6. 3. Molecular spectroscopy. Unit 6: Physical chemistry of spectroscopy, surfaces and chemical and phase equilibria

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1 6. 3 Molecular spectroscopy Spectroscopy in its various forms is a technique with wide applications across many disciplines. From qualitative analysis in toxicology through to quantitative measurements made on the atmosphere using remote-sensing satellites, the common strand is the use of the interaction between molecules and electromagnetic radiation. In this topic guide you will learn about some of the commonly used spectroscopic techniques and the theoretical models on which they are based and then examine some of the applications of these techniques. On successful completion of this topic you will: understand the origins and applications of molecular spectroscopy (LO3). To achieve a Pass in this unit you need to show that you can: examine the relationship between spectroscopic techniques and electromagnetic radiation (3.1) review theoretical models used in spectroscopy (3.2) explain the applications of practical spectroscopic techniques (3.3). 1

2 Key terms Wavelength: The length of a complete waveform. Frequency: The number of complete waveforms passing a point in one second. 1 Models and techniques Spectroscopy is the study of the way in which matter interacts with electromagnetic radiation. In this unit we will consider the way in which radiation of three different regions of the electromagnetic spectrum is absorbed. The electromagnetic spectrum Visible light, along with other familiar types of radiation, such as infrared radiation, microwave radiation and X-rays, is a form of electromagnetic radiation. All electromagnetic radiation consists of vibrating magnetic and electric fields which transfer energy from one point to another. The different types of radiation differ in their wavelength and frequency, and the whole range of electromagnetic radiation makes up the electromagnetic spectrum. Part of this spectrum, showing the frequencies and wavelengths of the different types of radiation, is shown in Figure Figure 6.3.1: The electromagnetic spectrum, showing the variation in frequency and wavelength over the spectrum. Frequency (Hz) Gamma-rays X-rays Ultraviolet Visible Infrared Near IR Thermal IR Far IR Microwaves Radar Radio, T.V. AM Wavelength 0.1 nm 1 nm 10 nm 100 nm 1000 nm 1 μm 10 μm 100 μm 1000 μm 1 mm 1 cm 10 cm 1 m 10 m 100 m 1000 m 400 nm 500 nm 600 nm 700 nm Blue Green Red Although the boundaries of the visible region of the electromagnetic spectrum are strictly defined by the frequencies that our eyes respond to, boundaries between other parts of the spectrum for example, microwave and infrared radiation may be rather more arbitrary. 2

3 Frequency, wavelength and velocity These three terms are linked by the equation below: (1) velocity, c (ms 1 ) = frequency, ν (s 1 or Hz) wavelength, λ (m) The velocity of all types of electromagnetic radiation is constant in a given medium: In a vacuum (and air), c = ms 1 In water, c = ms 1 Table 6.3.1: The effects of some different types of radiation used in spectroscopy. The use of different parts of the electromagnetic spectrum Region of spectrum Approximate frequency range used / Hz Effect on molecules radiowaves to Causes certain nuclei in molecules to align against a magnetic field. microwaves to Causes increase in rotational energy level. infrared to Causes increase in vibrational energy. visible and ultraviolet to Excites electrons to higher energy levels. X-rays Above about Causes ionisation of molecules. Table shows the effects of different types of radiation used in spectroscopy. In this topic guide you will look specifically at the use of microwave, infrared and visible/ultraviolet frequencies. Data about the radiation being used is often displayed in terms of its wavelength, although the wavelength of the radiation changes depending on the medium through which it travels. Converting between frequency and wavelength can easily be done using equation (1) above and data for the velocity of electromagnetic radiation. Wavenumber Data from infrared spectroscopy is often displayed using the wavenumber of the radiation, the number of waves per unit length (usually in one centimetre). Wavenumber is defined as the number of complete waveforms in 1 cm. So: 1 (2) wavenumber = wavelength in cm = wavelength in m Use equations (1) and (2) and the values for the velocity of light in air and water shown above to perform the following calculations. 1 A wave of infrared radiation in air has frequency Hz. Calculate (a) the wavelength in m (b) the wavenumber in cm 1. 2 The wavelength of microwave radiation in water is 1.74 cm. Calculate the frequency of the radiation in Hz. 3

4 Absorption and emission of radiation Molecules possess energy, which is associated with specific aspects of their behaviour. As well as translational energy (due to movement of the whole molecule), these can include: rotational energy (due to rotation of the molecule) vibrational energy (due to vibration of the covalent bonds within the molecule) electronic energy (the energy levels occupied by the electrons in the molecule). The way in which various types of radiation interact with matter can be explained by considering these different aspects of molecular behaviour. Key terms Quantum theory: A theoretical model developed at the beginning of the 20th century to describe the behaviour of matter on a sub-atomic level. Quantised: Energy is quantised if it can take only certain fixed values. Quantisation of energy Quantum theory states that all energy is quantised that is, it can take only certain fixed values, known as energy levels. After a molecule gains energy it occupies a new, higher energy level. For certain types of molecular energy, for example, translational energy, these energy levels are so close together that the effect of quantisation can be ignored. For rotational energy, vibrational energy and electronic energy the energy gaps between the levels become significant. The size of the energy gap will determine what type of radiation will be required to cause a transition to a higher energy level. This is because the energy of electromagnetic radiation is also quantised. According to quantum theory, electromagnetic radiation can be thought of as a stream of photons, each carrying a certain amount of energy. The value of energy associated with each photon is given by the Planck relation: (3) energy (in J) = Planck s constant, h (in J Hz 1 ) frequency (in Hz) E = hν h has the value J Hz 1 Figure 6.3.2: The spacing between energy levels determines the frequency of photons absorbed or emitted when the energy levels of molecules change. When a photon of radiation is absorbed, the molecule is described as being excited to a higher energy level, as shown in Figure Under certain circumstances, molecules may drop back down to a lower energy level; the energy lost is given out as a photon of radiation, which is also shown in Figure ΔE = hv = J IR radiation v = Hz ΔE = hv = J UV radiation v = Hz 4

