Chapter 2: Atomic Structure and Interatomic Bonding (Fall 2023/2024) PDF

Chapter 2 Fall 2023/2024 Dr. Zafar SREE University of Sharjah 1 Atomic Structure and Interatomic Bonding 2  Atomic Structure Each atom consists of a very small nucleus composed of protons and neutrons and is...

Chapter 2 Fall 2023/2024 Dr. Zafar SREE University of Sharjah 1 Atomic Structure and Interatomic Bonding 2  Atomic Structure Each atom consists of a very small nucleus composed of protons and neutrons and is encircled by moving electrons. Both electrons and protons are electrically charged, the charge magnitude being 1.602 × 10−19 C, which is negative in sign for electrons and positive for protons; neutrons are electrically neutral. Masses for these subatomic particles are extremely small; protons and neutrons have approximately the same mass, 1.67 × 10−27 kg, which is significantly larger than that of an electron, 9.11 × 10−31 kg. 3  Atomic Structure Each chemical element is characterized by the number of protons in the nucleus, or the atomic number (Z). The atomic mass (A) of a specific atom may be expressed as the sum of the masses of protons and neutrons within the nucleus. Atoms of some elements have two or more different atomic masses, which are called isotopes*. The atomic weight of an element corresponds to the weighted average of the atomic masses of the atom’s naturally occurring isotopes. The atomic mass unit (amu) may be used to compute atomic weight. *Although the number of protons is the same for all atoms of a given element, the number of neutrons (N) 4 may be variable.  Atomic Structure A scale has been established whereby 1 amu is defined as 1/12 of the atomic mass of the most common isotope of carbon, carbon 12 (12C) (A = 12.00000). Within this scheme, the masses of protons and neutrons are slightly greater than unity, and A≅Z+N In one mole of a substance, there are 6.022 × 1023 (Avogadro’s number) atoms or molecules. 1 amu/atom (or molecule) = 1 g/mol For example, the atomic weight of iron is 55.85 amu/atom, or 55.85 g/mol. 5  Atomic Structure Summary atom (mass): electrons – 9.11 x 10-31 kg protons } neutrons 1.67 x 10-27 kg atomic number = # of protons in nucleus of atom = # of electrons in neutral species atomic mass unit = amu = 1/12 mass of 12C A = Atomic wt = wt of 6.022 x 1023 molecules or atoms 1 amu/atom = 1 g/mol C 12.011 H 1.008 etc. 6 7 Atomic Structure (cont.) Some of the following properties are determined by an atom's electronic structure: 1) Chemical 2) Electrical 3) Thermal 4) Optical 8  Atomic Structure Electrons have wave-like and particle-like characteristics. The two atomic models are Bohr and wave mechanical. Whereas the Bohr model assumes electrons to be particles orbiting the nucleus in discrete paths, in wave mechanics we consider them to be wavelike and treat electron position in terms of a probability distribution. 9  ELECTRONS IN ATOMS Atomic Models Quantum mechanics: A set of principles and laws that govern systems of atomic and subatomic entities. Bohr atomic model: Electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. This model of the atom is represented in Figure 2.1. 10  Electron Energy States Another important quantum-mechanical principle stipulates that the energies of electrons are quantized—that is, electrons are permitted to have only specific values of energy. An electron may change energy, but in doing so, it must make a quantum jump either to an allowed higher energy (with absorption of energy) or to a lower energy (with emission of energy). Often, it is convenient to think of these allowed electron energies as being associated with energy levels or states. 11  Electron Energy States Electrons... have discrete energy values tend to occupy lowest available energy states 4d 4p N-shell n = 4 3d 4s Energy 3p M-shell n = 3 3s 2p L-shell n = 2 2s 1s K-shell n = 1 12  Quantum Numbers The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers. The Four Quantum Numbers that Describe an Electron 13  Electronic Structure Electrons have wave-like and particle-like characteristics. Two wave-like characteristics are Electron position in terms of probability density shape, size, orientation of probability density determined by quantum numbers Quantum # Designation/Values n = principal (shell) K, L, M, N, O (1, 2, 3, 4, etc.) l = azimuthal (subshell) s, p, d, f (0, 1, 2, 3,…, n-1) ml = magnetic (no. of orbitals) 1, 3, 5, 7 (-l to +l) ms = spin +½, -½ 14 Quantum Numbers In wave mechanics, every electron in an atom is characterized by four parameters called quantum numbers. The size, shape, and spatial orientation of an electron’s probability density (or orbital) are specified by three of these quantum numbers. Furthermore, Bohr energy levels separate into electron subshells, and quantum numbers dictate the number of states within each subshell. Shells are specified by a principal quantum number n, which may take on integral values beginning with unity; sometimes these shells are designated by the letters K, L, M, N, O, and so on, which correspond, respectively, to n = 1, 2, 3, 4, 5,... , as indicated in Table 2.1. 15 16 n-1 17 Shells and Subshells I In labeling shells and subshells in hydrogen-like atoms (and other atoms), we use: the quantum number n, followed by a letter designation for l (see table 3), and a subscript for the value of m. Table 2: Letter designation for n quantum numbers (shell). n value 1 2 3 4 Code letter K L M N Table 3: Letter designation for l quantum numbers (subshell). l value 0 1 2 3 4 5 6... Code letter s p d f g h i... Example: 2s denotes the n = 2, l = 0 state, and 2p−1 denotes the n = 2, l = 1 and m = −1 state. 18 19 The Aufbau Principle 1s 2s 2p The Aufbau6 principle for electron 3s 3p 3d configurations is based on the the fact 4s 4p 4d 4f that the total energy of the atom should be minimum. The ordering 5s 5p 5d 5f 5g of orbitals can be remembered by the way shown in figure 2.5. 6s 6p 6d 6f 6g 7s 7p and so on Figure 2.5: The order of filling of the subshells in most atoms (1–85), adapted from.. 6 From the german word for " to build-up" 20  SURVEY OF ELEMENTS Most elements: Electron configurations not stable. Element Atomic # Electron configuration Hydrogen 1 1s 1 Helium 2 1s 2 (stable) Lithium 3 1s 2 2s 1 Beryllium 4 1s 2 2s2 Boron 5 1s 2 2s 2 2p 1 Carbon 6 1s 2 2s 2 2p 2...... Neon 10 1s 2 2s 2 2p 6 (stable) Sodium 11 1s 2 2s 2 2p 6 3s 1 Magnesium 12 1s 2 2s 2 2p 6 3s 2 Aluminum 13 1s 2 2s 2 2p 6 3s 2 3p 1...... Argon 18 1s 2 2s 2 2p 6 3s 2 3p 6 (stable)......... Krypton 36 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable) Why not stable? Valence (outer) shell usually not completely filled. 21 Electron Configurations Valence electrons – those in outer unfilled shells Filled shells are more stable – require more energy to gain or lose electrons Valence electrons available for bonding and tend to determine an atom’s chemical properties example: C (atomic number = 6) 1s2 2s2 2p2 valence electrons 22  Electronic Configurations (cont.) ex: Fe (atomic # = 26) Electron configuration 1s2 2s2 2p6 3s2 3p6 3d 6 4s2 4d 4p N-shell n = 4 valence electrons 3d 4s Energy 3p M-shell n = 3 3s 2p L-shell n = 2 2s 1s K-shell n = 1 23 Shells and Subshells Figure 2.4: From MIT OCW. 24 25 The Periodic Table of the Elements Metal IA Key 0 1 29 Atomic number Nonmetal 2 H Cu Symbol He 1.0080 IIA 63.55 IIIA IVA VA VIA VIIA 4.0026 Atomic weight 3 4 5 6 7 8 9 10 Li Be Intermediate B C N O F Ne 6.941 9.0122 10.811 12.011 14.007 15.999 18.998 20.180 11 12 13 14 15 16 17 18 Na Mg VIII Al Si P S Cl Ar 22.990 24.305 IIIB IVB VB VIB VIIB IB IIB 26.982 28.086 30.974 32.064 35.453 39.948 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 39.098 40.08 44.956 47.87 50.942 51.996 54.938 55.845 58.933 58.69 63.55 65.41 69.72 72.64 74.922 78.96 79.904 83.80 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 85.47 87.62 88.91 91.22 92.91 95.94 (98) 101.07 102.91 106.4 107.87 112.41 114.82 118.71 121.76 127.60 126.90 131.30 55 56 Rare 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Cs Ba earth Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 132.91 137.33 series 178.49 180.95 183.84 186.2 190.23 192.2 195.08 196.97 200.59 204.38 207.19 208.98 (209) (210) (222) 87 88 Acti- 104 105 106 107 108 109 110 Fr Ra nide Rf Db Sg Bh Hs Mt Ds (223) (226) series (261) (262) (266) (264) (277) (268) (281) 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Rare earth series La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 138.91 140.12 140.91 144.24 (145) 150.35 151.96 157.25 158.92 162.50 164.93 167.26 168.93 173.04 174.97 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 Actinide series Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr (227) 232.04 231.04 238.03 (237) (244) (243) (247) (247) (251) (252) (257) (258) (259) (262) Figure 