Spectroscopy Primer for ultraviolet and visible absorbance spectroscopy by Stephanie Myers Summer 2015 Abstract: An overview of uv vis absorbance spectroscopy including Beer s Law, calibration curves, nongraphical standard addition and simple mixtures. 1
Light Light, or more properly electromagnetic radiation, is a form of energy that is described in two ways. It can be described as a wave (or ray) or as a particle. There is good experimental evidence for both models, so being able to use both is called particle wave duality. Terms associated with both models are commonly used; in fact, it is not uncommon to use particle and wave terminology in the same sentence. Electrons also have particle wave duality. Regardless of whether is it described as a particle or a wave, light is described by two components. One is its energy, the other its intensity. While these terms are often confused in common language, it is important to correctly use the terms for these two independent properties. As independent properties, light can be high energy and low intensity or vice versa. Light as a particle. When light is described as a particle, the particle is called a photon. The energy of a photon can be measured in the usual energy unit of joules. Normally, higher energy particles are thought of as moving faster, but, of course, electromagnetic radiation moves at the speed of light (c). A slightly better analogy is to think of the energy like a temperature. In fact, the energies of photons are sometimes expressed in units of temperature, although this is uncommon and not typical of chemical applications. In the particle model of light, intensity is simply the number of photons. Light as a wave. The horizontal component of a light wave is an expression of its energy. The horizontal component can be measured as wavelength (λ) the distance from crest to crest or valley tovalley. The unit would be some form of length units such as nm. The horizontal component can also be measured as frequency (γ), the time it takes for a wave to pass by. Thus the units of waves per time are generally just expressed as s 1 or Hz (1 Hz = 1 s 1 ). If you multiply frequency by wavelength, you get m/s which is, of course, speed. Therefore, since we are discussing light, λγ = c (1) It is important to recognize this expresses an inverse relationship between wavelength and frequency. That is if wavelength is long, frequency is short and vice versa. The wave model and the particle model both express energy and are therefore have related measurements. Frequency and energy are related by Planck s constant (h). hγ = E (2) By combining equations 1 and 2, the relationship between wavelength and energy can be determined. hc/λ = E (3) Consequently, high energy photons can also be described as high frequency and short wavelength; low energy photons are low frequency and long wavelength. The vertical component is the intensity component. Waves with higher amplitude are more intense. This connects to the particle model when you recognize that the effect of adding two waves with the same wavelength results in a single wave with the same wavelength, but twice the amplitude. Electromagnetic Spectrum. It is common to divide electromagnetic radiation into categories based on its energy. The categories are more or less assigned by the way that energy of light interacts with matter. Thus, the divisions between each category are not firm, but rather approximate values. 2
The only category that can properly be called light is the visible category. Visible light is, unsurprisingly, the only type of electromagnetic radiation we can see. The energy of visible light is typically expressed as wavelength with values of approximately 400 700 nm. Visible light can be further subdivided into colors in the typical rainbow order. Violet is high energy (400 nm) visible radiation; red is the low energy (700 nm) visible radiation. At slightly higher energies than visible light is ultraviolet light. Its name even means beyond violet. Its region is about 100 400 nm. Both ultraviolet and visible light interact with the valence electrons in atoms and molecules. At slightly lower energies than visible light is infrared radiation. Its name comes from the phrase inferior to red. The energy of infrared radiation is typically expressed in wavenumbers ( ) rather than wavelength. Wavenumbers are simply the reciprocal of the wavelength (4) and typical units are cm 1. At these energies, radiation interacts with bond vibrational energies. Lower in energy than infrared are microwave (rotational energies) and, lower yet, radiowaves (yes, the ones that carry a signal to your radio). At higher energies are x rays (interactions with innershell electrons) and at the highest energies, gamma rays (interactions with nuclear energies). Details of the electromagnetic spectrum are readily available in any analytical textbook. This primer primarily addresses visible and ultraviolet radiation although many principles also apply to other spectral regions. Absorbance Electromagnetic radiation can interact with the electrons in an atom. The energies of electrons are quantized. That is they have specific allowed energy values and energies