Uv-visible spectroscopy

analytical chemistry

1. Prepared by: Karwan O. Ali Yousif T. Maaroof Mzgin . M. Ayoob UV- VISIBLE SPECTROSCOPY

2. What is spectroscopy? The interactions of radiation and matter are the subject of the science called spectroscopy. Spectroscopic analytical methods are based on measuring the amount of radiation produced or absorbed by molecular or atomic species of interest

3. The Electromagnetic Spectrum

4. Light exhibits wave property during its propagation and energy particle during its interaction with matter. The double nature of light (waves and particles) is known as dualism. Dual nature of light

5. Light consist of energy packets, known as photons. The energy (E) of photons is proportional to the frequency i.e. related to c and  . It can be expressed by max plank relation: E = h  (  = C /  ) where h = max plank constant = 6.63 x 10 -27 erg., sec.) i.e. E   or E  1/   

6. For analytical purposes we use the region of I.R, visible and U.V radiations. UV radiation region is classified into : far UV from (10nm-200nm) and near UV from (200nm-380nm

7. Why Is a Red Solution Red?

8. When a molecule interact with radiant energy, the molecule is said to be excited , because the outer valence electrons undergo transition from original energy level ground state (E g) to an exited state ( E s). Interaction of a substance with EMR Excited state Es Ground state E g

9. When a molecule in the ground state absorbs EMR, 3 energy state transitions will take place. These types of transition are : 1) Electronic 2 ) Vibrational 3 ) Rotational.

10. When the molecule absorb Visible and U.V region. Raising electrons to a higher energy level, raising the Vibration of molecule, and increasing rotation of the molecule (Electronic transition energy + Vibrational transition energy + Rotational transition energy) 1) Electronic

11. When the molecule absorb I.R region. Raising the Vibration of molecule and increasing rotation of the molecule (Vibrational transition energy + Rotational transition energy) 2) Vibrational

12. When the molecule absorbs F.I.R and Microwave regions. Increasing rotation of the molecule (Rotational transition energy ). 3) Rotational

13. Absorption measurements based upon ultraviolet and visible radiation find widespread application for the quantitative determination of a large variety species [1] . Beer’s Law: A = -logT = logP /P = abc =  bc = 2 - log%T Where T = transmittance, T = percentage transmittance, P = transmitted power of radiation, Po = incident power of radiation, A = absorbance, a = absorptivity, b = path length, c = concentration,  = molar absorptivity, extinction coefficient An Introduction to Ultraviolet/Visible Molecular Absorption Spectrometry

14. The Quantitative Picture Where the absorbance A has no units, since A = log 10 P / P  Is the molar absorbtivity with units of L mol -1 cm -1 b is the path length of the sample in cm c is the concentration of the compound in solution, expressed in mol L -1 (or M , molarity)

15. The Beer-Lambert Law (Beer’s Law): A =  b c

16. Monochromatic incident radiation (all molecules absorb light of one  ) Absorbers independent (Absorbing molecules act independently of one another i.e., low c) Path length is uniform (all rays travel the same distance in sample) No scattering Absorbing medium is optically homogeneous Incident beam is not large enough to cause saturation All rays should be parallel to each other and perpendicular to surface of medium Assumptions in derivation of Beer’s Law

17. Deviations from Beer’s Law Real Limitations Beer’s law is successful in describing the absorption behavior of dilute solutions only ; in this sense it is a limiting law. At high concentrations ( > 0.01M ),the average distance between the species responsible for absorption is diminished to the point where each affects the charge distribution of its neighbors This interaction, in turn, can alter the species’ ability to absorb at a given wavelength of radiation thus leading to a deviation from Beer’s law [2] . A similar effect is sometimes encountered in solutions containing low absorber concentrations and high concentrations of other species, particularly electrolytes. Beer’s law is valid at low concentrations , but breaks down at higher concentrations For linearity, A < 1

18. Deviations from Beer's law also arise because ε is dependent upon the refractive index of the solution. Thus, if concentration changes cause significant alterations in the refractive index η of a solution, departures from Beer's law are observed. A correction for this effect can be made by substitution of the quantity εη /( η 2 + 2) 2 for ε in the Beer equation, as shown below [2 ] : A= [ εη b /( η 2 + 2) 2 ] bC In general, this correction is never very large and is rarely significant at concentrations less than 0.01 M.

