Topic 6 - Liquids and Solids PDF

CHM012 Chemistry for Engineers Topic 6: Liquids and Solids MA. KARLA B. CARMONA, M.Sc., R.Ch. Department of Chemistry College of Science and Mathematics MSU-Iligan Institute of Technology makarla.ba...

CHM012 Chemistry for Engineers Topic 6: Liquids and Solids MA. KARLA B. CARMONA, M.Sc., R.Ch. Department of Chemistry College of Science and Mathematics MSU-Iligan Institute of Technology [email protected] | Page  States of Matter ❖ The fundamental difference between states of matter is the strength of the intermolecular forces (IMF) of attraction. ❖ Stronger forces bring molecules closer together. ❖ Liquids are much denser and far less compressible than gases (strong IMF); assumes the shape of the container it occupies (weak IMF). ❖ Solids hold particles close together and to lock them virtually in place (strong IMF). ❖ Liquids and solids are the condensed states of matter because they are formed by forces that may involve: Covalent bonding Ionic bonding Intermolecular forces Topic 6: Liquids and Solids |Page 2  States of Matter ❖ The state of a substance depends largely on the balance between the kinetic energies of the particles (atoms, molecules or ions) and the interparticle energies of attraction. ❖ The interparticle attractions tend to draw the particles together (at room temp, gases < liquids < solids). ❖ Substance change from one state to another by increasing or decreasing temperature and pressure. ❖ Temperature (↑), KE (↑) ❖ Pressure (↑), IMF (↑) Topic 6: Liquids and Solids |Page 3  Intermolecular Forces ⮚ They are forces that occur between molecules. ⮚ The attractions between molecules are not nearly as strong as the intramolecular attractions (bonds) that hold compounds together. ⮚ Many physical properties reflect intermolecular forces, like boiling points, melting points, viscosity, surface tension, and capillary action. Types of Intermolecular Forces, IMFs (Weakest to strongest forces) The melting and boiling points of substances in which the particles are held together by chemical bonds tend ❖ dispersion forces (or London dispersion forces) to be much higher than those of ❖ dipole–dipole forces substances in which the particles are ❖ hydrogen bonding (a special dipole–dipole force) held together by intermolecular forces. ❖ ion–dipole forces (important in solutions) Note: The first two types are also referred to collectively as van der Waals forces. Topic 6: Liquids and Solids |Page 4  London Dispersion Forces They exist among noble gas atoms and nonpolar molecules. ❖ Instantaneous dipole that occurs accidentally in a given atom induces a similar dipole in a neighboring atom which instigates weak and short-lived interatomic attraction. ❖ The tendency of an electron cloud to distort is called its polarizability. (The greater the polarizability, the more easily the electron cloud can be distorted to give an instantaneous dipole; more polarizable molecules have larger dispersion forces ) Factors that Affect Dispersion Force in a Molecule 1. number of electrons in an atom (more electrons, more dispersion force) – large atoms easily polarizable. 2. size of atom or molecule/molecular weight – higher BP 3. shape of molecules with similar masses (more compact, less dispersion force) Topic 6: Liquids and Solids |Page 5  Dipole–Dipole Forces ⮚ Exhibited by molecules with polar bonds that behave in an electric field Attract each other electrostatically Also called dipole–dipole attraction ⮚ Dipoles find the best compromise between attraction and repulsion. ⮚ Dipole–dipole forces are effective only when molecules are very close together. ⮚ Characteristics: Only 1% as strong as covalent or ionic bonds Forces grow weaker as distance between dipoles increase a. The electrostatic interaction of two polar molecules b. The interaction of many dipoles in a condensed state Topic 6: Liquids and Solids |Page 6  Dipole–Dipole Forces Note: For molecules of approximately equal mass and size, the more polar the molecule, the higher its boiling point. Topic 6: Liquids and Solids |Page 7  Hydrogen Bonding ❖ Strong dipole–dipole forces can be noticed when H is bound to lone pairs on highly electronegative atoms like N, O, and F. ❖ Strength of interactions can be characterized by: Polarity of the bond Close approach of the dipoles Small size of the hydrogen atom ❖ Such bonding affects the physical properties of elements Important in organic molecules (example: Methanol, Ethanol) Note: Blue dotted lines represent intermolecular forces between the water molecules Topic 6: Liquids and Solids |Page 8  The Boiling Points of the Covalent Hydrides of the Elements in Groups 4A, 5A, 6A, and 7A Which Have a Greater Effect: Dipole–Dipole Interactions or Dispersion Forces? If two molecules are of comparable size and shape, dipole–dipole interactions will likely be the dominating force. If one molecule is much larger than another, dispersion forces will likely determine its physical properties. Topic 6: Liquids and Solids |Page 9  Ion–Dipole Interactions ❖ Exists between an ion and a polar molecule. ❖ Ion–dipole interactions are found in solutions of ions. ❖ The strength of these forces is what makes it possible for ionic substances to dissolve in polar solvents. Topic 6: Liquids and Solids |Page 10  Intermolecular Forces – Summary Topic 6: Liquids and Solids |Page 11  Example 1. Based on the following Lewis structures, which molecule has a higher boiling point? Why? Topic 6: Liquids and Solids |Page 12  Example 1. In which of these substances is hydrogen bonding likely to play an important role in determining physical properties: methane (CH4), hydrazine (H2NNH2), methyl fluoride (CH3F), hydrogen sulfide (H2S)? Topic 6: Liquids and Solids |Page 14  Characteristics of Liquid ⮚ Liquids exhibit low compressibility, lack of rigidity, and high density ⮚ Surface tension is the resistance of a liquid to an increase in its surface area – Liquids with large intermolecular forces tend to have high surface tensions ⮚ Capillary action is a spontaneous rising of a liquid in a narrow tube - involves adhesive and cohesive forces Adhesive forces attract the liquid to the wall of the tube. Cohesive forces attract the liquid to itself. ❖ Water has stronger adhesive forces with glass; mercury has stronger cohesive forces with itself. Topic 6: Liquids and Solids |Page 15  Characteristics of Liquid ⮚ Viscosity refers to the measure of a liquid’s resistance to flow. ⮚ Liquids with large intermolecular forces or molecular complexity tend to be highly viscous ⮚ viscosity increases with molecular weight ⮚ viscosity decreases with increasing temperature. Topic 6: Liquids and Solids |Page 16  Phase Change ⮚ Conversion from one state of matter to another is called a phase change. ⮚ Energy is either added or released in a phase change. ⮚ Phase changes: melting/freezing – the heat of fusion (ΔHfus) is the energy required to change a solid at its melting point to a liquid. vaporizing/condensing – the heat of vaporization (ΔHvap) is the energy required to change a liquid at its boiling point to a gas. subliming/depositing - the heat of sublimation (ΔHsub) is the energy required to change a solid directly to a gas. Topic 6: Liquids and Solids |Page 17  Heating Curves ❖ A plot of temperature vs. heat added is called a heating curve. ❖ Within a phase, the amount of heat needed to raise the temperature of a substance is the product of specific heat, sample mass, and temperature change. 𝐇𝐞𝐚𝐭 = 𝐦 𝐱 𝐂𝐩 𝐱 𝚫𝐓 ❖ The temperature of the substance does not rise during a phase change because the added energy is used to overcome the attractive forces between molecules. ❖ During the phase change, the product of mass and the heat of fusion or vaporization is heat. 𝐇𝐞𝐚𝐭 = 𝐦 𝐱 𝚫𝐇𝐯𝐚𝐩 Topic 6: Liquids and Solids |Page 18  Vapor Pressure ⮚ At any temperature, some liquid molecules have enough energy to escape the surface and become a gas. ⮚ Vapor pressure increases significantly with temperature. (As the temperature rises, the fraction of molecules that have enough energy to break free increases. ⮚ As more molecules escape the liquid, the pressure they exert increases. ⮚ The liquid and vapor reach a state of dynamic equilibrium: liquid molecules evaporate, and vapor molecules condense at the same rate. Substances with high vapor pressure, ⮚ The vapor pressure present at equilibrium is also called evaporate more quickly – Volatile equilibrium vapor pressure. Topic 6: Liquids and Solids |Page 19  Estimation of Vapor Pressure Using a Simple Barometer ⮚ Vapor pressure can be determined principally by the size of intermolecular forces in the liquid. ⮚ Liquids with large intermolecular forces have relatively low vapor pressures - molecules need a higher energy to escape the vapor phase. ⮚ Substances with large molar masses have low vapor pressures - attributed to larger dispersion forces. Topic 6: Liquids and Solids |Page 20  Boiling Point The boiling point of a liquid is the temperature at which its vapor pressure equals atmospheric pressure. The normal boiling point is the temperature at which its vapor pressure is 760 torr or 1 atm. Normal melting point: Temperature at which solid and liquid states have identical vapor pressure, and total pressure = 1 atm The effect of pressure on boiling point explains why it takes longer to cook food at high elevations than it does at sea level. Topic 6: Liquids and Solids |Page 21  Clausius–Clapeyron Equation ❖ The natural log of the vapor pressure of a liquid is inversely proportional to its temperature. This relationship is quantified in the Clausius–Clapeyron equation. ❖ When the values of ΔHvap and Pvap at constant temperature are known, it is easy to calculate the value of Pvap at another temperature. Note: R = 8.3145 J/mol K Topic 6: Liquids and Solids |Page 22  Example The vapor pressure of water at 25°C is 23.8 torr, and the heat of vaporization of water at 25°C is 43.9 kJ/mol. Calculate the vapor pressure of water at 50°C. Solution Given T1 = 25oC + 273.15 = 298.15 K T2 = 50oC + 273.15 = 323.15 K ∆Hvap = 43.9 kJ/mol P1 = 23.8 torr P2 = ? Topic 6: Liquids and Solids |Page 23  Phase Diagrams ❖ A convenient way of representing the phases of a substance as a function of its temperature and pressure ❖ Triple point: The temperature at which all three phases exist simultaneously ❖ Critical point: The critical pressure and critical temperature, together, define this point Critical pressure: Pressure required to produce liquefaction at critical temperature. Critical temperature: The temperature above which a liquid cannot be liquefied, irrespective of pressure applied Topic 6: Liquids and Solids |Page 24  Phase Diagram of Water ❖ At point X on the phase diagram, water is a solid ❖ As the external pressure is increased while the Liquid temperature remains constant, the solid/liquid line is crossed and the ice melts ❖ The solid/liquid boundary line is a negative slope Melting point of ice decreases with increased Solid external pressure ❖ At the melting point, liquid and solid are in dynamic X equilibrium When pressure is applied, the volume is reduced Gas A given mass of ice has more volume at 0°C than the same mass of water in liquid state Freezing point of water is less than 0°C when pressure is greater than 1 atm Topic 6: Liquids and Solids |Page 25  Phase Diagram of Carbon dioxide ❖ The liquid state does not exist at a pressure of 1 atm ❖ The solid/liquid line has a positive slope, since the density of solid carbon dioxide is greater than that of liquid carbon dioxide Interpretations: Solid/liquid line is a positive slope Triple point occurs at 5.1 atm and −56.6°C Critical point can be noticed at 72.8 atm and 31°C Sublimation occurs at −78°C Applications: Dry ice - A convenient refrigerant because it does not undergo the liquid phase under normal atmospheric conditions Liquid form is used in fire extinguishers at 25°C under high pressure Topic 6: Liquids and Solids |Page 26  Classification of Solids ❖ Amorphous solids have disordered structures. Example – Glass ❖ Crystalline solids have a highly regular arrangement of components. ❖ Positions of components are represented by lattice(s) – three-dimensional system of points that designates the position of the components of a substance. Topic 6: Liquids and Solids | Page 43  Classification of Solids Unit Cell The basis of a repeating pattern is the unit cell. The structure of a crystalline solid is defined by: the size and shape of the unit cell. the locations of atoms within the unit cell. Portion of a 3-D lattice Lattice Points Positions that define the overall structure of the crystalline compound are called lattice points. Each lattice point has an identical environment. Lattice vectors connect the points and define the unit cell. Topic 6: Liquids and Solids | Page 44  2-D Lattices Topic 6: Liquids and Solids | Page 45  3-D Lattices Topic 6: Liquids and Solids | Page 46  Primitive vs. Centered Lattices ⮚ Primitive lattices have atoms only in the lattice points. ⮚ Centered lattices have atoms in another regular location, most commonly the body-center or the face-center. ▪ A body-centered cubic (bcc) lattice – has one lattice point at the center of the unit cell; ▪ A face-centered cubic (fcc) lattice – has one lattice point at the center of each of the six faces of the unit