that do not match those values are not allowed in the atom. These allowed energy levels are called orbitals or more specifically, since they are the energies of electrons: electronic orbitals. Thus electromagnetic radiation can only interact with matter when the energy of the light exactly matches the energy difference in orbitals, i.e., the energy required to move an electron from one energy level to another. The ground state of the atom has its electrons arranged in the configuration with the lowest possible energy. This is the preferred and normal state of an atom. However, there are other energy levels that exist and if the right amount energy is provided to the atom, the electrons can move to these other levels creating an excited state. When a photon with an energy that exactly matches the energy difference between two electronic orbitals interacts with the substance, that energy may be used to move the electron to the higher energy state. If that occurs, the photon is said to be absorbed and no longer exists (as the light energy which was the photon becomes potential energy in the substance). This process is symbolically shown in Figure 1. If the photon is not absorbed, it continues on its path and is said to be transmitted. The energies of ultraviolet and visible radiation tend to be in the range sufficient to move an electron from its highest occupied orbital (a valence electron) to an unoccupied orbital that is close in energy. 3
Whether or not a photon of the correct energy is absorbed is a probability function that depends on the nature of orbitals. Some transitions between energy levels are favorable and a large percentage of the available photons are absorbed. These are called allowed transitions. Transitions that are not favorable are called forbidden. However, like many things, being forbidden does not mean that the transition will not occur, just that it is less likely. In atoms, the energy levels are very specific so the match between the energy of the photon and the difference in atomic energy levels must be nearly exact. However, in molecules, bond vibrations allow small differences in the electronic energy levels. Thus, while the exact energy difference is preferred, photons with energies close to that value are often absorbed as well. There are several other ways light and matter can interact, however, these are not addressed in this primer. Spectrometers The device used to measure the interaction of electromagnetic radiation is called a spectrometer or spectrophotometer. The components of this device can be described with a block diagram, as shown in Figure 2. In a spectrometer, the source provides the electromagnetic radiation. This is typically a tungsten (W) lamp for the visible spectrum or a deuterium (D 2 ) lamp for the ultraviolet spectrum. These provide all the wavelengths (energies) in that spectral region at high intensity. The monochromator (literally: one color maker ) divides light into its component wavelengths and allows only the chosen wavelength to continue to the sample. In reality, it is a small range of wavelengths that are allowed through. Because the source does not emit the same number of photons at every wavelength, the intensity of the output (P 0 ) is wavelength dependent. The sample cell holds the sample. It must be transparent to the light that being used for measurement otherwise you will be measuring the sample cell instead of the sample. For visible light, it is easy to choose a transparent cell as any colorless cell is transparent to visible light. However, glass and many plastics will absorb ultraviolet light so quartz cells are typically used for ultraviolet measurements. For solutions, the solvent must also be transparent to the light used. As will the cell, any colorless substance is transparent to visible light. However, if working in the ultraviolet region, you must choose more carefully. Fortunately, the common solvents (e.g., water, acetonitrile, short chain alcohols and alkanes) are transparent to ultraviolet light. 4
The pathlength (b) is the distance light travels through the cell. The longer this distance, the more molecules the photon might encounter, therefore the greater the chance the photon will be absorbed. The typical cell pathlength is 1.00 cm. The detector is a device (generally a photomultiplier tube) that changes photons into an electrical signal. Consequently, the detector is counting the number of transmitted photons, as the absorbed photons to do make it out of the sample. The detector can be set to give the output as transmittance (T), percent transmittance (%T) or absorbance (A). Transmittance is the ratio of transmitted photons (P) to number of photons that impacted the sample (P 0 ). To obtain a value for P 0, a blank is measured. A blank contains all the substances in the sample except the analyte (analyte = the substance under study). T = P/P 0 (5) Percent transmittance (%T) is simply this ratio times 100. %T = T x 100 = (P/P 0 ) X 100 (6) Absorbance (A) is the negative log of the transmittance. A = log(t) = log(p/p 0 ) = log (P 0 /P) (7) Absorbance is the most commonly used unit as it is directly proportional to the concentration of analyte. All