5 The spacing between energy levels for different types of molecular energy is compared in Table Table 6.3.2: The relationship between type of energy level and the typical spacing between the energy levels. Type of energy level Typical spacing between energy levels (J) Type of electromagnetic radiation absorbed rotational microwave vibrational infrared electronic visible/ultraviolet Look at the size of the spacing between the energy levels for each type of energy shown in Table Use Planck s relation (3) to calculate the frequency of the radiation required in each case to cause the molecule to be excited to the next energy level. The nature of spectra The data from spectroscopic investigations is usually presented in the form of a spectrum, in which the intensity of radiation absorbed, transmitted or emitted is plotted against the frequency of radiation. For example, Figure shows the appearance of a microwave (rotational) spectrum for the molecule carbon monoxide (CO). The y-axis shows the relative intensity of radiation absorbed at different frequencies. Figure 6.3.3: Microwave (pure rotational) spectrum of CO. Relative absorbance Frequency of electromagnetic radiation (10 11 Hz) Each peak in the spectrum can be linked to a particular transition between energy levels. The frequency of the peak depends on the difference in energy between the two levels. The intensity of the peak depends on the relative numbers of the transitions that occur. This depends on factors including the number of molecules occupying each energy level. The link between the energy levels, the possible transitions and the appearance of the spectrum will be explored in more detail in the next section. 5

6 In these calculations, c, the speed of light = ms 1 and h (Planck s constant) = J Hz 1. 1 The molecule carotene absorbs visible light. The maximum absorption occurs at a wavelength of 435 nm ( m). Calculate the frequency of this radiation and hence deduce the energy of the photon absorbed. 2 Propanone contains a C=O bond that absorbs infrared radiation with a wavenumber of 1710 cm 1. Calculate the wavelength (in m) and the frequency of this radiation. 3 In the pure rotational spectrum of carbon monoxide, the maximum absorbance occurs for radiation with a frequency of Hz. Calculate the energy of the photon absorbed at this frequency and the wavelength (in m) of the radiation. Portfolio activity (3.1) Obtain some spectra of simple molecules. Use each spectrum to explain what information can be deduced about the radiation that is absorbed by these molecules. You should choose an example from each of the three spectroscopic techniques studied in this section (microwave, infrared, visible/ultraviolet). In your answer, for each spectrum you should: extract information (for example, wavenumber or frequency) about the radiation absorbed by the molecule explain how this information can be used to deduce other information (wavelength, frequency or energy of the photon absorbed) about the radiation. Suitable examples of spectra to study could include: visible/uv spectra of benzene and other aromatic compounds, infrared spectra of simple alkenes or alcohols (e.g. propene or ethanol), or microwave spectra of simple gaseous molecules such as HCl or HCN. Key term Model: A scientific model is a way of visualising or making sense of a complex physical system. Models can be used to make predictions that can then be tested. A combination of the complex ideas from quantum theory and simple classical mechanics allows scientists to link the details of a molecular spectrum to the structure and identity of the molecule itself. Quantum numbers Quantum theory suggests that molecules can be described by a series of numbers, called quantum numbers, which determine the rotational, vibrational and electronic energy of a molecule. In the next section you will see how these quantum numbers link to the observed spectra of the molecules. 2 Rotational spectroscopy (microwave spectroscopy) The rigid rotor model Transitions between rotational energy levels correspond to the energy of a photon of radiation in the microwave region of the spectrum. The model used to explain the details of a rotational spectrum is most easily applied to a diatomic molecule. 6

7 Which of these molecules can give rise to a pure rotational spectrum in the gas phase: (a) H 2 (b) O 2 (c) H 2 O? Pure rotational spectra of molecules In this section, you will look at spectra that are described as pure rotational spectra. This means that the transitions that give rise to the spectra involve only rotational energy levels. If a change in rotational energy level is accompanied by a change in vibrational energy level then the spectrum obtained is described as a rotational-vibrational spectrum. Only molecules that possess a permanent electrical dipole, such as CO, will give rise to a pure rotational spectrum. Rotational spectra can only be obtained for molecules in the gas phase. Rigid rotor A diatomic molecule can be described by the rigid rotor model. In this model, the two atoms are rotating about their centre of mass. The distance between the two atoms (the bond length) remains constant. Figure 6.3.4: The rigid rotor model of a diatomic molecule. The rotational behaviour of the molecule is described using the atomic masses M 1 and M 2 and the bond length r. M 1 centre of mass M 2 r bond length Key terms Electrical dipole: Two electrical charges of equal magnitude but opposite sign, separated from each other by a (small) distance. Moment of inertia: A measurement of an object s resistance to angular acceleration. The energy of the rigid rotor depends on its moment of inertia, I. For this rigid rotor system: (1) I = μr 2 M 1 M 2 (2) where μ = M 1 + M 2 and is known as the reduced mass of the system. So this value of I is then used in the calculation of the energy of the molecule. Calculate a value of I, the moment of inertia, for the 12 C 16 O molecule. The masses are: 12 C = kg and 16 O = kg. The bond length is: m. Note: It is easy to calculate the mass of individual atoms from their isotopic masses. In the example above, one mole of 12 C atoms has a mass of 12 g (0.012 kg). The number of atoms in one mole is Avogadro s number, L (L = ), so the mass of an individual atom of 12 C = 0.012/ = kg. 7