cell. Topic 6: Liquids and Solids | Page 47  Cubic Structures ⮚ Not every part of an atom on a lattice point is completely within that unit cell. One can determine how many atoms are within each unit cell. ⮚ Eight cubes meet at a corner, therefore only 1/8 of that corner atom is within any one unit cell meeting there. ⮚ Two cubes meet at a face, therefore only 1/2 of that face atom is within any one unit cell meeting there. ⮚ A body-centered atom is entirely within the unit cell. Topic 6: Liquids and Solids | Page 48  X-Ray Analysis of Solids ❖ X-ray diffraction is used to determine Bragg Equation 𝑛𝜆 = 2𝑑 sin 𝜃 the structure of crystalline solids. Where: n - is an integer λ - is the wavelength of the X-rays ❖ Diffraction occurs due to: d - is the distance between atoms Constructive interference when θ - is the angle of incidence and reflection parallel beam waves are in phase Destructive interference when waves are out of phase ❖ Distance traveled by waves depends on the distance between the atoms. ❖ A diffractometer is used to carry out X- ray analysis of crystals Topic 6: Liquids and Solids | Page 49  Example X-rays of wavelength 1.54 Å were used to analyze an aluminum crystal. A reflection was produced at θ = 19.3 degrees. Assuming n = 1, calculate the distance d between the planes of atoms producing this reflection Solution given: λ = 1.54 Å θ = 19.3o n=1 d =? 𝑛𝜆 = 2𝑑 sin 𝜃 Topic 6: Liquids and Solids | Page 50  Classification of Solids https://byjus.com/chemistry/classification-of-solids-based-on-crystal-structure/ Topic 6: Liquids and Solids | Page 51  Types of Crystalline Solid ❖ Ionic solids possess ions at the points of the lattice that describe their structures ❖ Molecular solids have discrete covalently bonded molecules at each lattice point(s) ❖ An atomic solid has atoms at the lattice points that describe its structure Metallic solids - a special type of delocalized nondirectional covalent bonding Covalent – Network solids - the atoms bond to each other with strong directional covalent bonds Group 8A (18) solids - noble gas elements are attracted to each other with London dispersion forces Topic 6: Liquids and Solids | Page 52  Structures of Metals Closest packing is an arrangement that assumes that metal atoms are hard, uniform spheres. These spheres are packed in layers. Each successive layer is formed when spheres occupy a dimple formed by the spheres of the previous layer. Forms of closest packing: ⮚ aba packing ⮚ abc packing Topic 6: Liquids and Solids | Page 53  aba Packing ❖ The 2nd layer is like the 1st, but it is displaced, so that each sphere in the 2nd layer occupies a dimple in the 1st layer ❖ The spheres in the 3rd layer occupy dimples in the 2nd layer. Spheres in the 3rd layer lie directly over those in the 1st layer ❖ The resultant structures are called hexagonal closest packed (hcp) structures The spheres in every layer occupy the same vertical position When the spheres are aba closest packed, the unit cell is a hexagonal prism Topic 6: Liquids and Solids | Page 54  Hexagonal Closest Packing, hcp Topic 6: Liquids and Solids | Page 55  abc Packing ❖ The spheres in the 3rd layer occupy dimples in the 2nd layer ❖ Spheres in the 3rd layer do not rest above spheres in the 1st layer ❖ The 4th layer is like the 1st ❖ The resultant structure is termed a cubic closest packed (ccp) structure The spheres in every fourth layer occupy the same vertical position In abc packing, the unit cell is face-centered cubic Topic 6: Liquids and Solids | Page 56  Cubic Closest Packing, ccp Topic 6: Liquids and Solids | Page 57  Common Characteristics of the hcp and the ccp Structures Each sphere in both structures possesses 12 equivalent nearest neighbors Topic 6: Liquids and Solids | Page 58  Example Silver crystallizes in a cubic closest packed structure. The radius of a silver atom is 144 pm. Calculate the density of solid silver. Solution The unit cell of silver crystal is a face-centered cubic. The total number of silver atoms inside the unit cell = 4 atoms Topic 6: Liquids and Solids | Page 59  Example - continuation Solve for volume of the Ag crystal unit cell. 4r Using Pythagorean Theorem: a Topic 6: Liquids and Solids | Page 60  Example - continuation Solve for volume of the Ag crystal unit cell. 4r Using Pythagorean Theorem: a Topic 6: Liquids and Solids | Page 61  Bonding Models of Metal ⮚ A successful bonding model for metals must consider: Malleability Ductility