Week 11 Colour and Magnetism Workbook - Monash PDF

10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Week 11: Colour and magnetism - workbook Site: Monash Moodle1 Printed by: Kaltham Alzaabi...

10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Week 11: Colour and magnetism - workbook Site: Monash Moodle1 Printed by: Kaltham Alzaabi Unit: CHM1022 - Chemistry II - S2 2024 Date: Sunday, 6 October 2024, 10:00 AM Book: Week 11: Colour and magnetism - workbook https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 1/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Table of contents 1. Pre-workshop material 1.1. Revison 1.2. Colour 1.3. Spectro-chemical series 1.4. Magnetism 1.5. Measurement of magnetic properties 1.6. Activity 1.7. Activity solutions 2. Summary 3. Preparation quiz 4. Online lectures 5. Workshops https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 2/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1. Pre-workshop material Previously we have learnt that transition metal complexes are highly coloured and can have a variety of magnetic properties. These properties are due to the electronic configurations of the d-orbitals, which are best explained through the application of crystal field theory. The splitting of the d-orbitals into different energies allows for movement of electrons between d orbitals of different energy, and for different electronic configurations that depend on the relative energies of those split orbitals. Note, we will be only focusing on the first row of the transition metals (Figure 1). Figure 1: Examples of uses of the first row of the transition metals https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 3/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.1. Revison Revision from week 10: For octahedral complexes, the ligands approach the metal on the x-, y- and z-axes (Figure 2). Due to electrostatic repulsion, the orbitals which lie on these axes (dx2-y2 and dz2) have higher energy than the remaining orbitals (dxy, dyz, dxz) resulting in an energy gap. This energy gap for octahedral complexes is called Δoct. Figure 2: The five d-orbitals split into two energy levels for an octahedral complex. The size of Δoct Δoct is a measure of the energy gap created by the differing electrostatic repulsion between the d electrons of the metal and the ligands in an octahedral complex. Similar energy gaps exist for complexes with other geometries (e.g. Δtet for tetrahedral complexes), however we will mainly consider octahedral complexes here (although the principles explored will apply to all geometries). As we will see, the size of Δoct affects both the colour and magnetic properties of the complex. Note: the terms "high and low spin" will be defined shortly. Ligands can be separated into two differing groups, strong field ligands and weak field ligands, depending on the effect they have on the size of Δoct. Strong field ligands generally bind to the metal ion more strongly and therefore cause greater ligand to metal electron repulsion, causing Δoct to be large and leading to the complex having fewer unpaired electrons and being "low spin". An example of this is the cyanide ligand (CN-). Conversely, weak field ligands bind weakly to the metal centre, create less ligand to metal electronic repulsion, and thus cause smaller splittings between d orbitals. This leads to smaller values Δoct, more unpaired electrons and "high spin" electronic states. An example of this is the chloride ion (Cl-). Therefore depending on the ligands coordinated to the metal the size of the Δoct will differ, affecting which orbitals are occupied. For example, comparing the two complexes in Figure 3, we can see that for the strong field cyanide complex, the complex is yellow and the iron is in a low spin state, with all the electrons occupying the lower orbitals, whereas the aqua complex is green and in a high spin state with electrons in all the orbitals. The reasoning behind the differing colours and high spin/low spin configurations will be explored further in the following sections. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 4/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Figure 3: Strong field and weak field ligand effects on the colour and d-orbital configurations https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 5/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.2. Colour Please read The colours of transition metal complexes (page 784) of Chemistry, Blackman et al. (4th ed.) Transition metals are among the most highly coloured elements in the periodic table. For example, the colours of most natural gemstones and minerals are due to the presence of transition metals, even when, in some cases, they are only present in trace amounts. Figure 4 shows a wide variety of gemstones that have similar compositions except for the presence of different transition metals, leading to a variety of vibrant colours. Figure 5 shows further examples of gemstones based on colourless corundum (Al2O3) with trace transition metal impurities, including CrIII (Ruby - red) and TiIV (Sapphire - blue). Figure 4 The chemistry of gemstones. Figure 5 The colour of gemstones. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 6/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 What is Colour? We see colour due to the absorption and/or reflection of light. Colour is observed when an object reflects (or transmits) the respective colour, and absorbs the complementary colour. A good example of this is green leaves (Figure 6). The pigment that makes leaves green is known as chlorophyll. Chlorophyll absorbs red light and transmits green, therefore appearing green to our eyes. Figure 6 The colour of green leaves is due to chlorophyll absorbing red light. The same relationship between the light absorbed and the apparent colour observed applies to transition metal complexes. For example, the complex ion [Ti(H2O)6]3+ appears purple in colour (Figure 7) because it transmits light at the red and blue ends of the spectrum. Figure 7 The colour of [Ti(OH2)6]3+. The relationship between absorbed and observed colours is given in Table 1, and the relationship can be understood in crude terms by the "colour wheel" shown in Figure 8. To use the colour wheel, you first need to know the wavelength of light which is being absorbed (λmax). The colour observed is then the colour on the opposite side of the wheel. For example, if green light is absorbed (e.g. λmax = 520 nm) then the complex will appear red. Absorbed Colour λ (nm) Observed Colour λ (nm) Violet 400 Green-yellow 560 Blue 450 Yellow 600 Blue-green 490 Red 620 Yellow-green 570 Violet 410 https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 7/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Yellow 580 Dark blue 430 Orange 600 Blue 450 Red 650 Green 520 Table 1 Relationship between absorbed and observed colours. Figure 8 The colour wheel. It should be noted, however, that the colour wheel relationship between λmax and observed colour is only an approximation. In the case of the titanium complex, λmax = 490 nm (Figure 9), which the colour wheel indicates should result in complex which appears red. The absorption spectrum, however, is quite broad (which is typical), and there is considerably more light being absorbed at wavelengths longer than λmax (in the green-yellow region) compared to wavelengths below λmax. The cumulative effect of the broad and unsymmetrical shape of the absorption is to give a purple complex because it absorbs light in the yellow-green region but allows transmission of light at the blue and red ends of the spectrum. Figure 9 Absorption profile of [Ti(OH2)6]3+. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 8/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.3. Spectro-chemical series Origin of Colour in Transition Metal Complexes The splitting of d-orbitals into different energies due to the arrangement of ligands around a metal ion, as described by crystal field theory, leads to d-orbitals of different energies. A consequence of this is that if an electron in a lower energy d-orbital absorbs sufficient energy, it can move into a higher energy d-orbital (if there is room for another electron). This energy can be provided by light, and the energies needed for these d-d transitions typically correspond to the visible part of the electromagnetic spectrum. Consider again the [Ti(OH2)6]3+ complex. With an octahedral geometry and a d1 electronic configuration, there is one electron in the t2g orbitals and none in the eg orbitals. If, however, the t2g electron absorbs a photon of the right energy it can be promoted to a higher energy eg orbital. The energy of the photon the electron needs to absorb is that of the energy gap between the t2g and eg orbitals - i.e. Δoct. The energy is in turn related to the frequency (ν) or the wavelength (λ) of the light as follows: Δ Eelectron = Ephoton = h𝜈 = hc/𝜆 where h = Planck's constant (6.626 x 10-34 J.s) and c = the speed of light (3 x 108 m.s-1). In the case of [Ti(OH2)6]3+, the energy required corresponds to a max of ~ 490 nm, meaning it absorbs light in the green-yellow range and thus appears purple (Figure 10). Figure 10 Effects of energy transfer the colour of [Ti(OH2)6]3+. Ligand effects and the spectrochemical series The colours of metal complexes are related to the energy gaps between the non-degenerate d-orbitals (orbitals are not at the same energy level) The sizes of the energy gaps are related to the nature of the ligands coordinated to the metal. As mentioned earlier, ligands can be sorted according to how strongly they interact with the d-orbitals of the metal they are coordinated to. Ligands that interact strongly are known as strong field ligands. These will lead to large energy splittings (e.g. large Δoct), meaning electrons will need to absorb a relatively large amount of energy to make the d-d transition. Because of the inverse relationship between the energy of light and its wavelength (see equation below), this