10.8 Bond Order and Bond lengths Bond length estimation. 10.9 Bond Energies

1. June 8, 2009 – Class 33 and 34 Overview • 10.8 Bond Order and Bond lengths • Bond length estimation. • 10.9 Bond Energies • Bond-dissociation energy, average bond energy, calculation of enthalpy of reaction from bond energies. • 11.1 What a Bonding Theory Should Do • Potential energy of interaction of two hydrogen atoms • 11.2 Introduction to Valence Bond Theory • Localized electron model, application of the valence bond method to simple molecules.

2. Bond Order and Bond lengths • Bond Order (B.O.): describes if a bond is single (B.O. = 1), double (B.O. = 2), triple (B.O. = 3), or some intermediate value (structures with resonance). • This is concept that we will return to, in the next chapter! • Bond Length: the distance between the centres of two atoms joined by a covalent bond. • Higher bond order corresponds to shorter bond lengths, and, in general, to stronger bonds. • Bond length estimation: the length of the covalent bond between two atoms can be approximated as the sum of the covalent radii of the two atoms.

3. Bond Order and Bond lengths

4. Bond Order and Bond lengths Problem: Estimate the bond length for: • nitrogen-to-hydrogen in NH3 (measured: 101.7 pm) • bromine-to-chlorine in BrCl (measured: 213.8 pm) • carbon-to-hydrogen and carbon-to-bromine in CH3Br.

5. Bond Energies Bond Breakage: H2(g)  2 H(g) DH = D(H-H) = +435.93 kJ/mol Bond Formation: H2(g)  2 H(g) DH = -D(H-H) = -435.93 kJ/mol • Bond-dissociation energy (D): the quantity of energy required to break one mole of covalent bonds in a gaseous species, usually expressed in kJ/mol.

6. Bond Energies Bond Breakage: H-OH(g)  H(g) + OH(g) DH = D(H-OH) = +498.7 kJ/mol Bond Breakage: O-H(g)  H(g) + O(g) DH = D(O-H) = +428.0 kJ/mol • Average bond energy: the average of bond dissociation energies for a number of different species containing a particular covalent bond. • In H2O, more energy is required to break the first bond than the second. The second bond broken is the O-H radical. The O-H bond energy in H2O is the average of the two values: 463.4 kJ/mol.

7. Bond Energies

8. Calculation of enthalpy of reaction from bond energies Some of the BE are likely to be average bond energies rather than bond dissociation energies. Hypothetically, thermochemical data can be obtained from: gaseous reactants  gaseous atoms  gaseous products

9. Calculation of enthalpy of reaction from bond energies Note: In calculating DH for this reaction, some of the terms cancel out because the same bond types appear as both reactants and products (black bonds above). Only the net number and types of bonds broken (red bonds above) and formed (blue bonds above) are included in the calculation.

10. Calculation of enthalpy of reaction from bond energies

11. Problem: Estimate the enthalpy change for the following reaction: 2 H2(g) + O2(g)  2 H2O(g) Problem: Use bond energies to estimate the enthalpy of formation of NH3(g). (Recall, standard enthalpy of formation is the enthalpy change that occurs in the formation of 1 mole of substance from the reference forms of its components in their standard states.) Calculation of enthalpy of reaction from bond energies

12. What a Bonding Theory Should Do • Lewis theory is simple and structures can be determined rapidly. • It does not account for odd-electron species, resonance structures or the magnetic and spectral properties of molecules. • Example: Why is O2 paramagnetic? • VSEPR theory allows shape predictions • Neither yield quantitative information about bond lengths or energies

13. Introduction to Valence Bond Theory • Valence-bond method: treats a covalent bond in terms of the overlap of pure or hybridized orbitals. Electron probability (or electron charge density) is concentrated in the area of overlap. • This theory tells us what a covalent bond is and correlates molecular shapes to the interactions of atomic orbitals. • The basic principle of valence bond theory is that a covalent bond forms when half filled orbitals on two different atoms (atomic orbitals) overlap. Example: H2

14. Introduction to Valence Bond Theory

15. Introduction to Valence Bond Theory

16. Introduction to Valence Bond Theory • Localized electron model: according to valence bond theory, core electrons and lone-pair electrons retain the same orbital locations as in the separated atoms. • Charge density of the bonding electrons is concentrated in regions of orbital overlap. Example: Bonding in H2S. • Note: (+) and (-) signs denote phase signs, not charges!

17. Introduction to Valence Bond Theory Using the Valence-Bond Method to Describe a Molecular Structure. Describe the phosphine molecule, PH3, by the valence-bond method.. Step 1: Draw valence shell orbital diagrams for the separate atoms.

18. Introduction to Valence Bond Theory Step 2: Sketch the orbitals of the central atom (P) that are involved in the overlap. Recall:

19. Introduction to Valence Bond Theory Step 3: Complete the structure by bringing together the bonded atoms and representing the orbital overlap. Step 4: Describe the structure. PH3 is trigonal-pyramidal. Three H atoms lie in the same plane. The P is situated at the top of the pyramid. The three H-P-H bond angles are 90o. (Experimentally, they are measured to be between 93 and 94o.)

20. Introduction to Valence Bond Theory Problem: Use the Valence Bond Method to describe bonding and the expected molecular geometry in NI3.