these values (absorbance, transmittance, percent transmittance) are unitless. Nevertheless, you occasionally see AU looking like it is a unit. AU stands for absorbance unit but is not really a meaningful idea, it is more of a unit placeholder. A typical spectrophotometric measurement starts first with the choice of wavelength. Once the wavelength has been set, the blank is put in the sample compartment. The analyst informs the instrument that the blank is being measured, normally by pressing a button labeled 0 Absorbance (0 A) or 100% T. Then the blank is replaced with the sample and the absorbance (or transmittance) of the sample is measured. (This is normally displayed directly and does not require pushing any more buttons.) The blank measurement only has to be made 1) before the first measurement after the instrument has been turned on and 2) whenever the wavelength is changed. Absorbance Spectra One of the classic types of spectroscopic measurements is the determination of a spectrum. A spectrum is a graph of absorbance (y axis) versus wavelength (x axis) in the measurement of a single sample. (Infrared spectra typically use %T instead of absorbance and wavenumber instead of wavelength, but follow the same general principles.) Line Spectra. Line spectra consist of a series of lines, where each line represents a transition between the energy levels of orbitals. Line spectra are typical of atoms. Each line spectra is specific to the atom being measured. That is, if the wavelengths and relative heights of the lines match, the identity of the atom is confirmed. A typical line spectra is shown in Figure 3. 5
Figure 3. Line spectra for the sodium atom. From: http://faculty.sdmiramar.edu/fgarces/labmatters/instruments/aa/aas_instrument/aasinstruments.htm Band Spectra. However, it is more common to measure molecules than it is to measure atoms. (For example, while it might be intuitive to expect Cu 2+ to behave as an atom, in aqueous solutions it exists as [Cu(H 2 O) 4 ] 2+ and behaves as a molecule. Expect all non gases substances to behave as molecules.) Ultraviolet and visible (uv vis) spectra of molecules are band spectra with wide peaks rather than lines (Figure 4). Band spectra are characteristic spectra, so if the wavelength and relative height of the peaks do NOT match, you can confidently state the two substances are not the same, however you cannot confirm the identity of the substance. In other words, band spectra allows you to eliminate possible identities but not directly identify a substance. Uses of spectra. So one of the major uses of spectra is to get information about the identity of the analyte (qualitative information). This can be done, as described above, by matching to a known substance. If the molecule is not known, the wavelengths where absorption occurs can often be used as clues about its structure. In more sophisticated treatments of spectra you can even get direct information about orbital energies and other orbital characteristics. 6
Figure 4. Absorption spectrum of an organic molecule. From: http://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/spectrpy/images/cinnald1.gif Another use of the spectra is to determine the best conditions for quantitative analysis. Quantitative analysis is typically conducted at a single wavelength, so the spectra is used to choose this wavelength. Typically, the wavelength used for quantitative analysis is the wavelength with the highest value of absorbance, called λ max ( lambda max ). There are two advantages for choosing this wavelength: 1) the high absorbance values provide higher measurements and 2) because the absorbance tends to flatten at the top, small differences in wavelength do not have a large effect on the absorbance value. Both of these lead to more reliable measurements. Calibration/Quantitative Measurements For quantitative measurements, a calibration curve is used. Creation of a calibration curve requires a series of solutions with a known concentration of analyte (standards). The absorbance of each of these standards is measured at a single wavelength (normally the λ max ). The calibration curve is a graph of the absorbance (y axis) versus the concentration of analyte (x axis). (For example, Figure 5) Once a calibration curve is established, the equation of the line can be used to determine the concentration of an unknown analyte from its measured absorbance. At very high or very low absorbance values, spectrophotometric calibration curves often lose their linearity. This is understandable if you consider what the spectrophotometer is actually measuring. At low absorbance values, the spectrophotometer is comparing a very tiny difference in the number of photons. The normal variation in signal (called noise ) may be about the same or even more than that difference. Therefore, it is impossible to tell if the reduction in signal is due to the absorbance of the sample or noise. At high concentration values, there are very few photons reaching the detector so detecting anything other than zero photons depends on the sensitivity of the detector and a random chance of a photon getting through rather than the concentration of the sample. Beer s Law. The equation of the line for an absorbance calibration is described by the Beer Lambert Law, which is commonly called Beer s Law. Beer s Law is expressed as: A = abc (8) 7
