Chapter 2 CHEMICAL BONDS IONIC BONDS 2 1

Chapter 2. CHEMICAL BONDS IONIC BONDS 2. 1 The Ions That Elements Form 2. 2 Lewis Symbols 2. 3 The Energetics of Ionic Bond Formation 2. 4 Interactions Between Ions COVALENT BONDS 2. 5 Lewis Structures 2. 6 Lewis Structures of Polyatomic Species 2. 7 Resonance 2. 8 Formal Charge 2012 General Chemistry I 1

Key Ideas and Definitions Bond formation is accompanied by a lowering of energy: it is a favorable process. Formation of chemical bonds results in ionic lattices, molecules, and metallic lattices. It is fundamental to the production of compounds and so is central to the science of chemistry. Energy lowering is due to attractions between oppositely charged ions (ionic bonding), or between nuclei and shared electron pairs (covalent bonding). Ø Chemical bond is the link between atoms. - ionic bond i. e. Na+, Cl- covalent bond i. e. NH 3 - metallic bond i. e. Cu 2012 General Chemistry I 2

IONIC BONDS (Sections 2. 1 -2. 4) Ø Ionic model: the description of bonding in terms of ions An ionic solid is an assembly of cations and anions stacked together in a regular pattern, called a crystal lattice. 2. 1 The Ions That Elements Form Ø Cations are formed by removal of outermost electrons in the order np, ns, (n-1)d. Ø Main-group metal atoms lose their valence s- and/or pelectrons and acquire the electron configuration of the preceding noble gas atom. 2012 General Chemistry I 3

Ø Anions: Add electrons until the next noble-gas configuration is reached 2012 General Chemistry I 4

Self-Tests 2. 1 B and 2. 2 B 2. 1 B Write the electron configurations of (a) the Manganese (II) ion and (b) the lead (IV) ion. Solution: (a) Mn is [Ar] 3 d 5 4 s 2, hence Mn 2+ is [Ar] 3 d 5 (b) Pb is [Xe] 5 d 10 4 f 14 6 s 2 6 p 2, hence Pb 4+ is [Xe] 5 d 10 4 f 14 2. 2 B Write the chemical formula and electron configuration of the iodide ion. Solution: I needs to gain only one electron to achieve Xe electron structure, hence I- and [Xe] or [Kr] 4 d 10 4 s 2 4 p 6 2012 General Chemistry I 5

2. 2 Lewis Symbols Atoms and ions are conveniently represented by Lewis dot symbols, showing the element symbol, the valence electrons and charge, if any. Valence electrons – depicted as dots; a pair of dots for paired electrons. - Atoms - Cations and anions Here, we can use Lewis dot symbols to show electron transfer in the formation of cations and anions. 2012 General Chemistry I 6

Gilbert N Lewis 2012 General Chemistry I 7

2. 3 The Energetics of Ionic Bond Formation The formation of a typical ionic compound, such as sodium chloride can be broken down into three simple steps: 1. Ionization of gaseous metallic atom to give the cation. 2. Formation of gaseous non-metallic anion. 3. Condensation of the gaseous ions into a crystal lattice. The energies involved in these processes illustrate the favorability of ionic compound formation (see Fig. 2. 4, next slide): Na(g) → Na+(g) + e- (g) 494 k. J·mol-1 Cl(g) + e- (g) → Cl-(g) -349 k. J·mol-1 Na+(g) + Cl- (g) → Na. Cl(s) -787 k. J·mol-1 Na(g) + Cl(g) → Na. Cl(s) -642 k. J·mol-1 2012 General Chemistry I 8

Energetics of ionic compound formation. The difference in energy between the ions in the lattice and separated gaseous ions is called the lattice energy. 2012 General Chemistry I 9

2. 4 Interactions Between Ions - In an ionic solid, each cation is attracted to all the anions to a greater or lesser extent. This is a “global” characteristic of the entire crystal Ø Lattice energy: the difference in energy between the ions packed together in a solid and the ions widely separated as a gas - Strong electrostatic interactions in ionic solids → high melting points and brittleness 2012 General Chemistry I 10