leads to absorption of light at lower wavelengths. Conversely, ligands that interact weakly with the metal d-orbitals (weak field ligands) will lead to smaller splittings (e.g. small Δoct), meaning electrons need to absorb smaller energy packets to make the d-d transition (i.e. light at higher wavelengths). E = h𝝂 or E=hc/𝝀 A notable trend that has been observed over many different metal complexes is that the binding nature of a particular ligand remains the same irrespective of the central metal. For example, a weak field ligand such as chloride will be a weak field ligand in all of its complexes. Similarly, a strong field ligand such as cyanide will always be a strong field ligand. This leads to the "Spectrochemical Series" (Figure 11), where different ligands are listed according to whether they tend to be weak field (left hand side) or strong field (right hand side) ligands. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 9/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Figure 11 The spectrochemical series. For example, for Ti3+ complexes the order of Δoct and energy absorbed will be: [Ti(CN)6]3- > [Ti(NH3)6]3+ > [Ti(OH2)6]3+ A similar trend can be observed for Cr3+ complexes (Figure 12). Figure 12 Changes in the colour of Cr complexes due to changes in ligands. Other effects on colour The colour of complexes can also vary with a change in oxidation state; one example is given in Figure 13. Furthermore, as discussed previously, the way the d-orbitals are split into different energies is also dependent on ligand geometry. Different geometries give different splittings and thus different energy gaps across which d-d transitions occur. For example, typically Δtet ~ (4/9)Δoct. This in turn affects the colour observed for the complex. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 10/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Figure 13 Changes in colour due to changes in oxidation state. Tables 2 and 3 below highlight the variation of crystal field splitting energy (and consequently colour) across changes in metal, oxidation state, geometry and ligand. In particular, compare closely related complexes in Table 2 to see quantitatively the trends (colour vs. ligand, oxidation state, geometry) discussed above. You do not need to memorise these tables. Table 2 Crystal field splitting energies for some octahedral (Δo) and tetrahedral (Δt) transition-metal complexes. Note the energy values for Δo and Δt are in wavenumber units. Consider wavenumber proportional to energy (i.e. larger wavenumber, larger Δ in Joules). Table 3 Colours of some hexaaqua ions and other complex ions of the d-block metals. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 11/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.4. Magnetism Please read Bonding in transition metal complexes (page 779) of Chemistry, Blackman et al. (4th ed.) Magnetism and the transition metals Magnetism is a property observed in everyday life. Magnetism originates from the motion of charge particles such as electrons. These electrons spin around their axis and move in orbitals around the nucleus of the atom. These motions generate tiny electric currents in closed loops that in turn create magnetic dipole fields. When placed into a magnetic field, these tiny magnetic dipoles tend to then align with the external field. Magnetism The video below goes into more detail about the properties of magnetism Introduction to magnetism | Physics | Khan Academy https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnets-magnetic/v/introduction-to-magnetism If a material has all its electrons paired, then the magnetic effect of each electron is cancelled out by the other electron in the pair. Such a material is diamagnetic, and will not be attracted to a magnetic field (indeed, it will be slightly repelled). Most organic compounds, for example, are diamagnetic. If a material does have unpaired electrons, like many transition metal complexes, then it will be attracted to a magnetic field and it is said to be paramagnetic. The size of the attraction is proportional to the number of unpaired electrons - a complex with five unpaired electrons will show a much greater attraction than one with only one unpaired electron per complex. Many transition metal complexes are paramagnetic because they have unpaired electrons in the d orbitals. Furthermore, these unpaired electrons remain unpaired even after a complex is formed because the electrons used to create the coordination bonds come from the ligand (unlike covalently bonded molecules where the unpaired electrons on each individual atom end up being paired with unpaired electrons on neighbouring atoms to create the covalent bonds). The presence and number of unpaired electrons in a metal atom is therefore the key to understanding the magnetic properties of metal complexes (Figure 14), and Crystal Field Theory again plays an important part. Indeed, it has been shown experimentally that different metal complexes can show quite different magnetic properties, despite the metal atoms having the same number of d electrons, and Crystal Field Theory gives a very good explanation for this observation. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 12/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 Figure 14 Electronic configurations of a diamagnetic and a paramagnetic metal ion Consider, for example, the two complexes shown in Figure 3 in the Introduction (reproduced again in Figure 15). The first complex, [Fe(CN)6]4-, has cyanido ligands. These are strong field ligands (according to the Spectrochemical Series), and therefore they give a large energy gap between the t2g and eg orbitals for this octahedral complex. Now think about how the electrons fill those orbitals of differing energies. The Fe atom is in the 2+ oxidation state, and thus has a d6 electronic configuration. The first three electrons go in the lowest energy orbitals, t2g, with one electron per orbital. But the fourth electron now has a choice. If it goes in the lowest energy orbital with a vacancy, a t2g orbital, then there is an energy penalty to pay as you are pairing up electrons (Hund's rule, see Week 7). The other option is to put it in an eg orbital. This is a higher energy orbital, but it avoids having to pair up electrons. The same choice will also apply to the fifth and sixth electrons. Whichever choice is made ultimately depends on what is going to be the lowest energy. So, for the large value of Δoct in [Fe(CN)6]4-, it is lower energy to pair up electrons in the t2g orbitals before putting electrons in the eg orbitals. This leads to a "low spin" configuration. In this case, the result is a diamagnetic complex - i.e. all the electrons are paired up. In the case of [Fe(OH2)6]2+, the lower-field aqua ligands lead to much a smaller value for Δoct, and thus it is now lower energy to put electrons in the eg orbitals before pairing them up. The first three electrons go one-each in t2g orbitals, and the next two go one-each in the eg orbitals. The final electron needs to pair up (no more empty d orbitals), and it does that in the lower energy t2g level. This leads now to a paramagnetic metal ion with four unpaired electrons, which is the "high spin" possibility for d6. Figure 15 Strong field and weak field ligand effects on the colour and d-orbital configurations https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 13/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 In general, Crystal Field Theory leads to two possible configurations for octahedral complexes with d4, d5, d6 or d7 configurations (Figure 16), which correlates well with experimental observations (such as [Fe(CN)6]4- being diamagnetic and [Fe(OH2)6]2+ being paramagnetic). Large values of Δoct will result in the maximum amount of pairing of electrons before filling eg orbitals; this is the low spin configuration. Small values of Δoct will give high spin configurations - single electrons are placed in each orbital first, before pairing up any remaining electrons. For each of d1, d2, d3, d8, d9, d10 there is only one possible configuration whichever strategy is taken to fill the orbitals (prove this for yourself with e.g. d9). For complexes with other geometries (and thus different splittings of the d orbitals) it is often more straight forward. Square planar complexes are most often formed by metals with d8 configurations and are diamagnetic (there is a large energy gap between the highest and second-highest energy d orbitals - see the splitting diagram you worked out in Week 10 and assign electrons yourself to see how it gives a configuration with no unpaired electrons). For tetrahedral complexes the splitting of the orbitals is less (typically Δtet ~ 4/9(Δoct)), meaning that they are almost always high spin. Figure 16 High spin and low spin electronic configurations of octahedral transition metal ions https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 14/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.5. Measurement of magnetic properties Measurement of magnetic properties If we can experimentally measure the number of unpaired electrons (designated as n) in a complex, we can deduce a number of things about that complex, such as the identity of the metal, its oxidation state, its geometry, and/or whether it is high spin or low spin. We do this by measuring the response of the complex to a magnetic field. For the closely related complexes in Figures 14 and 15, the experiment is straightforward - if it is repelled by the magnetic field then it is the diamagnetic complex, whereas if it is attracted to the magnetic field then it is the paramagnetic option. But when both options are paramagnetic (e.g. an octahedral d5 complex which could be either high spin (five unpaired electrons) or low spin (one unpaired electron) - see Figure 17) we need to measure not just the fact that there is an attraction to the magnetic field, but also how strong that attraction is - more unpaired electrons will lead to a greater