# Electromagnetic spectrum and associated calculations

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1 SECTION 1 ELECTRONIC STRUCTURE Electromagnetic spectrum and associated calculations The work of Rutherford and others in the early part of the twentieth century resulted in the model of the atom in which negative electrons are arranged around a positive central nucleus. It is the electrons, rather than the nucleus, which take part in chemical reactions and so it is necessary to understand the electronic structure of an atom to explain its chemical properties. The key to understanding electronic structure and how electrons behave in an atom comes from the study of electromagnetic radiation. In 1864 James Maxwell developed a theory describing all forms of radiation in terms of oscillating or wave-like electric and magnetic fields in space. Hence radiation such as light, microwaves, X-rays, television and radio signals is collectively called electromagnetic radiation. Electromagnetic radiation may be described in terms of waves of varying length between m and m that travel in a vacuum at a constant velocity of approximately m s 1. Two simple waveforms are shown in Figure 1. The wavelength of a wave is the distance between adjacent wavecrests or high points (or successive troughs or low points). This distance is measured in metres (m) or an appropriate sub-multiple such as nanometres (nm). A nanometre is 10 9 metres. The symbol for wavelength is the Greek letter λ (lambda). Waves can also be specified by their frequency, symbol ν (Greek letter nu). For a wave travelling through some point in space the frequency is the rate of advance of any one wavecrest or the number of complete waves passing the point per unit time. The unit of measurement of frequency is the reciprocal of time in seconds (s 1 ) and this unit is called the hertz (Hz). Another unit of frequency often used by spectroscopists is the wavenumber, which is the reciprocal of the wavelength (1/λ). The wavenumber is the number of waves in one unit length of radiation, i.e. the number of waves per metre, and is measured in m 1. The symbol for wavenumber is ν. CHEMISTRY 1

2 ELECTRONIC STRUCTURE Figure 1 A λ = 800 nm B In Figure 1 the wavelength of wave A is twice that of wave B. Since both waves are travelling at the same speed, wave B completes two vibrations in the time wave A completes one. Thus the frequency of wave A is half that of wave B. The relationship between wavelength, frequency and velocity is: velocity = wavelength frequency (m s 1 ) (m) (s 1 ) c = λ ν λ = 400 nm The above relationships are summarised in Table 1. 2 CHEMISTRY

3 ELECTRONIC STRUCTURE Table 1 Quantity Symbol Units Description Wavelength λ (lambda) Metres (m) Distance between adjacent wave crests λ Velocity c m s 1 Rate of advance of any one wave crest Frequency ν (nu) Hertz (Hz) The number of wavelengths or cycles passing a point in 1 second 1 cycle per second = 1 Hz ν = c/λ or ν α 1/λ (for all electromagnetic radiation c is constant, m s 1 ) Wavenumber ν Waves per metre Number of waves in 1 metre (m 1 ) but many or in 1 centimetre of spectrometers radiation are calibrated in Often used in place of waves per cm (cm 1 ). frequency The complete electromagnetic spectrum is shown in Figure 2. Figure 2 ν = 1 λ γ RAYS m X-RAYS ULTRA- VIOLET Visible INFRA- RED MICRO- WAVE SHORT WAVE RADIO RADIO AND TV m VISIBLE SPECTRUM ( nm) Violet Blue Green Yellow Orange Red m ( nm) CHEMISTRY 3

4 ELECTRONIC STRUCTURE From Figure 2 it can be seen that visible light, which is that part of the electromagnetic spectrum that excites the nerve cells of the human eye, constitutes only a very small part of the total spectrum. When electromagnetic radiation interacts with matter, there is a transfer of energy from the radiation to the receiving body. Sitting out in the sun to get a sun-tan or cooking with microwave ovens are good examples of this. Energy can only be transferred in small bundles or packets, which are called quanta. These quanta of energy are of a definite size and therefore the transfer of energy can only occur in definite amounts. Because of this, it is necessary to consider that electromagnetic radiation is not only made up of waves, but can also be regarded as a stream of very small particles. These small particles are known as photons. Electromagnetic radiation is said to exhibit wave-particle duality, i.e. it may be considered to be a stream of photons with wave properties, the energy of the radiation being related to the wavelength or frequency of the radiation by the equation: for a photon, E = hν (where h is Planck s constant = J s) The relationship between the energy transferred by the emission or absorption of one mole of photons and the frequency of the radiation can be calculated as follows: for one mole of photons, E = Lhν or E = Lhc or E = Lhcν λ where ν is the wavenumber and L is the Avogadro constant. Using these relationships, the energy of radiation is calculated in J mol 1. Multiplying by 10 3 gives the energy in the more common unit kj mol 1. Questions 1. Calculate the energy, in kj mol 1, corresponding to (a) a wavenumber of 1000 cm 1 (b) a wavelength of 620 nm. 2. The bond enthalpy of a Cl Cl bond is 243 kj mol 1. Calculate the maximum wavelength of light that would break one mole of these bonds to form individual chlorine atoms. 4 CHEMISTRY