- Coulomb potential energy of the interactions of two individual ions: Here, e is the fundamental charge; z 1 and z 2 are the charge numbers of the two ions; r 12 is the distance between the centers of the ions; e 0 is the vacuum permittivity constant. - Molar potential energy of a three-dimensional crystal: d = distance between centers of neighboring ions (rcation + ranion) NA is the Avogadro number Ø The factor A is the Madelung constant, dependent on how the ions are arranged about one another in the 3 -dimensional lattice. 2012 General Chemistry I 11

One-Dimensional Crystal Model - In a one-dimensional crystal in which cations and anions alternate along a line: 2012 General Chemistry I 12

This implies Ep is most favorable for small ions with large charges. Also for a one dimensional model crystal, the Madelung constant A is 2 ln 2 = 1. 386. This compares well with values of A for real ionic crystals (Table 2. 2). For multi-charged ions (z 1 and z 2), z 2 is replaced by the absolute value of z 1 z 2 (its value without the negative sign). 2012 General Chemistry I 13

Self-Test 2. 3 A The ionic solids KCl and Ca. O crystallize to form structures of the same type. In which compound are the interactions between the ions stronger? Solution: The ions in Ca. O are both smaller and more highly charged, hence Ca. O has the stronger interactions. 2012 General Chemistry I 14

Attraction, Repulsion and the Born-Mayer Equation The previous discussion does not take into account cation-anion repulsion – the real potential energy of an ionic solid is a balance between attractive and repulsive interionic interactions. If a cation and anion are brought together (see Fig. 2. 7, opposite), potential energy decreases to a minimum value. Further decrease in d, leads to serious unfavorable repulsive interaction. 2012 General Chemistry I 15

Ø Born-Mayer equation with d* = 34. 5 pm repulsive effect This equation allows for repulsive interactions at small values of d: EP, min increases (becomes less favorable) when d approaches d* and is actually positive when d* > d. 2012 General Chemistry I 16

COVALENT BONDS (Sections 2. 5 -2. 8) 2. 5 Lewis Structures Some Definitions According to Lewis Theory Ø Covalent bond - a pair of electrons shared between two atoms - Octet rule: in covalent bond formation, atoms go as far as possible toward completing their octets by sharing electron pairs. - Valence of an atom is the number of bonds it can form. - A line (-) represents a shared pair of electrons. - Lone pairs of electrons – electron pairs not involved in bonding. - Lewis structure – atoms are indicated by chemical symbols, covalent bonds by lines, and lone pairs by pairs of dots. 2012 General Chemistry I 17

Self-Test 2. 4 A Write the Lewis structure for the “interhalogen” compound chlorine monofluoride, Cl. F, and state how many lone pairs each atom possesses in the compound. Solution 2012 General Chemistry I 18

2. 6 Lewis Structures of Polyatomic Species – A Lewis structure does not portray the 3 D shape of a molecule or ion, but simply displays which atoms are bonded together. - - bond order: the number of bonds that link a specific pair of atoms. 2012 General Chemistry I 19

Ø Writing a Lewis Structure 1. Count the total number of valence electrons, from the group numbers E. g. CO 2 4 + 2 x 6 = 16 (C in group IVA; O in group VIA) NOTE: if an anion (-), add the value of the charge; if a cation (+), subtract that value. 2. Calculate the total number of electrons that are needed if each atom had its own noble gas shell of electrons (2 for H and 8 for all others). E. g. for CO 2 there are 3 atoms (no H) and hence 24 noble gas shell electrons. 3. Subtract the number in 1 from the number in 2: this gives the number of shared (bonding) electrons present (and number of bonds = 1/2 that number). 4. Add electron pairs to “complete the octets”, as necessary. 5. Represent each bond by a line. 2012 General Chemistry I 20

