Inorganic Chemistry Notes PDF

Inorganic Chemistry I | Dr. Nyamato G.S. Inorganic Chemistry I Course Content: Early theories of the atom (Thomson’s model, Rutherford’s model, Bohr’s model and the hydrogen spectra); Particle-wave duality of matter; Qualitative treatment of the Schrodinger equation...

Inorganic Chemistry I | Dr. Nyamato G.S. Inorganic Chemistry I Course Content: Early theories of the atom (Thomson’s model, Rutherford’s model, Bohr’s model and the hydrogen spectra); Particle-wave duality of matter; Qualitative treatment of the Schrodinger equation in deduction of s, p, d, f orbitals; The Aufbau Principle, Pauli exclusion principle, Hund’s rule and the building up of the periodic table; Groups and periods of the periodic table; the periodic table and electron configuration. The Mole concept and balancing of ionic (redox) equations. Electronegativity, electron affinity, ionization energy; nature of ionic and covalent compounds-as influenced by these factors. Hybridization of atomic orbitals and shapes of simple molecules and ions; Common oxidation states of the elements; naturally occurring and artificially made isotopes and their applications. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. The Early Theories of the Atomic Structure The first clear atomic hypothesis for the existence of atoms was presented in 1803 by John Dalton (1766-1844). He suggested that: 1. All matter is composed of extremely small particles called atoms. 2. Atoms cannot be created nor destroyed-in a chemical reaction, atoms of different elements are separated, joined or rearranged. They are never changed into atoms of another element. 3. All atoms of the same element are alike and different from those of any other element. 4. A compound is a specific combination of atoms of more than one element. Towards the end of the 19th century, it was realized that the atom is not indivisible but consists of a number of sub-atomic particles. In 1897, J.J. Thomson (1856-1940) discovered the electron by experimenting with the cathode ray tube (is a tube that has a piece of metal, called an electrode, at each end. Each electrode is connected to a power source)-the bulky electronic part of an old television sets. When the power is turned on, the electrodes become charged and produce a stream of charged particles which travel from the cathode to the anode. Thomson used the cathode ray tube with a magnet and discovered that the green beam it produced was made up of negatively charged material. He performed a number of experiments and found that the mass of one of these particles was almost 2,000 times lighter than a hydrogen atom. Thus, it was determined that atoms contain electrons and since the atom was neutral, it was suggested that besides electrons, an atom also contained positive charges. In 1904, Thomson suggested that an atom consisted of a uniform positive sphere of matter on which electrons were embedded. This became to be known as the “plum budding” model of the atom. In 1910, Ernest Rutherford (1871-1937) did some experiments on Thomson’s plum budding model. The members of his lab fired a beam of positively charged particles called alpha particles at a very thin sheet of gold foil. It was observed that almost all the alpha particles passed directly through the foil without deflection. Although the explanation for these results was not immediately obvious, the findings were clearly inconsistent with Thomson’s model. By 1911, Rutherford was able to explain these observations. According to him, the greater part of the mass of an atom is concentrated in the part he called the nucleus. He postulated further © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. that most of the total volume of an atom is empty space in which electrons move around the nucleus. Thus, most of alpha particles passed through the foil because they did not encounter the minute nucleus of any gold foil atom. Occasionally, however, an alpha particle came close to a gold nucleus and the repulsion between the highly charged gold nucleus and the alpha particles was strong enough to deflect the less massive alpha particle. To explain his observations, Rutherford developed a new model of the structure of the atom. According to Rutherford, the electrons move about the nucleus in fixed orbits like planets revolving around the sun. According to classical physics, however, an electrically charged particle, such as an electron, moving in a circular path should continuously lose energy by emitting electromagnetic radiation. Hence, as the electron loses energy, it should spiral into the positively charged nucleus. This spiraling obviously does not occur since hydrogen atoms are stable. So, how can we explain this apparent violation of the laws of physics? Quantization of Energy When solids are heated, they emit radiation, as seen in the red glow of an electric stove burner and the bright white light of a tungsten lightbulb. The wavelength distribution of the radiation depends on temperature; a red-hot object is cooler than a white-hot one. During the late 1800s, a number of physicists were studying this phenomenon, trying to understand the relationship between the temperature and the intensity and wavelengths of the emitted radiation. The prevailing laws of physics could not account for the observations. 1n 1900 a German physicist named Max Planck (1858-1947) solved the problem by assuming that energy can be either released or absorbed by atoms only in discrete "chunks" of some minimum size. Planck gave the name quantum (meaning "fixed amount") to the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation. He proposed that the energy, E, of a single quantum equals a constant times the frequency of the radiation: © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. E = hν Where, h is called Planck's constant and has a value of 6.626 X 10-34 joule-second (J-s). According to Planck's theory, matter is allowed to emit and absorb energy only in whole- number multiples of hν, such as hν, 2hν, 3hν, and so forth. Because the energy can be released only in specific amounts, we say that the allowed energies are quantized-their values are restricted to certain quantities. Planck's revolutionary proposal that energy is quantized was proved correct, and he was awarded the 1918 Nobel Prize in Physics for his work on the quantum theory. The Photoelectric Effect and Photons A few years after Planck presented his theory, scientists began to see its applicability to a great many experimental observations. In 1905, Albert Einstein (1879-1955) used Planck's quantum theory to explain the photoelectric effect-the ejection of electrons from a metal surface upon exposure to photons of sufficiently high energy. Experiments had shown that light shining on a clean metal surface causes the surface to emit electrons. It was found that: 1. The frequency of the incident light must be greater than a certain value called the threshold frequency in order for the electrons to be emitted from the surface. 2. The kinetic energy, K.E, of the emitted electrons is directly proportional to the frequency of the incident light but independent of its intensity. 3. Electrons are emitted even if the intensity of radiation is very low provided the threshold frequency has been attained. To explain the photoelectric effect, Einstein assumed that the radiant energy striking the metal surface does not behave like a wave but rather as if it were a stream of tiny energy packets, called photons. Einstein deduced that each photon must have an energy equal to Planck's constant times the frequency of the light: Energy of photon = E = hν Thus, radiant energy itself is quantized. Under the right conditions, a photon can strike a metal surface and be absorbed. When this happens, the photon can transfer its energy to an electron in the metal. A certain amount of energy- called the work function-is required for an electron to overcome the attractive forces that hold it in the metal. If the photons have less energy than the work function, electrons do not acquire sufficient energy to escape from the metal surface, even if the light beam is intense. If light of a © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. high frequency is, therefore, used the electrons will not only be emitted but will also acquire some kinetic energy. Thus, E = hν = K.E + w Where w is the work done to overcome the attractive forces. Thus, K.E = hν-w. This shows that the higher the frequency, the greater the K.E of the ejected electrons. Einstein won the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect. The idea that the energy of light depends on its frequency helps us understand the diverse effects that different kinds of electromagnetic radiation have on matter. For example, the high frequency (short wavelength) of X-rays causes X-ray photons to have energy high enough to cause tissue damage and even cancer. Thus, signs are normally posted around X-ray equipment warning us of high-energy radiation. SAMPLE EXERCISE 1. Calculate the energy of one photon of yellow light with a wavelength of 589 nm. ν = c/λ ℎ𝑐 E = hν = = 2.03 ×105 J/mol 𝜆 2. (a) A laser emits light with a frequency of 4.69 X 1014 s-1. What is the energy of one photon of the radiation from this laser? (b) If the laser emits a pulse of energy containing 5.0 X 1017 photons of this radiation, what is the total energy of that pulse? (c) If the laser emits 1.3 x 10-2 J of energy during a pulse, how many photons are emitted during the pulse? Answers: (a) 3.11 X 10-19 J, (b) 0.16 J, (c) 4.2 X 1016 photons The Line Spectra (the hydrogen spectra) A particular source of radiant energy