5 ELECTRONIC STRUCTURE Electronic configuration and the Periodic Table If light from a tungsten filament lamp is passed through a glass prism, the light is split into the colours of the rainbow. This is known as a continuous spectrum as it consists of a continuous range of wavelengths. In contrast, if sufficient electrical energy is passed into a tube of gas at low pressure, the gas atoms or molecules are said to become excited and can emit electromagnetic radiation, e.g. light. When this is passed through a glass prism a line spectrum is obtained. A line spectrum shows up a characteristic number of discrete wavelengths. Glowing neon, for example, appears red to our eyes but when this red light is passed through a prism the light is shown to be composed of a few different colours and the spectrum consists of lines corresponding to the wavelengths of these different colours (see Figure 3). Spectra like this are known as emission spectra since light emitted by the gases is analysed by passing it through a prism. In modern spectrometers the light is separated into its different wavelengths using a diffraction grating instead of a prism. The light firstly passes through a series of narrow slits producing a fine beam or line of light before passing through the diffraction grating, and the emitted light is observed as a line spectrum, as shown in Figure 3. Figure 3: The emission spectrum of neon wavelength / nm Figure 3 shows that the red light seen from glowing neon is actually made up of light of different wavelengths mainly from the red end of the visible spectrum. Examination of the emission spectrum of hydrogen shows that this consists of a number of lines of precise frequency, corresponding to precise emissions of energy (Figure 4). CHEMISTRY 5

6 ELECTRONIC STRUCTURE Figure 4: The emission spectrum of hydrogen in the visible range (Balmer series) wavelength / nm These lines correspond to well-defined energy changes and by using the relationship E = Lhν the magnitude of these energy changes can be calculated. Atoms are said to become excited when they absorb energy and emission spectra arise from the movement of electrons from a higher to a lower energy when the excited atom returns to its ground state. The frequency of the line in the emission spectrum corresponds to the difference in energy between the two electronic energy levels. This is shown in Figure 5. Figure 5 E 3 E b = E 3 E 2 = hν b E 2 E a = E 3 E 1 = hν a E 1 It follows that since the differences in energy between the levels are fixed, the energy levels themselves must be fixed. Thus, since the electrons must occupy these energy levels, the electrons themselves must have fixed energies. In other words the energies of electrons are quantised and an atom can be considered to be emitting a photon of light energy when an electron falls back from a higher energy level to a lower energy level. Each line in the emission spectrum represents radiation of a specific wavelength or frequency from which these differences in energy can be calculated. 6 CHEMISTRY

7 ELECTRONIC STRUCTURE Although a hydrogen atom has only one electron, the emission spectrum of hydrogen has different series of lines in different parts of the electromagnetic spectrum. The differences in energy and hence the part of the electromagnetic spectrum in which the lines show up depend on the energy level to which the excited electron falls back. The full emission spectrum of hydrogen consists of one series of lines in the ultra-violet region, one series of lines in the visible region and several in the infra-red region. These series of lines are named after the scientists who discovered them (Table 2). Table 2 Name of series Energy level to which Part of the excited electron falls electromagnetic spectrum Lyman n = 1 Ultra-violet Balmer n = 2 Visible Paschen n = 3 Infra-red Brackett n = 4 Infra-red Pfund n = 5 Infra-red The electronic transitions that give rise to the Lyman, Balmer and Paschen series are shown in Figure 6. CHEMISTRY 7

8 ELECTRONIC STRUCTURE Figure 6 Energy level n=7 n=6 n=5 n=4 n=3 Paschen infra-red n=2 Balmer visible n=1 Lyman ultra-violet 8 CHEMISTRY

9 ELECTRONIC STRUCTURE The lines of the Lyman series correspond to changes in electronic energy levels from higher energy levels down to the n = 1 ground state. Figure 7: The Lyman series in the emission spectrum of hydrogen wavelength / nm It can be seen that as the energy increases, the energy levels become closer together until they converge. The difference in energy between the ground state and the convergence limit corresponds to the energy required for the electron to break away from the atom. This is its ionisation energy. Question Calculate the ionisation energy for hydrogen if the wavelength of the line at the convergence limit is 91.2 nm. Much of the work required to interpret and explain emission spectra was done by the Danish scientist Niels Bohr, who developed a model for the electronic structure of atoms. The equations derived from Bohr s model were used successfully to calculate values for the radius of the hydrogen atom and its energy levels, including its ionisation energy. The main points of Bohr s theory can be summarised as follows: the electron in a hydrogen atom exists only in certain definite energy levels a photon of light is emitted or absorbed when the electron changes from one energy level to another the energy of the photon is equal to the difference between the two energy levels ( E), which is related to the frequency by the equation E = hν. These definite quantities of energy possessed by electrons are known as quanta. CHEMISTRY 9

10 ELECTRONIC STRUCTURE Despite its success with hydrogen, Bohr s theory could not be used to explain the behaviour of atoms with more than one electron and a new science known as quantum mechanics was formulated. Quantum mechanics considers electrons as waves as well as particles and, although it is highly mathematical, the results of the theory are fairly straightforward. An electron can only possess certain fixed amounts of energy known as quanta. The energy of the electron can be defined in terms of quantum numbers. Electrons in atoms are arranged in a series of shells. Each shell is described by a number, known as the principal quantum number, n. The shells are numbered starting with the shell nearest the nucleus and working outwards. For the first shell n = 1, for the second shell n = 2 and so on. The higher the value of n, the higher the potential energy associated with the shell and the further from the nucleus the electron is likely to be found. The hydrogen atom has only one electron and its spectrum is fairly simple to interpret. Other elements are more complex and close examination of their spectra under high resolution shows that the lines are often not single lines but are split into doublets or triplets, etc. This suggests that the electron shells are further subdivided into subshells. These subshells are described by the letters s, p, d and f. Calculations using quantum mechanics show that all shells have an s subshell and all the shells except the first have a p subshell. Likewise all the shells except the first and second have a d subshell and so on, as shown in Table 3. The subshells within a shell have different energies, increasing s p d f. Table 3 Shell Subshells 1 1s 2 2s, 2p 3 3s, 3p, 3d 4 4s, 4p, 4d, 4f 10 CHEMISTRY