8 Key term Rotational constant: A constant with the symbol B, related to the moment of inertia of a molecule, which appears in equations for the rotational energy levels of molecules. Mathematically, B = h2 8π 2 I J 3 J 2 J 1 E = 12B E = 6B E = 2B J 0 E = 0 Figure 6.3.5: Relative energies of the rotational energy levels can be calculated using equation (2). Rotational energy levels Application of quantum theory suggests that a molecular rigid rotor can exist in several different rotational energy levels, each characterised by a different value of the rotational quantum number, J. J has integral values, so J = 0, 1, 2, etc. The energy of each of these energy levels (E j ) can then be calculated: h 2 (3) E =. J(J + 1) 8π 2 I To make the equation slightly simpler, the quantity h2 8π 2 I is often replaced by the term B, which is known as the rotational constant. So B = h2 8π 2 I (h = Planck s constant, J K 1 ) The equation for the energy levels of a rigid rotor now becomes: (4) E J = BJ(J + 1) In the lowest rotational energy level, J 0, J has a value of 0, so the energy of this level is also zero. The energy of the J = 1 energy level, J 1 = B 1 (1+1) = 2B. The relative energies of the first four rotational energy levels are shown in Figure The energy of the J o energy level = 0 and the energy of the J = 1 energy level = 2B. Calculate the energy of the energy levels J 2 to J 6. J 3 E = 12B J 2 J 3 ΔE = 6B J 2 E = 6B J 1 J 2 ΔE = 4B J 1 E = 2B J 0 J 1 ΔE = 2B J 0 E = 0 Selection rules At temperatures normally encountered in chemical systems, many different rotational energy levels will be populated by molecules. You might think that this could give rise to a large number of possible transitions, for example, J 0 J 1, J 0 J 2, J 1 J 4, etc. However, application of quantum theory shows us that in any transition between energy levels, the rotational quantum number can only change by a value of 1. This is known as the selection rule for rotational transitions: (5) ΔJ = ±1 So when electromagnetic energy is absorbed, only transitions such as J 0 J 1, J 1 J 2, etc. are allowed. These allowed transitions are shown in Figure Figure 6.3.6: The allowed transitions between the rotational energy levels. 8

9 Table 6.3.3: The energies of rotational transitions and the frequencies of radiation that will cause these transitions. Table shows the energies of these transitions and the frequency of radiation absorbed (= ΔE ) by this transition. h Transition Energy Frequency J 0 J 1 J 1 J 2 J 2 J 3 2B 4B 6B 2B h 4B h 6B h So the rotational spectrum of a diatomic molecule will consist of a series of peaks, spaced at regular intervals, as shown in Figure The interval between each peak corresponds to a frequency of 2B h. Figure 6.3.7: The pattern in frequencies absorbed by a rigid rotor molecule. Absorbance 2B h 2B h 2B h 2B h 4B h 6B h Frequency/H Z Look at the microwave (pure rotation) spectrum of 12 C 16 O shown in Figure Identify the transitions responsible for each of these peaks (Hint: start with the peak of the lowest frequency). Use the fact that the gap between peaks has a value of 2B to estimate a value of B, the h rotational constant for this molecule. Extension work: Use the value of I calculated in the activity on page 7 and the definition of B to calculate a value for the rotational constant of 12 C 16 O. Relative absorbance Frequency of electromagnetic radiation (10 11 Hz) Figure 6.3.8: The rotational spectrum of 12 C 16 O at 40 K. 9

10 Energy 30B 20B 12B 6B 2B 0 J 5 J 4 J 3 J 2 J 1 J 0 Relative population Figure 6.3.9: The relative population of each rotational energy level can be predicted from statistical ideas. In this diagram, the J 3 and J 4 energy levels are the most populated. Population of energy levels The relative number of molecules found in each rotational energy level depends on several factors: whether the rotational state of molecules in that energy level is permitted by quantum theory. For CO 2, for example, only states with even values of J are permitted. statistical calculation of the most probable rotational energies. As with the Maxwell distribution of molecular speeds (see Topic guide 6.1 section 1), at each temperature there will be one energy level which will be the most populated. A typical population of the energy level is shown in Figure Transitions from the most populated energy level are likely to be the most intense. Look at the microwave spectrum of 12 C 16 O in Figure 6.3.8, which was recorded at a temperature of 40 K. Suggest the most populated rotational energy level for this molecule (at 40 K). Applications of microwave spectroscopy Case study Research teams at the University of Arizona have been investigating the structure of transition metal hydrides. These could become very important in the development of hydrogen storage strategies, to enable greater use of hydrogen as a fuel. By determining the H H distances in the complex, the team was able to show that several transition metal hydrides with the formula MH 2 contained a hydrogen molecule bonded to the transition metal rather than two separate hydrogen atoms. Why is it usually difficult to measure the bond length of a H H bond by rotational spectroscopy? Suggest why it might be possible for a H H bond in the MH 2 complex. Calculation of bond lengths As noted previously, the peaks in a rotational spectrum occur at a spacing of (6) 2B h This means that a value of B can easily be deduced from a spectrum. From equation (1), a value of I can easily be calculated: h (7) I = 8π 2 B Now, from equation (1): I (8) I = μr 2, so r = μ (remember that μ = M 1 M 2 ) M 1 + M 2 So from knowledge of B, M 1 and M 2, the interatomic distance in a diatomic molecule can be calculated. M 1 and M 2 are in kg, and can easily be calculated from the mass number of the isotope present and Avogadro s number, L (L = ). 10

