Modern Analytical Cheymistry - Chapter 10

Chapter 10 Spectroscopic Methods of Analysis Before the beginning of the twentieth century most quantitative chemical analyses used gravimetry or titrimetry as the analytical method. With these methods, analysts achieved highly accurate results, but were usually limited to the analysis of major and minor analytes. Other methods developed during this period extended quantitative analysis to include trace level analytes. One such method was colorimetry. One example of an early colorimetric analysis is NesslerÕs method for ammonia, which was first proposed in 1856. Nessler found that adding an alkaline solution of HgI2 and KI to a dilute solution of ammonia produced a yellow to reddish brown colloid with the color determined by the concentration of ammonia. A comparison of the sampleÕs color to that for a series of standards was used to determine the concentration of ammonia. Equal volumes of the sample and standards were transferred to a set of tubes with flat bottoms. The tubes were placed in a rack equipped at the bottom with a reflecting surface, allowing light to pass through the solution. The colors of the samples and standards were compared by looking down through the solutions. Until recently, a modified form of this method was listed as a standard method for the analysis of ammonia in water and wastewater.1 Colorimetry, in which a sample absorbs visible light, is one example of a spectroscopic method of analysis. At the end of the nineteenth century, spectroscopy was limited to the absorption, emission, and scattering of visible, ultraviolet, and infrared electromagnetic radiation. During the twentieth century, spectroscopy has been extended to include other forms of electromagnetic radiation (photon spectroscopy), such as X-rays, microwaves, and radio waves, as well as 368 energetic particles (particle spectroscopy), such as electrons and ions.2 Chapter 10 Spectroscopic Methods of Analysis 369 10A Overview of Spectroscopy The focus of this chapter is photon spectroscopy, using ultraviolet, visible, and in-frared radiation. Because these techniques use a common set of optical devices for dispersing and focusing the radiation, they often are identified as optical spectros-copies. For convenience we will usually use the simpler term “spectroscopy” in place of photon spectroscopy or optical spectroscopy; however, it should be under-stood that we are considering only a limited part of a much broader area of analyti-cal methods. Before we examine specific spectroscopic methods, however, we first review the properties of electromagnetic radiation. 10A.1 What Is Electromagnetic Radiation Electromagnetic radiation, or light, is a form of energy whose behavior is described by the properties of both waves and particles. The optical properties of electromag-netic radiation, such as diffraction, are explained best by describing light as a wave. Many of the interactions between electromagnetic radiation and matter, such as ab-sorption and emission, however, are better described by treating light as a particle, or photon. The exact nature of electromagnetic radiation remains unclear, as it has since the development of quantum mechanics in the first quarter of the twentieth century.3 Nevertheless, the dual models of wave and particle behavior provide a use-ful description for electromagnetic radiation. Wave Properties of Electromagnetic Radiation Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space along a lin-ear path and with a constant velocity (Figure 10.1). In a vacuum, electromagnetic radiation travels at the speed of light, c, which is 2.99792 ´ 108 m/s. Electromagnetic radiation moves through a medium other than a vacuum with a velocity, v, less than that of the speed of light in a vacuum. The difference between v and c is small enough (< 0.1%) that the speed of light to three significant figures, 3.00 ´ 108 m/s, is sufficiently accurate for most purposes. Oscillations in the electric and magnetic fields are perpendicular to each other, and to the direction of the wave’s propagation. Figure 10.1 shows an example of plane-polarized electromagnetic radiation consisting of an oscillating electric field and an oscillating magnetic field, each of which is constrained to a single plane. Normally, electromagnetic radiation is unpolarized, with oscillating electric and Electric field Magnetic field Direction of propagation Figure 10.1 Plane-polarized electromagnetic radiation showing the electric field, the magnetic field, and the direction of propagation. 370 Modern Analytical Chemistry + l Ae Time or distance Figure 10.2 Electric field component of plane-polarized electromagnetic radiation. frequency The number of oscillations of an electromagnetic wave per second (n). wavelength The distance between any two consecutive maxima or minima of an electromagnetic wave (l). – magnetic fields in all possible planes oriented perpendicular to the direction of propagation. The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form E = Ae sin(2πnt + Φ) where E is the magnitude of the electric field at time t, Ae is the electric field’s maxi-mum amplitude, n is the frequency, or the number of oscillations in the electric field per unit time, and Φ is a phase angle accounting for the fact that the electric field’s magnitude need not be zero at t = 0. An identical equation can be written for the magnetic field, M M = Am sin(2πnt + Φ) where Am is the magnetic