11 ELECTRONIC STRUCTURE Each type of subshell (s, p, d and f) contains one or more energy levels or orbitals. These are defined by another quantum number, the angular momentum quantum number l. This is related to the shape of the orbital and is given the values 0, 1, 2,, (n 1) as shown in Table 4. Table 4 Value of n Value of l Energy level 1 0 1s 2 0 2s 1 2p 3 0 3s 1 3p 2 3d 4 0 4s 1 4p 2 4d 3 4f Like photons, electrons can be considered to behave as particles and also as waves. Their behaviour is governed by Heisenberg s uncertainty principle, which states that it is impossible to define with absolute precision both the position and the momentum of an electron at the same instant. This means that it is not possible to define a point in space where the electron is certain to be found and therefore it is necessary to define regions in space where the probability of finding an electron is high. These regions of high probability are called atomic orbitals. An atomic orbital is generally considered to be the volume in space where the probability of finding an electron is greater than 90%. The overall size of each orbital is governed by the value of n, the principal quantum number, while the actual shape of the orbital is given by the value of l, the angular momentum quantum number. All s orbitals (l = 0) are spherical in shape, the diameter of the sphere increasing as n increases (Figure 8). CHEMISTRY 11

12 ELECTRONIC STRUCTURE Figure 8 1s 2s 3s The probability of finding the s electron outwith the orbital is relatively low but not zero. For p, d and f orbitals, it is necessary to define a further quantum number, m l, known as the magnetic quantum number, and this gives the multiplicity and spatial orientation of the orbital. Table 5 shows how m l can have any integral value between l and +l. Table 5 Value of n Value of l Value of m l Type of atomic orbital s s 1 1, 0, +1 2p s 1 1, 0, +1 3p 2 2, 1, 0, +1, +2 3d The p orbitals, unlike the s orbitals, are not spherical in shape but have two lobes and are usually described as being dumb-bell in shape, as shown in Figure 9. Figure 9 Since for the p orbitals l = 1 there are three possible values of m l, namely 1, 0 and +1, there will be three p orbitals of equal energy (orbitals of equal energy are said to be degenerate). Because they have different values for m l, they will have different orientations in space in fact, they are arranged along the three mutually perpendicular principal axes x, y and z, as in Figure CHEMISTRY

13 ELECTRONIC STRUCTURE Figure 10 z y z y z y x x x p x p y p z Likewise with the d orbitals (l = 2), there are five possible values of m l ( 2, 1, 0, +1, +2) and so when n 3, there are five degenerate d orbitals. These have the individual names and shapes shown in Figure 11. Figure 11 z y z y x x z y d x 2 y 2 z y d z 2 z y x x x d xy d yz d xz Each type of subshell contains one or more orbitals and the number of orbitals in a subshell is summarised in Table 6. Table 6 Subshell Number of orbitals s 1 p 3 d 5 f 7 The three quantum numbers also allow us to define the orbital for an electron, as shown in Table 7. CHEMISTRY 13

14 ELECTRONIC STRUCTURE Table 7 Type of quantum Symbol Value Main orbital number property described Principal n 1, 2, 3, Orbital size/energy Angular momentum l 0, 1, 2, (n 1) Orbital shape Magnetic m l l, 0, +l Multiplicity and orbital orientation In about 1920 it was realised that an electron behaves as if it has a spin, just as the planet earth has a spin. To describe an electron in a manyelectron atom completely a fourth quantum number is therefore needed, namely the spin quantum number, m S. The spin quantum number can have one of only two values, +½ and ½. Thus, given values of the four quantum numbers, n, l, m l and m S, it is possible to define any single electron in an atom in terms of its energy and likely location. In 1925, Wolfgang Pauli proposed what is now known as the Pauli exclusion principle: no two electrons in any one atom can have the same set of four quantum numbers. This leads to two important conclusions: the maximum number of electrons in any atomic orbital is two if there are two electrons in an orbital, then they must have opposite spins (rather than parallel spins). The number of orbitals and electrons in each subshell is given in Table 8. Table 8 Type of subshell Number of orbitals Number of electrons s One s orbital 2 p Three p orbitals 6 d Five d orbitals 10 f Seven f orbitals CHEMISTRY

15 ELECTRONIC STRUCTURE In an isolated atom the orbitals within each subshell are degenerate. For example, the three different 2p orbitals (2p x, 2p y and 2p z ) in an atom have equal energy. Electronic configurations There are two main ways in which the electronic configurations of atoms can be expressed. Consider a hydrogen atom. It has one electron, which will occupy the orbital of lowest energy which is, of course, the 1s orbital. This can be expressed as 1s 1, i.e. one electron in the 1s orbital. Helium will have both its electrons in the 1s orbital and this can be written as 1s 2. The other way in which the electronic configuration can be expressed is by using a notation in which an orbital is represented by a box and each electron by an arrow. Using this notation the electronic configuration of hydrogen can be represented as H and helium can be represented as He 1s 1s One arrow pointing upwards and the other pointing downwards shows that the two electrons in the orbital have opposing spins, in keeping with the Pauli exclusion principle (Table 9). Table 9 1st electron n = 1 (first shell) l = 0 (s orbital) 2nd electron n = 1 (first shell) l = 0 (s orbital) m l = 0 m l = 0 m S = +½ m S = ½ If the electronic configuration of helium were to be represented with both arrows pointing in the same direction, i.e. parallel spins, this would be incorrect since it would not conform to the Pauli exclusion principle CHEMISTRY 15

