Bonding 5
1.Covalent Bonding
In this chapter we will discuss covalent bonding. Ionic and metallic bonding will be covered later.
A covalent bond involves the sharing of one or more pairs of electrons. When the atoms involved in the bond have the same electronegativity, as in Cl2 or O2, the electrons are shared equally. When the electronegativities differ, as in HCl or H2O, the electrons are shared unequally and the bond is polar; that is it has a positive end and a negative end. The more electronegative atom will bear a partial negative charge and the less electronegative atom will have a partial positive charge. Polarity will be discussed in greater detail at the end of this chapter.
2.Lewis Dot Structures
Covalent molecules are usually drawn showing the valence electrons as dots. Since the use of such drawings was popularized by G.N. Lewis, the British chemist and Nobel Laureate, the structures are often called "Lewis structures." Students typically call them "dot structures."
There are two rules which govern the drawing of Lewis structures. First, the structures must use the right number of electrons. If a structure has more electrons than do its individual atoms, it will have a negative charge. A structure with fewer electrons will have a positive charge. Second, the electrons are generally arranged so that each atom has the configuration of a noble gas. This will be two electrons for hydrogen and eight electrons (an octet) for other atoms. The formation of H2 from H atoms, each of which has a single valence electron, is:
Similarly the formation of Cl2 from Cl atoms, each of which has 7 valence electrons, is as below:
For more complicated molecules, it is convenient to draw pairs of electrons as lines. Thus we have
Sometimes the atoms in a molecule do not have enough electrons to both form the needed bonds and to give each atom an octet. Such a molecule, for example SO2 or N2, can form a valid structure by using double bonds. Some examples are:
3. Molecular Orbitals
The Lewis structure, with its emphasis on localized electron pairs, is part of a chemical bonding model called “valence bond theory.” Valence bond theory is simple to understand and easy to use. There is another bonding model which has far more predictive power than does VBT. Unfortunately this model, known as molecular orbital theory, is far more difficult to use and understand.
Molecular orbital theory is not covered in the AP syllabus and we will discuss it no further. However, it is used heavily in later chemistry courses. Knowing from the beginning that there is another way to view bonding may make the eventual introduction of molecular orbital theory less of a shock.
4. Resonance
Sulfur dioxide is noteworthy in that it has two possible structures -- one with a double bond on the left side and another with a double bond on the right side. One would expect, therefore, that each sulfur dioxide molecule would contain two non-equivalent bonds -- a single bond and a double bond. Since double bonds are shorter than single bonds, it is possible to determine experimentally whether this is true. It is not. The two bonds in a sulfur dioxide molecule are both equal and are intermediate in length between a single and a double bond. This can be explained using the concept of resonance.
Resonance requires that a molecule such as sulfur dioxide be described by drawing both possible structures with a double-headed arrow between them. Thus:
The two structures are called "resonance structures" and the actual structure is intermediate between them.
Another example of resonance is found in sulfur trioxide, SO3. In this compound there are three resonance structures, as shown below. Instead of a double bond and two single bonds, sulfur trioxide contains three equivalent bonds, each of which can be considered to be a 1 ⅓ bond.
Resonance occurs when a molecule can be drawn in several different ways, each differing only by the arrangement of electrons. Structures in which the atoms have different arrangements are not resonance structures. While resonance is a useful concept and is widely used by chemists, it is a misleading term. "Resonance" implies that the structures resonate. A resonating structure would exist in one form half the time and in the other form half the time. In fact a molecule which exhibits resonance has the same structure all the time. We just can't draw it.
Stating this differently, a molecule which exhibits resonance is like a mule. A mule is half horse and half donkey. But that does not mean that a mule is a horse half the time and a donkey the other half of the time. Molecular orbital theory, it should be noted, has no need for resonance structures.
5. Odd Electron Molecules — Free Radicals
There are a few cases of stable molecules with an odd number of electrons. An odd-electron molecule will never have an octet and will always have an unpaired electron. These molecules are therefore relatively unstable and quite reactive. Odd-electron molecules are generally called "free radicals." An example of a stable free radical is nitric oxide, shown below. Other resonance structures are possible. However because of the distribution of formal charge, which is discussed below, this structure is best.
6. Incomplete Octets — Lewis Acids
There are a few cases of stable molecules lacking one or more electron pairs. The examples you will see will almost always be boron or aluminum compounds, for example BCl3 or AlF3.
Compounds with incomplete octets have the ability to accept additional electron pairs, thus making them Lewis acids. A typical example, neglecting the unshared electron pairs, is:
7. Formal Charge
In many molecules some of the atoms are charged. This fact, upon which many organic reactions are based, is often explained in terms of something called “formal charge.”
Formal charge is the difference between the number of electrons possessed by a simple atom and the number of electrons “owned” by that same atom in a molecule. In calculating formal charge, bonding electrons are considered to be shared equally by the two atoms between which they lie. Strictly speaking, this is not true, since shared electrons will tend to associate more with the more electronegative atom. But it still works rather well. Note that the sum of the formal charges equals the charge on the molecule (or ion).
