Principles Of Inorganic Chemistry PDF

elab notes library SCH 100 Fundamentals of Inorganic Chemistry Course Outline The early theories of atomic structure. The fundamental particles of the ato...

elab notes library SCH 100 Fundamentals of Inorganic Chemistry Course Outline The early theories of atomic structure. The fundamental particles of the atom. Planck’s quantization of energy and the photoelectric effect. Rutherford’s planetary model and Bohr theory of atom. Failure of the Bohr theory. Qualitative treatment of the atomic orbitals (s, p, d and f).The aufbau principle and the periodic table. Common oxidation state of the element. Natural occurring and artificially made isotopes and their applications. Hybridization of atomic orbitals and shapes of simple molecules and ions. Electronegativity, electron affinity and ionization energy. Nature of ionic and covalent compounds as influenced by the above factors. The mole concept and its applications. General concepts of acid and bases. Strong and weak acids and bases. pH calculations. Balancing of redox reactions. Practicals. Identification of ions and cations in solution and titrations. Website: maktaba.elab.co.ke WhatsApp: +254 704 986 447 Email: [email protected] Table of Content Course Outline............................................................................................................................i Table of Content.........................................................................................................................ii Introduction................................................................................................................................1 UNIT OBJECTIVES..................................................................................................................2 Some Useful References and Recommended Reading:.............................................................2 Unit 1........................................................................................................................................3 1.0 Atomic Structure:...........................................................................................................3 1.1 Classical View of Atomic Structure...........................................................................3 1.2 Historical Development of Atomic Theory................................................................4 1.2.1 Thomson’s Plum Pudding or Raisin Bun Atomic Model (1856-1940).................4 1.2.2 Rutherford’s Nuclear Model of Atom (1871-1937)...............................................5 1.2.3 The Nature of Electromagnetic Radiation..............................................................6 1.2.4 Hydrogen Spectrum...............................................................................................7 1.2.5 Bohr Model of Atom (1913)..................................................................................9 1.2.5.1 Failures of the Bohr Model..................................................................................11 Unit 2......................................................................................................................................12 2.0 Quantum Model of an Atom........................................................................................12 2.1 De Broglie Equation- Dual Nature of Matter...........................................................13 2.2 Heisenberg Uncertainty Principle............................................................................14 2.3 Wave-Like Property of an Electron.........................................................................14 2.4 Schrödinger Wave Equation.....................................................................................15 2.5 Quantum Numbers and their Troperties...................................................................16 2.6 Atomic Wavefunctions.............................................................................................17 2.7 Pictorial Representation of Atomic Orbitals............................................................20 2.8 Nodal Surfaces and Electron Density Contour Plots of Atomic Orbitals................23 2.9 Electronic Configuration..............................................................................................23 2.9.1 Energy Levels in Hydrogen and Other Atoms.....................................................23 2.9.2 Aufbau Principle..................................................................................................26 2.9.3 Order of Orbital Filling in Polyelectronic Atoms:...............................................26 Unit 3......................................................................................................................................28 3.0 Periodic Table..............................................................................................................28 3.1 Periodic Trends of Atomic Parameters........................................................................29 3.2 Shielding..................................................................................................................29 3.3 Periodic Trend in Effective Nuclear Charge............................................................30 3.4 Sizes of Atoms and Ions...........................................................................................31 3.5 Periodic Trend in Atomic Radii...............................................................................32 3.6 Periodic Trend in Ionic Radii...................................................................................32 3.7 Periodic Trend in the First Ionization Energy..........................................................33 3.9 Periodic Trend in Electron Affinity.........................................................................36 3.10 Periodic Trend in Electronegativity.........................................................................37 3.11 Common Oxidation State of the Elements...............................................................38 Unit 4.....................................................................................................................................40 4.0 Electronic Structure and Chemical Bonding................................................................40 4.1 Lewis Theory...........................................................................................................40 ii 4.1.1 Lewis Symbols and Lewis Structures..................................................................40 4.1.2 Lewis Structures and Resonance..........................................................................42 4.2 Molecular Geometry and Bonding Theories............................................................42 4.2.1 Valence Shell Electron Pair Repulsion Theory (VSEPR)....................................42 4.2.3 Covalent Bonding and Orbital Overlap................................................................43 4.3 Valence Bond Theory (VBT)...................................................................................43 4.4 Molecular Geometry and Hybrid Orbitals...............................................................45 4.5 Hybridization Involving d Orbitals..........................................................................49 4.6 Multiple Bonds and Orbital Overlaps......................................................................51 4.7 Resonance Structures and Hybrid Orbitals..............................................................57 Unit 5.....................................................................................................................................60 5.0 Acid and Bases.............................................................................................................60 5.1 Lewis Definition.......................................................................................................61 5.2 Ionic Equilibrium in Aqueous Solutions..................................................................61 5.3 The Strength of the Acids and Bases.......................................................................62 5.4 Quantitative Measurement of pH.............................................................................62 5.5 The Dissociation of Water........................................................................................64 5.6 Important Generalization..........................................................................................64 5.7 Dissociation Constant of Acids and Bases...............................................................65 5.8 Buffer Solution.........................................................................................................66 5.8.1 An Equation for Buffer Solutions........................................................................66 5.8.2 Calculating pH Changes in Buffer Solutions.......................................................68 Unit 6.....................................................................................................................................70 6.0 Redox Reactions...........................................................................................................70 6.1 How Can We Tell When Redox Reaction is Taking Place?....................................70 6.2 Balancing Redox Reaction.......................................................................................71 6.2.1 Balancing Redox Reaction by Oxidation Number