Bond energies, as tabulated in Table 8.4 of your text (p 374) can be used much like heats of formation to calculate the heat (energy) involved in a reaction. Note that in the table all of the bond energies are positive values, so we have to think and assign the appropriate sign depending on what's occuring. Thus, it takes energy to break a bond (in a sense a bond is a situation where the energy is lower, or it wouldn't be a bond) - the tabulated bond energy is positive, but energy will be released when a bond is made - so in fact the bond energy is negative.
Let's try an example: How much energy is released in the complete combustion of methane?
Writing a balanced equation:
CH4 + 2 O2 CO2 + 2 H2O
From the table the bond energies are:
- C-H 413 kJ/mol
- O=O 495 kJ/mol
- C=O 799 kJ/mol
- O-H 467 kJ/mol
Combining the bond energies (reactants - products):
4 (413 kJ/mol) + 2 (495 kJ/mol) - 2 (799 kJ/mol) - 4 (467 kJ/mol) With the successes and failures of classical bonding models in mind, let's explore how we might view covalent bonding from a more modern, quantum, point of view.
2642 kJ/mol - 3466 kJ/mol = -824 kJ/mol
A Quantum View of Bonding
To do this we will need to look briefly again at atomic orbitals and ask what they can tell us about how atoms might share electrons.
But before we even do that, I want to look at some simple atoms and molecules calculated at the highest level of theory, and thus the best approximation we have of what real atoms and molecules look and behave like. In order to do these calculations, we are assuming our atoms or molecules are in a vacuum, and essentially alone in the Universe. First let's look at ionic bonding using the example of sodium chloride (one of the best "pure" ionic compounds). The images. animations etc. are available in the initial section on ionic bonds in the Bonding Supplement.
We have looked at a quantum model for ionic bond formation, now I want to continue our discussion with a model for covalent bond formation using two well studied diatomic molecules: Cl2 and H2. The animations and images are available in the Bonding Supplement.
In viewing these models we should keep in mind that:
With these thoughts in mind, lets look further at bonding and bond formation.
For both Cl2 and H2 you will note that we have a cylindrical distribution of the electrons in the single bond around the axis between the nuclei. Obviously in both cases the shapes of the orbitals have changed.
In order to understand this change, let's go back and review the shapes and electron distribution of atomic orbitals. The animations and images from this discussion are available at the Atomic Orbital Supplement.
For our discussion of bonding we need to look at s, p, and d orbitals. Higher orbitals are not involved in any of the substances we are interested in in this course.
Electronic Energy Levels Review:
Hybrid Atomic Orbitals
We've reviewed atomic orbitals and classical bonding theory, now our question is how can we best understand bonding in molecules, including their shapes etc., in light of modern theory (quantum mechanics)?
We need to keep in mind that our modern picture of simple molecules must be consistent with the classical picture, since it gave us good approximations to observation!
However, when we look at the atomic orbitals for the valence electrons they are generally not arranged in a way that would give the shapes predicted by VSEPR Theory. Thus, the four valence orbitals of atomic carbon are the spherical 2s orbital and the three mutually perpendicular 2p orbitals, while VSEPR predicts that carbon surrounded by four hydrogens will be tetrahedral in shape. [text Fig 9.1]
So what do we do? Recall that the specific shapes of the orbitals result from the interactions of the electrons with a central positive charge (and each other), so we might expect they would change shape if exposed to an external charge (like a second atom).
One way to model this new situation then is to assume that all four of the atomic orbitals are perturbed into a new configuration. If we assume they all have the same energy (required if they are to form a symmetrical set around the carbon nucleus, for example), then we can assume they each have the average energy of the original four orbitals. [text Fig 9.5] We can now come up with a new orbital set by adding the orbitals together, and keeping in mind that we must end up with the same number of orbitals as we started with. If we make this calculation we find there are now four equivalent orbitals arrayed in a tetrahedral geometry, just as we predicted with VSEPR Theory - ta da! [text Fig 9.3, 9.4 (xs)]
Remember, that with Hybrid Orbital Theory we are looking at individual atoms, not molecules. It is a Localized theory, all of our calculations and predictions are for the atoms. We make molecules by overlapping the new hybrid orbitals with other hybrid orbitals or with atomic orbitals of other atoms to make molecules.
Let's look now at some examples and illustrations in your text , noting single and multiple bonds etc.
Tetrahedral Electronic Geometry = sp3.
- Four orbitals (s + 3 p's) combined. (Note the sum of "exponents" = number of orbitals) [text Fig 9.3]
- Note in the following example text figures the side Hs should be behind the hybrid orbitals.
- Methane (CH4) - tetrahedral molecule. [text Fig 9.6]
- Ammonia (NH3) - trigonal bipyramidal molecule. [text Fig 9.7]
Trigonal Planar Electronic Geometry = sp2.
- Three orbitals (s + 2 p's) combined, one p orbital left as is. [text Fig 9.8, 9.9]
- Ethylene (H2CCH2) - each carbon has trigonal planar geometry. [text Fig 9.10, 9.12, 9.13]
Linear Electronic Geometry = sp1, or sp.
- Two orbitals (s + p) combined, two p orbitals left as is. [text Fig 9.14, 9.15, 9.16]
- Carbon dioxide (CO2) [text Fig 9.17, 9.18, 9.19]
- Nitrogen (N2) [text Fig 9.20]
Note we get two basic bond types when we overlap orbitals:
- Sigma (sigma) bonds: These are cylindrically symmetrical around the axis connecting the bonded atoms. Single bonds are always sigma bonds, and in a multiply bonded system the "first" or "central" bond is a sigma bond. [text Fig 9.20b]
- Pi (pi) bonds: these are made up of two lobes with planar symmetry round a plane though the nuclei of the two bonded atoms. The "second" and "third" bond of multiply bonded atoms are pi bonds. For systems with two pi bonds the bond panes are perpendicular to each other. [text Fig 9.20c].
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© R A Paselk
Last modified 13 April 2015