19. Chemical deviations from Beer’s law are caused by shifts in the position of a chemical or physical equilibrium involving the absorbing species. A common example of this behavior is found with acid/base indicators. Deviations arising from chemical factors can only be observed when concentrations are changed Chemical Deviations HIn K a H + + In - Red, l =600nm Colorless Phenolphthalein : If solution is buffered, then pH is constant and [HIn ] is related to absorbance. But, if un buffered solution , equilibrium will shift depending on total analyte concentration

20. instrument may be caused by fluctuations in the power-supply voltage, an unstable light source, or a non-linear response of the detector-amplifier system Polychromatic Radiation All monochromators, regardless of quality and size, have a finite resolving power and therefore minimum instrumental bandwidth. Polychromatic radiation (i.e., light of more than one  ) Instrumental Factors

21. Band A shows little deviation, because ε does not change greatly throughout the band. Band B shows marked deviations because ε undergoes significant changes in this region

22. The width of the image produced is thus an important measure of the quality of the performance of a spectrometer. The figure below shows the loss of detail that accompanies the use of wider slits. It is evident that an increase in slit width brings about a loss of spectral detail Effect of Slit Width on Absorbance Measurements

23. quantitative measurement of narrow absorption bands demand the use of narrow slits widths. Unfortunately, a decrease in slit width is accompanied by a second-order power reduction in the radiant energy; at very narrow settings spectral detail may be lost owing to an increase in the signal-to-noise ratio. In general, it is good practice to narrow slits no more than is necessary for good resolution for the spectrum at hand Another effect of slit width is the change of absorbance values that accompany a change in the slit width. The figure below illustrates this effect. Note that the peak absorbance values increase significantly (by as much as 70% in one instance) as the slit width decreases

24. The basic components of analytical instruments for absorption spectroscopy, as well as for emission and fluorescence spectroscopy, are remarkably alike in function and in general performance requirements whether the instruments are designed for ultraviolet (UV), visible, or infrared (lR) radiation. We often call the UV/visible and IR regions of the spectrum the optical region Instruments for Optical Spectrometry

25. a stable source of radiant energy a wavelength selector that isolates a limited region of the spectrum for measurement one or more sample containers a radiation detector, which converts radiant energy to a measurable electrical signal a signal processing and readout unit, usually consisting of electronic hardware and, in modern instruments, a computer. INSTRUMENT COMPONENTS

26. To be suitable for spectroscopic studies, a source must generate a beam of radiation that is sufficiently powerful to allow easy detection and measurement. In addition, its output power should be stable for reasonable periods of time. Typically, for good stability, a well-regulated power supply must provide electrical power for the source Spectroscopic Sources Spectroscopic sources are of two types: A- Continuum sources , which emit radiation that changes in intensity only slowly as a function of wavelength. B- Line sources , which emit a limited number of spectral lines, each of which spans a very limited wavelength range. The distinction between these sources is illustrated in Figure bellow. Sources can also be classified as continuous sources, which emit radiation continuously with time, or pulsed sources , which emit radiation in bursts

27. tungsten lamp of the type used in spectroscopy and its spectrum (b). Intensity of the tungsten source is usually quite low at wavelengths shorter than about 350 nm. Note that the intensity reaches a maximum in the near-IR region of the spectrum (<1200 nm in this case). Tungsten lamp