Method.................................71 6.2.2 Balancing Redox Reaction the Half-Equation Method........................................72 Unit 7.....................................................................................................................................76 7.0 Radioactivity................................................................................................................76 7.1 Characteristic of Radioactivity.................................................................................76 7.2 Types of Radiation...................................................................................................76 7.3 Effect of Radioactive Decay on Parent Nuclide.......................................................77 7.3.1 α-Particle Decay...................................................................................................77 7.3.2 β-Particle Decay...................................................................................................77 7.3.3 γ-Particle Decay...................................................................................................78 7.4 Properties of Radiation.............................................................................................78 7.5 Rate of Radioactive Decay and Half-Life................................................................79 7.6 Nucleus Fission and Fusion.....................................................................................80 7.6.1 Nucleus Fission....................................................................................................80 7.6.2 Nucleus Fusion.....................................................................................................80 iii  Introduction Fundamental of Inorganic chemistry is a core unit in chemistry at the undergraduate level for the Bachelor of Education as well as Bachelor of Science degrees. The unit aims at introducing the learner to various basic concepts in chemistry. It endeavours to equip the learner with sufficient knowledge to enable him/her to comprehend and relate to other concepts encountered at a later stage, as he/she dwells more in chemistry and other related sciences. Fundamental of Inorganic chemistry course requires a learner to have a good understanding of ‘O’ level chemistry. This is because it builds on the chemistry knowledge acquired at that level. The study unit begins with atomic structure with their electronic configurations, elements arrangement in the periodic table, bonding in molecules and the structure and shapes of molecules. This unit does not involve practical lessons, rather it emphasizes on acquisition of theoretical concepts. Practical lessons in this field of study would require equipment and skills beyond the scope of this course. In this unit you should be able to answer the questions provided in the text. The purpose of the questions is to enable you to evaluate your understanding of thoroughly the concepts presented in the lectures. Answers are provided at the end of this unit and you should not look at them before you are through with answering the questions. You should therefore be honest to yourself as you answer the questions. 1  COURSE OBJECTIVES At the end of this course you should be able to; (a) Describe the atomic structure (b) Explain the Schrödinger equation (c) Explain Pauli’s Exclusion Principle and write electronic configuration (d) Discuss the periodicity of the periodic table (e) Identify the shapes of orbitals (f) Discuss the various types of structures of molecules through their bonding. (g) Explain the structure of simple molecules in terms of Valence Shell Electron Pair Repulsion (VSEPR) Model, Molecular Orbital Theory, and Hybridization of Atomic Orbitals. h) Explain the concepts of acids and bases and calculate the pH. i) Identify and balance redox reactions j) Understand basics of radioactivity k) Use ideas, concepts and skills acquired in learning chemistry to solve problems in everyday life. Title of Couse: FUNDAMENTAL OF INORGANIC CHEMISTRY Code SCH 100 Lecturer(s) Prescribed Textbook None Some Useful References and Recommended Reading: 1 Petrucci R. H. and Harwood W. S., “General Chemistry: Principles and Modern Applications”. 7th edition. Prentice Hall. New Jersey. 2 McMarry J. and Fay R. C., “Chemstry”. Prentice Hall. New Jersey. 3 Raymond Chang, “Essential Chemistry”. McGraw-Hill Companies, Inc. Toronto 4 Hill G. C. and Holman J. S., “Chemistry in Context” 4 th edition 1995, Thomas Nelson and Sons Ltd Surry UK. 5 Any other college inorganic chemistry text book. 6 Internet Search WWW GENERAL There is no single prescribed textbook and you will be provided with comprehensive notes on the relevant subject matter. However, you may consult the above list of reference books for further information. Remember, what we do as lecturers will enable you to obtain your degree; what you do will make you a chemist. Reference books may be obtained from the library and /or from your lecturer 2  Unit 1 1.0 Atomic Structure: Objectives of unit 1 At the end of unit 1, one should be able to  Understand nature of electrons, protons and neutrons  Relate early theories of atomic structures and the experiments that led to them  Understand the nature of electromagnetic radiation  Understand the hydrogen spectrum and relate it to the Bohr atomic theory  Explain the failures of Bohr atom especially for multi-electron atom 1.1 Classical View of Atomic Structure The classical view of atomic structure was constructed with the body of knowledge accumulated in physics over several centuries preceding the 20th century. This body of knowledge is called classical physics. Known facts: Through experience, physicists have identified a long list of particles which make up the atoms. The most fundamental particles are: 1 Electrons 2 Protons 3 Neutrons Electrons The electron is negatively charged with a charge of -1.602189x10 -19 C (Coulombs). For convenience the charge of atomic and sub-atomic particles are described as multiple of this value (also known as electronic charge). Thus the charge of electron is usually referred to as -1. The mass of electron me=9.109534x10-31 kg =5.485x10-4 amu 1 atomic mass unit (amu)=1.660565x10-27 kg Symbol of electron is e-1. Protons The protons has a charge of +1 electronic charge or +1.602189x10-19 C The mass of proton mp=1.672648x10-27 kg =1.007276 amu Symbol p. Neutrons Neutrons have no charge. They are electrically neutral The mass of neutron mn=1.674954x10-27 kg =1.008665 amu 3 Symbol n. Atomic Mass Unit The mass of an atom is extremely small. The units of mass used to describe atomic particle is the atomic mass unit or (amu). An atomic mass unit (amu) is equal =1.660565x10-27 kg or =1.660565x10-24 g Hence mass of proton=1.007276 amu neutron=1.008665 amu electron=5.485x10-4 amu  From this comparison, we can see that the mass of proton and neutron are nearly identical.  The nucleus (protons plus neutrons) contain virtually all the mass of the atom.  The electrons while equal and opposite in charge to the protons have only 0.005% mass. 1.2 Historical Development of Atomic Theory The challenge was how these sub-atomic particles are arranged in an atom. Different atomic models were proposed. 1.2.1 Thomson’s Plum Pudding or Raisin Bun Atomic Model (1856-1940) Thomson didn’t know exactly how positive electric charge is distributed in an atom, so he considered the case that was easiest to describe mathematically. He developed a model in which a positive charge is uniformly distributed in a electron imbedded sphere in such a way that attraction of the positive charge just offsets the repulsion among the electrons. This somehow resembles raising pudding. Figure 1.1. Thomson’s plum pudding or raisin bun atomic model 4 1.2.2 Rutherford’s Nuclear Model of Atom (1871-1937) Rutherford used α-particles (alpha particles), doubly ionized helium atom, He 2+ to probe the structure of matter. Based on Thomson’s model of the atom Rutherford expected that most α particles would pass through atoms undeflected. However, also he expected that any of the positively charged α-particles that come close to an electron should be deflected to some extent. By measuring such deflection he hoped to gain information about distribution of electron in an atom. Rutherford assigned his assistant, Hans Geiger and an undergraduate student Ernest Marsden an experiment to bombarded very thin foil of metal such as gold, silver and platinum with α-partilces. They found that most of the particles went right through the foil and undeflected or deflected only slightly. Figure 1.2 Angular Distribution of Rutherford Scattering This was just what Rutherford had expected. However, much to Rutherford surprise, a few particles were deflected sharply and once in a while α-particles would bounce right back to the source. “It is about as incredible as of you had fired an inch shell at a piece of tissue paper and it came back and hit you”.-Rutherford Figure 1.3 Rutherford planetary or nuclear atomic model All the positive charge of an atom is concentrated at the centre of an atom in a tiny core called the nucleus. When positively charged α-particles approach a positively charged nucleus it is repelled and therefore sharply deflected. Electrons remain in the atom because they are strongly attracted to the positively charged nucleus. 