# Chapter 2: Atomic Structure and Chemical Bonding

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1 Chapter 2: Atomic Structure and Chemical Bonding Materials Molecules Atoms Atoms = protons (p) + neutrons (n) + electrons (e) Protons and neutrons are made of quarks Quantitative measurements need units: metric or S.I. (Systeme International) or mks (meter-kilogram-second) units meter (m) for length cubic meter (m 3 ) for volume kilogram (kg) for mass Kelvin (K) for temperature second (s) for time mole (mol) for amount of substance Chapter 2 1 Typical parameters: atoms are small Proton Neutron Electron Mass (kg) Charge (coulomb) Nuclear radius is measured in m = fm Electron radii measured in Å = 0.1 nm = m Fundamental charge = e = C Chapter 2 2 1

2 2.1 The Structure of Atoms Atomic number Z In neutral atom: # of protons = # of electrons = atomic number Z Value of Z is different for each element H (Z = 1), O (Z = 8), Fe (Z = 26) Isotopes Mass number Atomic number A Z X Element Same element (same Z) might have different # of neutrons (N) Same chemistry (same # of electron) Hydrogen: protium H-1; 1 H deutiruim H-2 or D 2 H tritium H-3 or T H Atomic mass unit (amu): 1/12 of C-12 (<1% of C-13, isotopically pure) Atomic mass A A Z + N Atomic weight (periodic table) weighted average of all isotopes Chapter Periodic Table of Elements Chapter 2 4 2

3 2.3 Electrons in Atoms One of the first models: Bohr atom Bohr assumed that electrons orbited the nucleus due to Coulomb forces Electrons could only be in one of infinitely many discrete states Explained spectra of H, He +, Li 2+ Not working for atoms with >1 electron Need a quantum mechanics approach Will summarize main points 1. Particles can have wave-like properties de Broglie suggested that any particles with momentum p(=m V, non-relativistically) displays wave-like properties: λ = h/p 2. Wave can have particle-like properties Light as a propagating wave of electric and magnetic fields Wavelength determines the colour Einstein showed that light is divided into packets of E (so called photons ) E = h f Chapter 2 5 The Heisenberg Uncertainty Principle 3. We can no longer describe a particle as having a precise position x and momentum p 4. The Heisenberg Uncertainty Principle We cannot know both x and p simultaneously with arbitrary precision There is a limit! δx δp h/ 2Π ħ We do know exactly where an electron is, we can t know how fast it is moving 5. Electrons in atoms can only be in certain states The energy is quantized only certain levels are permitted The level can change, but only if exactly the correct energy is emitted or absorbed 6. 4 quantum numbers: The state of an electron in an atom is described by a set of 4 quantum numbers principle quantum number n = 1, 2, 3, n subsidiary or azimuthal number L = 0, 1, 2, n-1 magnetic quantum number m L = 0, ±1, ±2, ±n-1 spin quantum number m S = ±½ 7. The Pauli Exclusion Principle: Two electrons in an atom can never have exactly the same set of all 4 quantum numbers (n, L, m L, m S ) Chapter 2 6 3

4 Possible electron states So what are the possible combinations of states? Notation n L 1 K 0 s 2 L 1 p 3 M 2 d 4 N 3 f We can describe an electron state as 1s or 3p or 5f Energy levels of the electron states the energy of an electron is determined by its state If there is only one electron in the atom, the energy depends on n alone If there are more electrons, they interact (repel each other), and so different states have different energies Chapter 2 7 Shell and Subshell Energies E Valence electrons The electrons in the outer shell (largest n) are called valence electrons Very important for chemical reactions and holding matter together If the outer shell is filled, the atom is inert If not, there is a tendency for the outer shell to become filled Principle quantum number, n Schematic representation of the relative energies of the electrons for various shells and subshells (adopted from Callister, Figure 2.4) Electronegative if it is almost full, the atom has a tendency to gain enough electrons to fill the shell Electropositive if it is almost empty, it easily losses the electrons in the outer shell Chapter 2 8 4

5 Periodic Table of Elements Chapter 2 9 Valence electrons The electrons in the outer shell (largest n) are called valence electrons Very important for chemical reactions and holding matter together If the outer shell is filled, the atom is inert If not, there is a tendency for the outer shell to become filled Electronegative if it is almost full, the atom has a tendency to gain enough electrons to fill the shell Electropositive if it is almost empty, it easily losses the electrons in the outer shell Chapter

6 Electronegativity Electronegativity is a degree to which an atom attracts electron to itself The electronegativity of the elements, adapted from Smith&Hashemi Chapter 2 11 Chemical reactivity: valence e-s Noble gases: s 2 p 6 configuration Ne: 1s 2 2s 2 p 6 Electronegative if it is almost full, the atom has a tendency to gain enough electrons to fill the shell Cl: 1s 2 2s 2 p 6 3s 2 p 5 or [Ne] 3s 2 p 5 Cl + 1e = Cl - negative ion (anion) Electropositive if it is almost empty, it easily losses the electrons in the outer shell (typically metals) K: 1s 2 2s 2 p 6 3s 2 p 6 4s 1 or [Ar] 4s K 1e = K + positive ion (cation) Oxidation number or oxidation state - not all allowed!!! Chapter