Efficient uniform conduction of heat and electricity in all directions Durable High melting points ⮚ Bonding models for metals include: Electron sea model Band model (Molecular Orbital model) Topic 6: Liquids and Solids | Page 63  Electron Sea Model ❖ A regular array of metal cations are considered to be in a sea of mobile valence electrons ❖ Mobile electrons conduct heat and electricity ❖ Ions can freely move around when the metal is hammered or drawn into a wire ❖ The electrical and thermal conductivity, ductility, and malleability of metals is explained by this model. a. Representation of an alkali metal (Group 1A) with one valence electron a. Representation of an alkaline earth metal (Group 2A) with two valence electrons Topic 6: Liquids and Solids | Page 64  Molecular Orbital Model ❖ As the number of atoms in a chain increases, the energy gap between the bonding orbitals and between the antibonding orbitals disappears, resulting in a continuous band of energy. Topic 6: Liquids and Solids | Page 65  Molecular Orbital Model Topic 6: Liquids and Solids | Page 65  Molecular Orbital Model Electrical conductivity in a conductor, semiconductor, and insulator. Topic 6: Liquids and Solids | Page 65  Molecular Orbital Model ⮚ Most metals have d and p orbitals to consider. ⮚ Their MO diagrams lead to more bands that better explain conductivity and other properties of metals. ⮚ The existence of empty molecular orbitals close in energy to filled molecular orbitals explains the thermal and electrical conductivity of metal crystals. ⮚ Metals conduct electricity and heat very efficiently because of the availability of highly mobile electrons. ⮚ These mobile electrons account for the efficiency of the conduction of heat through metals. Topic 6: Liquids and Solids | Page 66  Metal Alloys An alloy is a substance that contains a mix of elements and possesses metallic properties Classification of alloys: 1. Substitutional alloy - where some of the host metal atoms are replaced by other metal atoms of similar size. (Ex. Brass - Cu metal have been replaced by Zn atoms, Sterling silver - 93% Ag and 7% Cu) 2. Interstitial alloy - where some of the holes in the closest packed metal structure are occupied by small atoms. (Ex. Steel - contains C atoms in the holes of an Fe crystal) 3. Heterogeneous alloys - components not dispersed uniformly. Topic 6: Liquids and Solids | Page 67  Network Solids Network solids are those atomic solids that contain directional covalent bonds which form solids that can be viewed as “giant molecules” Properties: Brittle nature Ineffective conductors of heat and electricity Hard color less Important elements: insulator Carbon – ex. Diamond and graphite slippery Silicon black conductor Topic 6: Liquids and Solids | Page 68  Diamond ⮚ Hardest naturally occurring substance ⮚ Each C atom is surrounded by a tetrahedral arrangement of other C atoms ⮚ Structure as per the localized electron model: Stable structure is obtained via covalent bonds Formed by the overlap of sp3 hybridized C atomic orbitals ⮚ Structure as per the molecular orbital theory: Large gaps between filled and empty levels Electron transfer is not easy Topic 6: Liquids and Solids | Page 69  Graphite ⮚ Slippery, black, and a conductor of heat and electricity ⮚ Structure is based on layers of C atoms arranged in fused six-membered rings. ⮚ ⮚ Structure as per the localized electron model: Shows trigonal planar arrangement 120-degree bond angles sp2 hybridization - three sp2 orbitals on each C atom fuse to form σbonds with three other C atoms. One 2p orbital remains unhybridized, perpendicular to the plane. ⮚ Structure as per the molecular orbital theory: All orbitals combine to form π MOs - assist in the stability of graphite. Delocalized electrons account for good electrical conductivity. Topic 6: Liquids and Solids | Page 70  Semiconductors ⮚ They have a gap between the occupied MOs (valence band) and the unoccupied ones (conduction band). ⮚ Electrons must enter the conduction band for electron transfer. ⮚ Group IVA elements have gaps between the bands of 0.08 to 3.05 eV (7 to 300 kJ/mol). Note: Band gaps over 3.5 eV lead to the material being an insulator. Topic 6: Liquids and Solids | Page 71  Semiconductors ⮚ Among elements, only Group IVA, all of which have 4 valence electrons, are semiconductors. ⮚ Inorganic semiconductors (like GaAs) tend to have an average of 4 valence electrons (3 for Ga, 5 for