5 1.2.3 The Nature of Electromagnetic Radiation Electromagnetic radiation consists of packets (quanta) of oscillating electric and magnetic fields which are perpendicular to one another and traveling from the source in the form of a harmonic wave. The harmonic wave is characterized by properties such as frequency, wave length,  and the wave number, -1. Figure 1.4 Harmonic wave The wave length , is the distance between two successive crests or troughs in a wave and is expressed in meters, m. The frequency is the number of waves passing a point in unit time (usually one second). Its unit is the Hertz, Hz (i.e. cycles per second). The wave length and frequency are related by: c   where c is the velocity of the wave in the medium. In vacuum c = 2.998x108ms-1. The reciprocal of frequency is the period of oscillation, T. It indicates the time taken for one oscillation to pass a point. Hence, 1 T  The reciprocal of the wavelength, -1, is known as the wave number. The wave number indicates the number of waves accommodated in unit length. Thus, since c   then, 1    c 6 The SI unit for wave number is reciprocal metres, m -1, although most of the literature values are given in cm-1.The peak height of a wave is called the amplitude, A, of the wave. The electric and the magnetic fields interact with matter leading to a spectrum. The packets of electromagnetic radiation are known as quanta (singular: quantum) or photons. Each photon has energy, E, given by: E = hv where h = Planck’s constant = 6.6262x10-34Js. SAQ 1. For radiation having  = 2.0x10-7 m, calculate: (i) E (kJmole-1) (ii) v (iii) -1 Figure 1.5 The Electromagnetic Spectrum 1.2.4 Hydrogen Spectrum Each element display a characteristic spectrum as first pointed out by Kirchhorff in 1859. The law governing the distribution of lines in a spectrum was discovered by Balmer and Rydbeg. The interpretation of this law in terms of atomic structure began with the work of Bohr in 1913. It revealed that a study of spectra could provide a wealthy of information about the atomic structure. The study of these spectra has provided a key to the interpretation of many of the spectra of more complex atoms. In the visible region, the spectrum of hydrogen was known to consist of 4 main lines: Red 656.3 nm Blue 486.1 nm Violet 434.0 and 410.2 nm Denoted as Hα, Hβ, Hγ and Hδ. 7 Near the ultra violet there were other lines getting closer together converging to a limit of 364.6 nm continous H H H H spectrum (ultravioltet) 434.0 nm 486.1 nm 364.6 nm 656.3 nm (violtet) 410.2 nm (red) (red) Figure 1.6 The Balmer series of atomic hydrogen excited by electric discharge. The dark lines correspond to the bright emission lines of the spectrum. It was discovered by Balmer as early as 1885, that the wavelength (λ) of the nine lines, then known in this spectrum, could be accurately expressed by a single formula; kn 2  (1) n 2  22 Where k is a constant and n is an integer. The different wavelength corresponding to the lines Hα, Hβ, Hγ and Hδ etc. are obtained by putting the integers 3, 4, 5, 6 etc respectively in place of n. This set of line constitutes a spectral series and is known as the Balmer series. Expressing in terms of wave numbers, equation (1) is rearranged as 1  1 1    R 2  2  (2)  2 n  Where R is a constant called the Rydberg constant; R=109677.8 cm-1. n was an integer which can take all values greater than 2, n=3,4, 5…∞.  - the wave number, i.e. the number of wavelength in unit length. The hydrogen spectrum was investigated in the far (UV) ultra violet, IR (infra red) regions and revealed that there were few other series such as Lyman (UV region), Paschen and Brackett and Pfund. All these series were found to be in excellent agreement with the general equation 1  1 1    R 2  2  (3)   n1 n2  This is the universal formula for the atomic hydrogen spectrum. Where n1 and n2 are integers somehow defining the energy stages of the atom. 8 The atomic spectrum of hydrogen atom Series Region n1 N2 Lyman Ultravilotet 1 2, 3, 4, 5…..∞ Balmer Visible 2 3, 4, 5, 6…..∞ Paschen Near infrared 3 4, 5, 6, 7…..∞ Brackett Far infrared 4 5, 6, 7, 8…..∞ Pfund Far infrared 5 6, 7, 8, 9…..∞ Though equation (3) represented with great precision the entire known spectrum of atomic hydrogen, it was however an empirical formula described from experiment. The interpretation of this correct but underived formula was first given by theory of Niels Bohr (1913). 1.2.5 Bohr Model of Atom (1913) In order to explain the hydrogen spectrum, Bohr made the following assumptions governing the behaviour of electrons: 1. Electrons revolve in orbits of specific radius around the nucleus without emitting the radiation. 2. Within each orbit, each electron has a fixed amount of energy; electrons in orbits further from the nucleus have greater energies. 3. An electron may ‘jump’ from one orbit of high energy to another of lower causing the energy difference to be emitted as a photon of electromagnetic radiation such as light. 4. An electron may absorb a photon of radiation and jump from a lower-energy orbit to a higher-energy one. The energy emitted or absorbed corresponds to the difference in the energy for the initial and final state of the system. E final  E initial  E  hv Of the entire possible orbit only certain ones were acceptable – namely which had a specified angular momentum. He assumed circular electron orbit with quantized electronic angular momentum. 9  Figure 1.7. Bohr atomic model One of the implication of these quantized energy states is that only certain photon energy are allowed when electrons jump down from high to lower levels producing the hydrogen spectrum. n=6 n=5 n=4 n=3 n=2 n=1 Lyman Balmer Paschen Pfund series series series series Figure 1.8. Various series in hydrogen spectrum. For hydrogen the energy of electron in a n energy level is given by: Z 2 me 4 1 18 Z 2 En   2 2 2  2.18 x10 J 8h  0 n n2 or 10  Z 2 me 4 1 Z2 E n   2 2 2  13.6 2 eV 8h  0 n n Where m-mass of electron 9.1079x10-31 kg e-electronic charge 1.602x10-19 C h-Plank’s constant 6.626x10-34 J s ε0-permitivity of free space 8.854188x10-12 C2 s2 kg-1 m-3 Z-nuclear charge E  E n 2  E n1 1 1 E  2.18 x1018 Z 2  2  2  J  n1 n2  or  1 1  E  13.6 Z 2  2  2  eV  n1 n 2  1.2.5.1 Failures of the Bohr Model While the model was a major step towards understanding the quantum theory of the atom, it is not in fact a correct description of the nature of electron orbit. Some of the shortcomings of the models are:- 1. It fails to provide any understanding why some spectral lines are brighter than others. 2. There is no mechanism for the calculation of transition probability. 3. The Bohr model treats electrons as if they were miniature planet with definite radius and momentum. This is a direct violence of the Heisenberg uncertainty principle which dictates that position and momentum cannot be simultaneously determined. The Bohr model gives us a basic conceptual model of electrons orbit and energies. The precise details of spectra and charge distribution must be left to quantum mechanical calculations as with the Schrödinger equation. 11  Unit 2 Objectives of Unit 2  Provide evidence that matter has both wave and particle like properties  Relate particle and waves through the de Broglie equations  Explain the Heisenberg uncertainty principles  Understand the four Quantum numbers and how they relate with atomic orbitals  Draw the shapes of the atomic orbitals  Write electronic configurations for atoms and ions 2.0Quantum Model of an Atom Our current understanding of the electronic structure of an atom is expressed in terms of quantum mechanics. A fundamental concept of quantum mechanics is that all matter has wave and particle-like properties. 2.1 The Photoelectric Effect The photoelectric effect refers to the emission, or ejection, of electrons from the surface of, generally, a metal in response to incident light. Energy contained within the incident light is absorbed by electrons within the metal, giving the electrons sufficient energy to be 'knocked' out of, that is, emitted from, the surface of the metal. Using the classical Maxwell wave theory of light, the more intense the incident light the greater the energy with which the electrons should be ejected from the metal. That is, the average energy carried by an ejected (photoelectric) electron should increase with the intensity of the incident light. In fact, Lénard found that this was not so. Rather, he found the energies of the emitted electrons to be independent of the intensity of the incident radiation. Einstein (1905) successfully resolved this paradox by proposing that the incident light consisted of individual quanta, called photons that interacted with the electrons in the metal like discrete particles, rather than as continuous waves. For a given frequency, or 'color,' of the incident radiation, each photon carried the energy E = hv, where h is Planck's constant and v is the frequency. Increasing the intensity of the light corresponded, in Einstein's model, to increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant). Clearly, in Einstein's model, increasing the intensity of the incident radiation would cause greater numbers of electrons to be ejected, but each electron would carry the same average 12 energy because each incident photon carried the same energy. [This assumes that the dominant process consists of individual photons being absorbed by and resulting in the ejection of a single electron.] Likewise, in Einstein's model, increasing the frequency f, rather than the intensity, of the incident radiation would increase the average energy of the emitted electrons. Both of these predictions were confirmed experimentally. Moreover, the rate of increase of the energy of the ejected electrons with increasing frequency, which can be measured, enables one to determine the value of Planck's constant h. The photoelectric effect is perhaps the most direct and convincing evidence of the existence of photons and the 'corpuscular' nature of light and electromagnetic radiation. That is, it provides undeniable evidence of the quantization of the electromagnetic field and the limitations of the classical field equations of Maxwell. 