11 Calculate a value for r, the interatomic distance in the CO molecule. The mass of a 12 C atom = kg The mass of a 16 O atom = kg h (Planck s constant) = J Hz 1 (Hint: begin by using the spectrum and equations (6) and (7) to find a value for B and hence I. Finally use equation (8) and the masses provided to calculate r.) Key term (Electrical) dipole moment: A mathematical quantity to describe a dipole. Dipole moment = charge distance between the charges. Figure : The different modes of vibration of carbon dioxide. The symmetric C O stretch, mode V 1, is not infrared active. 3 Vibrational spectroscopy (infrared spectroscopy) The simple harmonic oscillator model As you saw in section 1 of this topic guide, transitions between vibrational energy levels correspond to the energy of a photon of radiation in the infrared region. In order for vibrating molecules to interact with electromagnetic radiation (i.e. to absorb infrared radiation), the vibration must involve a change in dipole moment. These modes of vibration are described as infrared active. There can be several ways for even simple molecules, such as carbon dioxide, to vibrate. These different modes of vibration are shown in Figure V 1 Symmetric C O stretch V 2 Bend V 3 Asymmetric C O stretch Take it further Animations of the different vibrational modes of molecules such as CO 2 are widely available on the net. Try which links the vibrational mode to the infrared spectrum. Simple harmonic oscillator The model used to describe a vibrating molecule is called the simple harmonic oscillator. For a diatomic molecule, this can be imagined as two masses connected by a spring. The properties of a simple harmonic oscillator depend on the two masses and a constant, k, which is called the force constant of the spring. 11

12 In simple harmonic motion, the force on the masses is proportional to the displacement of the spring, x (x = R r, the difference between the extension of the spring and its normal length). This is shown in Figure (1) F = kx Figure : The simple harmonic oscillator model, as applied to a diatomic molecule. Bond length, r force R force Frequency of vibration M 1 M 2 M 1 M 2 force constant = k The frequency at which this system vibrates will depend on the masses at either end of the spring (M 1 and M 2 ) and the stiffness of the spring. In the same way the frequency of vibration, ν, of a bond will depend on the masses of atoms that make up the bond and the strength (the force constant, k) of the bond. In fact (2) v = 1 2π k μ where μ = M 1 M 2 M 1 + M 2, the reduced mass of the system (see section 2 of this topic guide). Calculate the energy of the v = 1 and v = 2 vibrational energy levels. Vibrational energy levels As you saw in the section on rotational spectroscopy, quantum theory is applied to this simple situation. The result is that this simple molecular harmonic oscillator can exist in several different vibrational energy levels. The different vibrational energy levels have different values (0, 1, 2, etc) of the vibrational quantum number, v. Ev = (v + ½) h ν Where ν is the frequency of vibration of the molecule and v is the vibrational quantum number. Make sure that you do not confuse these two symbols! So, the energy of the lowest vibrational energy level, Eo, is equal to ½ h ν. The energies of the first few vibrational energy levels are shown in Figure Figure : The energies of the vibrational energy levels; the right-hand diagram shows these energies superimposed on a graph showing how potential energy varies with interatomic distance. V = 3 E 3 = 7 hν 2 V = 2 ΔE = hν E 2 = 5 hν 2 ΔE = hν E 3 E 2 V = 1 E 1 = 3 hν 2 ΔE = hν E 1 V = 0 E 0 = 1 2 hν E 0 r Interatomic distance, R 12

13 Take it further Vibrational energy levels are often shown superimposed on a graph showing the parabolic relationship between potential energy and interatomic distance. The derivation of this relationship and its limitations is discussed on websites such as Selection rules and population of energy levels You saw in the previous section how there are rules for the allowed transitions between rotational energy levels. The selection rule for transitions between vibrational energy levels has the same pattern: the vibrational quantum number can only change by a value of 1. (3) Δv = ±1 However, unlike in the rotational case, at room temperature almost all molecules are at the lowest energy level (v = 0). Thus the most important transition will be from v = 0 to v = 1. The energy difference between these two levels is easily calculated: ΔE = E 2 E 1 = 3 2 h ν 1 2 h ν = h ν But, as you can see from Figure , all the other allowed transitions have ΔE = h ν as well! The frequency of radiation, ν, which causes this transition is known as the fundamental vibrational frequency of the molecule (for a particular vibrational mode). Anharmonic oscillator The simple harmonic oscillator model works reasonably well for molecules in the lowest vibrational energy levels. However, for molecules in higher energy levels, the vibration of the molecule is no longer harmonic because the graph of potential energy of the molecule is not actually parabolic (see the Take it further feature above). The difference between the patterns of energy levels predicted by the harmonic and anharmonic oscillator models is shown in Figure Figure : The spacing of energy levels for the harmonic oscillator (left) and the anharmonic oscillator (right). V 4 V 3 V 4 V 3 V 2 V 2 V 1 ΔE = hν V 1 V 0 ΔE = hν V 0 ΔE = hν 13