response. In fact, if we measure the attraction carefully, we can even calculate the number of unpaired electrons directly from the measurement. This measurement can be done using a Guoy balance (Figure 17). Figure 17 Schematic representation of a Guoy balance In a Guoy balance the sample is placed in a glass tube and weighed with and without the magnetic field. Paramagnetic compounds will be attracted to the magnetic field, with the extent of attraction dependent on the number of unpaired electrons, n. In the set-up shown above, that will cause the sample to appear heavier than if there was no magnetic field (and a diamagnetic compound would appear slightly lighter). From the apparent change in weight of the sample caused by this attraction we can calculate the magnetic susceptibility, 𝜒. This is then used to calculate the molar magnetic suseptibility (i.e. it is corrected for how much sample you have), then used to calculate the effective magnetic moment, μeff using the following equation: μeff = 2.828 (𝜒M’ x T)1/2 where: μeff effective magnetic moment, Bohr magneton, B.M. (note: non-SI units used in magnetochemistry) 𝜒M’ molar magnetic susceptibility (corrected) T in Kelvin There are two main reasons as to why a unpaired electrons lead to paramagnetism, namely the inherent spin on an electron, and the orbital angular momentum from the electron orbiting around an atom. For first row transition metals the dominant contribution to paramagnetism is the electron spin, which allows us to use a simplified equation to calculate a 'spin-only' magnetic moment using only the number of unpaired electrons, as follows: μSO = √n(n+2) https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 15/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 (where n = numbers of unpaired electrons) For example, if we look at a high spin octahedral Cr2+ (d4 ion) complex: μSO = √n(n+2) = √4 x 6 = √24 = 4.90 B.M. cf. measured value μeff ~ 4.7-4.8 B.M. While this calculation is approximate, it does then allow us to estimate the number of unpaired electrons by comparison between calculated values of μSO and measured values of μeff. In the above example, while the high spin option (four unpaired electrons) gives μSO = 4.90 B.M., the low spin option (two unpaired electrons) would give μSO = 2.83 B.M. If the measured μeff is 4.73 B.M., then the complex is clearly closer to the first calculated value of μSO and thus it must be high spin. Some experimentally determined values of μeff and the relevant μSO calculated values for several octahedral complexes are given in the table below. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 16/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.6. Activity Coordination Complexes There are five coordination complexes shown below. For each of complex state the coordination geometry, oxidation state and number of d electrons. Then, based on the ligands present in each complex, decide if the complex is high or low spin and calculate the spin only magnetic moment. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 17/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 1.7. Activity solutions Coordination Complexes There are five coordination complexes shown below. For each of complex state the coordination geometry, oxidation state and number of d electrons. Then, based on the ligands present in each complex, decide if the complex is high or low spin and calculate the spin only magnetic moment. A) Octahedral, +2, 3d9, low spin, μSO: 1.73 B) Octahedral, +2, 3d7, high spin, μSO: 3.87 C) Octahedral, +3, 3d5, low spin, μSO: 1.73 D) Tetrahedral, +2, 3d8, low spin, μSO: 2.83 E) Tetrahedral, +2, 3d5, high spin, μSO: 5.92 https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 18/24 10/6/24, 10:05 AM Week 11: Colour and magnetism - workbook | MonashELMS1 2. Summary This week you will learn about how crystal field theory can be used to understand the origin of the colours of metal complexes, as well as the nature of their magnetic properties. In particular, the colour of metal complexes can be understood in terms of electrons moving between d orbitals of different energies. The colour is related to the amount of energy needed by the electrons to make these d-d transitions, and the amount of energy needed is in turn related to (a) the way the d orbitals are split (which is governed by geometry) and (b) the magnitude of the d orbital splitting (which is related to oxidation state and the nature of the ligands (through the spectrochemical series)). Magnetic properties arise from having unpaired electrons and are thus also dependent on how the electrons are distributed between the d orbitals. The size of the magnetic response is also proportional to the number of unpaired electrons. These magnetic properties can be understood by examining the nature and magnitude of d orbital splitting, even including cases where metals may have high spin or low spin configurations. https://learning.monash.edu/mod/book/tool/print/index.php?id=2780856 19/24