2.2 De Broglie Equation- Dual Nature of Matter Light can behave both as a wave and as particles (photons). Likewise all matter (e.g., electrons, protons & neutrons) can also behave as waves. From Einstein relativity theory, the fundamental law relating energy E, rest mass m0 and momentum p of a particle is 2 E    p  m0 c 2 2 2 c E The rest mass of a photon is zero, so m0=0 and therefore momentum is p  c From Plank’s quantum theory E  h Therefore E  h  mc 2 But p=mc h h p  mc   c  h Implying  p = wavelength of the moving particle; h: Planck's constant 6.626 x 10-34 J.s m: mass of the moving particle. That is, all particles in motion have a wavelength that depends on the particle’s momentum. The larger the momentum, the smaller the wavelength. 13  In 1927, Davisson and Germer at Bell Laboratories showed that when a beam of electrons was directed at a nickel crystal, a diffraction pattern was observed. 2.2 Heisenberg Uncertainty Principle Due to the dual nature of matter, both particles and wavelike properties, it is impossible to simultaneously know both the position and momentum of an object as small as an electron. h xp  2 Δx= errors in position Δp= errors in momentum 2.3 Wave-Like Property of an Electron An electron in an atom is viewed as a standing wave. Some common examples of standing waves are: a string attached at both ends to produce a musical tone in a guitar and violin. Figure 2.1 standing wave We use the mathematical function Ψ (called wavefunction) to describe the wave-like behavior of an electron in a region of space called the atomic orbital.  Ψ has positive and negative amplitudes, like any wave. 14  Figure 2.2  Due to the wave-like behavior of an electron, we cannot pin down its position and momentum at the same time (Heisenberg Uncertainty Principle).  In other words, we do not know the exact location of an electron and how it moves from one spot to another in an atom.  Instead, we can only speak of the probability of finding an electron in a given volume of space. This is given by the function Ψ2. 2.4 Schrödinger Wave Equation  Based on the wave-particle dual nature of electron, Schrödinger developed a partial differential equation to describe the behavior of an electron around an H atom. He received Nobel Prize in 1933. Schrödinger Equation for a hydrogen atom  This equation shows the relationship between the wave function of the electron Ψ, and E and V, the total and potential energies of the system, respectively. The derivation of this equation is beyond the scope of this course (will be derived in SCH 200).  There are many solutions to the Schrödinger's equation. Each solution is represented by the wavefunction, Ψ, which describes an atomic orbital. The Uncertainty Principle tells us that we cannot pin down the exact location and momentum of an electron at the same time. So chemists speak of "electron cloud" or electron density around a nucleus.  An atomic orbital is defined as the boundary surface encloses 95% of the electron density for a particular wavefunction Ψ. Each atomic orbital (Ψ) may be uniquely defined by a set of three quantum numbers: 15  n (the principal quantum number); l (the orbital angular quantum number) and ml (the magnetic quantum number).  Since electron behaves as if it is spinning about an axis, a spin quantum number m s is also required to uniquely described an electron in an atomic orbital. Figure 2.2 Spinning electron 2.5 Quantum Numbers and their Properties Symbol Name Allowed Properties Values n Principal n = 1, 2, 3,  determines the size and energy of an atomic orbital Quantum 4,... Number  As n increases, the number of allowed orbitals increases, the size and energies of those orbitals also increase. l Orbital l = 0, 1, 2,...,  Describe the shape of an atomic orbital Quantum n-1 Number ml Magnetic ml = -l,..., -(l-  Describe the directionality of an atomic orbital Quantum 1), 0, 1, 2,... Number +l ms Spin ms = - ½, + ½  Describes the orientation of the electron spin in space Quantum Number Orbitals with different l values are known by the following labels: lL 0 1 2345… Label s p dfgh… 16 2.6 Atomic Wavefunctions 1. A wavefunction ψ describes an atomic orbital. For most calculations, it is simpler to solve the wave equation if ψ is converted from the Cartesian coordinates (x, y, z) to spherical Ψ coordinates (r, θ,φ). The two sets of coordinates are related by: x  r sin  cos  y  r sin  sin  z  r cos Figure 2.3. The relationship between Cartesian and polar coordinates (diagram taken from Atkins & Shriver). 2 In spherical coordinates, y can be factored into a radial wavefunction R, and an angular wavefunction A: ( x , y , z )  R( r ) A( , ) 3 Radial wavefunction R(r):  Describes how the electron density changes with distance from the nucleus  s orbitals have finite electron density [ R (r )  0 ] at the nucleus but this drops off exponentially as the distance from the nucleus increases.  Other orbitals (e.g., p and d orbitals) have zero electron density [R (r) = 0] at the nucleus. 17 Figure 2.4 Plot of Radial Wavefunction (in atomic units) versus distance r (in atomic units) from the nucleus (diagram from Miessler & Tarr).  The point at which the radial wavefunction R (r )  0 (except the origin) is called a radial node.  The sign of the radial wavefunction R (r) changes (from +ve to -ve or vice versa) after passing the radial node  The number of radial nodes for a given orbital is given by: [ n  (l  1) ].  ns orbitals have (n-1) radial nodes. E.g. 2s has 1 radial node.  np orbitals have (n-2) radial nodes. e.g. 2p has 0 radial node, 3p has 1 radial node.  nd orbitals have (n-3) radial nodes. E.g. 3d has 0 radial node, 5d has 2 radial nodes.  nf orbitals have (n-4) radial nodes. E.g. 4f has 0 radial node.  1s orbital: no radial node.  2s orbital: two regions of maximum probability, separated by a spherical surface of zero probability. (1 radial node)  3s orbital: Three regions of maximum probability, separated by two radial nodes. 18 Figure 2.5 Boundary surface diagram of s orbitals and electron density plots showing the presence of radial nodes (diagram from Zumdahl). Radial distribution function 4r R (r ) 2 4  Tells us where an electron will be most likely found at a given distance from the nucleus.  Plots of radial distribution functions for 1s, 2s and 3s orbitals show that there is at least one maximum and the fact that an electron tends to be further from the nucleus as its principal quantum number n increases. Therefore the size of an atomic orbital gets increases as the principal quantum number n increases.  Plots of radial distribution functions for 3s, 3p and 3d orbitals show that s orbital has electron density closest to the nucleus than p and d orbitals. We say that an electron in a s orbital is more penetrating than that in a p or d orbital. 19  Plot of radial distribution function 4r R (r ) for 1s, 2s,2p, 3s, 3p, 3d orbitals 2 Figure 2.6 of the hydrogen atom (diagram from Miessler & Tarr). 5 Angular wavefunction A( , )  The angular wavefunction describes the shape of an atomic orbital and its orientation in space.  The angular function A( , ) is determined by the quantum numbers l and ml.  Angular node (nodal plane): the plane(s) on which the angular wavefunction A( , )  0. The sign of the angular wavefunction changes (from +ve to -ve or vice versa) after passing through an angular node. 2.7 Pictorial Representation of Atomic Orbitals  An atomic orbital is defined as a boundary surface which encloses 95 % of the electron density for a particular Ψ.  Atomic orbitals can be represented pictorially by boundary surface diagrams (H&S Fig. 1.9, 1.10, 1.11) or electron density contour plots (see overhead). 20 s orbitals  l = 0, ml = 0, the angular wavefunction A( , ) is independent of the angle q and f. Therefore, an s orbital is spherically symmetrical about the nucleus. Figure 2.7 Boundary surface diagram of an s orbital. (Figure taken from Shriver & Atkins) p orbitals  l = 1; ml = -1, 0, + 1. 3 possible orientation of p orbitals: along the x, y and z axes.  Dumb-bell shaped; electron density concentrated in identical lobes on either side of the nucleus.  pz orbital has an angular node [ A( , )  0 ] along the xy plane; px orbital has an angular node along the yz plane; py orbital has an angular node along the xz plane.  The electron density contour map shows that there is no radial node for the 2p orbitals but 1 radial node for the 3p orbitals. [see example 1] Figure 2.8. Boundary surface diagram of p orbitals. The lightly shaded lobe has a positive amplitude; the more darkly shaded lobe is negative (Figure taken from Shriver & Atkins). d orbitals  l = 2, ml = -2, -1, 0, + 1, 2. There are five d orbitals.  dxy, dyz, dxz, dx2-y2 have clover leaf shape and have 4 lobes of maximum electron probability centered in the plane indicated in the orbital label. The four lobes are separated by two nodal planes through the nucleus. 