14 The result of this anharmonic behaviour is that the spacing between the energy levels becomes closer together at higher energies. The selection rules for anharmonic oscillations are also different; Δv values of +2, +3 are permitted. The appearance of an infrared spectrum A graph of the appearance of the infrared spectrum of carbon dioxide can be seen at SPEC&Index=1#IR-SPEC. Each of the infrared active modes of CO 2 absorbs at a specific frequency. This corresponds to the frequency required for the transition v = 0 to v = 1. Take it further Databases of the infrared spectra of a wide range of substances are available on the Internet. Examples of these databases include: Go to SPEC&Index=1#IR-SPEC and estimate the wavenumber of the two main peaks shown in the graph. Calculate the frequency of the radiation absorbed (c = ms 1 ). Qualitative IR spectroscopy Link This section is covered in more detail in the presentation Interpreting spectra. Infrared spectra are normally presented to show the percentage transmission over a range of wavenumbers. A peak in such a spectrum is therefore seen as a dip in the percentage transmission. The shape of the peak and the fine structure sometimes seen in the peaks can be a result of the presence of rotational energy levels within each vibrational energy level, as well as the anharmonic nature of the oscillations at higher energy levels. For more complex molecules, the spectrum is normally interpreted by considering that bonds in the molecule may be identified by the specific wavenumber at which they will absorb infrared radiation. Detailed tables of absorption frequencies that are used to interpret these spectra are known as correlation tables. Take it further A useful table of infrared absorption frequencies, along with other useful and accessible background information about infrared spectroscopy, can be found at msu.edu/faculty/reusch/virttxtjml/spectrpy/infrared/infrared.htm#ir1. Different regions of infrared spectra can provide information about the presence of different types of bond. Figure gives some examples of important bonds found in each region. 14

15 Figure : Different regions of an infrared spectrum are associated with the presence of different types of bond. wavenumber/cm O H C=C fingerprint N H C=O region C H C C C O 500 Why would you expect bonds to H atoms to show absorption peaks at relatively high wavenumber values? Use ideas about simple harmonic oscillators in your answer. Use similar ideas to suggest why triple bonds also have absorption peaks at relatively high wavenumber values. Table is a simplified correlation table that will help identify bonds in molecules containing C, H and O atoms. Table 6.3.4: A simple correlation table showing the wavenumbers of the typical peaks for some common bonds in organic molecules. Bond Location Wavenumber / cm 1 O H alcohols, phenols carboxylic acids (non-hydrogen bonded) (hydrogen bonded, broad) (hydrogen bonded, very broad) C H alkanes and alkyl groups alkenes arenes C=C alkenes C=O aldehydes ketones carboxylic acids esters Look at the spectrum of 4-hydroxybenzoic acid. Draw out the structure of the molecule, and interpret the spectrum by identifying as many peaks as possible, using a suitable correlation table. Take it further Books that offer more guidance on the qualitative interpretation of infrared spectra include the classic Spectroscopic Methods in Organic Chemistry (D. Williams and I. Fleming, McGraw Hill, 2007). There is a helpful chapter on infrared spectra as well as coverage of UV-visible spectra (see next section). Quantitative infrared spectroscopy Infrared spectroscopy is less useful than UV-visible spectroscopy for quantitative use, but one area in which its use is widespread is in analysing the breath of drinkdriving suspects (see Case study on next page). 15

16 Link You can learn more about the use of infrared spectroscopy in analysing the breath of drink-driving suspects in the Unit 6 video clip. Case study A portable infrared spectrometer (known as an intoxilyser) has been developed for analysing the breath of drink-driving suspects. The suspect breathes into a sample chamber and a beam of infrared radiation is passed through the chamber. Filters are used to ensure only the frequencies of infrared radiation specific to the bonds in ethanol pass through the chamber. The absorbance of the sample is compared to the absorbance in the absence of the sample and the concentration can then be calculated by comparison with the absorbance of a reference sample of ethanol vapour of a known concentration. The C H and O H bonds in ethanol absorb infrared radiation strongly. Predict the wavenumbers at which they will absorb radiation. The wavenumber chosen to use in the intoxilyser corresponds to absorption by the C H bond. Suggest why this is chosen. (Hint: think about what other substances might be present in the breath of a suspect.) Key term Absorbance: A quantity given by the equation: absorbance, A = log I O, where I is the intensity of I the radiation reaching the sensor in the presence of the sample and I o is the intensity when the sample is not present. Beer-Lambert law for quantitative spectroscopy The example of the intoxilyser made use of absorbance by a vapour sample. Quantitative spectroscopy, whether using infrared or UV-visible spectroscopy, is more usually carried out using samples in solution and involves measuring the absorbance of the solution. For a sample in solution, the absorbance of a solution of a particular solute depends on the concentration of the solution and the path length of the radiation through the solution. Figure illustrates the meaning of these terms. Figure : The absorbance, A, of a solution depends on the concentration of a solution and the path length of the radiation through the solution. I 0 solution with concentration c I sensor source path length, I This relationship is summarised by the Beer-Lambert law: (4) A = I O = ε c I I where ε is the molar extinction coefficient of the solute (a measure of how strongly a substance absorbs radiation at a given wavelength; the units of ε are technically mol 1 dm 3 cm 1 but are usually not quoted) c is concentration of the solution in mol dm 3 I is the path length of the solution in cm. More details of how the Beer-Lambert law is used in spectroscopy will be found in Section 4 of this topic guide. 16