field’s maximum amplitude. An electromagnetic wave, therefore, is characterized by several fundamental properties, including its velocity, amplitude, frequency, phase angle, polarization, and direction of propagation.4 Other properties, which are based on these funda-mental properties, also are useful for characterizing the wave behavior of electro-magnetic radiation. The wavelength of an electromagnetic wave, l, is defined as the distance between successive maxima, or successive minima (see Figure 10.2). For ultraviolet and visible electromagnetic radiation the wavelength is usually expressed in nanometers (nm, 10–9 m), and the wavelength for infrared radiation is given in microns (mm, 10–6 m). Unlike frequency, wavelength depends on the electromag-netic wave’s velocity, where l = v = c (in vacuum) wavenumber The reciprocal of wavelength (n). Thus, for electromagnetic radiation of frequency, n, the wavelength in vacuum is longer than in other media. Another unit used to describe the wave properties of electromagnetic radiation is the wavenumber, n, which is the reciprocal of wave-length n = 1 Chapter 10 Spectroscopic Methods of Analysis 371 Wavenumbers are frequently used to characterize infrared radiation, with the units given in reciprocal centimeter (cm–1). EXAMPLE 10.1 In 1817, Josef Fraunhofer (1787–1826) studied the spectrum of solar radiation, observing a continuous spectrum with numerous dark lines. Fraunhofer labeled the most prominent of the dark lines with letters. In 1859, Gustav Kirchhoff (1824–1887) showed that the “D” line in the solar spectrum was due to the absorption of solar radiation by sodium atoms. The wavelength of the sodium D line is 589 nm. What are the frequency and the wavenumber for this line? SOLUTION The frequency and wavenumber of the sodium D line are n = c = 3.00 ´ 1089m/s = 5.09 ´ 1014 s 1 n = 1 = 589 ´ 10 9 m ´ 100 cm = 1.70 ´ 104 cm 1 Two additional wave properties are power, P, and intensity, I, which give the flux of energy from a source of electromagnetic radiation. Particle Properties of Electromagnetic Radiation When a sample absorbs electro-magnetic radiation it undergoes a change in energy. The interaction between the sample and the electromagnetic radiation is easiest to understand if we assume that electromagnetic radiation consists of a beam of energetic particles called photons. When a photon is absorbed by a sample, it is “destroyed,” and its energy acquired by the sample.5 The energy of a photon, in joules, is related to its frequency, wave-length, or wavenumber by the following equations E = hn power The flux of energy per unit time (P). intensity The flux of energy per unit time per area (I). photon A particle of light carrying an amount of energy equal to hn. hc l = hcn where h is Planck’s constant, which has a value of 6.626 ´ 10–34 J • s. EXAMPLE 10.2 What is the energy per photon of the sodium D line (l = 589 nm)? SOLUTION The energy of the sodium D line is hc (6.626 ´ 10 34 J • s)(3.00 ´ 108 m/s) l 589 ´ 10 9 m = 3.37 ´ 10 19 J 372 Modern Analytical Chemistry Wavelength (m) 10–14 10–12 10–10 10–8 10–6 10–4 10–2 100 102 Frequency (s–1) 1022 1020 1018 1016 1014 1012 1010 108 Type of transition Spectral region Nuclear g-ray Core-level electrons X-ray Valence electrons UV Molecular vibrations IR Molecular rotations; electron spin Microwave Nuclear spin Radio wave Visible Wavelength (nm) 380 480 580 680 780 Violet Blue Green Yellow Orange Red Figure 10.3 The electromagnetic spectrum showing the colors of the visible spectrum. Colorplate 9 shows the spectrum of visible light. electromagnetic spectrum The division of electromagnetic radiation on the basis of a photon’s energy. The energy of a photon provides an additional characteristic property of electro-magnetic radiation. The Electromagnetic Spectrum The frequency and wavelength of electromagnetic radiation vary over many orders of magnitude. For convenience, electromagnetic radiation is divided into different regions based on the type of atomic or molecular transition that gives rise to the absorption or emission of photons (Figure 10.3). The boundaries describing the electromagnetic spectrum are not rigid, and an overlap between spectral regions is possible. 10A.2 Measuring Photons as a Signal E2 E1 E0 Figure 10.4 Simplified energy level diagram showing absorption of a photon. In the previous section we defined several characteristic properties of electromag-netic radiation, including its energy, velocity, amplitude, frequency, phase angle, polarization, and direction of propagation. Spectroscopy is possible only if the pho-ton’s interaction with the sample leads to a change in one or more of these charac-teristic properties. Spectroscopy is conveniently divided into two broad classes. In one class of techniques, energy is transferred between a photon of electromagnetic radiation and the analyte (Table 10.1). In absorption spectroscopy the energy carried by a photon is absorbed by the analyte, promoting the analyte from a lower-energy state to a higher-energy, or excited, state (Figure 10.4). The source of the energetic state de-pends on the photon’s energy. The electromagnetic spectrum in Figure 10.3, for ex-ample, shows that absorbing a photon of visible light causes a valence electron in the analyte to move to a higher-energy level. When an analyte absorbs infrared radi-ation, on the other hand, one of its chemical bonds experiences a change in vibra-tional energy. ... - --nqh--