Bond Lengths and Energies

Skills to develop
Define bondlength and bond energy and note relationship between the two
Define bond order explain its relationship to bondlength or bond energy
Evaluate enthalpies of reactions using bond energies
Recognize covalent substances and characterize ionic character as difference in electonegativity
Describe trends in bondlengths of a series of related compounds


Bondlengths and Bond Energies

Distances between centers of bonded atoms are called bondlengths, or bond distances. Bondlengths vary depending on many factors, but in general, they are very consistent. Of course the bond orders affect bondlength, but bondlengths of the same order for the same pair of atoms in various molecules are very consistent. Thus, there are tables of interatomic distances or bondlengths in some standard handbooks.
Bondlength (pm) and bond energy (kJ/mol)

Bond Length Energy Bond Length Energy
H--H 74 436 H--C 109 413
C--C 154 348 H--N 101 391
N--N 145 170 H--O 96 366
O--O 148 145 H--F 92 568
F--F 142 158 H--Cl 127 432
Cl-Cl 199 243 H--Br 141 366
Br-Br 228 193 H--I 161 298
I--I 267 151
C--C 154 348
C--C 154 348 C=C 134 614
C--N 147 308 CºC 120 839
C--O 143 360
C--S 182 272 O--O 148 145
C--F 135 488 O=O 121 498
C--Cl 177 330
C--Br 194 288 N--N 145 170
C--I 214 216 NºN 110 945

Bondlengths are determined by X-ray diffraction of solids, by electron diffraction, and by spectroscopic methods (study the light absorbed or emitted by molecules).

The bondlengths ranges from the shortest of 74 pm for H-H to some 200 pm for large atoms, and the bond energies depends on bond order and lengths. sHalf of the bondlength of a single bond of two similar atoms is called covalent radius. The sum of two covalent radii of two atoms is usually the single bondlength. For example, the covalent radii of H and C are 37 and 77 pm respectively. The C-H bond is thus (37+77) 114 pm. Note that 77 pm = 154/2 pm.

The bond order is the number of electron pairs shared between two atoms in the formation of the bond. Bond order for C=C and O=O is 2. The amount of energy required to break a bond is called bond dissociation energy or simply bond energy. Since bondlengths are consistent, bond energies of similar bonds are also consistent. Thus, tables of bond energies are also of common occurence in handbooks. Some typical bondlengths in picometers (1 pm = 10-12 and bond energies in kJ/mol are given here to illustrate a general trend so that you are familiar with these quantities.

The bond energy is essentially the average enthalpy change for a gas reaction to break all the similar bonds. For the methane molecule, C(-H)4, 435 kJ is required to break a single C-H bond for a mole of methane, but breaking all four C-H bonds for a mole requires 1662 kJ. Thus the average bond energy is (1662/4) 416 (not 436) kJ/mol.

Bond energy is a measure of the strength of a chemical bond. The larger the bond energy, the stronger the bond.

Covalent Bonds

Bonds between the same type of atom are covalent bonds, and bonds between atoms when their electronegativity differs by a little (say 0.7) are also predominant covalent in character. There is also some covalent character between ions of what we usually call ionic solids. For example, bonds in the following substances are predominantly covalent:
Elements: H2, Li2, B2, C2, N2, O2, F2, Cl2, S8, P4, I2, diamond, graphite, silicon etc

Covalent compounds: H2O, NH2, CH4, H3C-CH3, H2C=CH2, SiO2, CO2, N2O4, NO2, SO2, SO2 etc.

Theoretically, even ionic bonds have some covalent character. Thus, the boundary between ionic and covalent bonds is a vague one.
For covalent bonds, bond energies and bondlengths depend on many factors: electron afinities, sizes of atoms involved in the bond, differences in their electronegativity, and the overall structure of the molecule. There is a general trend in that the shorter the bondlength, the higher the bond energy. However, there is no formula to show this relationship, because the variation is widespread. From a table of values, we can not grasp the trend easily. The best method to see the trend is to plot the data on a graph.