16 ELECTRONIC STRUCTURE because the two electrons would have the same values for all four quantum numbers (Table 10). Table 10 1st electron n = 1 (first shell) l = 0 (s orbital) 2nd electron n = 1 (first shell) l = 0 (s orbital) m l = 0 m l = 0 m S = +½ m S = +½ Before we can write the electronic configuration for multi-electron atoms, it is necessary to know the order in which the various orbitals are filled. The aufbau principle states that the orbitals of the lowest energy levels are always filled first. Thus, provided the relative energies of the orbitals are known, the electronic configuration can be deduced. Spectroscopic data give the following arrangement of the energies of the orbitals: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p increasing energy This may seem very complicated and another method of working out the increasing relative energies is given in Figure 12. Another useful method is to remember that electrons are assigned to orbitals in order of increasing (n + l). For two subshells with equal values of (n + l), electrons are assigned first to the orbital with lower n. Figure 12 1s 2s 3s 2p 3p 3d Write the orbitals in each shell as shown and then follow the diagonal arrows in order. 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p 8s 16 CHEMISTRY

17 ELECTRONIC STRUCTURE When the situation is reached where more than one degenerate orbital is available for the electrons, it is necessary to use Hund s rule of maximum multiplicity, which states that when electrons occupy degenerate orbitals, the electrons fill each orbital singly, keeping their spins parallel before spin pairing occurs. For example, the electronic configuration of a nitrogen atom using spectroscopic notation is written as follows: 1s 2 2s 2 2p 3 and using orbital box notation to show electron spins: 1s 2 2s 2 2p 3 (Compare these electronic configurations with the electron arrangement 2, 5 given in the Data Booklet). Question Using both spectroscopic and orbital box notations write down the electronic configurations for: (a) lithium (b) oxygen (c) sodium Remember that the (d) aluminium electronic configuration should have the same (e) phosphorus number of electrons in each (f) argon shell as the corresponding (g) calcium electron arrangement in the (h) Li + Data Booklet. (i) F (j) Mg 2+ (k) S 2 (l) K + The electronic configuration for neon, Ne, is 1s 2 2s 2 2p 6 and that of argon, Ar, is 1s 2 2s 2 2p 6 3s 2 3p 6. It is often acceptable to write the electronic configurations of other species in a shortened version, taking account of the electronic configuration of the preceding noble gas. For example, the electronic configuration for sodium can be written as [Ne] 3s 1, where [Ne] represents 1s 2 2s 2 2p 6, and that of calcium can be written as [Ar] 4s 2 where [Ar] represents 1s 2 2s 2 2p 6 3s 2 3p 6. CHEMISTRY 17

18 ELECTRONIC STRUCTURE The Periodic Table can be subdivided into four blocks (s, p, d and f) corresponding to the outer electronic configurations of the elements within these blocks. All the Group 1 elements (the alkali metals) have electronic configurations that end in s 1 and all the Group 2 elements (the alkalineearth metals) have electronic configurations that end in s 2. Because the elements in Groups 1 and 2 have their outermost electrons in s orbitals, these elements are known as s-block elements. The elements in Groups 3, 4, 5, 6, 7 and 0 are known as the p-block elements as their outermost electrons are in p subshells. The elements where d orbitals are being filled are known as the d-block elements and those in which f orbitals are being filled are the f-block elements. This is shown in Figure 13. Figure 13 s-block elements d-block elements p-block elements f-block elements Ionisation energy Figure 14 shows how the first ionisation energy varies with atomic number for elements 1 to 36. Figure 14 ionisation energy (kj mol 1 ) atomic number 18 CHEMISTRY

19 ELECTRONIC STRUCTURE The highest points are the noble gases (Group 0) and the lowest points are those of the alkali metals (Group 1). The first ionisation energy for an element E is the energy required to remove one mole of electrons from one mole of atoms in the gas state, as depicted in the equation E(g) E + (g) + e There are three main factors that affect the ionisation energies of an element: the atomic size the greater the atomic radius, the further the outermost electron is from the attraction of the positive nucleus and therefore the lower will be the ionisation energy the nuclear charge the more protons in the nucleus, the harder it will be to remove an electron and consequently the greater will be the ionisation energy the screening effect the inner electrons shield the outermost electrons from the attraction of the positively charged nucleus and so the more electron shells between the outer electron and the nucleus, the lower will be the ionisation energy. Looking at Figure 14 there are two obvious patterns. In general, the ionisation energy increases across a period the ionisation energy decreases down a group. However, looking more closely, it can be seen that the first ionisation energies do not increase smoothly across a period. This irregularity is evidence for the existence of subshells within each shell. For example, the reason that the first ionisation energy of boron is lower than that of beryllium can be explained by considering their electronic configurations: Be 1s 2 2s 2 B 1s 2 2s 2 2p 1 Accordingly, removal of the outer electron from a boron atom involves taking one electron from the 2p subshell, but with a beryllium atom this electron comes from the full 2s subshell. Since full subshells are relatively stable, it follows that the first ionisation energy of beryllium is greater than that of boron. CHEMISTRY 19