7 Periodic Table of Elements Chapter Types of atomic and molecular bonds Primary atomic bonds 1. Ionic (large interatomic forces, nondirectional, electron transfer, coulombic forces) 2. Covalent (large interatomic forces, localized (directional), electron sharing) 3. Metallic (large interatomic forces) nondirectional Secondary atomic and molecular bonds 1. Permanent dipole bonds 2. Fluctuating dipole bonds Chapter

8 Examples and characteristics of 5 types of bonds Bond type Examples Typical energies, ev/atom Distinct characteristics Ionic LiF, NaCl, CsCl 5-10 Nondirected bonding, giving structures of high coordination; no electrical conductivity at low temperature Covalent Diamond, Si, Ge 3-8 Spatially directed bonds, structures with low coordination; low conductivity at low temperature for pure crystals Metallic Li, Na, Cu, Ta Nondirected bond, structures of very high coordination and density; high electrical conductivity; ductility Fluctuating or permanent dipole Ne, Ar,Kr, Xe, CHCl Low melting and boiling points Hydrogen H 2 O, HF Increase in bonding energy over similar molecules without hydrogen bonds Chapter Ionic bonding Typically between highly electropositive (metallic) and electronegative (nonmetallic) elements NaCl Na 1s 2 2s 2 p 6 3s Cl 1s 2 2s 2 p 6 3s 2 p 5 Na + 1s 2 2s 2 p 6 Cl - 1s 2 2s 2 p 6 3s 2 p 6 Chapter

9 Force and Energy Diagram F net = F attactive + F repulvise The interionic energy can be defined as the energy needed to rip a compound into its components placed far apart (E NET ( ) = 0) 2 Z 1 Z 2 e b E NET = E attractive + E repulsive = + + n 4πε a a o Chapter 2 17 Q.: Calculate attractive force between Na + and Cl - ion at equilibrium interionic separation distance Chapter

10 Interionic Energies - the energy needed to rip a compound into its components placed far apart (E net ( ) = 0 2 Z1Z 2e b E net = Eattraction + Erepulsion = + + n 4Πε a a o Q2.: Calculate the net potential energy of a simple Na + Cl - ion pair in equilibrium (using the equation above) and assuming that n = 9 Chapter 2 19 Bonding Energies in Ionic Solids Typically large lattice energies (Table 2.6) kj/mol High melting temperatures 801 o C for NaCl For NaCl: E Na+Cl- = J = 4.63eV (2.315 per ion) Compare to 3.3eV (elsewhere): big difference! Chapter

11 Ionic Packing X-ray crystallography tells us most of ionic compounds (NaCl, CsCl, LiF, etc) are crystals Ionic radii of selected ions are listed in the table below (note increase in size, as their principle quantum number increases) No preferred orientation (nondirectional character of the ionic bond) Geometrical arrangements (coordination) and neutrality is maintained Cation Li+ Na+ K+ Rb+ Cs+ Ionic radius (nm) Anion Ionic radius (nm) F Cl Br I Chapter 2 21 Coordination and neutrality in ionic crystals CsCl: 8 Cl - ions can pack around Cs + R(Cs + )/R(Cl - )= = / = NaCl: 6 Cl - ions can pack around Na + R(Na + )/R(Cl - )= = / = Chapter

12 Evaluation of the Madelung Constant 1. Consider a cube of 8 ions 2. Consider a line of alternating in sign ions, with distance R between ions 3. Consider a lattice: lattice sum calculation can be used to estimate Madelung constant, α Structure α α = ± R j ij NaCl CsCl ZnS Chapter 2 23 Madelung constant for line of ions α N x R Chapter

13 Electronegativity Chapter Covalent bonding Takes place between elements with small difference in electronegativity - F, O, N, Cl, H, C, Si s and p electrons are commonly shared to attain noblegas electron configuration Multiple bonds can be formed by one atom Chapter

14 Hydrogen molecule 2 H: 1s H 2 1s 2 H +H H : H (electron pair covalent bond) Hydrogen molecule + + Bonding interaction Chapter 2 27 F 2s 2 2p 5 Other Covalent Molecules O 2s 2 2p 4 N 2s 2 2p 3 Bond energies and bond lengths of selected covalent bonds kj/mol (or ~ eV) 0.074nm (H 2 ) 0.18nm (C-Cl) Chapter

15 Covalent bonding by carbon C 1s 2 2s 2 2p 2 Formation of 4 equal covalent bond: hybridization sp 3 hybridization other hybridizations..? sp 2, sp Chapter 2 29 Carbon-containing molecules C and H: hydrocarbons Structural formulas: CH 4 (methane), C 2 H 6 (ethane), and C 4 H 10 (normal butane) Saturated C n H 2n+2 - strong bonds inside molecule, weak between molecules Unsaturated C n H 2n, C n H 2n-2 - generally more reactive Chapter

