Chem 321 Lecture 18 - Spectrophotometry

Chem 321 Lecture 18 - Spectrophotometry In the lab you will use spectrophotometric techniques to determine the amount of iron, calcium and magnesium in unknowns. Although the methods and instrumentation differ slightly from one experiment to another, many basic principles apply. Recall the electromagnetic radiation spectrum below. Electromagnetic Radiation Spectrum γ rays X-rays Ultraviolet Visible Infrared Microwave Radio increasing λ decreasing ν decreasing Ephoton Each region of this continuum consists of photons, each with a specific wavelength (λ), frequency (ν) and energy (Ephoton) related by: where h is Planck’s constant (6.63 x 10-34 J@s) and c is the speed of electromagnetic radiation in a vacuum (3.0 x 108 m/s). The visible portion of this spectrum consists of the familiar rainbow of colors ranging in wavelength from about 400 nm (violet end) to 750 nm (red end). The interaction of radiation with matter results in different effects, depending upon the photon energy involved. Radiation Atomic/Molecular Effect X-rays inner electron effects UV-VIS outer electron effects (excitation, ionization) IR molecular vibrations Microwave molecular rotations We will employ radiation in the ultraviolet and visible to analyze unknowns. Usually when visible radiation is absorbed by an atom (in the gas phase) an electron is excited to a higher energy level, then rapidly de-excites. Since electron energy levels are quantized, these excitation/de-excitation processes involve a very specific amount of energy. Hence, a very specific photon wavelength is absorbed. This results in a very specific absorption line spectrum (and emission line spectrum) that depends on the spacing between energy levels and is thus characteristic of a particular element. Part of the atomic absorption line spectrum (a plot of how much radiation is absorbed, absorbance, versus wavelength) for a sample containing iron, lead and copper is shown in Figure 12.1. Note the expanded x-axis scale and the rather sharp, discrete absorption bands. Figure 12.1 Portion of the absorption spectrum of a gas-phase sample containing lead, iron and copper The situation is slightly different when molecules absorb visible radiation. In contrast to individual atoms, molecules can vibrate and rotate. Associated with each electronic energy level is a series of closely-spaced vibrational levels. When visible radiation is absorbed, the molecule goes from its ground electronic state (E0) to an excited electronic state (E1) and to one of the many vibrational levels available in the excited state (Fig. 12.2). Consequently, the molecular absorption spectrum (in the gas phase) consists of a series of bands made up of closely-spaced lines due to excitation to various vibrational levels. Figure 12.2 Typical electronic transitions in a molecule following absorption of visible light In solution, where the absorbing molecules are surrounded by solvent, collisions tend to spread out the energy of a given quantum state, resulting in a rather broad continuous absorption band. The absorption spectra of various transition metal ion complexes in aqueous solution are shown in Figure 12.3. Note how much broader these absorption bands are compared to those for atoms in the gas phase. Notice that the absorption spectrum for Ni(H2O)62+(aq) indicates that this complex strongly absorbs around 400 nm (violet end of the visible light spectrum) and also around 700 nm (red end of the visible light spectrum). This means these wavelengths are removed from white light incident on an aqueous solution of this complex and what we see are the unabsorbed wavelengths that are associated with the blue-green-yellow portion of the visible light spectrum. Consequently, Ni(H2O)62+(aq) has a green color. Figure 12.3 Absorption spectra of various complex ions in aqueous solution The intensity of absorption depends on the concentration of the absorbing species and the probability that a particular transition will occur. The quantitative statement of this relationship is known as Beer’s law, which is: where A is absorbance; l is the pathlength the radiation takes through the sample (units of cm); c is the concentration of the light-absorbing substance (units of mol/L); ε is the molar absorptivity (units of L/mol-cm) Note that absorbance is a unitless quantity that is related to transmittance (T), the fraction of the incident radiation transmitted by the sample. If P0 is the radiant power (J/cm2-sec) of a radiation beam incident on the sample, and P is the transmitted radiant power, then and The transmittance scale is linear, ranging from 0 to 1. However, the absorbance scale is logarithmic. An absorbance of 1 corresponds to 10% of the light being transmitted, while A = 2 corresponds to only 1% of the radiation being transmitted. The relationship between absorbance and percent transmittance is illustrated in Figure 12.4. Figure 12.4 Relationship between absorbance and percent transmittance The molar absorptivity is related to the likelihood that a particular wavelength will be absorbed, hence ε and A vary with wavelength. Beer’s law suggests a linear relationship between absorbance and concentration. A typical spectrophotometric calibration curve is prepared by measuring absorbance as a function of analyte concentration at a specific wavelength and fixed pathlength. A plot of these data is expected to be linear with a slope of εl. However, deviations from a direct proportionality do occur because of limitations to Beer’s law. First, Beer’s law is successful in describing absorption behavior of dilute solutions only. As the light-absorbing analyte concentration increases, the distance between species is so small that they affect the charge distribution of each other and this will affect absorption properties. A similar effect can result from a high concentration of non-absorbing electrolytes in solution. Note that the concentration of the ironphenanthroline complex in the solutions measured in lab is μM, while that for the Ca2+ and Mg2+ analytes is ppm or sub-ppm. Even at these low levels, some effects are seen and a slightly non-linear calibration curve for calcium results. Associated with each analyte is a linear range - the range of concentrations for which there is a direct proportionality between absorbance and concentration. Generally one tends to make measurements within this range. A non-linear calibration curve can certainly be used, however, one must make the added assumption that whatever is responsible for this non-linear behavior in the standards is also true for the unknowns being measured. Another limitation results from an instrumental effect. Beer’s law applies only to monochromatic radiation, that is, only when a single wavelength is passing through the sample and being absorbed. In practice, however, a narrow band of wavelengths is used for the radiation beam. This is a problem if ε is changing significantly across this range of wavelengths. Consequently, absorption measurements are usually done at a broad maximum in the absorption spectrum (see band A in Fig. 12.5). In this region, the absorbance (and hence ε) is fairly constant (so Beer’s law holds and you get a linear calibration curve), and the signal is maximized for a given concentration. Using a range of wavelengths that is narrow compared to the absorption band and in which ε is fairly constant is equivalent to using monochromatic radiation. If measurements are made at a point of significantly changing absorbance (see band B in Fig. 12.5), a non-linear calibration curve results. Figure 12.5 External standard calibration curves as a function of the absorption spectrum region used for the absorbance measurements For the iron determination, you will prepare a standard containing the ironphenanthroline complex and record its absorption spectrum. A broad absorption maximum occurs around 510 nm for this complex, and this information is used to select the appropriate wavelength for the subsequent absorbance measurements on the standard and unknown samples. In many cases, large errors occur in the iron determination from use of the autopipet to deliver the stock solution when preparing the calibration standard solutions and the diluted unknown solutions. Remember that the autopipet is a “to contain” pipet and that all of the liquid must be expelled when taking an aliquot. Carefully check this as you use the autopipet. Another important consideration is that the stock solution (or any solution) should be thoroughly mixed before taking an aliquot. Invert and shake the stoppered volumetric flask many times to ensure this. The concentration of a diluted iron standard (Mdil) can be calculated from the molarity of the stock solution (Mstock) according to: where Vpipet is your calibration volume (close to 1 mL) for your autopipet, and n is the number of pipet volumes (1-5) of stock solution used for the diluted standard. This relationship can be rearranged to obtain the concentration of the unknown stock solution. First, the unknown absorbance is substituted into the equation of the calibration curve to determine the molarity of the diluted unknown sample. Then the molarity of the unknown stock solution is calculated from the above relationship.