28. Tungsten/halogen lamp Tungsten/halogen lamps, also called quartz/halogen lamps, contain a small amount of iodine within the quartz envelope that houses the filament. Quartz allows the filament to be operated at a temperature of about 3500 K, leading to higher intensities and extending the range of the lamp well into the UV. The lifetime of a tungsten/halogen lamp is more than double that of an ordinary tungsten lamp , which is limited by sublimation of tungsten from the filament. In the presence of iodine, the sublimed tungsten reacts to give gaseous WI2 molecules. These molecules then diffuse back to the hot filament where they decompose, redeposit W atoms on the filament, and release iodine. Tungsten/halogen lamps are finding ever-increasing use in spectroscopic instruments because of their extended wavelength range, greater intensity, and longer life

29. A deuterium lamp consists of a cylindrical tube containing deuterium at low pressure, with a quartz window from which the radiation exits Deuterium lamp

30. The word laser originally was the upper-case LASER, the acronym from Light Amplification by Stimulated Emission of Radiation. Lasers have become useful as sources in certain types of analytical spectroscopy. To understand how a laser works, consider an assembly of atoms or molecules interacting with an electromagnetic wave. Laser radiation is highly directional. Spectrally pure, coherent. and of high intensity. These properties have made possible many unique research applications that cannot easily be achieved with conventional sources Laser Sources

31. Spectroscopic instruments in the UV and visible regions are usually equipped with one or more devices to restrict the radiation being measured to a narrow band that is absorbed or emitted by the analyte. Such devices greatly enhance both the selectivity and the sensitivity of an instrument. In addition, for absorption measurements, narrow bands of radiation greatly diminish the chance of Beer's Jaw deviations due to polychromatic radiation. Many instruments use a monochromator or filter to isolate the desired wavelength band so that only the band of interest is detected and measured. Others use a spectrograph to spread out, or disperse, the wavelength so that they can be detected with a multichannel detector Wavelength Selectors

32. Monochromators generally have a diffraction grating to disperse the radiation into its component wavelengths, as shown in Figure bellow By rotating the grating, different Wavelengths can be made to pass through an exit slit Monochromators consist of: 1- entrance slit 2- collimating mirror or lens 3- a prism or grating 5- focal plane 6- exit slit Older instruments used prisms for this purpose Monochromators

33. Older instruments used prisms for this purpose

34. Radiation from a source enters the monochromator via a narrow rectangular opening, or slit. The radiation is then collimated by a concave mirror , which produces a parallel beam that strikes the surface of a reflection grating. Angular dispersion results from diffraction , which occurs at the reflective surface Grating Monochromator

35. The effective band width of the monochromator depends on the size and quality of the dispersing element, the slit widths, and the focal length of the monochromator. A high-quality rnonochromator will exhibit an effective band-width of a few tenths of a nanometer or less in the ultraviolet/visible region. The effective bandwidth of a monochromator that is satisfactory for most quantitative applications is about 1 to 20 nm. Many monochromators are equipped with adjustable slits to permit some control over the bandwidth. A narrow slit decreases the effective bandwidth but also diminishes the power of the emergent beam . Thus, the minimum practical bandwidth may be limited by the sensitivity of the detector For qualitative analysis , narrow slits and minimum effective bandwidths are required if a spectrum is made up of narrow peaks. For quantitative work. however, wider slits permit operation of the detector system at lower amplification, which in turn provides greater reproducibility of response.

36. Most gratings in modern monochromators are replica gratings , which are obtained by making castings of a master grating. The latter consists of a hard, optically flat, polished surface on which a suitably shaped diamond tool has created a large number of parallel and closely spaced grooves. A grating for the ultraviolet and visible region will typically contain 300 to 2000 grooves/mm. with 1200 to 1400 being most common. The construction of a good master grating is tediou s, time consuming, and expensive because the grooves must be identical in size, exactly parallel, and equally spaced over the length of the grating (3 to 10 cm). Replica gratings are formed from a master grating by a liquid resin casting process that preserves virtually perfectly the optical accuracy of the original master grating on a clear resin surface. This surface is ordinarily made reflective by a coating of aluminum or, some times, gold or platinum