21   dxy, and dx2-y2 are both centered in the xy plane while the lobes of dxy lie between the axis.  dz2 has two lobes along the z axis and a "belt" centered in the xy plane. Figure 2.9. Boundary surface diagram of d orbitals. The lightly shaded lobe has a positive amplitude; the more darkly shaded lobe is negative (Figure taken from Shriver & Atkins). 22 2.8 Nodal Surfaces and Electron Density Contour Plots of Atomic Orbitals Figure 2.10. Electron density contour plots for selected atomic orbitals showing radial or angular nodes (diagram taken from Miessler & Tarr). 2.9Electronic Configuration 2.9.1 Energy Levels in Hydrogen and Other Atoms 1 For H, the energy of the electron only depends on n, principal quantum number. The s, p, d, f orbitals have the same energy. 2 In the ground state, the electron in the H atom resides on the 1s orbital. 3 For other atoms with more than one electron, electron-electron repulsion and shielding play a role so energy depends on angular momentum quantum number l as well as the principal quantum number n. The energies of the atomic orbitals in multielectron atoms are arranged in the order: ns < np < nd < n f 23 Figure 2.11. Orbital energy level diagrams for a hydrogen atom and multielectron atoms (diagram taken from McMurry & Fay). 4 This ordering can be explained by considering the ability of having electron density closest to the positively charged nucleus in different atomic orbitals. Figure 2.12 Plot of radial distribution functions, 4 p r2R(r)2, for 1s, 2s, 2p, 3s, 3p, 3d orbitals versus radius r (diagram taken from Cotton, Wilkinson & Gaus). 24  The plot of radial distribution functions, 4 R (r ) , for 3s, 3p, 3d orbitals versus 2 2 5 radius (r) shows the first maximum for the s orbital is closest to the nucleus than the p or d orbitals, i.e., the s orbital has electron density closest to the nucleus. We say that electrons in an s orbital can penetrate closer to the nucleus than an electron in a p, d, or f orbital can.  Since orbitals with electron density closer to the nucleus are more stable, therefore, for a given n, the energy of the orbital increases in the order: s < p < d < f.  The effect is so pronounced for d and f electrons that they lie at higher energy than the s or p of the (n + 1 ) shell in some cases. E.g., Energy level of 3d > 4s, 4d > 5s; 4f > 5s, 5p. Figure. Relative energy level of various atomic orbitals in a multielectron atom (diagram from Rayner-Canham). Please note for the value of ns and (n - 1) d orbitals, there are 25 crossover points (e.g., 4s < 3d; 5s < 4d; 5s, 5p < 4f), this becomes important when filling electrons in multi-electron atoms. Electronic Configurations Describe how electrons distribute themselves in various orbitals in an atom. 2.9.2 Aufbau Principle  A set of rules guiding the filling order of orbitals. 1 Fill in electrons in the lowest energy orbital first. 2 Only two electrons with opposite spins per orbital (because Pauli exclusion principle says that no two electrons in an atom can have the same four quantum numbers). 3 If two or more degenerate orbitals (i.e. orbitals with the same energy) are available, electrons go into each degenerate orbital with parallel spins until the orbitals are half- fill (Hund's rule). 2.9.3 Order of Orbital Filling in Polyelectronic Atoms: Figure 2.13 Order of orbital filling in polyelectronic atoms 26 Filling of electrons for the first 30 elements Atom Atomic number Electronic configuration H 1 1s2 He 2 1s2 Li 3 1s22s1 Be 4 1s22s2 B 5 1s22s22p1 C 6 1s22s22p2 N 7 1s22s22p3 O 8 1s22s22p4 F 9 1s22s22p5 He 10 1s22s22p6 Na 11 1s22s22p63s2 Mg 12 1s22s22p63s2 Al 13 1s22s22p63s23p1 Si 14 1s22s22p63s23p2 P 15 1s22s22p63s23p3 S 16 1s22s22p63s23p4 Cl 17 1s22s22p63s23p5 Ar 18 1s22s22p63s23p6 K 19 1s22s22p63s23p64s1 Ca 20 1s22s22p63s23p64s2 Sc 21 1s22s22p63s23p64s23d1 Ti 22 1s22s22p63s23p64s23d2 V 23 1s22s22p63s23p64s23d3 Cr 24 1s22s22p63s23p64s13d5 Mn 25 1s22s22p63s23p64s23d5 Fe 26 1s22s22p63s23p64s23d6 Co 27 1s22s22p63s23p64s23d7 Ni 28 1s22s22p63s23p64s23d8 Cu 29 1s22s22p63s23p64s13d10 Zn 30 1s22s22p63s23p64s23d10 27  UNIT 3 Objectives of Unit 3  Understand how elements are arranged in the periodic chemistry  Explain the trend in properties of the elements such as ionization energy, electron affinity, atomic radius and electronegativity across the period and down the group. 3.0 Periodic Table 1 Elements are arranged with increasing atomic number in rows (called periods) and columns (called groups). 2 Elements in Groups 1 and 2 are also called s block elements: valence electrons fill in s orbitals. 3 Elements in Groups 13 to 18 are also called p block elements: valence electrons fill in p orbitals. 4 Elements in Groups 1, 2 and 13 - 18 are called main group elements. 5 Elements in Groups 3 - 11 are called transition metal because they have partially filled d orbitals. Elements in Groups 3 - 12 are called d block elements because valence electrons filled in d orbitals. 6 f block elements (also called Lanthanides and Actinides): valence electrons filling in f orbitals. 7 Elements in each group have similar valence-electron (electons in the outermost shell) configuration and therefore similar properties. Figure 3.1. The structure of the periodic table (diagram from Atkins & Shriver). 28  Figure 3.2. The modern periodic table 3.1 Periodic Trends of Atomic Parameters  Atomic properties such as effective nuclear charge, atomic radii, ionization energies, electron affinity and electronegativity are important in accounting for the chemical properties of an element. 3.2 Shielding 1. In atoms with more than one electrons, the effect of electron-electron repulsion depends on where the various electrons are located in the atom.  electrons in the outer shell (higher n) are pushed away by electrons in the inner shell (lower n). As a result, the net nuclear charge (or effective nuclear charge, Z eff) felt by an outer electron is substantially lower than the actual nuclear charge (Z). We say that the outer electrons are shielded from the full charge of the nucleus by the inner electrons.  Electrons in the same shell (same n) have an immediate effect in shielding the nuclear charge. 29   Electrons in the outer shell (higher n) do not shield the nuclear charge from the inner electrons (lower n)  In 1930, Slater formulated a set of rules for the effective nuclear charge felt by electrons in different atomic orbitals based on experimental data. The effective nuclear charge Zeff can be calculated by the following equation:  Zeff = Zactual - S  Z: atomic number (number of protons);  S: Slater screening constant;  The values of S are estimated as follows:  Write out the electron configuration of an element in groups of : (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f), (5s, 5p) etc.  Electrons with higher n do not shield those in lower n; S = 0.  If the electron in question resides in an s or p orbitals:  Each of the other electron in the same ns, np group, S = 0.35.  Each electron in the (n - 1) shell, S = 0.85.  Each electron in the (n - 2) and lower shell, S = 1.00  If the electron in question resides in a d or f orbitals:  Each of the other electron in the same nd, nf group, S = 0.35.  Each electrons in the (n - 1) shell, S = 1.00 Example: 1. Calculate the effective nuclear charge for the outermost electron in Oxygen. Given: Electron configuration of O: 1s22s22p4. 2. Calculate the effective nuclear charge on a 3d electron in a Nickel atom. Given: Electron configuration of Ni: 1s22s22p63s23p63d84s2. 3.3 Periodic Trend in Effective Nuclear Charge Below is a table of the values of effective nuclear charge (Zeff) for s and p electrons in elements Li - Ne: Element Li Be B C N O F Ne Z 3 4 5 6 7 8 9 10 30 1s 2.69 3.68 4.68 5.67 6.66 7.66 8.65 9.64 2s 1.28 1.91 2.58 3.22 3.85 4.49 5.13 5.76 2p 2.42 3.14 3.83 4.45 5.10 5.76 1. In the same atom, each electron with different n and l values can have a different Z eff because the repulsive effects due to the other electrons is different. E.g., the Z eff for the B atom: 1s >>2s > 2p and the size of orbitals is: 1s N > O > F > Ne 3.4 Sizes of Atoms and Ions  Since electrons can only be located by probability, there is no real boundary to an atom.  Radii of atoms and ions are obtained experimentally from measuring bond lengths in molecules, metals and ionic crystals by X-ray diffraction. 1. Covalent radii rcov:  defined as the half-distance between the nuclei of two atoms of the same element joined by a covalent bond.  E.g., Cl2: bond distance = 198 pm, atomic radius of Cl = (198)/2 = 99 pm. 2. Van der waal radius rvdw:  Defined as the half-distance between the nuclei of two non-bonded atoms or molecules.  Obtained from the closest approach between two non-bonded atoms or molecules in the solid state.  E.g., van der waal radius of Cl = 180 pm.  In general, rvdw > rcov. 3. Ionic radius:  defined as the distance between the nuclei of adjacent cations and anions in a purely ionic lattice. In general, ranions > rcov > rcation for any given element.  Cations: rNa+ = 116 pm; covalent radius rNa = 154 pm;  Why? From Na (1s22s22p63s1) to Na+ (1s22s22p6): Zeff increases since no. of electrons decreases. 31   Anions: the covalent radius rCl = 97 pm; rCl- = 167 pm;  Why? From Cl(1s22s22p63s23p5) to Cl- (1s22s22p63s23p6): Zeff decreases since no. of electrons increases. 3.5 Periodic Trend in Atomic Radii  Across a row, the atomic radius deceases because the n value for the outer shell remains the same but Zeff is increasing. o E.g. For row stared by Na outer shell is 3s 1, 3s2, 3s23p1, 3s23p2 ….,3s23p6, atomic radius decreases (from Na to Ar) because the Z value is increasing and the added electron do not completely shield the increase in Z.  