16 Benzene (C 6 H 6 ) important for some polymeric materials Chapter Metallic Bonding Consider Na metal: what holds it together? In solid state metal atoms are packed in a systematic pattern or crystal structure The valence electrons are weakly bonded to the positive-ion cores and can readily move as free electrons Positive ion cores Valence electrons in the form of electron charge clouds or electron gas Chapter

17 Nonlocalized behavior of electrons in metals High electrical conductivity - electrons move easily when E-field applied High thermal conductivity - the electrons can carry energy through metal High density - outer shell removed from atoms, so can be packed together High ductility - if metal distorted, bent, electrons can quickly move to compensate - metal bond is not directional Chapter Secondary Bonding Fluctuating or permanent dipoles (also called physical bonds, or van der Waals bonds or forces) weak relatively to the primary bonding (2-5eV/atom or ion) ~ 0.1eV/atom or ~ 10 kj/mol always present, but overwhelmed by other interaction most easily observed in inert gases dipoles to be considered Chapter

18 Electric dipole + - -a/2 0 + a/2 Dipole moment [debye]: µ = e a 2 ke ke U = + 2 x a x 2 consider a + and - charge (e) separated by a distance a What is the PE (U) of two dipoles in a distance x apart? a/2 0 + a/2 2 ke x + a x -a/2 x x + a/2 Chapter 2 35 Fluctuation Dipole Noble-gas elements: s 2 p 6 Stronger effect for larger electron shells Boiling temperature increases as a function of Z Schematic representation of how the van-der- Waals bond is formed by interaction of induced dipoles. Chapter

19 Permanent Dipoles When a covalent molecule has permanent dipole? Depends on geometry of the molecule CH 4? CH 3 Cl? H 2 O? Q.: Calculate the dipole moment associated with the ionic model of the water molecule. The length of the O-H bond is 0.097nm and the angle between the bonds is o. Hydrogen bond: permanent dipole-dipole interaction for the molecules with a hydrogen atoms bonded to a highly electronegative element (F, Cl, O, N) e.g.: H 2 O, polymeric materials Permanent dipole bond: a secondary bond created by the attraction of molecules that have permanent dipoles Chapter 2 37 Q.: Calculate the dipole moment associated with the ionic model of the water molecule. The length of the O-H bond is 0.097nm and the angle between the H-O-H bonds is o. Chapter

20 2.9 Mixed Bonding Ionic - Covalent Mixed Bonding AB: % _ ionic _ character = 100% 1 e 1 2 ( X A X B ) 4 where X A and X B are the electronegativity of the atoms A and B (Table above) e.g. ZnSe, GaAs Metallic - Ionic Mixed Bonding Typical for intermetallic compounds between elements with significant difference in electronegative e.g.: NaZn 13 Chapter 2 39 Summary Primary atomic bonds 1. Ionic (large interatomic forces, nondirectional, electron transfer, coulombic forces) 2 Z1Z 2e b E net = Eattraction + Erepulsion = + + n 4Πε a a 2. Covalent (large interatomic forces, localized (directional), electron sharing) 3. Metallic (large interatomic forces, nondirectional) o Secondary atomic and molecular bonds Dipole moment [debye]: µ = e a 1. Permanent dipole bonds 2. Fluctuating dipole bonds Chapter

21 Periodic Table of Elements Chapter 2 41 Problems 2.1 How many atoms are there in 1 g of copper? 2.2. What is the mass in grams of one atom of copper? 2.3 The first Canadian pennies were made in 1858 and had a diameter of 25.4 mm and weight of 4.54 grams. Composition of the penny was 95% copper, 4% tin, 1% zinc (weight %) alloy. (a) What are the atomic percentages of Cu, Sn and Zn in this alloy? (b) Imagine that you found 1234 such pennies in your backyard. The current scrap copper value is ~ \$3.4/kg (Cu). How much will you gain, if you give this treasure away as a scrap copper metal? 2.4 What is the chemical formula of an intermetallic compound that consists of 15.68wt% Mg and 84.32wt % Al? 2.5 Calculate the energy in joules and electron volts of the photon whose wavelength is 303.4nm. 2.6 A hydrogen atom exists with its electron in the n = 6 state. The electron undergoes a transition to the n = 2 state. Calculate (a) the energy of the photon emitted, (b) its frequency, and (c) its wavelength in nanometers. 2.7 Write the electron configuration of the following ions using the spdf notation (a) Mn 2+, Mn3+, Mn 7+ ; (b) S 4+, S 6+, S 2- ; (c) Mo 3+, Mo 4+, Mo Carbon tetrachloride (CCl 4 ) has a zero dipole moment. What does this tell us about the C-Cl bonding arrangement in this molecule? Chapter

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