37. Radiation Filters Filters operate by absorbing all but a restricted band of radiation from a continuum source. As shown in Figure bellow, two types of filters are used in spectroscopy; interference filters and absorption filters. Interference filters are typically used for absorption measurements , and they generally transmit a much greater fraction of radiation at their nominal wavelengths than do absorption filters

38. Interference Filters Interference filters are used with ultraviolet and visible radiation, as well as with wavelengths up to about 14 µm in the infrared region. As the name implies, an interference filter relies on optical interference to provide a relatively narrow band of radiation. typically 5 to 20 nm in width. As shown in Figure bellow, an interference filter consists of a very thin layer of a transparent dielectric material (frequently calcium fluoride or magnesium fluoride) coated on both sides with a film of metal that is thin enough to transmit approximately half the radiation striking it and to reflect the other half.

39. the radiant power transmitted, fluoresced, or emitted must be detected in some manner and converted into a measurable quantity. A detector is a device that indicates the existence of some physical phenomenon. Familiar examples of detectors include photographic film (for indicating the presence of electromagnetic or radioactive radiation. The human eye is also a detector; it converts visible radiation into an electrical signal that is passed to the brain via a chain of neurons in the optic nerve and produces vision. Detecting and Measuring Radiant Energy

40. The term transducer is used to indicate the type of detector that converts quantities, such as light intensity, pH, mass, and temperature, into electrical signals that can be subsequently amplified, manipulated, and finally converted into numbers proportional to the magnitude of the original quantity. A transducer is a type of detector that converts various types of chemical and physical quantities into electrical signals such as electrical charge, current, or voltage.

41. There are two general types of transducers : Photons All photon detectors are based on the interaction of radiation with a reactive surface either to produce electrons (photoemission) or to promote electrons to energy states in which they can conduct electricity (photoconduction). Only UV, visible, and near-IR radiation possess enough energy to cause photoemission to occur; thus, photoemissive detectors are limited to wavelengths shorter than about 2 µm (2000 nm). Types of Transducers

42. Thermal detectors  (Heat) detect a temperature change in a material due to photon absorption Thermal detectors can be used over a wide range of wavelengths .Their main disadvantages are slow response time and lower sensivity relative to other types of detectors. 

43. Widely used types of photon detectors include phototubes, photomultiplier tubes, silicon photodiodes, and photodiode arrays. Photon Detectors Phototubes The response of a phototube or a photomultiplier tube is based on the photoelectric effect. a phototube consists of a semicylindrical photocathode and a wire anode sealed inside an evacuated transparent glass or quartz envelope. The concave surface of the cathode supports a layer of photoemissive material. such as an alkali metal or a metal oxide. that emits electrons when irradiated with light of the appropriate energy. When a voltage is applied across the electrodes, the emitted photoelectrons are attracted to the positively

44. charged wire anode, In the complete circuit, a photocurrent then results that is easily amplified and measured. The number of photoelectrons ejected from the photocathode per unit time is directly proportional to the radiant power of the beam striking the surface. With an applied voltage of about 90 V or more, all these photoelectrons are collected at the anode to give a photocurrent that is also proportional to the radiant power of the beam. Photoelectrons: are electrons that are ejected from a photosensitive surface by electromagnetic radiation. Photocurrent: is the current in an external circuit that is limited by the rate of ejection of photoelectrons .  

45. The photomultiplier tube (PMT) is similar in construction to the phototube but is significantly more sensitive. Its photocathode is similar to that of the phototube, with electrons being emitted on exposure to radiation. In place of a single wire anode. however, the PMT has a series of electrodes called dynodes , The electrons emitted from the cathode are accelerated toward the first dynode. which is maintained 90 to 100 V positive with respect to the cathode. Each accelerated photoelectron that strikes the dynode surface produces several electrons, called secondary electrons, that are then accelerated to dynode 2, which is held 90 to 100 V more positive than dynode l. Again, electron amplification results. By the time this process has been repeated at each of the dynodes, 105 to 107 electrons have been produced for each incident photon. This cascade of electrons is finally collected at the anode to provide an average current that is further amplified electronically and measured.