Down a group, the increase in Zeff does not completely counteract the fact that the outer electrons are in orbitals with higher n, so radius increase down a group. o E.g. For group headed by Be outer shell is 2s 2, 3s2 , 4s2 , 5s2, 6s2, 7s2 , atomic size increases from Be to Ra. Table. Covalent radii (pm) of some selected elements Li Be B C N O 132 89 82 77 77 73 Na Mg Al Si P S 154 136 118 111 106 102 K Ca Ga Ge As Se 203 174 126 122 120 117 Rb Sr In Sn Sb Te 216 191 144 140 140 136 Atomic Number 3.6 Periodic Trend in Ionic Radii Going down a group in cations and anions:  e.g , Mg2+(2s22p6)--> Ca2+(3s23p6)--> Sr2+(4s24p6)--> Ba2+(2s22p6)  e.g , F-(2s22p6)--> Cl-(3s23p6)--> Br-(4s24p6)--> I-(2s22p6)  n value of outer orbital increase but not counteracted by the increasing Zeff. 32 Size of isoelectronic series (ions/atoms containing the same number of electrons):  e.g , O2-(2s22p6)--> F-(2s22p6)--> Ne(2s22p6)--> Na+(2s22p6) --> Mg2+(2s22p6)  Zeff increasing --> Since same no. of electrons and Z increasing.  R)O2-)> r(F-)> r(Ne)> r(Na+)> r(Mg2+) Ionic radii (pm) of some selected main group ions Li+ Be2+ O2- F- 60 31 140 136 Na+ Mg2+ Al3+ S2- Cl- 95 65 50 184 181 K+ Ca2+ Ga3+ Se2- Br- 133 99 62 198 Rb+ Sr2+ In3+ Sn4+ Te2- I- 248 113 81 71 221 216 3.7 Periodic Trend in the First Ionization Energy The ionization potential of an atom is the minimum energy required to remove an electron from a gaseous atom in its ground state. The magnitude of ionization potential is a measure of the effort required to force an atom to give up an electron, the higher the ionization energy, the more difficult it is to remove the electron. For many-electron atom, the amount of energy required to remove the first electron from the atom in its ground state is called the first ionization energy (I1) The second ionization energy (I2) and the third ionization energy (I3) are shown in the following equations Energy + X+ (g) X2+ (g) + e- Energy + X2+ (g) X3+ (g) + e- Where X is the element and (g) denotes the gaseous state. Higher ionization potentials labelled I2, I3, I4 and so on will correspond to the successive removal of additional electrons. The table below gives the first ionization energies of the first 21 elements. 33  Table 8-2; Ionization Potential (Energy) for the First 20 Elements Z Element First Second Third Fourth Fifth Sixth 1 H 1312 2 He 2373 5248 3 Li 520 7300 11808 4 Be 899 1757 14850 20992 5 B 801 2430 3660 25000 32800 6 C 1086 2350 4620 6220 38000 47232 7 N 1400 2860 4580 7500 9400 53000 8 O 1314 3390 5300 7470 11000 13000 9 F 1680 3370 6050 8400 11000 15200 10 Ne 2080 3950 6120 9370 12200 15000 11 Na 495.9 4560 6900 9540 23400 16600 12 MG 738.1 1450 7730 10500 13600 18000 13 Al 577.9 1820 2750 11600 14800 18400 14 Si 786.3 1580 3230 4360 16000 20000 15 P 1012 1904 2910 4960 6240 21000 16 S 999.5 2250 3360 3660 6990 8500 17 Cl 1251 2297 3820 5160 6540 9300 18 Ar 1521 2666 3900 5770 7240 8800 19 K 418.7 3052 4410 5900 8000 9600 20 Ca 589.5 1145 4900 6500 8100 11000 Ionization potentials are positive quantities. If the ionization Energy was plotted against the atomic number, the periodicity will be clearly evident. The 1st Ionization energy generally increases across the period. 34 Group I elements (alkali metals) have the lowest ionization energies. This is because the elements have one valence electron that is effectively shielded by the completely filled inner shells. Consequently, it is energetically easy to remove an electron from the atom of an alkali metal to form unipositive ion (Li+, Na+, K+ …………….). On the other hand non-metals have much higher ionization energies. The ionization energies of the metalloids usually fall between those of metals and non-metals. This explains why metals readily form cations while non-metals form anions. However, there are irregularities in the increase of the ionization energy across the periods. For example going across group 2 to 3, thus from Be to B and from Mg to Al. The group 3 elements have a single electron in the outermost sub level (ns 2 np1), which is well shielded by the inner electrons and the ns2 electrons. Less energy is therefore needed to remove a paired s electron from the same principle energy level. This brings about the lower ionization energies in group 3 elements compared with those in group 2 in the same period.  Periodic trends Atomic Number Figure. Ionization energies of the first 55 elements o Increase across each row, e.g. from Li to Ne; Na to Ar; K to Kr and so on (because Zeff increases and the electrons in a given orbital are held more tightly, therefore, to remove the electron from the atom requires more energy). o Group 1 Alkaline metals (i.e. Li, Na, K, Rb, Cs and Fr) have minimum I.E. (due to only single loosely held electron in the valence shell ns1). o Group 18 Noble gases (i.e. He, Ne, Ar, Kr, Xe and Rn) have the highest I.E. (due to filled valence shell, ns2np6; high Zeff valence electrons are tightly held). 35  o Minor irregularity occur from group 12 to group 13 elements also from group 15 to group 16 elements: o E.g. I.E. of Be (899.4 kJ/mol>I.E. of B (800.6 kJ/mol): due to completely filled ns2 configuration (2s2 in Be vs 2s22p1 in B); o I.E of N (1402.3 kJ/mol> I.E. of O (1313.9kJ/mol): due to half filled p orbital in N (2s22p3 in N vs 2s22p4 in O); o I.E decreases down a group, e.g. Li>Na>K>Rb>Cs>Fr; He>Ne>Ar>Kr>Xe>Rn. o Due to electrons filling in larger shell (larger n), further away from the nucleus. Therefore, valence electrons are well shielded from the nucleus by inner shell electrons and are loosely held. o The ionization energy increase only slightly across a row in the transition or lanthanides an actinides series. 3.9 Periodic Trend in Electron Affinity Electron Affinities The electron affinity of an atom is defined as the energy change obtained when a neutral atom in the gaseous state captures an electron. Thus, the energy is released by the reaction represented below: - X(g) + e-(g) →X- (g) + energy It is the reverse of the 1st ionization potential and may be looked at as the ability of an atom to accept one or more electrons. The largest electron affinities are those of the halogens. This is as expected since the addition of one electron yields the stable octet configuration of the 18 th group elements-the noble gases. X is an atom of an element. We assign a negative value to the affinity when energy is released. The more negative the electron affinity, the greater the tendency of the atom to accept an electron. The tendency to accept electrons increases as we move from left to right across the periodic table. Thus Electron Affinity becomes more negative. The E.A of metals are generally more positive (or less negative) than those of non-metals. The values differ little within a group, but the halogens have the most negative E.A values, while the noble gases that have filled outer s and p sub shells have no tendency to accept electrons. The E.A of oxygen has a negative value, which means that the process O (g) + e- O- (g) is favourable 36 While that of the O- is O- (g) + e- O2- (g) is positive (780kj/mol) meaning that this process is not favourable in the gas phase. 3.10 Periodic Trend in Electronegativity Electronegativity χ The tendency of an atom to attract electrons to itself in a chemical bond is referred to as electronegativity. The greater the electronegativity of an atom, the more strongly the atoms attracts the electrons of a bond. This concept was proposed by Linus Pauling in 1937. Electronegativity cannot be calculated accurately or measured directly. However, we expect it to depend on the magnitude of the charge and on the distance of the bonding pair of electrons from the nucleus. There are two important trends in electronegativity within the periodic table: - (a) electronegativity increases across a period as the charge increases (b) electronegativity generally decreases from top to bottom in a group; because with each successive shell, the bonding electrons are further from the nucleus. Because the electronegativity of an atom cannot be defined quantitatively, it cannot be given a precise value but approximate values. Table shows the electronegativity values 37 Table; Electronegativity χ of some elements Group 1 2 13 14 15 16 17 18 Period 1 H He 2.2 - 2 Li Be B C N O F Ne 1.0 1.5 2.0 2.5 3.1 3.5 4.1 - 3 Na Mg Al Si P S Cl Ar 1.0 1.2 1.3 1.7 2.1 2.4 2.8 - 4 K Ca Ga Ge As Se Br Kr 0.9 1.0 1.8 2.0 2.2 2.5 2.7 3.1 5 Rb Sr In Sn Sb Te I Xe 0.9 1.0 1.5 1.7 1.8 2.0 2.2 2.4 Increase of electronegativity-----------------------------------------→ Important application: Could use χ to estimate bond polarity  Atoms with similar electronegativity (   0.4 ) form nonpolar bonds.  Atoms whose electronegativity differs by more than 2 form ionic bonds.  Atoms whose electronegativity differ by less than 2 form cavalent bonds. 3.11 Common Oxidation State of the Elements Oxidation number is the apparent charge assigned to an atom in a molecule or in a compound. Some oxidation numbers are fixed: Elements Oxidation number O -2 except in peroxide H +1 except in hydride Group 1 metals +1 Group 2 metals +2 Halogens -1 except in oxygen compounds 38 39  UNIT 4 Objectives of Unit 4  Draw Lewis structure of simple molecules and ions  Use VSEPR theory to predict electronic and molecular geometry of simple molecules and ions  Explain the concept of hybridization  Identify hybridization in simple molecules and ions  Explain resonance and give examples in simple molecules 4.0Electronic Structure and Chemical Bonding There are four different but related approaches to explain how atoms combine to form covalent bond: 1) Lewis dot structure. 