where A is the measured absorbance, c is the concentration, b is the pathlength and a is the absorptivity. Thus, the slope of the line in a calibration curve is equal to the absorptivity times the pathlength (ab). Beer s Law predicts that the y intercept will be zero. This is a result of how measurements are made, as you tell the instrument that the blank (where analyte concentration is zero) has an absorbance of zero when you press the 0 A/100% T button. If a blank was not used to set the zero on the instrument, or if there is sufficient error in the measurements, the calibration curve might have a nonzero y intercept. In that case corrected absorbance should be used in a Beer s Law calculation where the corrected absorbance (A corr ) is the difference between the measured absorbance and the y intercept or the absorbance of the blank (A blank ). A corr = A measured A blank = A measured y intercept (9) If the equation of the line is used directly there is no need for correction use the same value you graphed. (i.e., if you graphed measured absorbance, use that in your calculation; if you graphed correct absorbance, use that!) 0.800 0.700 0.600 absorbance 0.500 0.400 0.300 0.200 0.100 0.000 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 concentration of iron (ppm) Figure 5. Calibration Curve for trisphenanthrolineiron(ii) ion at 520 nm. The absorbance (A) is the typical measurement recorded by the spectrophotometer and b is the distance the light travels through the sample cell. Both are described in the section on spectrophotometers. Concentration can be expressed in any unit, provided it is used consistently throughout the experiment. Typical concentration units are: molarity (M), parts per million (ppm), and mg/l. The absorptivity (a) is a proportionality factor between absorbance and concentration. Its value depends on the wavelength of measurement, the identity of the analyte and the units of concentration and pathlength. When molarity is used for concentration and cm for pathlength, absorptivity can be symbolized as ε which stands for molar absorptivity. Molar absorptivity (ε) is often expressed without units as the symbol defines the units as M 1 cm 1 and you sometimes see Beer s Law written as: A = εbc (10) It should be obvious from the spectra that different wavelengths absorb differently and will, therefore, have a different absorptivity. However, the value of wavelength (λ) is not part of the calculation. Consequently, while all Beer s Law problems will include the wavelength so that the 8
experiment is correctly and completely described, the value of wavelength is not the absorptivity nor is it part of the calculation. Some spectra (see previous section) will use absorptivity or molar absorptivity on the y axis instead of absorbance. This accounts for potential differences in concentration and gives a spectra that is more directly linked to identity. The identity of the analyte also has a significant influence on absorptivity values. As you should recall from the section on absorbance, the signal comes from photons moving an electron to a higher energy level. Some of these transitions are more favorable ( allowed ) than others. For allowed transitions, most of the photons are absorbed and the absorbance is high. Forbidden transitions have a low absorbance as few electrons are promoted. What makes a transition allowed or forbidden is beyond the scope of this primer. Even when this information is known, values are normally determined experimentally for the most accurate values. Sometimes the actually identity of the analyte is less straightforward than it appears on the surface. For example, copper(ii) ion in water is a light, pale blue. This is actually the color of the complex ion: [Cu(H 2 O) 4 ] 2+. When ammonia is added, the color becomes a dark navy blue because the [Cu(NH 3 ) 4 ] 2+ ion is formed. Because they are two different compounds, they will have different values of λ max (only slightly different as they are both shades blue) and the calibration measurements should be conducted at different wavelengths. In addition, if ammonia is added is excess, the amount of copper determines the amount of the complex ion so either concentration of copper or concentration of [Cu(NH 3 ) 4 ] 2+ can be used for the x axis of the calibration curve. However, if ammonia is not in excess, the absorbance will depend on the amount of ammonia instead of the amount of copper and graphing the data as concentration of copper will give you an error. Standard Addition. As an alternative to a calibration curve, the concentration of analyte can also be determined by standard addition. In this experiment, the absorbance of a sample is measured then a known amount of analyte is added to a specific amount of sample and the absorbance of the mixture measured. When the two measurements are compared, the concentration of analyte in the substance can be determined. (11) where: A 1 = absorbance of the analyte in the sample; A 2 = absorbance of analyte in the sample standard mixture; k = proportionality constant for the analyte including pathlength and absorptivity; c x = concentration of the analyte in the sample; c m = concentration of the analyte in the mixture. Since the analyte and the wavelength are the same, the proportionality constants are the same and will cancel. 