46. One of the major advantages of photomultipliers is their automatic internal amplification . About 10 6 to 10 7 electrons are produced at the anode for each photon that strikes the photocathode of a photomultiplier tube . Photomultiplier tubes are among the most widely used types of transducers for detecting ultraviolet/visible radiation. With modern electronic instrumentation, it is possible to detect the electron pulses resulting from the arrival of individual photons at the photocathode of a PMT. The pulses are counted, and the accumulated count is a measure of the intensity of the electromagnetic radiation impinging on the PMT. Photon counting is advantageous when light intensity, or the frequency of arrival of photons at t\1e photocathode, is low.

47. Photoconductive transducers consist of a thin film of a semiconductor material, such as lead sulfide, mercury cadmium telluride (MCT), or indium antimonide , deposited often on a nonconducting glass surface and sealed in an evacuated envelope. Absorption of radiation by these materials promotes nonconducting valence electrons to a higher energy state, which decreases the electrical resistance of the semiconductor. Typically, a photoconductor is placed in series with a voltage source and a load resistor, and the voltage drop across the load resistor serves as a measure of the radiant power of the beam of radiation. The PbS and InSb detectors are quite popular in the near-IR region of the spectrum. The MCT detector is useful in the mid- and far-IR regions when cooled with liquid N2 to minimize thermal noise. Photoconductive Cells:

48. Diode-Array Detectors Silicon photodiodes have become important recently because 1000 or more can be fabricated side by side on a single small silicon chip. (The width of individual diodes is about 0.02 mm). With one or two of the diode-array detectors placed along the length of the focal plane of a monochromator. All wavelengths can be monitored simultaneously, thus making high-speed spectroscopy possible. Silicon photodiode detectors respond extremely rapidly, usually in nanoseconds.

49. They are more sensitive than a vacuum phototube but considerably less sensitive than a photomultiplier tube.  

50. Sample containers, which are usually called cells or cuvettes must have windows that are transparent in the spectral region .Thus as shown in the figure below, quartz or fused silica is required for the UV region (wavelengths less than 350nm nm) and may be used in the visible region and out to about 3000 nm (3 µm) in the IR region. Silicate glass is ordinarily used for the 375 to 2000 nm region because of its low cost compared with quartz . Plastic cells are also used in the visible region . The most common window material for IR studies is crystalline sodium chloride , which is soluble in water and in some other solvents. Sample Containers

51. The best cells have windows that are perpendicular to the direction of the beam in order to minimize reflection losses. The most common cell path length for studies in the UV and visible regions is 1 cm; matched, calibrated cells of this size are available from several commercial sources. Many other cells with shorter and longer path lengths can be purchased.

52. For reasons of economy, cylindrical cells are sometimes used. Fingerprints, grease, or other deposits on the walls markedly alter the transmission characteristics of a cell . Thus, thorough cleaning before and after use is need , and care must be taken to avoid touching the windows after cleaning is complete. Matched cells should never be dried by heating in an oven or over a flame because this may cause physical damage or a change in path length ..

53. Photometers provide simple, relatively inexpensive tools for performing absorption measurements. Filter photometers are often more convenient and more rugged and are easier to maintain and use than the more sophisticated spectrophotometers. Furthermore, photometers characteristically have high radiant energy throughputs and thus good signal-to-noise ratios even with relatively simple and inexpensive transducers and circuitry. Photometers have the advantages of simplicity, ruggedness, and low cost .

54. Spectrophotometers offer the considerable advantage that the wavelength can be varied continuously, thus making it possible to record absorption spectra and is a scanning instrument (i.e. a spectrophotometer has a monochromator for separating the individual wavelengths of light). Several dozen models of spectrophotometers are available commercially. Most spectrophotometers cover the UV /visible and occasionally the near-infrared region, while photometers are most often used for the visible region.. Both photometers and spectrophotometers can be obtained in single- and double-beam varieties.