In a discussion of bond energies, this link has shown how energy varies as two H atoms approach each other in the formation of a H-H covalent bond:



Covalent bonds such as H-Cl, H-I etc are polar, because the bonding electrons are attracted to the more electronegative atoms, Cl and I in these cases. In general, the higher the electronegativity difference, the more polar are the bonds. In particular, H-F, and H-O bonds are very polar.

Example 1.

Use the table of bond energies to find the DHo for the reaction:
H2(g) + Br2(g) ® 2 HBr(g)
Solution


From the Table of bondlength and bond energy given above, a table below is obvious: Changes DHo
H-H ® H + H 436
Br-Br ® Br + Br 193
H + H + Br + Br ® 2 H-Br 2*(-366)
= -732
Overall (add up)
H-H + Br-Br ® 2 H-Br -103

Discussion


Another approach is shown below. Write the bond energy below the formula, and then apply the principle of conservation of energy.
Bonds broken Bonds formed
H-H + Br-Br 2 H-Br
DHo 436 + 193 -2*366
energy released
DHo = 436 + 193 - 2*366 = -103

Exercise


Evaluate the energy changes for the following reactions
H H H H
\ / | |
C=C + H-H -> H-C-C-H
/ \ | |
H H H H

Ans: - 124 kJ
H Cl
| |
H-C-H + Cl-Cl -> H-C-Cl + H-H
| |
H H

Confidence Building Questions
Which bond in the list has the highest bond energy,
H-H, H-O, H-F, H-I or I-I?
Hint . . .H-F

Discussion: Describe the trends in bondlength and bond energy from the Table above.


Which bond of the following list has the lowest bond energy, H-H, C-C, N-N, O-O, Cl-Cl, Br-Br, I-I? Note that all these are single bonds.
Hint . . .O-O

Discussion: The bondlengths and energies of two possible ones are compared here. I-I, 267 pm, 153 kJ/mol; O-O, 148 pm, 145 kJ/mol.


For carbon-carbon bonds, which one has the highest bond energy, single bond, double bond, or triple bond.
Hint . . .tripple bond has the highest bond energy

Discussion: Bond energies: single, 348; double, 614; triple, 839 kJ/mol. The higher the bond order, the more the bond energy.


Define bond energy

HInt....The energy required to break a mole of bonds is the bond energy.
Discussion: Energy is always required to break a chemical bond. Chemical bonds store energy

Syllabus for GATE (CY- CHEMISTRY)