may emit a single wavelength, as in the light from a laser or produce radiation containing many different wavelengths, as in the light from lightbulbs and stars. When the radiation containing many different wavelengths is separated into its different wavelength components, a spectrum is produced. The resulting spectrum consists of a continuous range of colors-violet merges into blue, blue into green, and so forth, with no blank spots. This rainbow of colors, containing light of all wavelengths, is called a continuous spectrum. The most © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. familiar example of a continuous spectrum is the rainbow produced when raindrops or mist acts as a prism for sunlight. Not all radiation sources produce a continuous spectrum. When a high voltage is applied to tubes that contain different gases under reduced pressure, the gases emit different colors of light. The light emitted by neon gas is the familiar red-orange glow of many "neon" lights, whereas sodium vapor emits the yellow light characteristic of some modern streetlights. When light coming from such tubes is passed through a prism, only a few wavelengths are present in the resultant spectra, as shown in below. Each wavelength is represented by a colored line in one of these spectra. A spectrum containing radiation of only specific wavelengths is called a line spectrum. When scientists first detected the line spectrum of hydrogen in the mid-1800s, they were fascinated by its simplicity. At that time, only the four lines in the visible portion of the spectrum were observed. These lines correspond to wavelengths of 410 nm (violet), 434 nm (blue), 486 nm (blue-green), and 656 nm (red). In 1885, a Swiss schoolteacher named Johann Balmer showed that the wavelengths of these four visible lines of hydrogen fit an intriguingly simple formula that related the wavelengths of the visible line spectrum to integers. Soon Balmer's equation was extended to a more general one, called the Rydberg equation, which allowed the calculation of the wavelengths of all the spectral lines of hydrogen: 1 1 1 = RH (𝑛21 − ) 𝜆 𝑛2 2 In this formula λ is the wavelength of a spectral line, RH is the Rydberg constant (1.096776 X 107 m-I), and n1 and n2 are positive integers, with n2 being larger than n1. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Later, additional lines were found to occur in the ultraviolet and infrared regions of the hydrogen spectrum; Lyman series (UV region), Paschen series (IR), Brackett series (IR) and Pfund series (IR). For Lyman series: n1 = 1, n2 = 2, 3, 4, 5 … Balmer series, n1 = 2, n2 = 3, 4, 5 … Paschen series, n1 = 3, n2 = 4, 5, 6 … Brackett series, n1 = 4, n2 = 5, 6, 7 … Pfund series, n1 = 5, n2 = 6, 7, 8 … Bohr’s model of the atom In 1913, a Danish Physicist Neil Bohr (1885-1962) proposed a model of the atom that could account for the spectra of hydrogen-like atoms using Rutherford’s planetary model and Planck’s quantum theory. The theory is based on the following postulates: 1. Electrons in an atom rotate only on specific or definite circular orbits. Each orbit is associated with a definite amount of energy and the energy of the electron remains constant so long as it stays in that orbit. If an electron is at an orbit near the nucleus, the atom possesses minimum energy. Such a state is called the unexcited state. When an electron moves to the next or further orbits, its energy increases and the state of the atom is excited. 2. The emission or absorption of energy, in the form of radiation, can only occur when an electron moves from one stationary state to another. This energy is emitted or absorbed as a photon, E = hν. Starting with these postulates and using classical equations for motion and for interacting electrical charges, Bohr calculated the energies corresponding to each allowed orbit for the electron in the hydrogen atom. Ultimately, the energies that Bohr calculated fit the formula: 1 1 E = (-hcRH) (𝑛2 ) = (-2.18 × 10-18 J) (𝑛2 ) Where h, c, and RH are Planck's constant, the speed of light, and the Rydberg constant, respectively. Each orbit corresponds to a different value of n, and the radius of the orbit gets larger as n increases. What happens to the orbit radius and the energy as n becomes infinitely large? The radius increases as n2, so we reach a point at which the electron is completely separated from the nucleus. When n = ∞, the energy is zero: 1 E = (-2.18 × 10-18 J) (∞2) = 0 © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. When an electron makes a transition from a state of energy Ei to a final state of energy Ef, the change in energy is: ΔE = Ef - Ei = Ephoton = hν Thus, ℎ𝑐 1 1 ΔE = hν = = (-2.18 × 10-18 J) (𝑛2 𝑓 − ) 𝜆 𝑛2 𝑖 If we solve for 1/λ, we find that this equation derived from Bohr's theory corresponds to the Rydberg equation, which was obtained using experimental data: 1 1 1 = -RH (𝑛2 𝑓 − ) 𝜆 𝑛2 𝑖 Thus, the existence of discrete spectral lines can be attributed to the quantized jumps of electrons between energy levels. Limitations of the Bohr Model ▪ While the Bohr model explains the line spectrum of the hydrogen atom, it cannot explain the spectra of other atoms. ▪ Bohr also avoided the problem of why the negatively charged electron would not just fall into the positively charged nucleus by simply assuming it would not happen. ▪ Bohr assumed that an electron is located at definite distance from the nucleus and is revolving around it with definite velocity, i.e. associated with a fixed value of momentum. This is against the Heisenberg’s uncertainty principle according to which it is impossible to determine simultaneously with certainty the position and the momentum of a particle. The Wave Behaviour of Matter In the years following the development of Bohr's model for the hydrogen atom, the dual nature of radiant energy became a familiar concept. Depending on the experimental circumstances, radiation appears to have either a wavelike or a particle-like (photon) character. Louis de Broglie (1892-1987), who was working on his Ph.D. thesis in physics at the Sorbonne in Paris, argued that because electromagnetic radiation could be considered to consist of particles, called photons, yet at the same time exhibit wave-like properties, then the same might be true of electrons. De Broglie suggested that as the electron moves about the nucleus, it is associated with a particular © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. wavelength. He went on to propose that the characteristic wavelength of the electron, or of any other particle, depends on its mass, m, and on its velocity, v, (where h is Planck's constant): ℎ 𝜆= 𝑚𝑣 The quantity mv for any object is called its momentum. Because de Broglie's hypothesis is applicable to all matter, any object of mass m and velocity v would give rise to a characteristic matter wave. However, the above equation indicates that the wavelength associated with an object of ordinary size, such as a golf ball, is so tiny as to be completely out of the range of any possible observation. This dual nature is called wave-particle duality. The German physicist Werner Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. The limitation becomes important only when we deal with matter at the subatomic level (that is, with masses as small as that of an electron). Heisenberg's principle is called the uncertainty principle. When applied to the electrons in an atom, this principle states that it is inherently impossible for us to know simultaneously both the exact momentum of the electron and its exact location in space. De Broglie's hypothesis and Heisenberg's uncertainty principle set the stage for a new and more broadly applicable theory of atomic structure. In this new approach, any attempt to define precisely the instantaneous location and momentum of the electron is abandoned. The wave nature of the electron is recognized, and its behavior is described in terms appropriate to waves. The result is a model that precisely describes the energy of the electron while describing its location not precisely, but in terms of probabilities. In 1926 the Austrian physicist Erwin Schrodinger (1887-1961) proposed an equation, now known as Schrodinger's wave equation that incorporates both the wave-like behavior and the particle-like behavior of the electron. To do so, he introduced the wavefunction, ψ (psi), a mathematical function of the position coordinates x, y, and z which describes the behaviour of an electron. The Schrodinger equation, of which the wavefunction is a solution, for an electron free to move in one dimension is: © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. where me is the mass of an electron, V is the potential energy of the electron, and E is its total energy. Although the wave function itself has no direct physical meaning, the square of the wave function, ψ2, provides information about an electron's location when the electron is in an allowed energy state. That is, the probability of finding an electron at a given location is proportional to the square of the wavefunction at that point. According to this interpretation, there is a high probability of finding the electron where ψ2 is large, and the electron will not be found where ψ2 is zero. For the hydrogen atom, the allowed energies are the same as those predicted by the Bohr model. However, the Bohr model assumes that the electron is in a circular orbit of some particular radius about the nucleus. In the quantum mechanical model, the electron's location cannot be described so simply. According to the uncertainty principle, if we know the momentum of the electron with high accuracy, our simultaneous knowledge of its location is very uncertain. In the quantum mechanical model, we therefore speak of the probability that the electron will be in a certain region of space at a given instant. As it turns out, the square of the wave function, ψ2, at a given point in space represents the probability that the electron will be found at that location. For this reason, ψ2 is called either the probability density or the electron density. One way of representing the probability of finding the electron in various regions of an atom is as shown below. The regions with a high density of dots correspond to relatively large values for ψ2 and are therefore regions where there is a high probability of finding the electron. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Atomic Orbitals The wavefunction of an electron in an atom is called an atomic orbital. Each orbital describes a specific distribution of electron density in space, as given by the orbital's probability density. Chemists use hydrogenic atomic orbitals to develop models that are central to the interpretation of inorganic chemistry, and we shall spend some time describing their shapes and significance. Each of the wave functions obtained by solving the Schrodinger equation for a hydrogenic atom is uniquely labelled by a set of three integers called quantum numbers. These quantum numbers are designated n, l, and ml: n is called the principal quantum number, l is the orbital angular momentum quantum number (formerly the ‘azimuthal quantum number’), and ml is called the magnetic quantum number. Each quantum number specifies a physical property of the electron: 1. The principal quantum number, n, specifies the energy, i.e. the average radius of the energy level, and can have positive integral values of 1, 2, 3, and so forth. A level is a region in space where electrons with the same value of n are located. As n increases, the orbital becomes larger, and the electron spends more time farther from the nucleus. An increase in n also means that the electron has a higher energy and is therefore less tightly bound to the nucleus. 2. The angular momentum quantum number, l, defines the shape of the orbital and can have integral values from 0 to (n - 1) for each value of n. l characterizes the energy sub- level which is an ingredient of the level n. The value of l for a particular sub-level is generally designated by the letters s, p, d, and f, corresponding to l values of 0, 1, 2, and 3, respectively. Usually in atoms, l does not go beyond 3. The collection of orbitals with the same value of n is called an electron shell. All the orbitals that have n = 3, for © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. example, are said to be in the third shell. Further, the set of orbitals that have the same n and l values is called a subshell. Each subshell is designated by a number (the value of n) and a letter s, p, d or f (corresponding to the value of l). For example, the orbitals that have n = 3 and l = 2 are called 3d orbitals and are in the 3d subshell. Value of l 0 1 2 3 Letter used s p d f 3. The magnetic quantum number, m1, describes the orientation of the orbital in space and for a sub-level with quantum number l, there are 2l+1 individual orbitals. These orbitals are distinguished by the magnetic quantum number, ml, which can have the 2l +1 integer values from -l down to +l. For example, a d subshell of an atom (l = 2) consists of five individual atomic orbitals that are distinguished by the values ml -2, -1, 0, +1, +2. Thus there is only one orbital in an s subshell (l = 0), the one with ml = 0: this orbital is called an s orbital. There are three orbitals in a p subshell (l = 1), with quantum numbers ml = -1, 0, +1; they are called p orbitals. The five orbitals of a d subshell (l = 2) are called d orbitals, and so on. The Table below summarizes the possible values of the quantum numbers l and ml for values of n through n = 4. From the Table, the total number of orbitals in a shell is n2, where n is the principal quantum number of the shell. Relationship among Values of n, l, and m1 through n = 4 n Possible Subshell Possible values of Number of Total Number Values of l Designation ml Orbitals in of Orbitals in subshell shell 1 0 1s 0 1 1 2 0 2s 0 1 1 2p -1, 0, 1 3 4 3 0 3s 0 1 1 3p -1, 0, 1 3 2 3d -2, -1, 0, 1, 2 5 9 4 0 4s 0 1 1 4p -1, 0, 1 3 2 4d -2, -1, 0, 1, 2 5 3 4f -3, -2, -1, 0, 1, 2, 3 7 16 The restrictions on the possible values of the quantum numbers give rise to the following very important observations: © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. 1. The shell with principal quantum number n will consist of exactly n subshells. 2. Each subshell consists of a specific number of orbitals. Each orbital corresponds to a different allowed value of ml. 3. The total number of orbitals in a shell is n2, where n is the principal quantum number of the shell. The resulting number of orbitals for the shells-1, 4, 9, 16---is related to a pattern seen in the periodic table: We see that the number of elements in the rows of the periodic table-2, 8, 18, and 32-equals twice these numbers. Representation of Orbitals The s Orbitals All of the s orbitals (1s, 2s, 3s, 4s, and so forth) are spherically symmetric. Recall that the l quantum number for the s orbitals is 0; therefore the ml quantum number must be 0. Therefore, for each value of n, there is only one s orbital. An s orbital is normally represented by a spherical surface with the nucleus at its center. The surface is called the boundary surface of the orbital and defines the region of space within which there is a high probability (typically 90%) of finding the electron. The p Orbitals The electron density in p orbitals is not distributed in a spherically symmetric fashion as in an s orbital. Instead, the electron density is concentrated in two regions on either side of the nucleus, separated by a node at the nucleus. We say that this dumbbell-shaped orbital has two lobes. For each value of n, the three p orbitals have the same size and shape but differ from one another in spatial orientation. We usually represent p orbitals by drawing the shape and orientation of their wave functions, as shown below. It is convenient to label these as the px, py and pz orbitals. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. The d Orbitals They are determined by quantum number l = 2. Thus, there are five possible values for the ml quantum number: -2, -1, 0, 1, and 2. The different d orbitals in a given shell have different shapes and orientations in space, as shown below. The dxy, dxz and dyz lie in the xy, xz, and yz planes, respectively, with the lobes oriented between the axes. The lobes of the dx2- y2 orbital also lie in the xy plane, but the lobes lie along the x and y axes. The dz2 orbital looks very different from the other four: There are in fact six possible combinations of double dumb-bell shaped orbitals around three axes: three with lobes between the axes, as in dxy, dxz and dyz, and three with lobes along the axis. One of these orbitals is dx2-y2. The dz2 orbital can be thought of as the superposition of two contributions, one with lobes along the z- and x-axes and the other with lobes along the z- and y-axes. Even though the dz2 orbital looks different from the other d orbitals, it has the same energy as the other four d orbitals. When n is 4 or greater, there are seven equivalent f orbitals (for which l = 3). The shapes of the f orbitals are even more complicated than those of the d orbitals. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Many Electron Atoms The Aufbau principle Although the shapes of the orbitals for many-electron atoms are the same as those for hydrogen, the presence of more than one electron greatly changes the energies of the orbitals. In hydrogen the energy of an orbital depends only on its principal quantum number, n. For example, the 3s, 3p, and 3d subshells all have the same energy. In a many-electron atom, however, the electron-electron repulsions cause the different subshells to be at different energies. The building-up principle (Aufbau) is a procedure for arriving at the lowest energy electron configuration of many electron atoms. Simply put, the principle states that: electrons of a many electron atom occupy the orbitals in the order of increasing energy. The order of increasing energy of the atomic orbitals in many-electron atoms is described by Kletchkovsky’s rule: the energy of the orbitals increase in accordance with the increase in the sum of the principal and orbital quantum numbers, n+l. when the sum values are equal, then energy is less in the orbital with a bigger value of l and a small value of n. For example: a) 3d orbital has a sum of n+l = 3+2 = 5 b) 4p orbital has a sum of n+l = 4+1 = 5 Thus, 3d has less energy since its l value is bigger and n value is smaller. Using this rule, we can show that the energy of orbitals rise in the following manner: 1s ˂ 2s ˂ 2p ˂ 3s ˂ 3p ˂ 4s ˂ 3d ˂ 4p ˂ 5s ˂ 4d ˂ 5p ˂ 6s ˂ 4f ˂ 5d ˂ 6p ˂ 7s ˂ 5f……. Orbital quantum number, l 0 1 2 3 Principal quantum number, n 1 1s 2 2s 2p 3 3s 3p 3d 4 4s 4p 4d 4f 5 5s 5p 5d 5f 6 6s 6p 6d 7 7s 7p 7d © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Electron Spin and the Pauli Exclusion Principle When scientists studied the line spectra of many-electron atoms in great detail, they noticed a very puzzling feature: Lines that were originally thought to be single were actually closely spaced pairs. In 1925 the Dutch physicists George Uhlenbeck and Samuel Goudsmit proposed a solution to this dilemma. They postulated that electrons have an intrinsic property, called electron spin, which causes each electron to behave as if it were a tiny sphere spinning on its own axis. This observation led to the assignment of a new quantum number for the electron, the spin magnetic quantum number, is denoted ms (the subscript s stands for spin). Two possible values are allowed for ms, +½ or -½, which was first interpreted as indicating the two opposite directions in which the electron can spin. A spinning charge produces a magnetic field. The two opposite directions of spin therefore produce oppositely directed magnetic fields, as shown below. These two opposite magnetic fields lead to the splitting of spectral lines into closely spaced pairs. In 1925 the Austrian-born physicist Wolfgang Pauli (1900-1958) discovered the principle that governs the arrangements of electrons in many-electron atoms. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers n, l, ml, and ms. For a given orbital, the values of n, l, and m1 are fixed. Thus, if we want to put more than one electron in an orbital and satisfy the Pauli Exclusion Principle, our only choice is to assign different ms, values to the electrons. Because there are only two such values, we conclude that an orbital can hold a maximum of two electrons and they must have opposite spins. ELECTRON CONFIGURATIONS The way in which the electrons are distributed among the various orbitals of an atom is called the electron configuration of the atom. The most stable electron configuration of an atom- the ground state-is that in which the electrons are in the lowest possible energy states. If there were no restrictions on the possible values for the quantum numbers of the electrons, all the electrons would crowd into the 1s orbital because it is the lowest in energy. The Pauli Exclusion Principle tells us, however, that there can be at most two electrons in any single orbital. Thus, the orbitals © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. are filled in order of increasing energy, with no more than two electrons per orbital. For example, consider the lithium atom, which has three electrons. The 1s orbital can accommodate 2 of the electrons. The third one goes into the next lowest energy orbital, the 2s. This electron configuration is usually represented by the symbol of the occupied subshell and a superscript, indicating the number of electrons in that subshell. Thus, the electron configuration for lithium is written as Is22s1. This configuration can also be represented in what is called an orbital diagram, where each orbital is denoted by a box and each electron by a half arrow. i.e. Li 1s 2s A half arrow pointing up represents an electron with a positive spin magnetic quantum number (ms = +½) and a half arrow pointing down represents an electron with a negative spin magnetic quantum number (ms = -½). In fact, chemists and physicists often refer to electrons as "spin-up" and "spin-down" rather than specifying the value for ms. Electrons having opposite spins are said to be paired when they are in the same orbital. An unpaired electron is one not accompanied by a partner of opposite spin. In the lithium atom, the two electrons in the ls orbital are paired and the electron in the 2s orbital is unpaired. Hund’s rule Let’s now consider the electron configurations of the elements change as we move from element to element across the periodic table. Hydrogen has one electron, which occupies the ls orbital in its ground state. H : 1s1 He : 1s2 1s 1s The next element, helium, has two electrons. Because two electrons with opposite spins can occupy an orbital, both of helium's electrons are in the ls orbital. The two electrons present in helium complete the filling of the first shell. This arrangement represents a very stable configuration, as is evidenced by the chemical inertness of helium. For the third electron of lithium, the change in principal quantum number represents a large jump in energy and it represents the start of a new shell occupied with electrons. The element that follows lithium is beryllium; its electron configuration is ls22s2. Boron, atomic number 5, has the electron configuration ls22s22p1. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. The fifth electron must be placed in a 2p orbital because the 2s orbital is filled. Because all the three 2p orbitals are of equal energy, it does not matter which 2p orbital is occupied. With the next element, carbon, we encounter a new situation. We know that the sixth electron must go into a 2p orbital. However, does this new electron go into the 2p orbital that already has one electron, or into one of the other two 2p orbitals? This question is answered by Hund's rule, which states that for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized. This means that electrons enter each orbital of a given type singly and with identical spins before any pairing of electrons of opposite spins occurs within those orbitals. Thus, a carbon atom in its ground state has two unpaired electrons. Similarly, for nitrogen in its ground state, Hund's rule requires that the three 2p electrons singly occupy each of the three 2p orbitals. For oxygen and fluorine, we place four and five electrons, respectively, in the 2p orbitals. To achieve this, we pair up electrons in the 2p orbitals. Hund's rule is based in part on the fact that electrons repel one another. By occupying different orbitals, the electrons remain as far as possible from one another, thus minimizing electron-electron repulsions. Condensed Electron Configurations The filling of the 2p subshell is complete at neon, which has a stable configuration with eight electrons (an octet) in the outermost occupied shell. The next element, sodium, atomic number 11, marks the beginning of a new row of the periodic table. Sodium has a single 3s electron beyond the stable configuration of neon. We can therefore abbreviate the electron configuration of sodium as Na: [Ne]3s1 Writing the electron configuration as [Ne]3s1 helps focus attention on the outermost electrons of the atom, which are the ones largely responsible for the chemical behavior of an element. In general, in writing the condensed electron configuration of an element, the electron configuration of the nearest noble-gas element of lower atomic number is represented by its chemical symbol in brackets. For example, we can write the electron configuration of lithium as Li: [He]2s1 We refer to the electrons represented by the symbol for a noble gas as the noble-gas core of the atom. More usually, these inner-shell electrons are referred to as the core electrons. The © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. electrons given after the noble-gas core are called the outer-shell electrons. The outer-shell electrons include the electrons involved in chemical bonding, which are called the valence electrons. For lighter elements (those with atomic number of 30 or less), all of the outer-shell electrons are valence electrons. ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE The periodic table is structured so that elements with the same pattern of outer-shell (valence) electron configuration are arranged in columns. For example, the electron configurations for the elements in groups 2 (2A) and 13 (3A) are given below. It’s evident that all the 2 elements have ns2 outer configurations, while the all the 13 elements have ns2np1 configurations. Group 2 (2A) Group 13 (3A) Be [He]2s2 B [He]2s2p1 Mg [Ne]3s2 Al [Ne]3s2p1 Ca [Ar]4s2 Ga [Ar]3d104s24p1 Sr [Kr]5s2 In [Kr]4d105s25p1 Ba [Xe]6s2 Tl [Xe]4f145d106s26p 1 Ra [Rn]7s2 Earlier, we saw that the total number of orbitals in each shell is equal to n2: 1, 4, 9, or 16. Because each orbital can hold two electrons, each shell can accommodate up to 2n2 electrons: 2, 8, 18, or 32. The structure of the periodic table reflects this orbital structure. The first row has two elements, the second and third rows have eight elements, the fourth and fifth rows have 18 elements, and the sixth row has 32 elements (including the lanthanide metals). Some of the numbers repeat because we reach the end of a row of the periodic table before a shell completely fills. For example, the third row has eight elements, which corresponds to filling the 3s and 3p orbitals. The remaining orbitals of the third shell, the 3d orbitals, do not begin to fill until the fourth row of the periodic table (and after the 4s orbital is filled). Likewise, the 4d orbitals do not begin to fill until the fifth row of the table, and the 4f orbitals don't begin filling until the sixth row. All these observations are evident in the structure of the periodic table. Hence, the periodic table is the best guide to the order in which orbitals are filled- the electron configuration of an element can easily be written based on its location in the periodic table (as summarized in the table below). Notice that the elements can be grouped by the type of orbital into which the electrons are placed. On the left are two columns of elements (depicted in blue). These elements, known as the © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. alkali metals (group 1A) and alkaline earth metals (group 2A), are those in which the valence s orbitals are being filled. On the right is a pink block of six columns. These are the elements in which the valence p orbitals are being filled. The s block and the p block of the periodic table together are the representative elements, which are sometimes called the main-group elements. In the middle of the periodic table is a gold block of ten columns containing the transition metals. These are the elements in which the valence d orbitals are being filled. Below the main portion of the table are two tan rows containing 14 columns. These elements are often referred to as the f-block metals, because they are the ones in which the valence f orbitals are being filled. Recall that the numbers 2, 6, 10, and 14 are precisely the number of electrons that can fill the s, p, d, and f subshells, respectively. Recall also that the 1s subshell is the first s subshell, the 2p is the first p subshell, the 3d is the first d subshell, and the 4f is the first f subshell. The Figure below gives the valence ground-state electron configurations for all the elements. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Elements in the same column of the table contain the same number of electrons in their valence orbitals, the occupied orbitals that hold the electrons involved in bonding. For example, O ([He]2s22p4) and S ([Ne]3s23p4) are both members of group 6A. The similarity of the electron distribution in their valence s and p orbitals leads to similarities in the properties of these two elements. When we compare O and S, however, it is apparent that they exhibit differences as well, not the least of which is that oxygen is a colorless gas at room temperature, whereas sulfur is a yellow solid. One of the major differences between atoms of these two elements is their electron configurations: the outermost electrons of O are in the second shell, whereas those of S are in the third shell. Thus, electron configurations can be used to explain differences as well as similarities in the properties of elements. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. EFFECTIVE NUCLEAR CHARGE Because electrons are negatively charged, they are attracted to nuclei, which are positively charged. Many of the properties of atoms depend on their electron configurations and on how strongly their outer electrons are attracted to the nucleus. The force of attraction between an electron and the nucleus depends on the magnitude of the net nuclear charge acting on the electron and on the average distance between the nucleus and the electron. The force of attraction increases as the nuclear charge increases, and it decreases as the electron moves farther from the nucleus. In a many-electron atom, each electron is simultaneously attracted to the nucleus and repelled by the other electrons. Estimation of the net attraction of each electron to the nucleus by considering how it interacts with the average environment created by the nucleus and the other electrons in the atom gives rise to what is called effective nuclear charge, Zeff· The effective nuclear charge acting on an electron in an atom is smaller than the actual nuclear charge because the effective nuclear charge also accounts for the repulsion of the electron by the other electrons in the atom-in other words, Zeff < Z. A valence electron in an atom is attracted to the nucleus of the atom and is repelled by the other electrons in the atom. In particular, the electron density that is due to the inner (core) electrons is particularly effective at partially canceling the attraction of the valence electron to the nucleus. We say that the inner electrons partially shield or screen the outer electrons from the attraction of the nucleus. We can therefore write a simple relationship between the effective nuclear charge, Zeff, and the number of protons in the nucleus, Z: Zeff = Z - S The factor S is a positive number called the screening constant. It represents the portion of the nuclear charge that is screened from the valence electron by the other electrons in the atom. Periodic Trends in Atomic Radii ▪ Within each column (group), atomic radius tends to increase from top to bottom. This trend results primarily from the increase in the principal quantum number (n) of the outer electrons. As we go down a column, the outer electrons have a greater probability of being farther from the nucleus, causing the atom to increase in size. ▪ Within each row (period), atomic radius tends to decrease from left to right. The major factor influencing this trend is the increase in the effective nuclear charge © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. (Zeff) as we move across a row. The increasing effective nuclear charge steadily draws the valence electrons closer to the nucleus, causing the atomic radius to decrease. Periodic Trends in Ionic Radii Like the size of an atom, the size of an ion depends on its nuclear charge, the number of electrons it possesses, and the orbitals in which the valence electrons reside. The formation of a cation vacates the most spatially extended occupied orbitals in an atom and decreases the number of electron-electron repulsions. Therefore, cations are smaller than their parent atoms. The opposite is true of anions. When electrons are added to an atom to form an anion, the increased electron-electron repulsions cause the electrons to spread out more in space. Thus, anions are larger than their parent atoms. For ions carrying the same charge, size increases as we move down a column in the periodic table. As the principal quantum number of the outermost occupied orbital of an ion increases, the radius of the ion increases. A group of ions, all containing the same number of electrons, is called an isoelectronic series. For example, each ion in the isoelectronic series O2-, F-, Na+, Mg2+, Al3+ has 10 electrons. In any isoelectronic series we can list the members in order of increasing atomic number; therefore, nuclear charge increases as we move through the series. Because the number of electrons remains constant, the radius of the ion decreases with increasing nuclear charge, as the electrons are more strongly attracted to the nucleus. IONIZATION ENERGY The ionization energy of an atom or ion is the minimum energy required to remove an electron from the ground state of the isolated gaseous atom or ion. The first ionization energy, I1, is the energy needed to remove the first electron from a neutral atom. The second ionization energy, I2, is the energy needed to remove the second electron, and so forth, for successive removals of additional electrons. The greater the ionization energy, the more difficult it is to remove an electron. The values of ionization energy for a given element increase as successive electrons are removed: I1 < I2 < I3, and so forth. This trend exists because with each successive removal, an electron is being pulled away from an increasingly more positive ion, requiring increasingly more energy. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Every element exhibits a large increase in ionization energy when electrons are removed from its noble-gas core. This observation supports the idea that only the outermost electrons, those beyond the noble-gas core, are involved in the sharing and transfer of electrons that give rise to chemical bonding and reactions. The inner electrons are too tightly bound to the nucleus to be lost from the atom or even shared with another atom. ELECTRON AFFINITIES The energy change that occurs when an electron is added to a gaseous atom is called the electron affinity because it measures the attraction, or affinity, of the atom for the added electron. For most atoms, energy is released when an electron is added. It is important to understand the difference between ionization energy and electron affinity: Ionization energy measures the ease with which an atom loses an electron, whereas electron affinity measures the ease with which an atom gains an electron. CHEMICAL BONDS, LEWIS SYMBOLS, AND THE OCTET RULE Whenever two atoms or ions are strongly attached to each other, we say there is a chemical bond between them. There are three general types of chemical bonds: ionic, covalent, and metallic. The term ionic bond refers to electrostatic forces that exist between ions of opposite charge. Ionic substances generally result from the interaction of metals on the left side of the periodic table with nonmetals on the right side (excluding the noble gases, group 8A). A covalent bond results from the sharing of electrons between two atoms. The most familiar examples of covalent bonding are seen in the interactions of nonmetallic elements with one another. Metallic bonds are found in metals, such as copper, iron, and aluminum. Each atom in a metal is bonded to several neighboring atoms. The bonding electrons are relatively free to move throughout the three- dimensional structure of the metal. Lewis Symbols The electrons involved in chemical bonding are the valence electrons, which, for most atoms, are those residing in the outermost occupied shell of an atom. The American chemist G. N. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Lewis (1875-1946) suggested a simple way of showing the valence electrons in an atom and tracking them in the course of bond formation, using what are now known as Lewis electron-dot symbols, or merely Lewis symbols. The Lewis symbol for an element consists of the chemical symbol for the element plus a dot for each valence electron. Sulfur, for example, has the electron configuration [Ne]3s23p4; its Lewis symbol therefore shows six valence electrons:... S... The dots are placed on the four sides of the atomic symbol: the top, the bottom, and the left and right sides. The Octet Rule Atoms often gain, lose, or share electrons to achieve the same number of electrons as the noble gas closest to them in the periodic table. The noble gases have very stable electron arrangements, as evidenced by their high ionization energies, low affinity for additional electrons, and general lack of chemical reactivity. Because all noble gases (except He) have eight valence electrons, many atoms undergoing reactions also end up with eight valence electrons. This observation has led to a guideline known as the octet rule: Atoms tend to gain, lose, or share electrons until they are surrounded by eight valence electrons. An octet of electrons consists of full s and p subshells in an atom. In terms of Lewis symbols, an octet can be thought of as four pairs of valence electrons arranged around the atom. There are many exceptions to the octet rule, but it provides a useful framework for introducing many important concepts of bonding. IONIC BONDING When sodium metal, Na(s), is brought into contact with chlorine gas, Cl2(g), a violent reaction ensues. The product of this very exothermic reaction is sodium chloride, NaCl(s). The formation of Na+ from Na and Cl- from Cl2 indicates that an electron has been lost by a sodium atom and gained by a chlorine atom-we can envision an electron transfer from the Na atom to the Cl atom. Two of the atomic properties we discussed earlier give us an indication of how readily electron transfer occurs: the ionization energy, which indicates how easily an electron can be removed from an atom, and the electron affinity, which measures how much an atom wants to gain an electron. Electron transfer to form oppositely charged ions occurs when one of the atoms readily © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. gives up an electron (low ionization energy) and the other atom readily gains an electron (high electron affinity). Thus, NaCI is a typical ionic compound because it consists of a metal of low ionization energy and a nonmetal of high electron affinity. Ionic substances possess several characteristic properties. They are usually brittle substances with high melting points. They are usually crystalline. Furthermore, ionic crystals often can be cleaved; that is, they break apart along smooth, flat surfaces. These characteristics result from electrostatic forces that maintain the ions in a rigid, well-defined, three-dimensional arrangement COVALENT BONDING The vast majority of chemical substances do not have the characteristics of ionic materials. Most of the substances with which we come into daily contact-such as water-tend to be gases, liquids, or solids with low melting points. Many, such as gasoline, vaporize readily. Many are pliable in their solid forms-for example, plastic bags and paraffin. For the very large class of substances that do not behave like ionic substances, what is the nature of bonding between their atoms? G. N. Lewis reasoned that atoms might acquire a noble- gas electron configuration by sharing electrons with other atoms. A chemical bond formed by sharing a pair of electrons is called a covalent bond. The hydrogen molecule, H2, provides the simplest example of a covalent bond. When two hydrogen atoms are close to each other, electrostatic interactions occur between them. The two positively charged nuclei repel each other, the two negatively charged electrons repel each other, and the nuclei and electrons attract each other. Because the H2 molecule exists as a stable entity, the attractive forces must exceed the repulsive ones. Thus, the atoms in H2 are held together principally because the two nuclei are electrostatically attracted to the concentration of negative charge between them. In essence, the shared pair of electrons in any covalent bond acts as a kind of "glue" to bind atoms together. BOND POLARITY AND ELECTRONEGAT IVITY The concept of bond polarity helps describe the sharing of electrons between atoms. A nonpolar covalent bond is one in which the electrons are shared equally between two atoms, as in © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. the Cl2 and N2. In a polar covalent bond, one of the atoms exerts a greater attraction for the bonding electrons than the other. Electronegativity is defined as the ability of an atom in a molecule to attract electrons to itself. The greater an atom's electronegativity, the greater is its ability to attract electrons to itself. The electronegativity of an atom in a molecule is related to its ionization energy and electron affinity, which are properties of isolated atoms. The ionization energy measures how strongly a gaseous atom holds on to its electrons, while the electron affinity is a measure of how strongly an atom attracts additional electrons. An atom with a very negative electron affinity and high ionization energy will both attract electrons from other atoms and resist having its electrons attracted away; it will be highly electronegative. Within each period there is generally a steady increase in electronegativity from left to right; that is, from the most metallic to the most nonmetallic elements. With some exceptions (especially within the transition metals), electronegativity decreases with increasing atomic number in any one group. DRAWIN G LEWIS STRUCTURES Lewis structures can help us understand the bonding in many compounds and are frequently used when discussing the properties of molecules. For this reason, drawing Lewis structures is an important skill that you should practice. Procedure: 1. Sum the valence electrons from all atoms. For an anion, add one electron to the total for each negative charge. For a cation, subtract one electron from the total for each positive charge. 2. Write the symbols for the atoms to show which atoms are attached to which, and connect them with a single bond. Chemical formulas are often written in the order in which the atoms are connected in the molecule or ion. The formula HCN, for example, tells you that the carbon atom is bonded to the H and to the N. In many polyatomic molecules and ions, the central atom is usually written first, as in CO32- and SF4. 3. Complete the octets around all the atoms bonded to the central atom. Remember, however, that you use only a single pair of electrons around hydrogen. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. 4. Place any leftover electrons on the central atom, even if doing so results in more than an octet of electrons around the atom. 5. If there are not enough electrons to give the central atom an octet, try multiple bonds. Use one or more of the unshared pairs of electrons on the atoms bonded to the central atom to form double or triple bonds. EXAMPLES 1. Draw the Lewis structure for phosphorus trichloride, PC13, BrO3- ion, ClO2- ion, PO43- ion and HCN. MOLECULAR SHAPES Lewis structures, unfortunately, do not indicate the shapes of molecules; they simply show the number and types of bonds between atoms. The overall shape of a molecule is determined by its bond angles, the angles made by the lines joining the nuclei of the atoms in the molecule. The bond angles of a molecule, together with the bond lengths, accurately define the shape and size of the molecule. Most molecules conform to the general formula ABn in which the central atom A is bonded to n B atoms. For example, both CO2 and H2O are AB2 molecules, whereas SO3 and NH3 are AB3 molecules, and so on. The possible shapes of ABn molecules depend on the value of n. An AB2 molecule must be either linear (bond angle = 180°) or bent (bond angle ≠ 180°). For example, CO2 is linear, and SO2 is bent. For AB3 molecules, the two most common shapes place the B atoms at the comers of an equilateral triangle. If the A atom lies in the same plane as the B atoms, the shape is called trigonal planar. If the A atom lies above the plane of the B atoms, the shape is called trigonal pyramidal. In general, the shape of any particular ABn molecule can usually be derived from one of the five basic geometric structures shown below. Why do so many ABn molecules have shapes related to these basic structures, and can we predict these shapes? When A is a representative element (one of the elements from the s block or p block of the periodic table), we can answer these questions by using the valence-shell electron-pair repulsion (VSEPR) model. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. THE VSEPR MODEL Imagine tying two identical balloons together at their ends as shown in (a) below; the balloons naturally orient themselves to point away from each other-they try to “get out of each other’s way” as much as possible. If a third balloon is added, the balloons orient themselves toward the vertices of an equilateral triangle, as shown in (b). If a fourth balloon is added, they adopt a tetrahedral shape, (c). © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Somehow, electrons in molecules behave like the balloons shown above. Recall that a single covalent bond is formed between two atoms when a pair of electrons occupies the space between the atoms. A bonding pair of electrons thus defines a region in which the electrons will most likely be found. We will refer to such a region as an electron domain. Likewise, a nonbonding pair (or lone pair) of electrons defines an electron domain that is located principally on one atom. For example, the Lewis structure of NH3 has four electron domains around the central nitrogen atom (three bonding pairs and one nonbonding pair): nonbonding pair.. H N H H bonding electrons Each multiple bond in a molecule also constitutes a single electron domain. Thus, O3 has three electron domains around the central oxygen atom (a single bond, a double bond, and a nonbonding pair of electrons):...... :O.. O O.. In general, each nonbonding pair, single bond, or multiple bond produces an electron. In general, each nonbonding pair, single bond, or multiple bond produces an electron domain around the central atom. The VSEPR model is based on the idea that electron domains are negatively charged and therefore repel one another. Like the balloons