55. Single beam spectrometers Single beam spectrometers are relatively cheap, simple, portable & ideally suited to quantitative analysis . It is not possible to scan through the entire spectrum with such an instrument because both the source intensity & the detector response vary with the wavelength. To record an accurate value of the absorbance it is necessary to zero the instrument on a reference/blank before every measurement. Thus, this is essentially a single wavelength measurement of absorbance.

56. Voltage fluctuations and changes in light source present a problem When a heavy load is placed on the electric power system, lights dim and later brighten *If measurements are being taken on the spectrophotometer at the same time, the readings will be unreliable *Aging lamp source may momentarily flicker and cause the readings to be unstable and errorneous So, a single-beam instrument requires a stabilized voltage supply to avoid errors resulting from changes in the beam intensity during the time required to make the 100% T measurement and determine %T for the analyte. Disadvantages of single-beam spectrophotometer

57. The second type of double-beam instrument. Here the beams are separated in time by a rotating sector mirror that directs the entire beam from the monochromator first through the reference cell and then through the sample cell. The pulses of radiation are recombined by another sector mirror, which transmits one pulse and reflects the other to the transducer. As shown by the insert labeled "front view ", the motor-driven sector mirror is made up of pie-shape segments, half of which are mirrored and half of which are transparent. The mirrored sections are held in place by blackened metal frames that periodically interrupt the beam and prevent its reaching the transducer. The double-beam-in-time approach is generally preferred because of the difficulty in matching the two detectors needed for the double-beam-in-space design Double-Beam in time spectrophotometers

58. Double-Beam in space spectrophotometers Many modern photometers and spectrophotometers are based on a double-beam design. A double-beam-in-space instrument in which two beams are formed in space by a V-shape mirror called a beamsplitter . One beam passes through the reference solution to a photodetector , and the second simultaneously traverses the sample to a second, matched detector. The two outputs are amplified, and their ratio (or the logarithm of their ratio) is determined electronically or by a computer and displayed by the readout device.

59. The determination of an analyte’s concentration based on its absorption of ultraviolet or visible radiation is one of the most frequently quantitative analytical methods. One reason for its popularity is that many organic and inorganic compounds have strong absorption bands in the UV/Vis region of the electromagnetic spectrum . There are many application Environmental Applications Clinical Applications Industrial Analysis Forensic Applications Quantitative Applications

60. Methods for the analysis of waters and wastewaters relying on the absorption of UV/Vis radiation are among some of the most frequently employed analytical methods. Environmental Applications

61. UV/Vis molecular absorption is one of the most commonly employed techniques for the analysis of clinical samples, several examples of which are listed in Table below. The analysis of clinical samples is often complicated by the complexity of the sample matrix, which may contribute a significant background absorption at the desired wavelength . Clinical Applications

62. The Application of UV/Vis Molecular Absorption to the Analysis of Clinical Samples

63. UV/Vis molecular absorption is used for the analysis of a diverse array of industrial samples, including pharmaceuticals, food, paint, glass, and metals. In many cases the methods are Products that have been analyzed in this fashion include antibiotics, hormones, vitamins, and analgesics. One example of the use of UV absorption is in determining the purity of aspirin tablets. Industrial Analysis

64. UV/Vis molecular absorption is routinely used in the analysis of narcotics and for drug testing. One interesting forensic application is the determination of blood alcohol using the Breathalyzer test. In this test a 52.5-mL breath sample is bubbled through an acidified solution of K 2 Cr 2 O 7 . Any ethanol present in the breath sample is oxidized by the dichromate, producing acetic acid and Cr 3+ as products. Forensic Applications

65. The energy at which the absorption occurs, as well as the intensity of the absorption, is determined by the chemical environment of the absorbing moiety. For example, benzene has several ultraviolet absorption bands due to p  p* transitions. The position and intensity of two of these bands, 203.5 nm (e = 7400) and 254 nm (e = 204), are very sensitive to substitution. For benzoic acid, in which a carboxylic acid group replaces one of the aromatic hydrogens , the two bands shift to 230 nm (e = 11,600) and 273 nm (e = 970). Several rules have been developed to aid in correlating UV/Vis absorption bands to chemical structure. Qualitative Applications