17 Link The idea of molecular orbitals, and the difference between σ and π orbitals, was introduced in Unit 5: Chemistry for applied biologists. 4 Electronic transitions (ultraviolet and visible spectroscopy) Transitions between orbitals Electrons in atoms and molecules occupy specific orbitals, which can be thought of as regions of space with a particular 3-dimensional shape and possessing a fixed amount of energy. Transitions between these orbitals (from the highest occupied molecular orbital to the lowest unoccupied molecular orbital) give rise to a spectrum in the ultraviolet and visible region because the energy difference between these orbitals often corresponds to a wavelength of light between 200 nm and 800 nm. Molecular orbitals Atomic orbitals are characterised by three different quantum numbers, n, l and m, which relate to the energy, angular momentum and magnetic properties of the electrons within them. Molecular orbitals are formed from the interaction of the atomic orbitals of the atoms bonded together in the molecule. The molecular orbitals that make up a C=C double bond in ethene are shown in Figure Figure : σ and π bonding orbitals. σ bonding orbital C C π bonding orbital π* antibonding orbital C σ* antibonding orbital Figure : σ* and π* antibonding orbitals. C The σ and π orbitals shown in Figure are described as bonding orbitals because there is significant electron density between the two atoms. The nuclei of the atoms are therefore mutually attracted by an electrostatic force. σ and π orbitals can also be antibonding where there is less electron density between the atoms than in the original atomic orbitals. Antibonding orbitals are denoted by an asterisk: σ* and π*. The antibonding orbitals for the C=C double bond in ethene are shown in Figure When two atomic orbitals combine, two molecular orbitals are formed a bonding orbital and a non-bonding orbital, although in most molecules at room temperature only the bonding orbitals are occupied, because the bonding orbitals have a lower energy than the antibonding orbitals, as shown in Figure Figure : The relative energy of σ and σ* orbitals. π* antibonding orbital σ* energy S ΔE S σ* antibonding orbital σ 17

18 Transitions between molecular orbitals For a simple alkane molecule, for example, hexane, the only molecular orbitals involved in electronic transitions are the σ and σ*. The presence of a C=C bond in, say, a cyclohexene molecule means that π and π* will also be present. If a C=O bond is present in, say, propanone, there will be π and π* orbitals but the lone pair of electrons on the oxygen atom occupy what is called a nonbonding orbital, given the symbol n. As with rotational and vibrational spectroscopy there are restrictions on the transitions that can actually take place. The selection rules are more complex than those for rotational and vibrational transitions, however, and even forbidden transitions may be observed, although with low probability. The allowed transitions are: σ to σ* π to π* n to σ*. n to π* can also occur although it is technically forbidden. This makes the intensity low. The energy gaps corresponding to these transitions are determined by the relative energies of the orbitals involved. These are shown in Figure Figure : The relative energy gaps for transitions between common types of molecular orbitals. Energy σ* π* σ σ* n σ* n π π* n π* π σ C C C = C C = O C = O As most of the energy gaps shown in the diagram are relatively large, the frequency of radiation required to cause the excitation is high, and so the wavelength will be short. So, for simple alkanes, alkenes and carbonyl compounds absorption occurs in the ultraviolet region, with wavelengths between 150 nm and 280 nm. Of these, only those between about 200 nm and 280 nm are useful in spectroscopy. Figure shows four different transitions between orbitals. Put these in increasing order of energy gap. Hence suggest the order of the wavelengths of radiation causing these transitions, starting with the shortest wavelength. Functional groups giving rise to the absorption of ultraviolet or visible radiation are described as chromophores. 18

19 Some simple organic chromophores, and the wavelengths (λ max ) at which they absorb the maximum intensity of radiation, are shown in Table Table 6.3.5: Absorption wavelengths and intensity of some simple chromophores. The intensity of the absorption (measured by the value of ε, the molar extinction coefficient) are also shown in the table. Chromophore Typical λ max (nm) Transition causing this absorption Typical intensity C=C 175 π π* strong (ε = ) C=O π π* n π* moderately strong (ε = 5000) weak (ε =15) C C 175 π π* strong (ε = ) Key term Delocalised: Electrons are delocalised if they are free to move over a system of three or more atoms. Figure : The π and π* orbitals from two conjugated π bonds form four new π and π* orbitals. Conjugation Some molecules absorb strongly at wavelengths of longer than 200 nm. They do so because of the presence of a conjugated system. This is one in which the electrons from several p orbitals (or π bonds) form a delocalised system. The formation of a delocalised system is shown in Figure π 4 π* π π 3 * π π* π 2 π 3 * π 2 (LUMO) (HOMO) C = C π 1 C = C C = C As you will observe from the diagram, the effect of the conjugation is to reduce the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) the gap between π 2 and π 3 * in the conjugated system is much less than between π and π* in the simple C=C bond. Hence the energy required for the transition is reduced, the frequency of the radiation is lowered and the wavelength is increased. The greater the conjugation, the smaller the energy gap for the transition and hence long conjugated systems absorb at much longer wavelengths, even into the visible region. Table shows the typical wavelength at which some conjugated chromophores absorb radiation. As a rough guide, every extra conjugated double bond is likely to increase λ max by about 30 nm. 19