9 (11b) Standard addition is particularly useful when something other than the analyte is affecting the absorbance of the sample (an interference ). By using this method, the sample is in both measurements and the only change is the amount of analyte. Therefore the change is absorbance is attributed only to the analyte and this method gives a better measurement of analyte concentration. This works best if only a small volume of standard in relatively high concentration is added. Students generally find appropriately expressing the concentration of the mixture in terms of analyte and standard concentration the most difficult part of this calculation. Concentrations cannot be added directly, only moles or mass can. Thus, a general expression of c m is: (12)
where V x is the volume of sample; V s is the volume of standard, V t is the total volume and c s is the concentration of standard. As volumes are not additive, it is best practice to dilute the mixture to a known total volume. However, if the standard and sample are similar (e.g., both dilute, aqueous solutions) it is not uncommon to use the sum of V x and V s for the total volume. Another way to create the solutions for standard addition is to dilute both the sample and the standard sample mixture to the same volume. Instead of c x in equation 11, you would use c dil. (13) This has two advantages. First, since you would have the same amount of sample in both solutions, the effect of the interference would be exactly the same and completely accounted for. Second, because the concentration of analyte in the diluted sample (c dil ) is also a fraction with the same denominator as the concentration of analyte in the mixture, the total volume also cancels and the math is simplified. Use of standard addition makes measurements of complex samples more reliable. However, it does assume that both solutions are in the linear portion of the calibration curve and this version of standard addition does not test for that. Secondly, this method of standard addition does not have a convenient way to evaluate the error associated with the measurement. It is possible to account for these problems by doing standard addition graphically, using a series of solutions with increasing amounts of added analyte and the same total volume. However, that method is not addressed in this primer. Mixtures: when 2 or more substance absorb. Another possible complication in Beer s Law measurements is in a mixture where two substances are absorbing at the same wavelength. Just because 2 substances do not have the same λ max, does not mean that one substance does not affect the absorbance of another. The substance may be absorbing but at less than its maximum value. Absorbance measurements that are due to the absorbance of two substances are not uncommon in molecular measurements. As the peak of each substance is broad, the possibility of overlap is fairly high and any overlap will affect the absorbance measurement. In the case where two substances are being absorbed at the same wavelength, the measured absorbance is simply the sum of the absorbance of each substance. A measured = A 1 + A 2 = a 1 bc 1 + a 2 bc 2 (14) where c 1 is the concentration of substance 1 and c 2 is the concentration of substance 2; a 1 is the absorptivity of substance 1 at the experimental wavelength (which is NOT necessarily λ max!) and a 2 is the absorptivity of substance 2 at the experimental wavelength; b is the pathlength of the spectrophotometer which must be the same for both substances as the experiment is measuring both simultaneously (in the same container). Absorptivities can be easily determined by measuring a standard of each substance by itself at the experimental wavelength. To determine the concentration of both substances in a sample, measure at two wavelengths and algebraically solve for the two equations for both unknowns. Summary Absorbance spectrophotometry is a very common technique used for both qualitative and quantitative analysis. A spectrophotometer compares the number of photons that are transmitted through a blank to the number of photons transmitted through a sample to determine the transmittance (T) from which it then computes absorbance (A). Information about the identity of the sample can be determined using a spectrum, a graph of absorbance versus wavelength. Atoms produce a line spectra, a series of narrow peaks. If 2 atomic 10