3.1: The periodic (atomic mass, size, ionization energies, and electronegativity) table of the elements, from.. 26 Periods and Groups I 7 horizontal rows called periods several columns or groups having similar valence electron structures, as well as chemical and physical properties: Group 0: inert gases, filled electron shells and stable electron con- figuration. Groups VIIA & VIA: elements with one (halogens) or two deficient electrons from stable structure. Groups IA & IIA: alkali and alkaline earth metals having, respectively, one and two excess electrons vs. stable configuration. Group IIIB to IIB: transition metals with partially filled d-electron states and in some case one or two electrons in the next higher energy shell. Groups IIIA to VA: elements with characteristics intermediate between metals and nonmetals because of their valence electron structure. 27 Periods and Groups II Elements in each column: Similar valence electron structure inert gases give up 1e- give up 2e- accept 2e- accept 1e- give up 3e- H He Li Be O F Ne Na Mg S Cl Ar K Ca Sc Se Br Kr Rb Sr Y Te I Xe Cs Ba Po At Rn Fr Ra Electropositive elements: Electronegative elements: Readily give up electrons Readily acquire electrons to become + ions. to become - ions. 28  Electronegativity Ranges from 0.7 to 4.0, Large values: tendency to acquire electrons. Smaller electronegativity Larger electronegativity 29 Periods and Groups III Example Give the electron configurations for the following ions: Fe2+, Cu + , and B r – Fe2+: 1s22s22p63s23p63d6 (that of Fe is 1s22s22p63s23p63d64s2) Cu + : 1s22s22p63s23p63d10 (that of Cu is 1s22s22p63s23p64s13d10) B r – : 1s22s22p63s23p63d104s24p6 (that of Br is [Ar]3d104s24p5) 30 Periods and Groups IV Example Determine whether each of the following electron configurations is an inert gas, a halogen, an alkali metal, an alkaline earth metal, or a transition metal. Justify your choices. 1 1s22s22p63s23p63d74s2 2 1s22s22p63s23p6 3 1s22s22p5 4 1s22s22p63s2 5 1s22s22p63s23p63d24s2 6 1s22s22p63s23p64s1 31 Periods and Groups V 1 1s22s22p63s23p63d74s2 has an incomplete d subshell: transition metal 2 1s22s22p63s23p6 has filled 3s and 3p subshells: inert gas 3 1s22s22p5 has one electron deficient from having a filled L shell: halo- gen 4 1s22s22p63s2 has two s electrons: alkaline earth 5 1s22s22p63s23p63d24s2 has an incomplete d subshell: transition metal 6 1s22s22p63s23p64s1 has a single s electron: alkali metal 32 Metallicity and Electronegativity I The property of metallicity can be defined as the tendency of an atom to donate electrons to metallic or ionic bonds. Metallicity increases from top to bottom and from right to left on the periodic chart. It is far more common to describe the properties of atoms in terms of their electronegativity, which is the opposite of the metallicity. The periodic trends in size are the same as those for metallicity. It is also worth remembering that cations (positive ions) are smaller than neutral atoms, while anions (negative ions) are larger. Ions always shrink with increasing positive charge and expand with increasing negative charge. Mass increases with atomic number. 33 Metallicity and Electronegativity II IA 0 1 2 H He 2.1 IIA IIIA IVA VA VIA VIIA – 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 1.0 1.5 2.0 2.5 3.0 3.5 4.0 – 11 12 13 14 15 16 17 18 Na Mg VIII Al Si P S Cl Ar 0.9 1.2 IIIB IVB VB VIB VIIB IB IIB 1.5 1.8 2.1 2.5 3.0 – 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 0.8 1.0 1.3 1.5 1.6 1.6 1.5 1.8 1.8 1.8 1.9 1.6 1.6 1.8 2.0 2.4 2.8 – 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 0.8 1.0 1.2 1.4 1.6 1.8 1.9 2.2 2.2 2.2 1.9 1.7 1.7 1.8 1.9 2.1 2.5 – 55 56 57–71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Cs Ba La–Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 0.7 0.9 1.1–1.2 1.3 1.5 1.7 1.9 2.2 2.2 2.2 2.4 1.9 1.8 1.8 1.9 2.0 2.2 – 87 88 89–102 Fr Ra Ac–No 0.7 0.9 1.1–1.7 Figure 3.3: The electronegativity values for the elements, from.. 34 Three Types of Primary/Chemical Bonds I Three primary or chemical bonds (strong bonds) in solids: 1 ionic, 2 covalent, and 3 metallic. They all involve the valence electrons. They depend on the electronic structure of the constituent atoms. Remark The more electrons per atom that take place in this process, the higher the bond "order" (e.g., single, double, or triple bond) and the stronger the connection between atoms. 