20 Table 6.3.6: Absorption wavelengths and intensity of some conjugated chromophores. Chromophore λ max (nm) Relative intensity C=C C=C 217 Strong benzene ring Strong Moderate Weak carotene 460 Strong The effect of solvents Ultraviolet and visible spectra are obtained from samples of organic molecules that are dissolved suitable solvents. The nature of the solvent affects the wavelength of the radiation absorbed for the different transitions. With more polar solvents, such as ethanol, the following shifts occur: π to π* transitions occur at longer wavelengths (described as a red shift) n to π* transitions occur at shorter wavelengths (described as a blue shift). These changes occur because, although π, π* and n orbitals are all stabilised in a polar solvent, the stabilisation is more significant for the π* and n orbitals. An example of this is shown for propanone in Table The λ max of the n to π* transition is shown for a range of solvents. Table 6.3.7: The effect of solvents on the absorption wavelength of an n π* transition. Solvent λ max (nm) hexane 280 ethanol 271 water 257 Predict the λ max of the n to π* transition for a solution of propanone in trichloromethane solvent. The polarity of trichloromethane is intermediate between that of hexane and ethanol. d-d transitions The previous sections have been largely concerned with the formation of absorption spectra of organic molecules. 20

21 Case study Heavy metal ions, such as copper, mercury and lead, are often present in water leaching from industrial sites, for example, spoil heaps containing waste from mining and metal extraction processes. Spectrophotometry, in which the absorbance of solutions is measured over particular frequency ranges, provides a simple method for detecting these ions and obtaining an approximate value for their concentration, using the Beer-Lambert law. Highly coloured complexes are produced by adding suitable ligands to the solutions; at low concentrations the colour of these complexes will be very faint and the absorbance difficult to measure. Techniques to overcome this problem include forming the complex on the surface of a solid support that selectively traps the metal ions. One ligand often used to form complex ions is edta (ethylenediaminetetraacetic acid). Use research to find the structure of edta and explain how it bonds strongly to Cu 2+ ions. Solutions of transition metal ions, such as Cu 2+, also absorb strongly in the visible region of the spectrum. This is due to a transition between the d-orbitals of the transition metal ion. Transition metal ions such as Cu 2+ have several d electrons, distributed between the five different atomic orbitals that make up the d subshell. Key term Complex ion: A central metal ion surrounded by ligands that bond to it by dative covalent bonds. Figure : The presence of ligands alters the energies of the 3d orbitals in Cu 2+ (aq); the d-orbitals become split into two sets with different energies. The presence of water molecules increases the energies of the electrons in these orbitals. However, because the water molecules that surround the Cu 2+ ion are arranged in a specific geometric arrangement, forming a complex ion, some of the d-orbitals are affected more than others. As a result the d-orbitals are split by the presence of solvents such as water (see Figure ). energy average energy of d-orbitals surrounded by ligands ΔE some d-orbitals interact with ligands more strongly Cu 2+ (g) Cu 2+ (aq) The size of the energy gap (ΔE) between the two sets of d-orbitals corresponds to the absorption of a photon of light in the visible region of the spectrum for Cu 2+ (aq) this is at a wavelength of about 590 nm. 21

22 The appearance of ultraviolet-visible spectra Figure : The UV-visible spectrum of nitrobenzene (which contains a conjugated system). Logarithm epsilon Wavelength (nm) UV-visible spectra are usually displayed as a plot of absorbance against wavelength (although, as in Figure , absorbance may be replaced by ε, the molar extinction coefficient which is related to absorbance by the Beer-Lambert law). As shown in Figure , even compounds that largely absorb in the ultraviolet region may show some absorbance in the visible region (and vice versa) and so the wavelength range shown in the spectrum often spans both regions of the spectrum hence the term UV-visible spectrum. The UV-visible spectrum in this case shows a simple curve so only one value of λ max is recorded; if the curve has several peaks then several different λ max values may be recorded for a single molecule. Estimate a value of λ max for nitrobenzene from Figure Compare this spectrum with that of benzene (available from Look at the structure of nitrobenzene and suggest why the λ max for nitrobenzene differs from that for benzene. Quantitative spectra The main application of UV-visible spectra is in the quantitative analysis of organic molecules and inorganic ions. Quantitative analysis makes use of the Beer-Lambert law introduced in the previous section: A = ε c l For the substance under investigation, a UV-visible spectrum is obtained (using a 1 cm path length) and the absorbance at the λ max wavelength is recorded. If the ε value for the absorbance at that wavelength is known, then the concentration can be determined by simple substitution into the Beer-Lambert equation. 22