spectra produce peaks at the same wavelengths with the same relative heights, the spectra must be of the same atom. Molecules produce band spectra, with one or more wide and possibly overlapping peaks. If 2 molecular spectra produce peaks at the same wavelengths with the same relative heights, the spectra might be of the same molecule. However if the spectra are different, the molecules are definitely not the same. The spectra is also used to determine the best conditions for quantitative experiments, which are conducted at a single wavelength. In general, the best wavelength to use is the λ max, the wavelength with the highest absorbance value. To obtain quantitative information, the absorbance of a series of solutions with a known concentration (standards) are measured at the chosen wavelength. From these measurements, a calibration curve (graph of absorbance versus concentration) is constructed. Then the absorbance of a solution with unknown concentration can be measured and the calibration curve used to determine the concentration. The relationship between absorbance and concentration can be described with Beer s Law. Beer s Law says that absorbance is proportional to concentration. The proportionality constant is called absorptivity which is dependent on the identity of the compound and the wavelength of measurement. 11
Spectroscopy questions Assume all measurements are made in a spectrophotometer with a 1.00 cm pathlength unless otherwise specified. 1. Consider the spectrum below. Questions a f refer to this spectrum. a. Is the spectrum above a band spectrum or a line spectrum? b. What is its λ max? c. What region of the spectra is shown here? d. If the concentration of the solution was 45.0 ppm, what is the absorptivity of the substance at λ max? at 450 nm? e. How will the spectra look if a higher concentration of the same ion where measured? f. How will the spectra look if a 1.00 mm sample cell is used instead of the 1.00 cm cell? g. Is the substance in the spectra below, the same as the substance in the spectra above? Justify your answer. 12
2. Copper(II) ion in aqueous ammonia produces a blue solution. Copper(II) ion in aqueous hydrochloric acid produces a green solution. Based on this evidence, which of the following statements are true? a. The spectra of the two solutions will have different λ max values. b. The ion being measured in the same in both solutions. c. The concentration of copper in both solutions is different. d. The slope of the calibration curve will be the same. e. If the concentration of copper is the same, the absorbance of the two solutions at must be the same at their λ max. 3. Consider the spectrum below. a. What region of the spectra is being studied? b. Are G and 6 TG atoms or molecules? How can you tell? c. What is the λ max of G? d. What is the λ max of 6 TG? e. If G has a concentration of 0.25 mm, what is its absorptivity at 250 nm? 13
f. If G has a concentration of 0.25 mm, what is its absorptivity at 350 nm? g. If 6 TG has a concentration of 0.40 mm, what is its absorptivity at 250 nm? h. If 6 TG has a concentration of 0.40 mm, what is its absorptivity at 350 nm? i. A solution contains 0.52 mm of G and 0.03 mm of 6 TG. What will be the absorbance of this solution at 250 nm? At 350 nm? j. How will the solution look to you if you add more G to make a higher concentration? 4. Properly complete the following statements using: increasing, decreasing, staying the same, changing in an unknown direction, or unrelated to this property. a. When the energy of light increases, its wavelength is. b. When the energy of light increases, its frequency is. c. When the wavelength of light increases, its frequency is. d. When light changes from red to blue, its wavelength is. e. When the intensity of light increases, its energy is. f. When intensity of radiation increases, the amplitude of the wave is. g. When the energy of light increases, the number of photons is. h. As you move from ultraviolet to visible radiation, the energy is. i. If absorbance is increasing, the number of transmitted photons is. j. In a series of red solutions, the color of the solutions gets darker red, absorbance is. k. In a series of red solutions, the color of solutions gets darker red, λ max is. l. If absorptivity is increasing, transmittance is. 5. What is the absorbance of each? a. a solution with a transmittance of 0.570 b. a solution with 43.5%T c. a 0.084 mm X(aq) in a 5.00 cm cell if the molar absorptivity of X is 365. d. 59.5% of photons are transmitted through a cell 14
6. What is the percent transmittance of each? a. a solution with an absorbance of 0.015 b. a solution with a transmittance of 0.272 c. a 0.084 mm X(aq) in a 5.00 cm cell if the molar absorptivity of X is 365. 7. Chromatography catalogs often list the uv cut off value for various solvent. This is the wavelength below which uv absorbance starts to become significant. Why are these numbers of value to anyone doing uv spectroscopy? 