35  Ionization Process metal atom + nonmetal atom donates accepts electrons electrons Dissimilar electronegativities ex: MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4 [Ne] 3s2 Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 [Ne] [Ne] 36 Ionic Bonding Occurs between + and - ions. Requires electron transfer. Large difference in electronegativity required. Example: NaCl (salt) Na (metal) Cl (nonmetal) unstable unstable electron Na (cation) stable + - Cl (anion) Coulombic stable Attraction 37 Interatomic Bonding I Attractive forces: F A depends on the bondings between atoms. Repulsive forces: F R depend on the nuclear and electronic repulsions. Net force: F N = F A + F R 38 Interatomic Bonding II ∫ E = F dr and E N = E A + E R (6) + Attractive force F A Attraction Minimum energy at r0 which is called Force F 0 Interatomic separation r the bonding energy. Note that a Repulsive force F R Repulsion r0 similar outline holds for multi-atom Net force F N system for solid materials. – (a) + Repulsive energy E R Repulsion Potential energy E Remark Interatomic separation r 0 Bonding energy and energy-interatomic Net energy E N Attraction distance vary from one material to E0 another and define many of the material Attractive energy E A properties, such as melting temperature – (b) (↑ T m ↑ E 0 ) , solids (↑ E 0 ) , gases Figure 4.1: Attractive vs repulsive forces/potentials (↓ E 0 ) vs interatomic distance, from.. 39 Ionic Bonding (cont.) Energy – minimum energy most stable Net energy = sum of attractive and repulsive energies Equilibrium separation when net energy is a minimum EN = EA + ER Repulsive energy ER Interatomic separation r Net energy EN Fig. 2.10(b), Callister & Rethwisch 10e. Attractive energy EA 40 Ionic Bonding (cont.) Predominant bonding in Ceramics Examples: NaCl MgO CaF2 CsCl Give up electrons Acquire electrons 41 Three Types of Primary/Chemical Bonds II Ionic bonding: nondirectional bonding (strong Coulomb interaction) be- tween metallic (easily give up their valence electrons) and nonmetallic elements (the horizontal extremities of the ta- ble of the elements), such as NaCl, MgO (usually when the electronegativity difference > 2). Coulombic bonding force Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Na+ Cl– Figure 4.4: Ionic bonding in NaCl, from. 42 Three Types of Primary/Chemical Bonds III Na has 11 electrons, 1 more than needed for a full outer shell (Neon) and Cl has 17 electron, 1 less than needed for a full outer shell (Argon) Electron transfer reduces the energy of the system of atoms, that is, electron transfer is energetically favorable. Note rel- ative sizes of ions: Na shrinks and Cl expands 11 Protons Na 1S2 2S2 2P6 3S1 donates e- 11 Protons Na+ 1S2 2S2 2P6 10 e- left 17 Protons Cl 1S2 2S2 2P6 3S2 3P5 receives e- 17 Protons Cl- 1S2 2S2 2P6 3S2 3P6 18 e- e- Na Cl Na+ Cl- Figure 4.5: Ionic bonding in NaCl, from. 43 Three Types of Primary/Chemical Bonds IV Covalent bonding: stable electron configuration as a result of sharing of electrons between adjacent atoms (directional bond), such as in nonmetallic elemental molecules (H2, Cl2), heteroge- neous molecules (CH4, H2O) and elemental solids (Si, SiC, C). Usually when the electronegativity difference < 0.4) H Shared electron Shared electron from carbon from hydrogen H C H H Figure 4.6: Four covalent bondings in CH4 molecule, from. 44 Covalent Bonding: Bond Hybridization Carbon can form sp3 hybrid orbitals Fig. 2.14, Callister & Rethwisch 10e. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.) Fig. 2.13, Callister & Rethwisch 10e. 45  Covalent Bonding (cont.) Hybrid sp3 bonding involving carbon Example: methane CH4 C: each has 4 valence electrons, needs 4 more H: each has 1 valence electron, needs 1 more Electronegativities of C and H are similar so electrons are shared in sp3 hybrid covalent Fig. 2.15, Callister & Rethwisch 10e. (Adapted from J.E. Brady and F. Senese, Chemistry: bonds. Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.) 