66. 1-Limited since few resolved peaks Unambiguous identification not usually possible. Why we cannot use UV / visible Spectroscopy in Qualitative Analysis ? Loss of fine structure for acetaldehyde when transfer to solvent from gas phase Also need to consider absorbance of solvent  

67. 2. Solvent can affect position and shape of curve . polar solvents broaden out peaks, eliminates fine structure .   Loss of fine structure for 1,2,4,5-tetrazine as solvent polarity increases

68. 3.Solvent can also absorb in UV- vis spectrum.   Solvent for the ultraviolet and visible regions

69. Molecular absorption, particularly in the UV/Vis range, has been used for a variety of different characterization studies, including determining the stoichiometry of metal–ligand complexes and determining equilibrium constants. Stoichiometry of a Metal, Ligand Complex The stoichiometry for a metal–ligand complexation reaction of the following general form can be determined by one of three methods: the method of continuous variations, the mole-ratio method, and the slope-ratio method Characterization Applications

70. also called Job’s method, is the most popular. In this method a series of solutions is prepared such that the total moles of metal and ligand, n tot , in each solution is the same. Thus, if ( n M ) i and ( n L ) i are, respectively, the moles of metal and ligand in the i - th solution, Then The relative amount of ligand and metal in each solution is expressed as the mole fraction of ligand, ( X L) i , and the mole fraction of metal, ( X M) i , Method of continuous variations

71. A plot of A vs volume ratio (volume ratio = mole fraction) gives maximum absorbance when there is a stoichiometric amount of the two.

72. A procedure for determining the stoichiometry between two reactants by preparing solutions containing different mole ratios of two reactants . In the mole-ratio method the moles of one reactant, usually the metal, are held constant, while the moles of the other reactant are varied. The absorbance is monitored at a wavelength at which the metal–ligand complex absorbs. A plot of absorbance as a function of the ligand-to-metal mole ratio ( n L / n M ) has two linear branches that intersect at a mole ratio corresponding to the formula of the complex. Mole-ratio method

73. Figure (a)shows a mole-ratio plot for the formation of a 1:1 complex in which the absorbance is monitored at a wavelength at which only the complex absorbs.

74. Figure (b) shows a mole-ratio plot for a 1:2 complex in which the metal, the ligand, and the complex absorb at the selected wavelength.

75. A procedure for determining the stoichiometry between two reactants by measuring the relative change in absorbance under conditions when each reactant is the limiting reagent . In the slope-ratio method two sets of solutions are prepared. The first set consists of a constant amount of metal and a variable amount of ligand, chosen such that the total concentration of metal, C M, is much greater than the total concentration of ligand, C L. Under these conditions we may assume that essentially all the ligand is complexed. The concentration of a metal–ligand complex of the general form M x L y is Slope-ratio method

76. Determine endpoint by following change in absorbance of: 1) reactant (decrease) 2) product (increase) 3) titrant (increase after endpoint)   Example Titration curves for where S = analyte being titrated, T = titrant, P = product   Photometric Titrations

77. where S = analyte being titrated, T = titrant, P = product

78. References 1- Douglas A. skoog , Donald M. West, F. james Holler, Stanley R. Crouch. (2013). Fundamentals of analytical chemistry. 9 th ed . Belmont, USA: Mary finch. pp:651-674 . 2- Douglas A. Skoog , F. James Holler , Stanley R. Crouch. (2007). Principles of instrumental analysis. 6 th ed. Belmont , USA: David Harris.pp:335-367. 3- Tony O.(2000). Fundamentals of modern Uv -Visible spectroscopy. 1 st ed. Germany: Agilent technologies .pp:36-43. 4- David H.(2000). Modern analytical chemistry. 1 st ed . London: James M smith. Pp : 394-407.