8. A solution containing 64.1 ppm of Z had an absorbance of 0.231 in a 1.00 cm cell at 388 nm. a. What is the absorptivity of Z? b. If another solution of Z had an absorbance of 0.767 under the same condition, what is the concentration of Z? 9. A solution containing 40.00 ppm of B had an absorbance of 0.425 in a 1.00 cm cell at 690 nm. If 5.00 ml of this solution was diluted with water to 100.0 ml, what is the absorbance of the new solution at 690 nm? 10. A compound has a molar mass of 616.0 g/mol and an absorptivity of 789.0 M 1 cm 1 at 620 nm. A sample containing 1.4516 g of this compound was dissolved in 150.0 ml of water, then 25.00 ml of reagent was added (to create the color) to a 10.00 ml aliquot of this solution. The resulting solution with both the reagent and analyte were diluted to a total volume of 50.00 ml. What is the absorbance of the final solution in a 1.000 cm cell at 620 nm? 11. Use the calibration curve in Figure 5 to solve these problems. a. A solution containing trisphenanthrolineiron(ii) had an absorbance of 0.191 at 520 nm. What is the concentration of iron in this solution? b. 0.7168 g of sample was dissolved to make 250.0 ml of solution X. A 5.00 of o phenanthroline solution and 20 drops of sodium citrate were mixed with 10.00 ml of solution X and the entire thing diluted to 100.0 ml to create solution Y. The absorbance of solution Y was 0.523 at 520 nm. What is the %Fe in the sample? c. A vitamin tablet was boiled in acid to dissolve it and the filtered solution was diluted with water to make a total volume of 100.0 ml. A 5.00 ml aliquot of this solution was diluted to 100.0 ml. Various reagents were added to a 10.00 ml aliquot of the diluted solution and then were diluted to make 100.0 ml of solution. The solution of diluted vitamin and reagents had an absorbance of 0.194. How many mg of Fe were in the vitamin tablet? 15
12. Use the following data to construct a calibration curve and determine the concentration of unknown as given. What is the molar absorptivity of the analyte? solution [X] (M) Absorbance At 254 nm Standard 1 0.03584 0.097 Standard 2 0.05719 0.169 Standard 3 0.1289 0.365 Standard 4 0.2305 0.682 Standard 5 0.3161 0.997 Sample??? 0.719 13. A series of solutions were made using an analytical standard with a concentration of 183.1 ppm copper and concentrated ammonia. Each solution was diluted to a total volume of 25.00 ml. Use the following data to construct a calibration curve and determine the molar absorptivity of the analyte. When a 5.00 ml of sample was mixed with 15.00 ml of ammonia and diluted to a total volume of 25.00 ml, the absorbance of the resulting solution was 0.157. What is the concentration of copper in the sample? Solution Volume Cu (ml) Volume NH 3 (ml) absorbance 1 1.00 15.00 0.170 2 2.00 15.00 0.239 3 4.00 15.00 0.424 4 5.00 15.00 0.480 14. a. A series of standard aqueous solutions were made in the following manner: 0.8661 g of Ni(NO 3 ) 2 2H 2 O was dissolved to make 100.0 ml of stock solution; 10.00 ml of stock solution was diluted to a total of 50.00 ml to make solution A; solution B was made by diluting 5.00 ml of stock to 50.00 ml; solution C was made by diluting 10.00 ml of solution A to 25.00 ml and solution D was made by diluting 10.00 ml of solution B to 25.00 ml. Find the parts per million of nickel(ii) ion in each solution. The absorbance of each solution was measured at 525 nm, results are in the table below. Graph the Beer s Law curve. Solution absorbance Stock 1.442 A 0.670 B 0.358 C 0.286 D 0.145 16
14b. A 0.3481 g sample containing nickel was dissolved in 25.00 ml of nitric acid. The resulting solution was diluted to a total volume of 150.0 ml. A 10.00 ml aliquot of that solution was diluted to 50.00 ml. The absorbance of the diluted solution was measured at 525 nm and found to be 0.508. What is the percent of nickel in the original sample? 15. The absorbance of a sample solution was 0.155. When 5.00 ml of sample was mixed with 1.00 ml of 125.0 ppm Co 2+ the resulting solution had an absorbance of 0.424. Assuming that absorbance is proportional to the concentration of cobalt(ii) ion and that volumes are additive, what is the concentration of cobalt in the sample? 16. The absorbance of benzene in a sample solution was measured at 254 nm and had a value of 0.142. When 0.096 g of pure benzene was added to 0.274 g of pure sample, the absorbance of the resulting solution was 0.533 at 254 nm. What is the percent of benzene in the sample? 17. 5.00 ml of solution containing iron was mixed with 10.00 ml of o phenanthroline and diluted to a total volume of 50.00 ml. The absorbance of the resulting solution at 615 nm was 0.339. When 5.00 ml of sample solution, 2.00 ml of 57.6 ppm Fe 2+ standard and 10.00 ml of o phenanthroline were mixed and diluted to 50.00 ml, the absorbance of the resulting solution was 0.735. What is the concentration of iron in the sample solution? 18. Substance X has a molar absorptivity of 5.15 at 400 nm. Solution Y has a molar absorptivity of 0.236 at 400 nm. a. In a mixture where [X] = 0.482 M and [Y] = 0.537 M, what is the absorbance at 400 nm? b. In a mixture where [X] = 0.017 M and [Y] = 0.447 M, what is the absorbance at 400 nm? 19. Substance R has a λ max of 500 nm. Substance S has a λ max of 650 nm. A standard solution of R has a concentration of 74.2 ppm and an absorbance of 0.972 at 500 nm and an absorbance of 0.276 at 650 nm. A standard solution of S has a concentration of 35.9 ppm and an absorbance of 0.102 at 500 nm and of 0.564 at 650 nm. A sample solution that is a mixture of R and S has an absorbance of 0.741 at 500 nm and 1.602 at 650 nm. What is the concentration of R and of S in the sample solution? 20. A green solution has a λ max of about 690 nm, which is the red region of the spectra. An orange solution has a λ max of 450, the blue region of the spectra. Explain this phenomena and predict the λ max of a yellow solution. 17