20 ELECTRONIC STRUCTURE A similar argument can be used to explain the higher first ionisation energy of magnesium (1s 2 2s 2 2p 6 3s 2 ) compared to aluminium (1s 2 2s 2 2p 6 3s 2 3p 1 ). The higher first ionisation energy of nitrogen compared to oxygen can also be explained by considering their electronic configurations: N 1s 2 2s 2 2p 3 or 1s 2 2s 2 2p 3 O 1s 2 2s 2 2p 4 or 1s 2 2s 2 2p 3 Since half-full subshells are relatively stable and because nitrogen has a half-full subshell it has a higher ionisation energy than oxygen. A similar argument can be used to explain the higher first ionisation energy of phosphorus compared to sulphur. There will also be electron electron repulsions between two electrons in the same orbital. Likewise the relative values of first, second and subsequent ionisation energies can be explained in terms of the stabilities of the electronic configurations from which the electrons are removed. For example, the sodium atom, Na, has electronic configuration 1s 2 2s 2 2p 6 3s 1 and the first ionisation energy of sodium is small (502 kj mol 1 ). The sodium ion, Na +, has the electronic configuration of the noble gas neon, 1s 2 2s 2 2p 6, and because this is a more stable electronic configuration, the second ionisation energy of sodium is significantly greater (4560 kj mol 1 ). This second electron to be removed from the sodium is in a shell much closer to the attraction of the nucleus and therefore much more energy is required to overcome this attraction. Spectroscopy Just as specific lines in the emission spectra of elements give information about the electronic structure of these elements, the technique of atomic emission spectroscopy (AES) can be used to detect the presence of these elements. Each individual element provides a characteristic spectrum that can be used to identify that particular element. Both AES and atomic absorption spectroscopy (AAS) involve transitions between electronic energy levels in atoms. Individual spectral lines correspond to definite electronic transitions. In general the energy difference corresponds to the visible region of the 20 CHEMISTRY

21 ELECTRONIC STRUCTURE electromagnetic spectrum (approximate wavelength nm) but in some applications the ultra-violet region (approximate wavelength nm) is used. In AES a gaseous sample is excited with thermal or electrical energy, causing electrons to be promoted to higher energy levels. The wavelength of the radiation emitted as the electrons fall back to lower energy levels is recorded. This technique can be used to detect metal elements in, for example, foodstuffs or effluent water since each element has a known characteristic spectrum. The element present can also be determined quantitatively by measuring the intensity of the emitted radiation. The greater the amount of that element present in the sample, the greater will be the intensity of its characteristic radiation. AES detects both metallic and non-metallic elements. In fact, the element helium was discovered by the English scientist Sir Norman Lockyer, who pointed his telescope at the sun during the eclipse of 1868 and examined the light using a spectroscope. He observed bright emission lines but found it impossible to identify the source of the strong yellow light on earth. In 1870 Lockyer suggested that the spectrum was due to an unknown element which he thought was a metal and named helium after the Greek sun god, Helios. Lockyer was eventually knighted for his discovery but initially he was ridiculed. His critics were silenced when the Scottish chemist Sir William Ramsay managed to isolate helium from the uranium-containing mineral cleveite. Ramsay went on to discover the entire group of noble gases and was awarded the Nobel Prize for chemistry in In AAS electromagnetic radiation is directed through a gaseous sample of the substance. Radiation corresponding to certain wavelengths is absorbed as electrons are promoted to higher energy levels. The wavelength of the absorbed radiation is measured and used to identify each element, as each element has a characteristic absorption spectrum. The amount of the species present in the sample can also be determined by quantitative measurement of the amount of light absorbed by the atomised element. The measured absorbance is proportional to the concentration of the element in the sample. CHEMISTRY 21

23 SECTION 2 CHEMICAL BONDING Atoms are held together in substances by chemical bonds and an understanding of chemical bonding is central to our understanding of chemistry, since the breaking and the forming of new bonds is basically what happens in chemical reactions. A chemical bond will form when atoms or molecules can rearrange their electrons in such a way as to bring about a new arrangement of electrons and nuclei of lower energy than before the bonding occurred. A chemical bond can be considered to be the localisation of negative electrons holding together two adjacent positive nuclei (Figure 16). Figure A simple summary of bonding covered in Higher Chemistry is shown in Figure 17 where EN = difference in electronegativity values between the two atoms forming the bond. Figure 17 non-polar covalent polar covalent ionic EN = 0 EN increasing usually low melting high melting and and boiling points boiling points non-conductors conduct electricity in of electricity solution and when molten Figure 17 illustrates that non-polar covalent bonding and ionic bonding are considered as being at opposite ends of a bonding continuum with polar covalent bonding lying between these two extremes. This is very much a simplified summary with metallic bonding being ignored. There are also well-known exceptions such as carbon in the form of graphite, which can conduct electricity. Electronegativity differences between atoms of different elements are helpful but do not always predict the type of bonding correctly. For CHEMISTRY 23