2) Valence Shell Electron Pair Repulsion theory (VSEPR). 3) Hybridization of atomic orbital. In this lesson we will describe the interactions between atoms called chemical bonds. Most of our discussion will centre on the simplest method of representing chemical bonding, known as the Lewis theory. We will explore, however, another relatively simple theory, one for prediction probable shape-Valence – Shell Electron – Pair Repulsion (VSEPR) theory. The subject of chemical bonding in more depth will be examined in SCH 200-(Atomic Structure and Chemical Bonding), especially molecular orbital theory. 4.1 Lewis Theory Some fundamental ideas in Lewi’s theory are: 1. Electrons, especially those of the outermost (valence) electronic shell, play a fundamental role in chemical bonding. 2. In some cases electrons are transferred from one atom to another. Positive and negative ions are formed and attract each other through electrostatic forces called ionic bonds. 3. In other cases one or more pairs of electrons are shared between atoms; this sharing of electrons is called a covalent bond. 4. Electrons are transferred, or shared, in such a way that each atom acquires an especially stable electron configuration. Usually this is a noble gas configuration, one with eight outer shell electrons, or an octect. 4.1.1 Lewis Symbols and Lewis Structures A Lewis symbol consists of a chemical symbol to represent the nucleus and core (inner shell) electrons of an atom, together with dots placed around the symbol to represent the valence (outer shell) electrons. Examples. Lewis structure for: Na electron configuration [Ne]3s1 is 40  Na N electron configuration [He]2s22p3 is N O electron configuration [He]2s22p4 is O Study question 1 Write the Lewis symbols for the following elements: H, He, Li, C, N, O, F, Ne, Cl, Na, Mg, Al, K and Ca. A Lewis structure is a combination of Lewis symbols that represent either the transfer or sharing of electrons in a chemical bond.  Ionic bonding (transfer of electrons) + - Na + Cl Na Cl - Cl 2+ Mg + 2 Cl Mg - Cl  Covalent bonding (sharing of electrons Hydrogen molecule is written showing a pair of dots between hydrogen atoms, incating that the hydrogen share the pair of electrons in covalent bond H + H H H Two hydrogen A hydrogen atom molecule The shared pair is usually represented by a line. E.g. H H Atoms other than hydrogen also form covalent bonds H + Cl H Cl Cl + Cl Cl Cl 41 Exercise 1 Write Lewis structures of the following ionic compounds: a) BaO; b) MgCl2;c) Aluminium oxide 2 Write Lewis structures of the following covalent compounds: a) F2; b) H2O; c) NH3 d) CH4 e) O2 f) N2 4.1.2 Lewis Structures and Resonance The Lewis structure of ozone O3 are: O O O or O O O Which of the two Lewis structure for O3 is correct? In fact, neither is correct by itself. Whenever it is possible to write more than one Lewis structure for a molecule the actual electronic structure is an average of the various possibilities called a resonance hybrid. Ozone does not have:  One O=O double bond and  One O-O single bond as individual structure imply, rather ozone has two equivalent O-O bonds that one can think of as having a bond order of 1.5 midway between pure single bond and pure double bond. Both have an identical length of 1.28 Å. The idea of resonance between two or more Lewis structure is indicated by drawing the individual Lewis structure and using double headed “resonance arrow” to show that both contribute to the resonance hybrid. O O O O O O Study question Draw the resonance structure of carbonate ion, CO32-. 4.2 Molecular Geometry and Bonding Theories 4.2.1 Valence Shell Electron Pair Repulsion Theory (VSEPR) (Molecular geometry or shape of molecules)  Lewis structures say nothing about bond angles.  A structure should be considered which let all the electron pairs of the valence shell of central atom try to get further away from each other. Repulsion between lone pairs is greater than those between bonding electrons. The order of repulsive energy is: Lp-Lp>Lp-Bp>Bp-Bp 42 O C O Linear H Cl Linear O H H V-shaped Cl B Trigonal planar Cl Cl N H H Triangular pyramidal H H C H Tetrahedral H H 4.2.3 Covalent Bonding and Orbital Overlap The VSEPR model is a simple method which allows us to predict molecular geometry BUT it does NOT explain why bond exist between atoms.  How can we explain molecular geometry and basis of bonding at the same time? o Quantum mechanism and molecular orbitals are used. 4.3 Valence Bond Theory (VBT)  Combine Lewis idea of electron pair bonds with electron orbitals (quantum mechanic).  Covalent bond occurs when atom shares electrons.  Concentrate electron density between nuclei.  The build up of electrons density between two nuclei occurs when a valence atomic orbital of one atom overlap with one of another.  The orbital share a region of space i.e. they overlap.  The overlap of orbital allows two electron of opposite spin to share the common space between the nuclei forming a covalent bond. 43   In the hydrogen m molecule for instance the H-H bond result from overlap of two singly occupied H 1s orbitals. H + H H H 1s 1s H2 molecule  In the valence bond model, the strength of covalent bond depends on amount of overlap. The greater the overlap, the stronger the bond. This in turn, means that bond formed by overlap other than s- orbitals have directionalities to them. In the fluorine molecule, F2, for instance each atom has electron configuration: [He]2s22pz22py22px1 Meaning that the fluorine bond results from overlap of two singly occupied two 2p orbitals. The 2p orbitals must point directly to one another for optimum overlap to occur, and the F-F form bond along the orbitals. F F F + F 2p 2p F2 molecule F F atom atom In HCl, the covalent bond involves overlap of 1s orbital (nondirectional) with chlorine 3p orbital and formed along p-axis. 1s 3p HCl molecule The key ideas of valence bond theory can be summarized by few statements: i. Covalent bonds are formed by overlap of atomic orbitals, each of which contains 1 electron of opposite spin. ii. Each of the bonded atoms maintains its own atomic orbitals, but the electron pair in the overlapping pair is shared by both atoms. iii. The greater the amount of orbital overlap the stronger the bond. This leads to a directional character to the bond when other than s – orbitals are formed. 44 4.4 Molecular Geometry and Hybrid Orbitals Hybrid Orbitals For polyatomic molecules we would like to be able to explain: The number of bonds formed Their geometries sp Hybrid Orbitals Consider the Lewis structure of gaseous molecules of BeF2:  The VSEPR model predicts this structure will be linear  What would valence bond theory predict about the structure? The fluorine atom electron configuration:  1s22s22p5  There is an unpaired electron in a 2p orbital  This unpaired 2p electron can be paired with an unpaired electron in the Be atom to form a covalent bond The Be atom electron configuration:  1s22s2  In the ground state, there are no unpaired electrons (the Be atom is incapable of forming a covalent bond with a fluorine atom  However, the Be atom could obtain an unpaired electron by promoting an electron from the 2s orbital to the 2p orbital: 45 This would actually result in two unpaired electrons, one in a 2s orbital and another in a 2p orbital  The Be atom can now form two covalent bonds with fluorine atoms  We would not expect these bonds to be identical (one is with a 2s electron orbital, the other is with a 2p electron orbital) However, the structure of BeF2 is linear and the bond lengths are identical  We can combine wavefunctions for the 2s and 2p electrons to produce a "hybrid" orbital for both electrons  This hybrid orbital is an "sp" hybrid orbital  The orbital diagram for this hybridization would be represented as: 46 Note:  The Be 2sp orbitals are identical and oriented 180° from one another (i.e. bond lengths will be identical and the molecule linear)  The promotion of a Be 2s electron to a 2p orbital to allow sp hybrid orbital formation requires energy. o The elongated sp hybrid orbitals have one large lobe which can overlap (bond) with another atom more effectively o This produces a stronger bond (higher bond energy) which offsets the energy required to promote the 2s electron sp2 and sp3 Hybrid Orbitals Whenever orbitals are mixed (hybridized):  The number of hybrid orbitals produced is equal to the sum of the orbitals being hybridized  Each hybrid orbital is identical except that they are oriented in different directions BF3 Boron electron configuration:  The three sp2 hybrid orbitals have a trigonal planar arrangement to minimize electron repulsion 47 NOTE: sp2 refers to a hybrid orbital being constructed from one s orbital and two p orbitals. Although it looks like an electron configuration notation, the superscript '2' DOES NOT refer to the number of electrons in an orbital.  