PHYSICAL CHEMISTRY
Structure: Quantum theory: principles and techniques; applications to a particle in a box,harmonic oscillator, rigid rotor and hydrogen atom; valence bond and molecular orbital theories,Hückel approximation; approximate techniques: variation and perturbation; symmetry, point groups; rotational, vibrational, electronic, NMR, and ESR spectroscopy
Equilibrium: Kinetic theory of gases; First law of thermodynamics, heat, energy, and work; second law of thermodynamics and entropy; third law and absolute entropy; free energy; partial molar quantities; ideal and non-ideal solutions; phase transformation: phase rule and phase diagrams - one, two, and three component systems; activity, activity coefficient, fugacity, and fugacity coefficient; chemical equilibrium, response of chemical equilibrium to temperature and pressure; colligative properties; Debye-Hückel theory; thermodynamics of electrochemical cells; standard electrode potentials: applications - corrosion and energy conversion; molecular partition function (translational, rotational, vibrational, and electronic).
Kinetics: Rates of chemical reactions, temperature dependence of chemical reactions; elementary, consecutive, and parallel reactions; steady state approximation; theories of reaction rates - collision and transition state theory, relaxation kinetics, kinetics of photochemical reactions and free radical polymerization, homogeneous catalysis, adsorption isotherms and heterogeneous catalysis.
INORGANIC CHEMISTRY
Main group elements: General characteristics, allotropes, structure and reactions of simple and industrially important compounds: boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes. Hydrides, oxides and oxoacids of pnictogens (N, P), chalcogens(S, Se & Te) and halogens, xenon compounds, pseudo halogens and interhalogen compounds. Shapes of molecules and hard- soft acid base concept. Structure and Bonding (VBT) of B, Al, Si, N, P, S, Cl compounds. Allotropes of carbon: graphite, diamond, C60. Synthesis and reactivity of
inorganic polymers of Si and P.
Transition Elements: General characteristics of d and f block elements; coordination chemistry: structure and isomerism, stability, theories of metal- ligand bonding (CFT and LFT), mechanisms of substitution and electron transfer reactions of coordination complexes. Electronic spectra and magnetic properties of transition metal complexes, lanthanides and actinides. Metal carbonyls,
metal- metal bonds and metal atom clusters, metallocenes; transition metal complexes with bonds to hydrogen, alkyls, alkenes and arenes; metal carbenes; use of organometallic compounds as catalysts in organic synthesis. Bioinorganic chemistry of Na, K. Mg, Ca, Fe, Co, Zn, Cu and Mo.
Solids: Crystal systems and lattices, miller planes, crystal packing, crystal defects; Bragg’s Law, ionic crystals, band theory, metals and semiconductors, Different structures of AX, AX2, ABX3 compounds, spinels. Instrumental methods of analysis: Atomic absorption and emission spectroscopy including ICP-AES, UV- visible spectrophotometry, NMR, mass, Mossbauer spectroscopy (Fe and Sn), ESR spectroscopy, chromatography including GC and HPLC and electro-analytical methods(Coulometry, cyclic voltammetry, polarography – amperometry, and ion selective electrodes).
ORGANIC CHEMISTRY
Stereochemistry: Chirality of organic molecules with or without chiral centres. Specification of configuration in compounds having one or more stereogenic centres. Enantiotopic and diastereotopic atoms, groups and faces. Stereoselective and stereospecific synthesis. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism. Configurational and conformational effects on reactivity and selectivity/specificity.
Reaction mechanism: Methods of determining reaction mechanisms. Nucleophilic and electrophilic substitutions and additions to multiple bonds. Elimination reactions. Reactive intermediates- carbocations, carbanions, carbenes, nitrenes, arynes, free radicals. Molecular rearrangements involving electron deficient atoms.
Organic synthesis: Synthesis, reactions, mechanisms and selectivity involving the following-alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids and their derivatives, halides, nitro compounds and amines. Use of compounds of Mg, Li, Cu, B and Si in organic synthesis. Concepts in multistep synthesis- retrosynthetic analysis, disconnections, synthons, synthetic equivalents, reactivity umpolung, selectivity, protection and deprotection of functional groups.
Pericyclic reactions: Electrocyclic, cycloaddition and sigmatropic reactions. Orbital correlation, FMO and PMO treatments.
Photochemistry: Basic principles. Photochemistry of alkenes, carbonyl compounds, and arenes. Photooxidation and photoreduction. Di-π- methane rearrangement, Barton reaction.
Heterocyclic compounds: Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole and their derivatives.
Biomolecules: Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, structural features of proteins, nucleic acids, steroids, terpenoids, carotenoids, and alkaloids.
Spectroscopy: Principles and applications of UV-visible, IR, NMR and Mass spectrometry in the determination of structures of organic molecules.

Syllabus for NET (JOINT CSIR-UGC TEST for JRF and LS)

CHEMICAL SCIENCES PAPER I - SECTION B



(1) Structure and Bonding: Atomic orbitals, electronic configuration of atoms (L-S coupling) and the periodic properties of elements; ionic radii, ionisation potential, electron affinity, electronegativity; concept of hybridization. Molecular orbitals and electronic configuration of homonuclear and heteronuclear diatomic molecules. Shapes of polyatomic molecules; VSEPR, theory. Symmetry elements and point groups for simple molecules. Bond lengths, bond angles, bond order and bond energies. Types of Chemical Bond (weak and strong) intermolecular forces, structure of simple ionic and covalent solids, lattice energy.