46  Covalent Bonding Similar electronegativities  share electrons Bonds involve valence electrons – normally s and p orbitals are involved Example: H2 H2 Each H: has 1 valence e-, needs 1 more H H Electronegativities are the same. shared 1s electron shared 1s electron from 1st hydrogen from 2nd hydrogen atom atom Fig. 2.12, Calliser & Rethwisch 10e. 47 Three Types of Primary/Chemical Bonds V Remark For two atoms with an electronegativity difference of between 0.4 and 2.0, a polar covalent bond is formed–one that is neither truly ionic nor totally covalent, such as HF. The percent ionic character (%IC) of a bond between elements A and B (A being the most electronegative) may be approximated by: % I C = 100 × 1 − exp −0.25(ξA − ξ B )2 (7) 48  Mixed Bonding Most common mixed bonding type is Covalent-Ionic mixed bonding % ionic character = x ( 100 %) where XA & XB are electronegativities of the two elements participating in the bond Ex: MgO XMg = 1.2 XO = 3.5 æ - (3.5-1.2)2 ö ç % ionic character = 1- e 4 ÷ x (100%) = 73.3% ç ÷ è ø 49 Metallic Bonding Electrons delocalized to form an “electron cloud” Fig. 2.19b, Callister & Rethwisch 10e. 50 Three Types of Primary/Chemical Bonds VI Metallic bonding: nondirectional, found in metals and their alloys; maxi- mum 3 valence electrons not bound to any particular atom in the solid matrix and are free to drift throughout the entire metal generating an electron cloud that glues together the positive ion cores. Ion cores + + + + – – – + + + + – – – + + + + – – – + + + + Sea of valence electrons Figure 4.7: Metal bondings model, from. 51  Secondary Bonding Arises from attractive forces between dipoles Fluctuating dipoles ex: liquid H 2 asymmetric electron clouds H2 H2 + - + - H H H H secondary secondary bonding bonding Permanent dipoles + - secondary + - -general case: bonding H Cl secondary H Cl -ex: liquid HCl bonding -ex: polymer linear polymer molecule 52 Secondary Interatomic Bonds I Secondary, Van der Waals, or physical bond (no electron transfer or shared interaction of atomic or molecular dipoles) are weak ( < 1 eV/atom) in comparison to the primary bonds and should normally exist between all atoms and molecules. They are the result of molecular dipoles and coulombic attraction between: 1 fluctuating induced dipoles (due to the distortion of electric symmetry because of vibrational motion of atoms that would induce the same with adjacent atoms, e.g. H2, Cl2, etc.), 2 permanent dipole bonds because of electric dissymmetry (polar molecules such as H2O, HCl), and 3 polar molecule-induced dipole bonds (a polar molecule induces a dipole in a nearby nonpolar atom/molecule) 53 Secondary Interatomic Bonds II O H H - + + Dipole Figure 4.8: Hydrogen bond secondary bond formed between two permanent dipoles in adjacent water molecules: the H end of the molecule is positively charged and can bond to the negative side of another H2 O molecule (the O side of the H2 O dipole), from. 54 Bonding in Real Materials Remark In many materials more than one type of bonding is involved: ionic and covalent in ceramics, covalent and secondary in polymers, covalent and ionic in semiconductors. Figure 4.9: Bonding in real materials, from. 55 Bonding Energy and Melting Temperatures for Various Substances 56  Properties Related to Bonding I: Melting Temperature (Tm) Bond length, r Melting Temperature, Tm Energy r Bond energy, Eo ro r Energy smaller Tm unstretched length larger Tm ro r Eo = The larger Eo, the higher Tm “bond energy” 57  Properties Related to Bonding II: Coefficient of Thermal Expansion (αl) Coefficient of thermal expansion, αl length, L o ΔL Lo = αl (T2 -T1) unheated, T1 ΔL heated, T 2 unstretched length r Energy o The smaller Eo, the larger αl. r larger αl Eo Eo smaller αl 58 Summary: Properties Related to Bonding Type and Bonding Energy Ceramics Large bond energy high Tm (Ionic & covalent bonding): large E small αl Metals Variable bond energy moderate Tm (Metallic bonding): moderate E moderate αl Polymers Weak bond energy (between chains) (Covalent & Secondary): Secondary bonding responsible for most physical properties low Tm small E large αl 59 Summary Make sure you understand language and concepts related to: Atomic number, Atomic weight, Bonding energy, Coulombic force, Cova- lent bond, Dipole (electric), Electron state, Electronegative, Electropositive, Hydrogen bond, Ionic bond, Metallic bond, Mole, Molecule, Periodic table, Polar molecule, Primary bonding, Secondary bonding, Van der Waals bond, Valence electron. 60 References 1 David W. Ball and Tomas Baer. Physical Chemistry. Cengage Learning, 2nd edition, 2014. 2 William D. Callister and David G. Rethwisch. Materials Science and Engineering: an introduction. John Wiley & Sons, 8th edition, 2010. 61