E. g. for CO 2, the figure is 24 – 16 = 8 (4 bonds: two “double bonds”) Hence the Lewis diagram is The above works well only for molecules that obey the octet rule. For certain molecules (like BF 3, radicals, and high valence compounds like SF 6), this rule is ignored. 2012 General Chemistry I 21

Ø Writing a Lewis Structure: Rules of Thumb - Terminal atom: bonded to only one other atom - Central atom: bonded to at least two other atoms – Usually, element with lowest I 1 or lowest electronegativity is central atom. E. g. , in HCN, carbon has lowest I 1 and is least electronegative: hence it is the central atom. – Usually, there is symmetrical arrangement around central atom. E. g. , in SO 2, OSO is symmetrical, with S central and O terminal. – Oxoacids have H atoms mostly bonded to O atoms. E. g. , H 2 SO 4 is actually (HO)2 SO 2, with two O atoms and two OH groups bonded to S. – For organic compounds, the atoms are arranged into groups, as suggested by the standard molecular formula. E. g. , CH 3 COOH = one CH 3 group and one COOH group. 2012 General Chemistry I 22

Examples . . : . . . 2012 General Chemistry I 23

Self-Test 2. 5 A Write a Lewis structure for the cyanate ion, NCO- (sometime written CNO-). 2012 General Chemistry I

Self-Test 2. 6 A Write a Lewis structure for the urea molecule, (NH 2)2 CO 2012 General Chemistry I 25

2. 7 Resonance – Multiple Lewis structures: many compounds can be represented by different Lewis structures in which the location of electrons (but not nuclei) differ. They are known as resonance structures, each making a contribution to the real structure of the molecule (called a “resonance hybrid”). – The resonance symbol is a double-headed arrow (↔), indicating a blend of the contributing structures: – Resonance implies delocalization: in which a shared electron pair is distributed over several pairs of atoms and cannot be identified with just one pair of atoms. 2012 General Chemistry I 26

Ø Benzene, C 6 H 6 - No reactions typical of compounds with double bonds - All the carbon-carbon bonds with the same length - Only one 1, 2 -dichlorobenzene exists. 2012 General Chemistry I 27

Self-Test 2. 7 B Write Lewis structures contributing to the resonance _ hybrid for the nitrite ion, NO 2 2012 General Chemistry I 28

) 2012 General Chemistry I 29

2. 8 Formal Charge Ø Formal charge – the charge an atom would have if the bonding were perfectly covalent in the sense that the atom had exactly a halfshare of the bonding electrons. V = the number of valence electrons in the free atom L = the number of electrons present on the bonded atom as lone pairs B = the number of bonding electrons on the atom - A Lewis structure in which the formal charges of the individual atoms are closest to zero typically represents the lowest energy arrangement of the atoms and electrons. 2012 General Chemistry I 30

– Formal charge exaggerates the covalent character of bonds by assuming that the electrons are shared equally. – Oxidation number (state) exaggerates the ionic character of bonds. It represents the atoms as ions, and all the electrons in a bond are assigned to the atom with the lower ionization energy. formal charge 2012 General Chemistry I oxidation state 31

Self-Test 2. 8 B Suggest a likely structure for the oxygen difluoride molecule. Write its Lewis structure and formal charges. 2012 General Chemistry I 32

Chapter 2. CHEMICAL BONDS EXCEPTIONS TO THE OCTET RULE 2. 9 Radicals and Biradicals 2. 10 Expanded Valence Shells 2. 11 The Unusual Structures of Some Group 13/III Compounds IONIC VERSUS COVALENT BONDS 2. 12 Correcting the Covalent Model: Electronegativity 2. 13 Correcting the Ionic Model: Polarizability THE STRENGTH AND LENGTHS OF COVALENT BONDS 2. 14 Bond Strength 2. 15 Variation in Bond Strength 2. 16 Bond Lengths 2012 General Chemistry I 33