(2) Acids and Bases: Bronsted and Lewis acids and bases, pH and pKa, acid-based concept in non-aqueous media; HSAB concept. Buffer solution.

(3) Redox Reactions: Oxidation numbers. Redox potential. Electrochemical series. Redox indicators.

(4) Energetics and Dynamics of Chemical Reactions: Law of conservation of energy. Energy and enthalpy of reactions. Entropy, free-energy, relationship between free energy change and equilibrium. Rates of chemical reactions (first-and second - order reactions). Arrhenius equation and concept of transition state. Mechanisms, including SN1 and SN2 reactions, electron transfer reactions, catalysis. Colligative properties of solutions.

(5) Aspects of s.p.d.f. Block Elements: General characteristics of each block. Chemical principles involved in extractions and purification of iron, copper, lead, zinc and aluminium. Coordination chemistry: structural aspects, isomerism, octahedral and tetrahedral crystal - field splitting of dorbitals. CFSE, magnetism and colour of transition metal ions. Sandwich compounds, metal carbonyls and metal clusters. Rare gas compounds, non-stoichiometric oxides. Radio activity and transmutation of elements. Isotopes and their applications.

(6) IUPAC Nomenclature of Simple Organic and Inorganic Compounds.

(7) Concept of Chirality: Recognition of symmetry elements and chiral structures; R-S nomenclature, diastereoisomerism in acyclic and cyclic systems; E-Z isomerisms. Conformational analysis of simple cyclic (chair and boat cyclo hexanes) and acyclic systems. Interconversion of Fischer, Newman and Sawhorse projections.

(8) Common Organic Reactions and Mechanisms: Reactive intermediates. Formation and stability of carbonium ions, carbanians, carbenes, nitrenes, radicals and arynes. Nucleophilic, electrophilic, radical substitution, addition and elimination reactions. Familiar name reactions: Aldol, Perkin, Stobbe, Dieckmann condensations; Hofmann, Schmidt, Lossen, Curtius, Beckmann and Fries rearrangements; Reimer - Tiemann, Reformatsky and Grignard reactions. Diels - Alder reactions; Clasien rearrangements; Friedeal - Crafts reactions; Wittig reactions; and Robinson annulation. Routine functional group transformations and interconversions of simple functionalities. Hydroboration, Oppenaur oxidations; Clemmensen, Wolff- Kishner, Meerwein-Ponndorf-Verley and Birch reductions.

(9) Elementary principles and applications of electronic, vibrational, NMR, EPR and Mass Spectral techniques to simple structural problems.

(10) Data Analysis: Types of errors, propagation of errors, accuracy and precision, least-squares analysis, average standard deviation.



CHEMICAL SCIENCES PAPER II



1. Quantum Chemistry: Planck’s quantum theory, wave-particle duality. Uncertainty Principle, operators and commutation relations: postulates of quantum mechanics and Schrodinger equation: free particle, particle in a box, degeneracy, harmonic oscillator, rigid rotator and the hydrogen atom. Angular momentum, including spin; coupling of angular momenta including spin-orbit coupling.

2. The variation method and perturbation theory. Application to the helium atom; antisymmetry and Exclusion Principle, Slater determinantal wave functions. Terms symbols and spectroscopic states.

3. Born-Oppenheimer approximation. Hydrogen molecule ion. LCAO-MO and VB treatments of the hydrogen molecule; electron density, forces and their role in chemical binding. Hybridization and valence MOs of H2O, NH3 and CH4. Huckel pi-electron theory and its applications to ethylene, butadiene and benzene. Idea of self-consistent fields.

4. Group theoretical representations and quantum mechanics: vanishing of integrals; spectroscopic selection rules for vibrational, electronic, vibronic and Raman spectroscopy. MO treatment of large molecules with symmetry.