24 CHEMICAL BONDING example, consider the two compounds sodium hydride (NaH) and water (H 2 O): sodium hydride: EN for Na = 0.9 EN for H = 2.2 so EN = = 1.3 water: EN for H = 2.2 EN for O = 3.5 so EN = = 1.3 It might therefore be expected that both compounds will have the same type of bonding, most likely polar covalent. However, sodium hydride is a solid at room temperature and when melted and electrolysed, hydrogen gas is produced at the positive electrode. This demonstrates that sodium hydride is ionic and also that it contains the hydride ion, H. Water, of course, has polar covalent bonding. Electronegativity values and their differences are useful indicators of the type of bonding but it is also necessary to study the properties of the substance for confirmation or otherwise. In general, ionic bonds involve metals from the left-hand side of the Periodic Table combining with non-metals from the far right-hand side. Covalent bonding usually occurs when the two bonding elements are non-metals that lie close to each other in the Periodic Table. Ignoring metallic bonding, most chemical bonds are somewhere between purely covalent and purely ionic. Covalent bonding Consider what happens when two hydrogen atoms approach one another to form a hydrogen molecule. Each of the hydrogen atoms has a single proton in its nucleus and a single electron in the 1s orbital. These are shown separated in Figure 18. Figure CHEMISTRY

25 CHEMICAL BONDING When the atoms move closer together (Figure 19) the electrostatic attraction between the nucleus of one atom and the electron of the other becomes significant and a drop in potential energy results. Figure If the atoms become too close together, the repulsive force between the nuclei becomes more important and the potential energy increases again. The most stable situation, Figure 20, when the potential energy is at its lowest, is where the forces of attraction and repulsion balance. Figure Each atom now has a share of both electrons and there is a region of common electron density between the two nuclei. This electron density exerts an attractive force on each nucleus, keeping both atoms held tightly together in a covalent bond. Figure 21 shows the energy changes that occur when the orbitals from two hydrogen atoms overlap to form a covalent bond. Figure potential energy bond dissociation energy r o distance between the two nuclei (r) CHEMISTRY 25

26 CHEMICAL BONDING From Figure 21 it can be seen that in the formation of a covalent bond there is a merging or overlap of atomic orbitals the atoms take up position at a distance such that the forces of repulsion and attraction balance. This distance is known as the bond length (r o ). a certain amount of energy is released to the surroundings. This same amount of energy must be supplied to the molecule to break the bond. The energy required to break one mole of these bonds is known as the bond enthalpy, or bond dissociation energy. A single covalent bond contains a shared pair of electrons. When two pairs of electrons are shared a double bond forms, as in oxygen (O=O). When three pairs of electrons are shared a triple bond forms, as in nitrogen (N N). In 1916 the American chemist G N Lewis introduced the theory of the shared electron pair constituting a chemical bond. To honour his contribution electron-dot (or dot-and-cross) diagrams are known as Lewis electron-dot diagrams or simply Lewis diagrams. For example, the Lewis diagram for hydrogen is: H H If we wish to show that each of the bonding electrons is from a different hydrogen atom the dot-and-cross variation can be used: H H Similar diagrams for fluorine and nitrogen are: and F F or F xf xx x N N or N x N x x Question xx x x x Draw Lewis diagrams for (a) chlorine (e) hydrogen cyanide, HCN (b) hydrogen fluoride (f) methane (c) carbon dioxide (g) water (d) ammonia 26 CHEMISTRY

27 CHEMICAL BONDING Some of the above questions contain pairs of electrons that are not involved in bonding. Such non-bonding pairs of electrons are often known as lone pairs. For example, in water H O x x H there are two bonding pairs of electrons ( x) and two non-bonding pairs of electrons ( ). The total number of bonding and non-bonding pairs of electrons becomes important in determining the shapes of molecules (see page 29). Sometimes both the electrons making up a covalent bond come from the same atom. This type of covalent bond is known as a dative covalent bond (or co-ordinate covalent bond). An example of the formation of a dative covalent bond is when ammonia gas is passed into a solution containing hydrogen ions to form the ammonium ion, NH 4+ : NH 3 (g) + H + (aq) NH 4+ (aq) The Lewis dot-and-cross diagram for this reaction is: H H x H x x N + H + H xn H x x H H + = electron from nitrogen x = electron from hydrogen The hydrogen ion has no electrons and both electrons for the dative covalent bond come from the lone pair on the nitrogen atom. Once a dative covalent bond has formed it is the same as any other covalent bond. In the ammonium ion all four N H bonds are identical. Resonance structures High in the upper atmosphere, a layer of ozone gas, O 3, protects us from the intense ultra-violet radiation coming from the sun. All the O O bonds in ozone are of equal length, suggesting that there is an CHEMISTRY 27

28 CHEMICAL BONDING equal number of bonding pairs on each side of the central O atom. This is at odds with drawing a Lewis electron-dot diagram since double bonds are much shorter than single bonds: O O O This is more simply represented as: + O O O One way to get ground the problem of the single and double bonds being of different lengths is to draw equivalent diagrams known as resonance structures: + + O O O or O O O It is important to understand that neither structure is a satisfactory representation of the bonding since the two terminal oxygen atoms in ozone are known to be equivalent. The actual bonding is midway between these two resonance structures and is best represented by a single composite structure in which two of the bonding electrons are delocalised or spread symmetrically over the three oxygen atoms. The delocalised electrons are represented by the dotted line: + O O O It is important to realise that ozone has only one actual structure. It does not flip from one resonance structure to another. Resonance structures can also be drawn for the carbonate ion. This time there are three equivalent structures, whose equal contribution by complete delocalisation of charge is denoted by the double-headed arrows, : O O O C C C O O O O O O In fact, experimental data show that all the bonds in the carbonate ion are the same length and all the bond angles are the same. 28 CHEMISTRY