An s orbital can also mix with all 3 p orbitals in the same subshell CH4 Thus, using valence bond theory, we would describe the bonds in methane as follows: each of the carbon sp3 hybrid orbitals can overlap with the 1s orbitals of a hydrogen atom to form a bonding pair of electrons NOTE: sp3 refers to a hybrid orbital being constructed from one s orbital and three p orbitals. Although it looks like an electron configuration notation, the superscript '3' DOES NOT refer to the number of electrons in an orbital. ANOTHER NOTE: the two steps often observed when constructing hybrid orbitals is to 1) promote a valence electron from the ground state configuration to a higher energy orbital, and then 2) hybridize the appropriate valence electron orbitals to achieve the desired valence electron geometry (i.e. the correct number of hybrid orbitals for the appropriate valence electron geometry) H2O Oxygen 48 4.5 Hybridization Involving d Orbitals Atoms in the third period and higher can utilize d orbitals to form hybrid orbitals PF5 49 Similarly hybridizing one s, three p and two d orbitals yields six identical hybrid sp3d2 orbitals. These would be oriented in an octahedral geometry.  Hybrid orbitals allows us to use valence bond theory to describe covalent bonds (sharing of electrons in overlapping orbitals of two atoms)  When we know the molecular geometry, we can use the concept of hybridization to describe the electronic orbitals used by the central atom in bonding Steps in predicting the hybrid orbitals used by an atom in bonding: 1. Draw the Lewis structure 2. Determine the electron pair geometry using the VSEPR model 3. Specify the hybrid orbitals needed to accommodate the electron pairs in the geometric arrangement NH3 1. Lewis structure 2. VSEPR indicates tetrahedral geometry with one non-bonding pair of electrons (structure itself will be trigonal pyramidal) 3. Tetrahedral arrangement indicates four equivalent electron orbitals 50 Valence Electron Pair Number of Orbitals Hybrid Orbitals Geometry Linear 2 Sp Trigonal Planar 3 Sp2 Tetrahedral 4 Sp3 Trigonal Bipyramidal 5 sp3d Octahedral 6 sp3d2 4.6 Multiple Bonds and Orbital Overlaps Two types of bond Sigma (σ) and pi (π) bonds 51 The "internuclear axis" is the imaginary axis that passes through the two nuclei in a bond: The covalent bonds we have been considering so far exhibit bonding orbitals which are symmetrical about the internuclear axis (either an s orbital - which is symmetric in all directions, or a p orbital that is pointing along the bond towards the other atom, or a hybrid orbital that is pointing along the axis towards the other atom) Bonds in which the electron density is symmetrical about the internuclear axis are termed "sigma" or "" bonds In multiple bonds, the bonding orbitals arise from a different type arrangement:  Multiple bonds involve the overlap between two p orbitals  These p orbitals are oriented perpendicular to the internuclear (bond) axis This type of overlap of two p orbitals is called a "pi" or " " bond. Note that this is a single  bond (which is made up of the overlap of two p orbitals) In  bonds:  The overlapping regions of the bonding orbitals lie above and below the internuclear axis (there is no probability of finding the electron in that region)  The size of the overlap is smaller than a  bond, and thus the bond strength is typically less than that of a  bond Generally speaking: 52   A single bond is composed of a  bond.  A double bond is composed of one  bond and one  bond.  A triple bond is composed of one  bond and two  bonds. C2H4 (ethylene; see structure above)  The arrangement of bonds suggests that the geometry of the bonds around each carbon is trigonal planar  Trigonal planar suggests sp2 hybrid orbitals are being used (these would be  bonds) What about the electron configuration? Carbon: 1s2 2s2 2p2  Thus, we have an extra unpaired electron in a p orbital available for bonding  This extra p electron orbital is oriented perpendicular to the plane of the three sp2 orbitals (to minimize repulsion):  The unpaired electrons in the p orbitals can overlap one another above and below the internuclear axis to form a covalent bond 53   This interaction above and below the internuclear axis represents the single  bond between the two p orbitals Experimentally:  we know that the 6 atoms of ethylene lie in the same plane.  If there was a single  bond between the two carbons, there would be nothing stopping the atoms from rotating around the C-C bond.  But, the atoms are held rigid in a planar orientation.  This orientation allows the overlap of the two p orbitals, with formation of a bond.  In addition to this rigidity, the C-C bond length is shorter than that expected for a single bond.  Thus, extra electrons (from the  bond) must be situated between the two C-C nuclei. C2H2 (acetylene)  The linear bond arrangement suggests that the carbon atoms are utilizing sp hybrid orbitals for bonding  This leaves two unpaired electrons in p orbitals  To minimize electron replusion, these p orbitals are at right angles to each other, and to the internuclear axis: 54   These p orbitals can overlap two form two  bonds in addition to the single  bond (forming a triple bond) Delocalized Bonding localized electrons are electrons which are associated completely with the atoms forming the bond in question In some molecules, particularly with resonance structures, we cannot associate bonding electrons with specific atoms C6H6 (Benzene) Benzene has two resonance forms  The six carbon - carbon bonds are of equal length, intermediate between a single bond and double bond 55   The molecule is planar  The bond angle around each carbon is approximately 120° The apparent hybridization orbital consistent with the geometry would be sp2 (trigonal planar arrangement)  This would leave a single p orbital associated with each carbon (perpendicular to the plane of the ring) With six p electrons we could form three discrete  bonds  However, this would result in three double bonds in the ring, and three single bonds  This would cause the bond lengths to be different around the ring (which they are not)  This would also result in one resonance structure being the only possible structure The best model is one in which the  electrons are "smeared" around the ring, and not localized to a particular atom 56   Because we cannot say that the electrons in the  bonds are localized to a particular atom they are described as being delocalized among the six carbon atoms Benzene is typically drawn in two different ways:  The circle indicates the delocalization of the p bonds 4.7 Resonance Structures and Hybrid Orbitals Structure of NO3- The Lewis structure of NO3- ion suggests that three resonance structures describe the molecular structure  For any individual Lewis resonance structure the electronic structure for the central N atom is predicted to be sp2 hybrid orbitals participating in  bonds with each of the O atoms, and an electron in a p orbital participating in a  bond with one oxygen (forming a double bond)  Two of the O atoms are predicted to have sp3 hybrid orbitals, with one orbital participating in a  bond with the central N atom and the other orbitals filled with non-bonding electron pairs. The other O atom is predicted to have sp2 hybrid orbitals, with one orbital participating in a  bond with the central N and two orbitals filled with non-bonding pairs of electrons. Furthermore, this last O atom is participating in a double bond with the central N atom and therefore should have an electron in a p orbital to participate in a  bond with the central N How will this arrangement look as far as the orbital diagrams? 57   There are 24 valence electrons in the expected valence orbitals above  Summing the valence electrons from the formula gives: (3 x 6) for O, plus 5 for N, plus 1 for ionic charge = 24 What might we expect for the electron configuration if we just started with the N atom?  We would predict that the N can only make two  bonds, it would have one pair of non-bonding electrons, and a p electron left over to participate in a  bond with one of the  bonds  This is different from what the Lewis structure shows, and from our prediction of hybrid orbitals from the expected geometry  If we look at the sp3 O atoms above we see that they actually have 7 electrons (1 more than expected), while the sp2 O atom has the expected 6. Furthermore, the N atom (in the correct sp2 configuration) has 4 electrons (1 less than expected)  The "extra" electron from the ionic charge is correctly accounted for in the summation of electrons 58 Thus, the correct way to determine electron configurations appears to be:  begin by predicting the hybridization orbitals  then determine lone pair arrangements and s and p bonding electrons for each atom  confirm that all bonding electrons are correct and that the total of electrons is correct 59  UNIT 5 Objectives of Unit 5  Understand acid and bases in the Brønsted and Lowry sense and Lewis sense  Differentiate weak and strong acids  Calculate PH and POH of strong and weak acids and bases 5.0Acid and Bases Arrhenius definition of an acid is a substance that provides hydrogen ions, H +, when dissolved in water, and one definition of a base is a substance that provides hydroxide ions, OH- , when dissolved in water. Arrhenius definition of a base is restricted to those substances which react with H+ ion to form water. In order to widen the scope of acid- base reaction and include non-aqueous systems and a wider range of bases, Brønsted and Lowry independently suggested the following definition in 1923. An acid is a proton donor And A base is a proton acceptor, Thus the relationship between an acid and its corresponding base is - HB H+ + B Acid proton base proton donor proton acceptor HB and B- are said to be conjugate and to form conjugate acid – base pair. HB is the conjugate acid of B- and B- is the conjugate base of HB.