5. Spectroscopy: Theoretical treatment of rotational, vibrational and electronic spectroscopy. Principles of magnetic resonance, Mossbauer and photoelectron spectroscopy.

6. Thermodynamics: First law of thermodynamics, relation between Cp. and CV; enthalpies of physical and chemical changes; temperature dependence of enthalpies. Second law of thermodynamics, entropy, Gibbs-Helmoholtz equation. Third law of thermodynamics and calculation of entropy.

7. Chemical Equilibrium: Free energy and entropy of mixing, partial molar quantities, Gibbs-Duhem equation. Equilibrium constant, temperature-dependence of equilibrium constant, phase diagram of one-and two-component systems, phase rule.

8. Ideal and Non-ideal solutions. Excess functions, activities, concept of hydration number: activities in electrolytic solutions; mean ionic activity coefficient; Debye-Huckel treatment of dilute electrolyte solutions.

9. Electrochemistry: Electrochemical cell reactions, Nernst equation, Electrode Kinetics, electrical double layer, electode/electrolyte interface, Batteries, primary & secondary Fuel Cells, corrosion and corrosion prevention.

10. Surface Phenomena: Surface tension, adsorption on solids, electrical phenomena at interfaces, including electrokinetic, micelles and reverse micelles: solubilization, micro-emulsions. Application of photoelectron spectroscopy. ESCA and Auger spectroscopy to the study of surfaces.

11. Statistical Thermodynamics: Thermodynamic probability and entropy; Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Partition function: rotational translational, vibrational and electronic partition functions for diatomic molecules; calculations of thermodynamic functions and equilibrium constants. Theories of specific heat for solids.

12. Non-equilibrium Thermodynamics: Postulates and methodologies, linear laws, Gibbs equation, Onsager reciprocal theory.

13. Reaction Kinetics: Methods of determining rate laws. Mechanisms of photochemical, chain and oscillatory reactions. Collision theory of reaction rates; steric factor, treatment of unimolecular reactions. Theory of absolute reaction rates, comparison of results with Eyring and Arrhenius equations. Ionic reactions: salt effect. Homogeneous catalysis and Michaelis-Menten kinetics; heterogeneous catalysis.

14. Fast Reaction: Luminescence and Energy transfer processes. Study of kinetics by stoppedflow technique, relazation method, flash photolysis and magnetic resonance method.

15. Macromolecules: Number-average and weight average molecular weights; determination of molecular weights. Kinetics of polymerization. Stereochemistry and mechanism of polymerization.

16. Solids: Dislocation in solids, Schottky and Frenkel defects, Electrical properties; Insulators and semiconductors; superconductors; band theory of solids, Solid-state reactions.

17. Nuclear Chemistry: Radioactive decay and equilibrium. Nuclear reactions; Q value, cross sections, types of reactions, Chemical effects of nuclear transformations; fission and fusion, fission products and fission yields. Radioactive techniques; tracer technique, neutron activation analysis, counting techniques such as G.M. ionization and proportional counter.

18. Chemistry of Non-transition Elements: General discussion on the properties of the nontransition elements; special features of individual elements; synthesis, properties and structure of their halides and oxides, polymorphism of carbon, phosphorus and sulphur. Synthesis, properties and structure of boranes, carboranes, borazines, silicates carbides, silicones, phosphazenes, sulphur -nitrogen compounds: peroxo compounds of boron, carbon and sulphur; oxy acids of nitrogen, phosphorus, sulphur and halogens, interhalogens pseudohalides and noble gas compounds.

19. Chemistry of Transition Elements: Coordination chemistry of transition metal ions; Stability constants of complexes and their determination; stabilization of unusual oxidation states. Stereochemistry of coordination compounds. Ligandfield theory, splitting of d-orbitals in low-symmetry environments. Jahn-Teller effect; interpretation of electronic spectra including charge transfer spectra; spectrochemical series, nephelauxetic series Magnetism: Dia-, para-, ferro- and antiferromagnetism, quenching of orbital angular moment, spinorbit coupling, inorganic reaction mechanisms; substitution reactions, trans effect and electron transfer reactions, photochemical reaction of chromium and ruthenium complexes. Fluxional molecules iso-and heteropolyacids; metal clusters. Spin crossover in coordination compounds.