29 CHEMICAL BONDING Resonance structures differ in the number of bonding pairs between a given pair of atoms. Resonance structures differ only in the positions of the electron pairs, not in the position of the atoms. Question Draw the two equivalent resonance structures for sulphur dioxide, SO 2. Shapes of molecules and polyatomic ions The shapes of molecules or polyatomic ions (e.g. NH 4+ ) can be predicted from the number of bonding electron pairs and the number of non-bonding electron pairs (lone pairs). This is because the direction which covalent bonds take up in space is determined by the number of orbitals occupied by electron pairs and the repulsion between these orbitals. The repulsive effect of a non-bonded pair or lone pair of electrons is greater than that of a bonded pair and so the trend in repulsive effect is: bonded pair:bonded pair < bonded pair:lone pair < lone pair:lone pair The shape adopted by the molecule or polyatomic ion is the one in which the electron pairs in the outer shell get as far apart as possible. In other words, the shape in which there is the minimum repulsion between the electron pairs. Consider some examples: (a) Two filled orbitals, both bonding pairs, e.g. beryllium chloride, BeCl 2 (g) In the beryllium chloride molecule beryllium has two outer electrons and each chlorine atom contributes one electron and so there is a total of four electrons, i.e. two electron pairs, involved in bonding. These two bonding pairs will be as far apart as possible at 180 o and so the beryllium chloride molecule is linear: Cl Be Cl (b) Three filled orbitals, all bonding pairs, e.g. boron trifluoride, BF 3 In the boron trifluoride molecule boron has three outer electrons and each fluoride atom contributes one electron to the structure. In total there are six electrons involved in bonding, resulting in three bonding pairs. Repulsions are minimised between these three bonding pairs when the molecule is flat and the bond angles CHEMISTRY 29

30 CHEMICAL BONDING are 120 o. The name given to this shape of molecule is trigonal planar (or simply trigonal): F B F F (c) Four filled orbitals, all bonding pairs, e.g. methane, CH 4 In methane, the central carbon atom has four outer electrons and each hydrogen atom contributes one electron to the structure and so there is a total of eight electrons involved in bonding, resulting in four electron pairs. The methane molecule is tetrahedral because this is the shape in which there is minimum repulsion between these electron pairs. The exact bond angles in methane are found using X-ray diffraction to be o, which is the true tetrahedral value: H H C H H Four filled orbitals, three bonding pairs and one lone pair, e.g. ammonia, NH 3 In ammonia, the central nitrogen atom has five outer electrons and each hydrogen atom contributes one electron. There is a total of four electron pairs, but only three are bonding pairs, i.e. there are three N H bonds while one pair of electrons is a non-bonding or lone pair. The arrangement of the electron pairs is tetrahedral but since there are only three bonds the shape is said to be pyramidal. There is greater repulsion between the lone pair and the three bonding pairs than there is between the three different bonding pairs with the result that the bonds are pushed closer together by the lone pair. Instead of a bond angle of o, the three bonds are angled at 107 o to each other: H N H H 30 CHEMISTRY

31 CHEMICAL BONDING Four filled orbitals, two bonding pairs and two lone pairs, e.g. water, H 2 O In water, the central oxygen atom has six outer electrons and each hydrogen atom contributes one electron. There is a total of four electron pairs, but only two are bonding pairs. In other words, there are two O H bonds and two non-bonding or lone pairs. The arrangement of the electron pairs is tetrahedral but since there is greater repulsion between the two lone pairs than between the lone pairs and the two bonding pairs the outcome is that the bonds are pushed even closer together in water than in ammonia. In water the bond angle is approximately 105 o and the shape of the water molecule is bent: H O H It is worth noting that if the lone pair on the nitrogen in ammonia were to form a dative covalent bond with a hydrogen ion to form the ammonium ion, there would be four equivalent bonding pairs and no non-bonding pairs. The shape of the ammonium ion would therefore be tetrahedral and all the bond angles would be o, as in methane: H + H N H H (d) Five filled orbitals, all bonding pairs, e.g. gaseous phosphorus(v) chloride, PCl 5 (g) In gaseous phosphorus(v) chloride the central phosphorus atom has five outer electrons and each chlorine atom contributes one electron to make five electron pairs. There will be no lone pairs as there will be five P Cl bonds. The shape of the molecule is trigonal bipyramidal: Cl Cl Cl P Cl Cl CHEMISTRY 31

32 CHEMICAL BONDING With no lone pairs on the central phosphorus atom, the bond angles between the three central chlorine atoms are 120 o. The upper chlorine atom has bond angles of 90 o to the three central chlorine atoms as does the lower chlorine atom. The bond angle between the upper and lower chlorine atom is 180 o. Five filled orbitals, three bonding pairs and two lone pairs, e.g. chlorine(iii) fluoride, ClF 3 In chlorine(iii) fluoride the central chlorine atom has seven outer electrons and each fluorine atom contributes one electron to make five electron pairs in total. Three of these will be bonding pairs and two will be lone pairs. The five electron pairs will be in a trigonal bipyramidal arrangement but the actual shape of the molecule depends on the arrangement of the bonds. There are three possible options (showing all electron pairs as solid lines in this case): F F F Cl F Cl F Cl F F F F Considering all the repulsive forces between the electron pairs and taking into account that there is greatest repulsion at 90 o and least at 180 o, and also remembering that the trend in repulsive effect is bonded pair:bonded pair < bonded pair:lone pair < lone pair:lone pair, the most stable option is: F Cl F F The ClF 3 molecule is said to be T-shaped. 32 CHEMISTRY

