intensity after it passes through the sample and Io is the initial light intensity. The relation between A an

28、d T is:A = -log T = - log （I / Io）. Absorption of light by a sampleModern absorption instruments can usually display the data as either transmittance, %-transmittance, or absorbance. An unknown concentration of an analyte can be determined by measuring the amount of light that a sample absorbs and applying Beers law. If the absorptivi