23 The absorbance of a solution of benzene in hexane was 2.96 at λ max = 204 nm. The concentration of the solution was mol dm 3. Calculate the value of ε for absorbance at this wavelength. Manganate ions, present in the salt potassium manganate, are intensely coloured transition metal ions with a λ max value of 528 nm. The absorbance of a solution of manganate was measured as 2.04 using a sample with a path length of 1 cm. Calculate the concentration of the manganate ions. The value of ε at 528 nm is Calculate the concentration of the solution. Values of ε can be obtained by measuring the absorbance of a solution of known concentration. If ε values are relatively high, then UV-visible spectra can provide information about the concentration of quite dilute solutions, making it an ideal technique for quantitative measurement of impurities in samples. Portfolio activity (3.2) Choose spectra for some simple molecules. Suitable spectra could include the microwave (pure rotational) spectrum of CO 2, infrared spectrum for propanal and the UV-visible spectrum for buta-1,3-diene. Use suitable theoretical models to explain how each spectrum arises. In your answer, for each type of spectroscopy: state the main features of the model, including any relevant equations used to describe the energy differences between energy levels of the system include a copy of the spectrum show how at least one peak in the spectrum can be accounted for using this model comment on any other useful information about the molecule that can be derived using information from the spectrum. Link The interpretation of ultraviolet and visible spectra to identify organic groups, chromophores and metal cations is covered in the presentation Interpreting spectra. 5 Interpreting spectra Infrared spectroscopy The main features of the interpretation process are summarised below: groups of atoms (for example carbonyl groups, C=O) can be identified from their approximate position in the spectrum the exact wavenumber can give information about the location of the group (for example, a C=O in a carboxylic acid) only infrared active vibrations can be detected, so C C is not usually observed some groups give rise to multiple peaks in a single spectrum with similar frequencies peaks relating to C H bonds can provide data about structural features such as CH 2, CH 3 or pattern of substitution in benzene rings hydrogen bonding affects the wavenumber and shape of the peak the region below 1300 cm 1 is known as the fingerprint region and can be used to identify the molecule by comparison with databases. 23

24 UV-visible spectroscopy The main features of the interpretation process are summarised below: chromophores can be identified by their λ max value and/or ε value λ max is affected by amount of conjugation, or (for benzene) by presence of different substituents nature of solvent must be taken into account as it will shift λ max slightly. Analytical chemist, quality control I work for a large pharmaceutical company that produces a range of drugs in tablet form. Quality control of the mass of the drug present in each tablet is absolutely critical and I head up a team that develops analytical methods based on UV/vis spectroscopy. Previous research will have identified a complexing reagent that reacts with the drug to produce a complex which absorbs strongly in the visible (or ultraviolet) region and the λ max value of the complex will have been identified. Our job is to find a suitable method for extracting the drug from our tablets into solution and to form the complex that can be analysed using our UV/vis spectrophotometers. Once we have a reliable method for doing this, we will produce accurate calibration data to relate the absorption data from the spectrophotometer to the concentration of the drug. In theory, according to the Beer-Lambert law, this should be a linear relationship, but in reality that is not always the case so calibration data are essential. Once we have this data, we can begin using the new spectrophotometric method in our quality control protocol. Portfolio activity (3.3) Describe and explain the range of applications of spectroscopic techniques. You should explain at least one way in which a substance can be identified using spectroscopy, one way in which its structure can be deduced and one way in which its concentration can be calculated. Suitable examples could include: how the infrared spectrum of a molecule such as methyl salicylate can be used to made deductions about its structure how the UV-visible spectrum of a transition ion such as Co 2+ (aq) can be used to calculate its concentration. In your answer you should: include a relevant spectrum for any substance you discuss annotate the spectrum to show the data which you can extract from the spectrum explain how these data are used to derive the information required. 24

25 Checklist At the end of this topic guide you should be familiar with the following ideas: electromagnetic radiation can interact with chemical substances in several regions of the electromagnetic spectrum including microwave, infrared and visible/ultraviolet absorption of radiation by substances gives rise to spectra that can be used to provide information about the structure and/or concentration of the substance quantum theory is used to explain how molecular rotation and vibration give rise to discrete, quantised energy levels; electron energies in molecules and atoms are also quantised excitation to higher energy levels occurs when specific frequencies of radiation are absorbed, as described by the equation ΔE = hv interpretation of rotational spectra (microwave) allows information about bond lengths to be deduced interpretation of vibrational spectra (infrared) and electronic spectra (UV/vis) allows the presence of specific bonds or groups of atoms to be deduced by using suitable correlation tables application of the Beer-Lambert law (A = ε c l) allows the concentration of substances to be calculated from spectroscopic absorption data. Further reading Elements of Physical Chemistry (Atkins and de Paula, 2009) covers the theoretical principles underlying rotational, vibrational and electronic spectroscopy in Chapters 19 and 20. A classic text to cover the interpretation of infrared and UV/visible spectra of organic molecules (as well as other techniques such as NMR and mass spectroscopy) is Spectroscopic Methods in Organic Chemistry (Williams and Fleming, 2007). Detailed correlation tables are included alongside worked examples and problems. UV/visible spectroscopy is also covered well in Modern Chemical Techniques (Faust, 1997) published by the Royal Society of Chemistry and also freely available online as a pdf file. This also covers the spectra of inorganic complexes. Acknowledgements The publisher would like to thank the following for their kind permission to reproduce their photographs: Corbis: David Sutherland All other images Pearson Education Every effort has been made to trace the copyright holders and we apologise in advance for any unintentional omissions. We would be pleased to insert the appropriate acknowledgement in any subsequent edition of this publication. 25

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