Lecture 12. Assessing and using Lewis structures
Tuesday 27 February 2024
Examples of Lewis structures of molecules and polyatomic ions. More on resonance forms and formal charge assignments. Assessing Lewis structures using formal charge. Exceptions to the octet rule: Expanded octets, incomplete octets, and odd-electron species. Bond lengths and bond energies . Electron groups and steric number (SN). Interpreting Lewis structures to obtain electron group geometries and molecular shapes (VSEPR theory).
Reading: Tro NJ. Chemistry: Structure and Properties (3rd ed.) - Ch.5, §5.5-5.8 (pp.228-242)
Summary
We work further with Lewis structures, writing out valid structures for molecules and polyatomic ions, identifying cases of equivalent and nonequivalent resonance forms, and paying particular attention to formal charge assignments for every atom.
We also look at exceptions to the octet rule. There are three classes of these exceptions, and these occur when valence elections are insufficient or odd in number, as well as for period 3 and larger atoms which can expand upon octets. It is this latter case that is of primary importance to us, as it encompasses so much of the structural chemistry of the heavier elements. Expanded octets, exhibited by molecules such as XeF4, PCl5, and SF6, give rise to the more exotic molecular shapes of the single-center atom structures that we are mainly considering. (Remember though that expanded octets are not available to central atoms of Period 2 elements.) We briefly consider how the molecules with the Group 2A and 3A elements beryllium and boron as a central atom yield incomplete octets, making them reactive toward molecules that can offer a lone pair to form a new covalent bond, called a coordinate covalent bond. The bond formation completes the octet for such atoms. Finally, the case for odd numbers of electrons is introduced.
Bond lengths, bond energies, and bond order.
In a simple diatomic molecule (as shown at right), the bond length is the distance between the nuclei of the two bonded atoms. In other words, it is the length of the bond axis, or straight line connecting the nuclei. Bond length is often measured in a nonstandard unit, the ångstrom (Å):
1 Å = 10−10 m = 0.1 nm = 100 pm
Bond lengths for bonds between and among hydrogen and period 2 elements are typically in a fairly narrow range centered on a value a little over 1.0 Å.
Bond energy, or the strength of a bond, corresponds to the amount of energy necessary to separate a pair of covalently bonded atoms. For example, the chemical equation for the dissociation of the diatomic hydrogen molecule,
H2(g) → H(g) + H(g) bond energy = + 436.4 kJ/mol
represents an energy-requiring process, so that bond energy is a positive value by convention.
Bond axis and bond length are fundamental to molecular geometry. Although we illustrate these here with a simple diatomic molecule, these are more general terms, applying as well to all pairs of bonded atoms in polyatomic molecules and ions. Bond energies are of great practical importance to chemical thermodynamics, and any theory of chemical bonding must attempt to account for the variations in bond lengths and energies among different molecules.
Bond length and bond energy trends: We introduce the term bond order to help us classify bonds and note how bond lengths and energies vary with bond order. The Lewis structures of nitrogen (N2) and ethylene (C2H4) illustrate the fact that more than one covalent bond can form between a pair of atoms. For now we will associate the number of covalent bonds between two atoms in a molecule with bond order - bond order = 1 for a single covalent bond, bond order = 2 for a double bond, and bond order = 3 for a triple bond. Not surprisingly, bond length decreases and bond energies increase with increasing bond order. For example, for bonding between carbon and nitrogen, a single bond (C-N, 1.43 Å or 143 pm) is "worth" (on average, of a number of molecules featuring C-N bonds) 276 kJ/mol, whereas a double bond (C=N, 1.38 Å or 138 pm) is worth 615 kJ/mol. The triple bond is only 1.16 Å long, and would cost (on average) or 891 kJ/mol to break.
Bond energies and lengths: Take-home messages
- Typical bond energies for single covalent bonds are on the order of ~ 400 kJ/mol
- Double bonds have higher energies, triple bonds higher yet
- Bond lengths are typically on the order of ~ 1.0 – 1.5 Å (or 100-150 pm; 1 Å = 10−10 m, 1 pm = 10−12 m
- For a given pair of bonded atoms double bonds are shorter than single bonds and triple bonds are shorter than double bond
- Larger atoms form longer bond bonds
- Bond energies and lengths generally correlate: shorter bonds imply stronger bonds (higher bond energies, and vice-versa.
Electron groups and steric number (SN)
Once we are able to draw valid Lewis structures for simple molecules, we can use them to predict properties of the substances made up by them. Doing this requires however further conceptual deveopment and additional tools that aid our interpretation of Lewis structures. Since the properties of substances in bulk are in principle explained by the three-dimensional structures and polarities or charges of the constituent molecules or polyatomic ions, the most important skill to learn in making use of Lewis structures is to predict molecular shape and polarity from them. To this end, it is convenient to define the steric number (abbreviated SN) for the central atom in the structure of a molecule or polyatomic ion, and we can derive this from any valid Lewis structure representing that species. This amounts simply to a count of the number of bonded atoms plus the number of lone pairs present on the central atom. Tro's text refers to this count, what we are calling steric number, as the "number of electron groups". Since we end up counting a peripherally bonded atom only once, even if it is double- or triple-bonded to the central atom, we sometimes use the term electron domain (Tro's "electron groups") instead of electron pair in determining a value for SN. The value we assign to SN is the same as the number of electron domains (electron groups).
Note that any atom obeying the octet rule will not have SN > 4. This will be a very common situation, and we'll begin by analyzing the possible molecular shapes for steric number equal to 2, 3 and 4.
Molecular structure: The five basic shapes
Lewis structures do not by themselves give us the ability to predict three-dimensional structure of the bonded atoms in molecules and polyatomic ions. But with the help of an additional interpretive tool, called valence shell electron pair repulsion (VSEPR), specific inferences of the likely geometric shapes can be made based on the steric nunber determined from Lewis structures. For a good website for viewing molecular structures, try ChemEd Digital Library Models 360. In using Lewis structures to determine molecular polarity, we are using them in a further interpretive analysis.