above, electron domains try to stay out of one another’s way. The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them. In fact, the analogy between electron domains and balloons is so close that the same preferred geometries are found in both cases. Hence, the shapes of different ABn molecules or ions depend on the number of electrons domains surrounding the central A atom. The arrangement of electron domains about the central atom of an ABn molecule or ion is called its electron-domain geometry. In contrast, the molecular geometry is the arrangement of © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. only the atoms in a molecule or ion-any nonbonding pairs are not part of the description of the molecular geometry. In the VSEPR model, we predict the electron domain geometry. From knowing how many electron domains are due to nonbonding pairs, we can then predict the molecular geometry of a molecule or ion from its electron-domain geometry. EXERCISE 1. Use the VSEPR model to predict the molecular geometry of (a) O3, (b) SnC13- (c) IF5 Answers: (a) bent; (b) trigonal pyramid (c) Square pyramid 2. Predict the electron-domain geometry and the molecular geometry for (a) SeCl2, (b) CO32- Answers: (a) tetrahedral, bent; (b) trigonal planar, trigonal planar COVALEN T BONDING AND ORBITAL OVERLAP The marriage of Lewis's notion of electron-pair bonds and the idea of atomic orbitals leads to a model of chemical bonding called valence-bond theory. In the Lewis theory, covalent bonding occurs when atoms share electrons, which concentrates electron density between the nuclei. In the valence-bond theory, we visualize the buildup of electron density between two nuclei as occurring when a valence atomic orbital of one atom shares space, or overlaps, with that of another atom. The overlap of orbitals allows two electrons of opposite spins to share the common space between the nuclei, forming a covalent bond. For example, in H2, each atom of hydrogen has a single electron in a 1s orbital and as the orbitals overlap, electron density is concentrated between the nuclei. Because the electrons are simultaneously attracted to both nuclei, they hold the atoms together, forming a covalent bond. Similarly, the same idea applies to HCl where the 3p orbital of Cl overlaps with the 1s orbital of H. Consider the electron configuration of Be (1s22s2) in its ground state. On the basis of its electron configuration, Be cannot form a covalent bond because it does not have unpaired © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. electrons. However, the element forms divalent compounds such as BeH2, BeCl2 etc. Similarly, B has only one unpaired electron (1s22s22p1) and yet it is trivalent. How can we explain the valences of these elements on the basis of the number of unpaired electrons and overlap of atomic orbitals? This is only possible with the theory of hybridization, according to which different orbitals, before overlapping and bond formation, mix and pool their energy and form new orbitals known as hybrid orbitals. EXAMPLES i. BeF2 The valence shell electronic configuration of Be is 2s2. Since there are no unpaired electrons, Be cannot form covalent bonds in its ground state. Thus, in BeF2, the Be atom is not in its ground state but in the excited state. To get it in the excited state, one of the 2s electrons is "promoted" to a 2p orbital: 1s 2s 2p 1s 2s 2p The Be atom now has two unpaired electrons and can therefore form two covalent bonds with the F atoms. The 2s and 2p orbitals are then “combined” or “mixed” generating new orbitals. Like p orbitals, each of the new orbitals has two lobes. Unlike p orbitals, however, one lobe is much larger than the other. The two new orbitals are identical in shape, but their large lobes point in opposite directions. These two new orbitals are hybrid orbitals. Because we have hybridized one s and one p orbital, we call each hybrid an sp hybrid orbital. According to the valence-bond model, a linear arrangement of electron domains implies sp hybridization. Thus, for BeF2, the orbital diagram for the formation of the two sp hybrid orbitals is written as: © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. 1s sp 2p The electrons in the sp hybrid orbitals can form two electron bonds with the two fluorine atoms. ii. BF3 B in ground state 1s 2s 2p B in excited state 1s 2s 2p In BF3, mixing the 2s and two of the 2p orbitals yields three equivalent sp2 hybrid orbitals. These three hybrid orbitals are directed towards the three corners of an equilateral triangle in a plane having an angle of 120°. The three sp2 hybrid orbitals make three equivalent bonds with three fluorine atoms, leading to the trigonal planar geometry of BF3. iii. CH4 An s orbital can also mix with all three p orbitals in the same subshell. For example, the carbon atom in CH4 forms four equivalent bonds with the four equivalent bonds with four hydrogen atoms. The process results from the mixing of the 2s and all the three 2p atomic orbitals of carbon to create four equivalent sp3 hybrid orbitals. The repulsion between the four orbitals is smallest if they point to the corners of a regular tetrahedron and make a bond angle of 109°28ʹ. Each of the four sp3 hybrid orbitals is singly © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. occupied and overlaps with the 1s orbital of four hydrogen atoms and forms four equivalent bonds in CH4 molecule. The idea of hybridization is used in a similar way to describe the bonding in molecules containing nonbonding pairs of electrons. In H2O, for example, the electron domain geometry around the O atom is approximately tetrahedral. Thus, the four electron pairs can be envisioned as occupying sp3 hybrid orbitals. Two of the hybrid orbitals contain nonbonding pairs of electrons, while the other two are used to form bonds with hydrogen atoms. Hybridization Involving d Orbitals The concept of hybridization can be applied to molecules where the central atom has more than an octet of electrons around it, such as PF5 and SF6. This is achieved by utilizing unfilled d orbitals with the same value of the principal quantum number, n. Mixing one s orbital, three p orbitals, and one d orbital leads to five sp3d hybrid orbitals. These hybrid orbitals are directed toward the vertices of a trigonal bipyramid, e.g. in PCl5. Similarly, mixing one s orbital, three p orbitals, and two d orbitals gives six sp3d2 hybrid orbitals that are directed toward the vertices of an octahedron. Overall, hybrid orbitals provide a convenient model for using valence bond theory to describe covalent bonds in molecules with geometries that conform to the electron-domain geometries predicted by the VSEPR model. The picture of hybrid orbitals has limited predictive value. However, when we know the electron-domain geometry, we can employ hybridization to describe the atomic orbitals used by the central atom in bonding. The following steps allow us to predict the hybrid orbitals used by an atom in bonding: 1. Draw the Lewis structure for the molecule or ion. 2. Determine the electron-domain geometry using the VSEPR model. 3. Specify the hybrid orbitals needed to accommodate the electron pairs based on their geometric arrangement. These steps are illustrated by the figure below which shows how hybridization employed by N in NH3 is determined. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. EXERCISE 1. Indicate the hybridization of orbitals employed by the central atom in (a) NH2-, (b) SF4 Answers: (a) sp3 (b) sp3d 2. Predict the electron-domain geometry and the hybridization of the central atom in (a) SO32- (b) SF6. Answers: (a) tetrahedral, sp3; (b) octahedral, sp3d2 MULTIPLE BONDS In the covalent bonds we have considered thus far, the electron density is concentrated along the line connecting the nuclei {the internuclear axis). In other words, the line joining the two nuclei passes through the middle of the overlap region. These bonds are called sigma (σ) bonds. To describe multiple bonding, we must consider a second kind of bond that results from the overlap between two p orbitals oriented perpendicularly to the internuclear axis. This sideways overlap of p orbitals produces a pi (Π) bond. A Π bond is a covalent bond in which the overlap regions lie above and below the internuclear axis. In almost all cases, single bonds are σ bonds. A double bond consists of one σ bond and one Π bond, and a triple bond consists of one σ bond and two Π bonds. For example in ethylene, the σ bonding framework is formed from sp2 hybrid orbitals on the carbon atoms. The unhybridized 2p orbitals on the C atoms are used to make a Π bond. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. The Mole Concept-assignment In everyday life we use counting units such as a dozen (12 objects) and a gross (144 objects) to deal with modestly large quantities. In chemistry the unit for dealing with the number of atoms, ions, or molecules in a common-sized sample is the mole, abbreviated mol. A mole is the amount of matter that contains as many objects (atoms, molecules, or whatever objects we are considering) as the number of atoms in exactly 12 g of isotopically pure 12C. From experiments, scientists have determined this number to be 6.0221421 X 1023. Scientists call this number Avogadro's number, in honor of the Italian scientist Amedeo Avogadro (1776-1856). EXERCISE: Converting Moles to Number of Atoms 1. Calculate the number of H atoms in 0.350 mol of C6H12O6. Answers: Moles C6H12O6----> molecules C6H12O6----> atoms H = 2.53 X 1024 H atoms. 