As). Topic 6: Liquids and Solids | Page 72  Semiconductors - Doping Doping – is changing the conductivity of semiconductors by adding an element with more or fewer electrons n-type semiconductor: A substance whose conductivity is increased by doping with atoms that have more valence electrons than those in the host crystal. n-type have more electrons, so the negative charge travels in the conductance band. p-type semiconductors: A substance whose conductivity is increased by doping with atoms having fewer valence electrons than the atoms of the host crystal. p-type have fewer electrons, so the “hole” travels in the valence band. Topic 6: Liquids and Solids | Page 73  Molecular Solids ⮚ Possess strong covalent bonding within molecules but weak forces between molecules ⮚ Forces among the molecules depend on the nature of the molecules. CO2, I2, P4, and S8 - No dipole moment; possess London dispersion forces. Molecules that possess dipole moments have greater intermolecular forces, especially when hydrogen bonding is viable. Solid CO2 (Dry Ice) Solid H2O (Ice) Topic 6: Liquids and Solids | Page 74  Ionic Solids ⮚ In ionic solids, the lattice comprises alternately charged ions. Held together by strong electrostatic forces between oppositely charged ions. ⮚ Structure is based on closest packing of spheres so that: Electrostatic attraction between oppositely charged ions is maximized. Repulsion among ions with like charges is minimized. ⮚ Attractions increases with increasing charges, and ions size decreases. ⮚ Ionic solids have very high melting and boiling points and are quintessential crystals. Topic 6: Liquids and Solids | Page 75  Ionic Solids Most favorable structures have cation–anion distances as close as possible, but the anion–anion and cation–cation distances are maximized. Three common structures for 1:1 salts: 1. CsCl structure 2. NaCl (rock salt) structure 3. Zinc blende (ZnS) structure Topic 6: Liquids and Solids | Page 76  Effect of Ion Size on Structure ⮚ The size of the cation compared to the anion (radius ratio) is the major factor in which structure is seen for ionic compounds. For spheres of a given diameter, the holes increase in size in the order: trigonal < tetrahedral < octahedral Topic 6: Liquids and Solids | Page 77  Example Determine the net number of Na+ and Cl− ions in the sodium chloride unit cell. Solution NaCl structure is a cubic closest pack thus forms a face-centered cubic unit cell. Cl- Chloride ion: Cl- Na+ Sodium ion: Na+ Formula Unit: Na4Cl4 Empirical Formula: NaCl Topic 6: Liquids and Solids | Page 79  Types and Properties of Solids Type of Solid: Atomic Molecular Ionic Network Metallic Group 8A Structural Unit: Atom Atom Atom Molecule Ion Type of Bonding: Directional Nondirectional covalent London Polar molecules: Ionic covalent bonds involving electrons dispersion dipole–dipole bonds that are delocalized forces interactions throughout the crystal Nonpolar molecules: London dispersion forces Typical Hard Wide range of hardness Soft Hard Properties: High melting Wide range of melting Very low Low melting point High melting point points melting point point Examples: Insulator Conductor Insulator Insulator Diamond Silver Argon(s) Ice (solid H2O) Sodium chloride Iron Dry ice (solid CO2) Calcium fluoride Brass Topic 6: Liquids and Solids | Page 80  Example Using the table on the types and properties of solids, classify each of the following substances according to the type of solid it forms a. Gold b. Carbon dioxide c. Lithium fluoride d. Krypton Solution: a. Solid gold is an atomic solid with metallic properties. b. Solid carbon dioxide contains nonpolar carbon dioxide molecules and is a molecular solid. c. Solid lithium fluoride contains Li1 and F2 ions and is a binary ionic solid. d. Solid krypton contains krypton atoms that can interact only through London dispersion forces. It is an atomic solid but has properties characteristic of a molecular solid with nonpolar molecules. Topic 6: Liquids and Solids | Page 82  References T.L. Brown, H.E. Lemay, B.E. Bursten, and C.J. Murphy. Chemistry: The Central Science, 12th ed. Prentice Hall, 2012. (Chapter 11 and 12) M.S. Silberberg. Principles of General Chemistry. McGraw Hill Higher Education, 2007 (Chapter 12) S.S. Zumdahl, S.A. Zumdahl, D.J. DeCoste. Chemistry: An Atoms First Approach. 3rd ed. Cengage Learning, 2021. (Chapter 9) Supplemental Notes Web references TOPIC 2 Chemical Bonding | Page 83