2. 9 Radicals and Biradicals Ø There are three types of molecules for which the octet rule of Lewis has to be dropped: 1. Odd-electron molecules (radicals) 2. High valence molecules (hypervalent compounds) (See 2. 10) 3. Low valence molecules (especially of group IIA and IIIA elements) (See 2. 11) 2012 General Chemistry I 34

Ø Radicals are species with at least one unpaired electron. They are often highly reactive. Examples Biradicals: molecules with two unpaired electrons 2012 General Chemistry I

Self-Test 2. 9 A Write a Lewis structure for the hydrogenperoxyl radical, HOO. (etc). 2012 General Chemistry I 36

2. 10 Expanded Valence Shells High valence compounds of elements in and beyond period 3 require Lewis structures that disobey the octet rule - more than 8 electrons are associated with the central atom in a Lewis structure. These are often called hypervalent compounds. Examples: 2012 General Chemistry I 37

– Variable covalence: the ability of certain elements to form different numbers of covalent bonds. Prevalent in elements of the p block in and beyond period 3. PCl 3(l) + Cl 2(g) PCl 5(s) Phosphorus trichloride Phosphorus pentachloride 2012 General Chemistry I 38

Self-Test 2. 10 A Write a Lewis structure for xenon tetrafluoride, Xe. F 4, and give the number of electrons in the expanded valence shell. 2012 General Chemistry I 39

Self-Test 2. 11 A Calculate the formal charge for the two Lewis structures of the phosphate ion shown in (27). 2012 General Chemistry I 40

2. 11 The Unusual Structures of Some Group IIIA/13 Compounds – Incomplete octet: many of the compounds of group IIIA are characterized by fewer than eight valence electrons around the central atom: 2012 General Chemistry I 41

– Their chemistry is dominated by completing octets using a coordinate covalent bond, in which both electrons come from a terminal atom. 2012 General Chemistry I 42

IONIC VERSUS COVALENT BONDS (Sections 2. 12 -2. 13) 2. 12 Correcting the Covalent Model: Electronegativity – Many covalent compounds have polar covalent bonds (with partial ionic character). – Polar covalent bond: a bond in which ionic contributions to resonance result in partial (d+ and d-) charges (the actual charges on the atoms in a molecule). Bond electrons in the resonance hybrid are shared unevenly. 2012 General Chemistry I 43

– An electric dipole results when a partial positive charge is next to an equal but opposite partial negative charge. It can be represented in two ways: - electric dipole moment (m): size of an electric dipole Debye For a Cl-H bond: m = ~1. 1 D, indicating considerable ionic character (~23%) 2012 General Chemistry I 44

Electronegativity Ø Electronegativity (c) was first defined by Linus Pauling (1932) as the electron-pulling power of an atom when it is part of a molecule. Pauling’s electronegativity scale is based on the difference in bond dissociation energies (in e. V) between A-A, B-B, and A-B. The electronegativity difference between two elements A and B is: c. A – c. B = {D(A-B) – ½[D(A-A) + D(B-B)}1/2 In time, the electronegativity of fluorine was chosen as 4. 0, and electronegativities of other elements are determined relative to this (maximum) value. See next slide for electronegativities of main group elements (Fig. 2. 12) 2012 General Chemistry I 45

Electronegativities of Main Group elements (Fig. 2. 12) c increases from left to right and from bottom to top 2012 General Chemistry I 46

Linus Pauling 2012 General Chemistry I 47

Robert Mulliken devized an electronegativity scale based on ionization energy and electron affinity: - Mulliken scale: c = ½(I 1 + Eea) (average of the ionization energy and electron affinity) Is a bond, covalent, polar covalent or ionic? -Rough rules of thumb based on electronegativity difference (Fig. 2. 13): ionic polar covalent Examples: Na. Cl or KF : ionic C-O : polar covalent Ca-O : ionic 2012 General Chemistry I 48