33 CHEMICAL BONDING (e) Six filled orbitals, all bonding pairs, e.g. sulphur hexafluoride, SF 6 In sulphur hexafluoride, the central sulphur atom has six outer electrons and each fluorine atom contributes one electron, resulting in six electron pairs, all of which are bonding pairs. The shape of the molecule is: F F F S F F F If this molecule were constructed in a solid shape it would be a regular octahedron and therefore the SF 6 molecule is octahedral in shape. Bearing in mind that the number of electron pairs decides the shape of molecules, Table 11 provides a useful summary of molecular shapes. Table 11 Total number of electron pairs Arrangement of electron pairs 2 Linear 3 Trigonal 4 Tetrahedral 5 Trigonal bipyramidal 6 Octahedral Question Draw molecules of the following species showing their shapes: (a) PCl 3 (d) PF 5 (g) NF 3 (b) SnCl 4 (e) BeF 2 (h) BH 4 (c) BrF 4 (f) H 2 S CHEMISTRY 33

34 CHEMICAL BONDING Ionic lattices, superconductors and semiconductors Ionic lattice structures Ionic compounds have high melting and boiling points and are solids at room temperature. They are brittle when hit hard unlike metals, which are both malleable and ductile. In ionic compounds the ions are held together by the attraction of their opposite electrical charges. Each positive ion (cation) attracts several negative ions (anions) and vice versa in a structure known as an ionic lattice. There are no molecules or even pairs of ions in ionic solids but a huge lattice of ions clumped together with each ion pulling others of the opposite charge around it. Ionic solids do not conduct electricity as the ions are trapped in the lattice, but in the liquid state the ions are mobile and the compound is then able to conduct electricity. The exact arrangement of the ions in an ionic lattice varies according to the particular ions. In an ionic lattice the positive and negative ions may have similar sizes or may be quite different in size. The geometry of the crystalline structure adopted by the compound depends on the relative sizes of the ions. In sodium chloride each Na + ion is surrounded by six Cl ions and vice versa. This is known as 6:6 co-ordination. The sodium chloride lattice structure has a face-centred cubic arrangement and this structure is generally adopted by ionic compounds in which the anion is somewhat bigger than the cation. The ionic radius of Na + is 95 pm and that of Cl is 181 pm. Figure 22 Na + Cl 34 CHEMISTRY

35 CHEMICAL BONDING Many ionic compounds adopt the sodium chloride structure (Figure 22) because it is the optimum arrangement for ions of relative sizes similar to those of Na + and Cl. The optimum arrangement is a compromise between maximum attraction of oppositely charged ions and minimum repulsion of ions of the same charge. When the positive and negative ions have similar sizes, the crystalline structure adopted is more likely to be that of caesium chloride (Figure 23), which has 8:8 co-ordination. The ionic radius for Cs + is 174 pm, which is fairly similar to that of Cl (181 pm). Figure 23 Cl Cs + As well as the sodium chloride and caesium chloride lattices there are other types of ionic crystalline structures. The sodium chloride structure (often known as the rock salt structure) is adopted by many classes of compounds, particularly the alkali metal halides except for CsCl, CsBr and CsI. Question Which structure, that of NaCl or CsCl, is likely to be adopted by the following ionic compounds? (a) NiO (b) MgO (c) CsBr (d) CaO Different structures are found in compounds where the ratio of positive to negative ions is not 1:1. For example, in rutile, TiO 2, each titanium ion is surrounded by six oxide ions and each oxide ion is surrounded by three titanium ions and so the rutile structure has 6:3 co-ordination. Superconductors Metals are good electrical conductors because of the mobile electrons in the metallic lattice. At ordinary temperatures metals have some resistance to the flow of electrons. In 1911, Onnes, a Danish scientist who was the first to liquefy helium, discovered that when mercury is cooled to about 4 K ( 269 o C) it loses all resistance to electrical flow. CHEMISTRY 35

36 CHEMICAL BONDING Thus, a current once started will flow continuously. This phenomenon is known as superconductivity and superconductors are materials that conduct electricity with no resistance. This means that superconductors can carry a current indefinitely without losing any energy. Onnes found that several metals, such as copper, lead, tin and silver, lose all electrical resistance when cooled to a low enough temperature. When the temperature is lowered (using liquid helium), the atoms vibrate less and the resistance decreases smoothly until the critical temperature, T c, of the metal is reached. At this point the resistance drops abruptly to zero. Figure 24 electrical resistance 0 T c temperature/k The critical temperatures of these metals are too low to have many practical applications since achieving temperatures near absolute zero (0 K or 273 o C) is very difficult and costly. In 1986 a superconductor with a critical temperature over 30 K was discovered. This instigated more research throughout the world, culminating in the discovery of a metallic oxide of yttrium, barium and copper with a critical temperature of about 92 K. This compound, YBa 2 Cu 3 O 7, is called a superconductor because of the molar ratio of the three metals. This higher critical temperature meant that liquid nitrogen (boiling point 77 K), which is relatively cheap and readily available, as well as being easy to handle, could be used as the coolant instead of liquid helium. Compounds such as the superconductors are known as ceramic superconductors. They have higher critical temperatures than purely metallic ones but there is still a problem forming ceramics into wires, as ceramics are less ductile than metals. 36 CHEMISTRY

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