20. Chemistry of Lanthanides and Actinides: Spectral and magnetic properties; Use of lanthanide compounds as shift reagents.

21. Organometallic Chemistry of Transition Elements: Synthesis, structure and bonding, organometallic reagents in organic synthesis and in homogeneous catalytic reactions (hydrogenation, hydroformaylation, isomerisation and polymerization); pi-acid metal complexes, activation of small molecules by coordination.

22. Topics in Analytical Chemistry: Adsorption partition, exclusion electrochromatography, Solvent extraction and ion exchange, methods. Application of atomic and molecular absorption and emission spectroscopy in quantitative analysis Light scattering techniques including nephelometry and Raman spectroscopy. Electronalytical techniques: voltammetry, cyclic, voltammetry, polarography, amperometry, coulometry and conductometry ion-elective electrodes. Annodic stripping voltammetry; TGA, DTA, DSC and online analyzers.

23. Bioinorganic Chemistry: Metal ions in Biology, Molecular mechanism of ion transport across membranes; ionophores. Photosynthesis, PSL, PSH; nitrogen fixation, oxygen uptake proteins, cytochromes and ferrodoxins.

24. Aromaticity: Huckel’s rule and concept of aromaticty (n) annulenes and heteroannulenes, fullerenes (C60)

25. Stereochemistry and conformational Analysis: Nwere method of asymmetric synthesis (including enzymatic and catalytic nexus), enantio and diastereo selective synthesis. Effects of conformation on reactivity in acyclic compounds and cyclohexanes.

26. Selective Organic Name Reactions: Favorskli reaction; Stork enamine reaction; Michael addition, Mannich Reaction; Sharpless asymmetric epoxidation; Ene reaction, Barton reaction, Hofmann-Loffler-Freytag reaction, Shapiro reaction, Baeyer-Villiger reaction, Chichibabin reaction.

27. Mechanisms of Organic Reactions: Labelling and Kinetic isotope effects, Hamett equation, (sigma-rho) relationship, non-classical carbonium ions, neighbouring group participation.

28. Pericyclic Reactions: Selection rules and stereochemistry of electrocyclic reactions, cycloaddition and sigmatropic shifts, Sommelet, Hauser, Cope and Claisen rearrangements.

29. Heterocyclic Chemistry: Synthesis and reactivity of furan, thiophene, pyrrole, pyridine, quinoline, isoquinoline and indole; Skraup synthesis, Fischer indole synthesis.

30. Reagents in Organic Synthesis: Use of the following reagents in organic synthesis and functional group transformations; Complex metal hydrides, Gilman’s reagent, lithium dimethylcuprate, lithium disopropylamide (LDA) dicyclohexylcarbodimide. 1,3-Dithiane (reactivity umpolung), trimethylsilyl iodide, tri-n-butyltin hybride, Woodward and prevost hydroxylation, osmium tetroxide, DDQ, selenium dioxide, phase transfer catalysts, crown ethers and Merrifield resin, Peterson’s synthesis, Wilkinson's catalyst, Baker yeast.

31. Chemistry of Natural Products: Familiarity with methods of structure elucidation and biosynthesis of alkaloids, terponoids, steroids, carbohydrates and proteins.

32. Bioorganic Chemistry: Elementary structure and function of biopolymers such as proteins and nucleic acids.

33. Photochemistry: Cis-trans isomeriation, Paterno-Buchi reaction, Norrish Type I and II reactions, photoreduction of ketones, di-pimethane rearrangement, photochemistry of areanes.

34. Spectroscopy: Applications of mass, UV-VIS, IR and NMR spectroscopy for structural elucidation of compound.

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