Self-Test 2. 12 A In which of the following compounds do the bonds have greater ionic character: (a) P 4 O 10 or (b) PCl 3? Solution Difference in c for P and O = 1. 2 Difference in c for P and Cl = 1. 0 Hence the bonds in (a) have greater ionic character. 2012 General Chemistry I 49

2. 13 Correcting the Ionic Model: Polarizability – All ionic bonds have some covalent character. – Highly polarizable atoms and ions readily undergo a large distortion of their electron cloud. i. e. large anions and atoms such as I-, Br-, and Cl – Polarizing power is the property of ions (and atoms) that cause large distortions of electron clouds. It increases with decreasing size and increasing charge of a cation i. e. small and/or highly charged cations Li+, Be 2+, Mg 2+, and Al 3+ 2012 General Chemistry I 50

Self-Test 2. 13 A In which of the compounds Na. Br and Mg. Br 2 do the bonds have greater covalent character? Solution Mg 2+ is a smaller cation than Na+, hence Mg. Br 2 has bonds with greater covalent character. 2012 General Chemistry I 51

THE STRENGTHS AND LENGTHS OF COVALENT BONDS (Sections 2. 14 -2. 16) 2. 14 Bond Strength Ø Dissociation energy (D): energy required to separate the bonded atoms (Fig. 2. 15). - The bond breaking is homolytic, which means that each atom retains one of the electrons from the bond. 2012 General Chemistry I 52

- Average dissociation energy is for one type of bond found in many different molecules (Tables 2. 3 and 2. 4). E. g. the average C-H single bond dissociation energy gives average strength of bonds in a selection of organic molecules, such as methane (CH 4), ethane (C 2 H 6), and ethene (C 2 H 4) 2012 General Chemistry I 53

2. 15 Variation in Bond Strength Factors influencing bond strength Figs. 2. 16, 2. 17 Figs. 2. 18, 2. 19, 2. 20 Bond dissociation energies of N 2, O 2, and F 2 (Fig. 2. 16) (in k. J/mol) 2012 General Chemistry I 54

Strengths of single and multiple C-C bonds (Fig. 2. 16) (in k. J/mol) Strengths of H-halogen bonds (Fig. 2. 18) (in k. J/mol) 2012 General Chemistry I 55

2. 16 Bond Length Ø Bond length: the distance between the centers of two atoms joined by a covalent bond - It corresponds to the internuclear distance at the potential energy minimum for the two atoms - It affects the overall size and shape of a molecule, evaluated by using spectroscopy or x-ray diffraction methods Factors influencing bond length 2012 General Chemistry I 56

Ø Covalent radius is the contribution an atom to the length of a covalent bond. - Bond length is approximately the sum of the covalent radii of the two atoms. - Decreases from left to right (increasing Zeff) - Increases in going down a group (size of valence shells and better shielding by inner core electrons) 2012 General Chemistry I 57

INFRARED SPECTROSCOPY Ø Infrared radiation: electromagnetic radiation with longer wavelengths (lower frequencies) than red light ~ 1000 nm or ~ 3× 10 14 Hz -Molecules become vibrationally excited when they absorb infrared radiation of correct energy. - “stretching” mode: the atoms moving closer and away again. “bending” mode: bond angles periodically increase and decrease. Ø Vibrational frequencies - The stiffness of a bond measured by its force constant, k Force = -k × displacement by Hooke’s law - Vibrational frequency, n, of a bond between two atoms A and B of mass m. A and m. B: 2012 General Chemistry I m = effective mass (or reduced mass) 58

Ø Normal (fundamental) modes of vibration A nonlinear molecule consisting of N atoms → 3 N-6 normal modes A linear molecule → 3 N-5 normal modes i. e. H 2 O, n = 3 → 3 normal modes CO 2, n = 3 → 4 normal modes Ø Characteristic frequencies of functional groups detectable in a spectrum - fingerprint region: a complex series of absorptions 2012 General Chemistry I 59