2. How many oxygen atoms are in (a) 0.25 mol Ca(NO3)2 and (b) 1.50 mol of sodium carbonate? Answers: (a) 9.0 x 1023, (b) 2.71 X 1024 Oxidation-Reduction Reactions Oxidation refers to the loss of electrons, and reduction refers to the gain of electrons. Thus, oxidation-reduction reactions occur when electrons are transferred from an atom that is oxidized to an atom that is reduced. The concept of oxidation state/oxidation number was devised as a way of tracking track of the electrons in oxidation-reduction reactions. Oxidation occurs when the oxidation number increases, whereas reduction occurs when the oxidation number decreases. For example, consider the reaction that occurs when zinc metal is added to a strong acid: 0 +1 +2 0 Zn(s) + 2H+(aq) Zn2+(aq) + H2(g) The oxidation number of Zn changes from 0 to +2, and that of H changes from + 1 to 0. Thus, this is an oxidation-reduction reaction. Electrons are transferred from zinc atoms to hydrogen ions, and therefore Zn is oxidized and H+ is reduced. Hence, oxidation is the process of donating electrons, which is accompanied by a rise in the oxidation state. The substance that makes it © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. possible for another substance to be oxidized is called either the oxidizing agent or the oxidant. The oxidizing agent removes electrons from another substance by acquiring them itself; thus, the oxidizing agent is itself reduced. Similarly, a reducing agent, or reductant, is a substance that gives up electrons, thereby causing another substance to be reduced. The reducing agent is therefore oxidized in the process. Consider the following redox reaction that occurs in the nickel-cadmium (nicad) battery, a rechargeable "dry cell" used in battery-operated devices, to generate electricity: 0 +4 -2 +1 -2 +2 -2 +1 +2 -2 +1 Cd(s) + NiO2(s) + 2H2O(l) Cd(OH)2(s) + Ni(OH)2(s) Cd increases in oxidation state from 0 to +2, and Ni decreases from +4 to +2. Because the Cd atom increases in oxidation state, it is oxidized (loses electrons) and therefore serves as the reducing agent. The Ni atom decreases in oxidation state as NiO2 is converted into Ni(OH)2. Thus, NiO2 is reduced (gains electrons) and therefore serves as the oxidizing agent. EXERCISE Identify the oxidizing and reducing agents in the oxidation-reduction reaction 2 H2O(1) + Al(s) + MnO4-(aq) ---> Al(OH)4-(aq) + MnO2(s) Answer: Al(s) is the reducing agent; MnO4-(aq) is the oxidizing agent. BALANCING OXIDATION-REDUCTION EQUATIONS Whenever we balance a chemical equation, we must obey the law of conservation of mass: The amount of each element must be the same on both sides of the equation. (Atoms are neither created nor destroyed in any chemical reaction.) In addition, gains and losses of electrons must be balanced. In other words, if a substance loses a certain number of electrons during a reaction, then another substance must gain that same number of electrons. (Electrons are neither created nor destroyed in any chemical reaction.) In many simple chemical reactions, balancing the electrons is handled "automatically"; we can balance the equation without explicitly considering the transfer of electrons. Many redox reactions are, however, more complex and cannot be balanced easily without taking into account the number of electrons lost and gained in the course of the reaction. In this section we examine the method of half reactions, which is a systematic procedure for balancing redox equations. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Half-Reactions Although oxidation and reduction must take place simultaneously, it is often convenient to consider them as separate processes. For example, the oxidation of Sn2+ by Fe3+: Sn2+(aq) + 2Fe3+(aq) Sn4+(aq) + 2Fe2+(aq) Oxidation: Sn2+(aq) Sn4+(aq) + 2e- half-reactions Reduction: 2Fe3+(aq) + 2e- 2+ 2Fe (aq) Notice that electrons are shown as products in the oxidation process, whereas electrons are shown as reactants in the reduction process. The use of half-reactions provides a general method for balancing oxidation-reduction equations. Generally, H+ (for acidic solutions), OH- (for basic solutions), and H2O are often involved as reactants or products in redox reactions. Unless H+, OH- , or H2O are being oxidized or reduced, they do not appear in the skeleton ionic equation. Their presence, however, can be deduced during the course of balancing the equation. For balancing a redox reaction that occurs in acidic aqueous solution, the procedure is as follows: 1. Divide the equation into two half-reactions, one for oxidation and the other for reduction. 2. Balance each half-reaction. a) First, balance the elements other than H and O. b) Next, balance the O atoms by adding H2O as needed. c) Then, balance the H atoms by adding H+ as needed. d) Finally, balance the charge by adding e- as needed. 3. Multiply the half-reactions by integers, if necessary, so that the number of electrons lost in one half-reaction equals the number of electrons gained in the other. 4. Add the two half-reactions and, if possible, simplify by canceling species appearing on both sides of the combined equation. 5. Check to make sure that atoms and charges are balanced. As an example, consider the reaction between permanganate ion (MnO4-) and oxalate ion (C2O42-) in acidic aqueous solution. When MnO4- is added to an acidified solution of C2O42-, the © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. deep purple color of the MnO4- ion fades, as illustrated below. Bubbles of CO2 form, and the solution takes on the pale pink color of Mn2+. Titration of an acid solution of Na2C2O4 with KMnO4(aq): (a) As it moves from the burette to the reaction flask, the deep purple MnO4- is rapidly reduced to extremely pale pink Mn2+ by C2O42-. (b) Once all the C2O42-in the flask has been consumed, any MnO4- added to the flask retains its purple color, and the end point corresponds to the faintest discernible purple color in the solution. (c) Beyond the end point the solution in the flask becomes deep purple because of excess MnO4-. The ionic equation for the reaction can be written as: MnO4-(aq) + C2O42-(aq) Mn2+(aq) + CO2(g) ▪ To complete and balance this equation, we first write the two half-reactions (step 1). MnO4-(aq) Mn2+(aq) C2O42-(aq) CO2(g) ▪ Next, complete and balance each half-reaction. First, we balance all the atoms except for H and O (step 2a). MnO4-(aq) Mn2+(aq) C2O42-(aq) 2CO2(g) ▪ Next we balance O (step 2b). © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. MnO4-(aq) Mn2+(aq) + 4H2O(l) ▪ The eight hydrogen atoms now in the products must be balanced by adding 8 H+ to the reactants (step 2c): 8H+(aq) + MnO4-(aq) Mn2+(aq) + 4H2O(l) ▪ There are now equal numbers of each type of atom on the two sides of the equation, but the charge still needs to be balanced. The total charge of the reactants is 8(1+) + (1-) = 7+, and that of the products is (2+) + 4(0) = 2+. To balance the charge, we must add five electrons to the reactant side (step 3d): 5e- + 8H+(aq) + MnO4-(aq) Mn2+(aq) + 4H2O(l) ▪ Balance the charge in the other half-reaction: C2O42-(aq) 2CO2(g) + 2e- ▪ Now we need to multiply each half-reaction by an appropriate integer so that the number of electrons gained in one half-reaction equals the number of electrons lost in the other (step 3). Thus, 10e- + 16H+(aq) + 2MnO4-(aq) 2Mn2+(aq) + 8H2O(l) 5C2O42-(aq) 10CO2(g) + 10e- 16H+(aq) + 2MnO4-(aq) + 5C2O42-(aq) 2Mn2+(aq) + 8H2O(l) + 10CO2(g) If a redox reaction occurs in basic solution, the equation must be completed by using OH- and H2O rather than H+ and H2O. One way to balance these reactions is to balance the half- reactions initially as if they occurred in acidic solution. Then, count the H+ in each half-reaction, and add the same number of OH to each side of the half-reaction. In essence, what you are doing is "neutralizing" the protons to form water on the side containing H+, and the other side ends up with the OH-. This procedure is illustrated in the following example. CN-(aq) + MnO4-(aq) CNO-(aq) + MnO2(s) (basic solution) Step 1: Half-reactions: CN-(aq) CNO-(aq) MnO4-(aq) MnO2(s) Step 2: Balance each half-reaction as if it took place in acidic solution. © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. H2O(aq) + CN-(aq) CNO-(aq) + 2H+(aq) + 2e- 3e- + 4H+(aq) + MnO4-(aq) MnO2(s) + 2H2O(l) Step 3: We now add OH- to both sides of both half reactions to neutralize H+. 2OH-(aq) + H2O(l) + CN-(aq) CNO-(aq) + 2H+(aq) + 2e- + 2OH-(aq) 3e- + 4H+(aq) + MnO4-(aq) + 4OH-(aq) MnO2(s) + 2H2O(l)+ 4OH-(aq) Step 4: We now "neutralize" H+ and OH- by forming H2O when they are on the same side of either half-reaction, and then cancel the water molecules that appear as both reactants and products: 2OH-(aq) + H2O(l) + CN-(aq) CNO-(aq) + 2H2O(l) + 2e- 3e- + MnO4-(aq) + 4H2O(l) MnO2(s) + 2H2O(l)+ 4OH-(aq) 2OH-(aq) + CN-(aq) CNO-(aq) + H2O(l) + 2e- 3e- + MnO4-(aq) + 2H2O(l) MnO2(s) + 4OH-(aq) Step 5: Equalize the number of e-. 6OH-(aq) + 3CN-(aq) 3CNO-(aq) + 3H2O(l) + 6e- 6e- + 2MnO4-(aq) + 4H2O(l) 2MnO2(s) + 8OH-(aq) 3CN-(aq) + 2MnO4-(aq) + H2O(l) 3CNO-(aq) + 2MnO2(s) + 2OH-(aq) EXERCISE 1. Complete and balance the following equations by the method of half-reactions: a) Cr2O72-(aq) + Cl-(aq) Cr3+(aq) + Cl2(g) (acidic solution) Answer: 14H+(aq) + Cr2O72-(aq) + 6Cl-(aq) 2Cr3+(aq) + 3Cl2(g) + 7H2O(l) Cu(s) + NO3-(aq) Cu2+(aq) + NO2(g) (acidic solution) b) Answer: 4H+(aq) + Cu(s) + 2NO3-(aq) Cu2+(aq) + 2NO2(g) + 2H2O(l) NO2-(aq) + Al(s) NH3(aq) + Al(OH)4-(aq) (basic solution) c) Answer: NO2-(aq) + 2Al(s) + 5H2O(l) +OH-(a) NH3(aq) + 2Al(OH)4-(aq) d) Cr(OH)3(s) + ClO-(aq) CrO42-(aq) + Cl2(g) (basic solution) © 2016  Inorganic Chemistry I | Dr. Nyamato G.S. Answer: 2Cr(OH)3(s) + 6ClO-(aq) 2CrO42-(aq) + 3Cl2(g) + 2OH-(aq) + 3H2O(l) © 2016