In carbon monoxide, for example, carbon possesses a pair of non-bonding electrons and shares three pairs of bonding electrons. Thus it has 5 electrons. Make sure that you see this! Since by itself a carbon atom has 4 valence electrons, carbon has gained an electron and therefore has a formal charge of -1. Using similar logic we find that an oxygen atom in CO has 5 electrons. Since it starts with 6 electrons, this gives it a formal charge of +1.
Formal charges in resonance structures are determined separately for each structure and then averaged together. Consider, for example, the nitrate ion.Nitrogen, which normally has 5 electrons, now has a half share in four electron pairs. Thus it has a charge of +1. The double-bonded oxygen has two unshared pairs and a half share in two bonding pairs. This gives a total of 6 electrons, which is exactly what oxygen starts with. Thus its formal charge is zero. The single bonded electrons each have 3 unshared pairs and a half share of one bonding pair – for a total of 7 electrons. Since oxygen starts with 6 valence electrons, it now has a charge of -1. Thus each of the three resonance structures has the formal charge distribution shown below:
Note that for each of the three resonance structures the formal charges add up to -1, which is the charge of a nitrate ion. The actual formal charges are the averages of the charges on the individual resonance structures. Thus the formal charge on the central nitrogen atom would remain at +1. However, the formal charge on each oxygen atom would be -2/3.
Creating these charge separations requires energy. So a structure in which none of the atoms is charged will be in a lower energy state than a structure containing charged atom. However nitrate, like many other molecules, does not have a valid Lewis structure with no formal charges.
As a final example, let us use formal charges to explain why the structure of N2O is NNO and not NON. First consider the molecule NON. Its three resonance structures have the formal charge distributions shown below:
Here even the middle structure, which distributes its charge more evenly than do the other two, has a substantial charge separation. Further, all three structures place a +2 charge on the very electronegative oxygen atom. This, also, requires energy.
Compare this sorry state with the formal charge distribution available to NNO. Its three resonance structures are drawn below:
The two structures on the left are good. They have small charge separations and don't place a positive charge on the oxygen. While the right-hand is energetically less desirable than the others, there is no need to use it when two low-energy alternatives are available. This simple model does not allow us to determine the relative importance of each of the three resonance structures. However, if we were to assume that NNO was an equal mixture of the two left-hand structures, with the structure on the right having relatively little importance, we would be close to right.
Thus NON, having no low-energy resonance structures, does not exist. NNO does.
8. Molecular Shapes – the VSEPR Model
One of the more elegant parts of bonding theory is the way in which it lets us use a few simple rules to predict molecular shapes. Predicting shapes is based on the idea that the most stable structure for a molecule is the one in which the electron pairs on the central atom are as far apart as possible. This idea is known as the valence shell electron pair repulsion model – V.S.E.P.R.
To use VSEPR theory we must first know the shapes in which each possible number of electron pairs will arrange themselves in order to minimize their repulsive forces. You should be aware that, for reasons which will be discussed later in this chapter, double and triple bonds count only as a single bonding pair.
Two electron pairs will arrange themselves on opposite sides of the central atom, giving a linear molecule. Three electron pairs will go to the corners of an equilateral triangle, giving a shape which can be called either trigonal or triangular. Four electron pairs will go to the corners of a tetrahedron. Five electron pairs will go to the corners of a trigonal bipyramid and six electron pairs will go to the corners of an octahedron. This is summarized in Table 1.
Table 1. Shapes which Maximize Electron Separation
This would be very simple indeed if we had only to consider bonding pairs. Carbon dioxide (2 bonds) is linear; sulfur trioxide (3 bonds) is trigonal planar (triangular); methane (4 bonds) is tetrahedral; phos-phorus pentachloride (5 bonds) is trigonal bipyramidal; sulfur hexafluoride (6 bonds) is octahedral.
However many molecules have unshared electron pairs as well as bonding pairs. Although the unshared pairs cannot actually be “seen,” they exert influence on the geometry of the molecule. Thus water has its four electron pairs arranged tetrahedrally around the central atom. But since the molecular shape does not include the two unshared pairs,the water molecule is considered to be “bent”.
Before we continue to make matters more complex, let us deal with an issue of pronunciation. The structure of PCl5 is a bipyramid (bi pyr' a mid'). The adjective used to describe a bipyramid is bipyramidal (bi' pyr a' mid al). The widely used (mis)pronunciation bi pyr a mid' al is wrong!
At this point we must discuss not only molecular shapes but also bond angles. A regular tetrahedron (e.g. methane) has a bond angle of 109.5°. We would therefore expect the H-O-H bond angle in water to also be 109.5°. However it is not; the bond angle in water is 105°. Not only do unshared pairs occupy space around the central atom, they occupy more space than do bonding pairs. The proper way to phrase this is to say that unshared pairs repel other electrons more than do bonding pairs, thus pushing the bonding pairs close together. This is particularly important in molecules where the central atom has five electron pairs, as is discussed below.
The problem with the trigonal bipyramid, the arrangement which is assumed by five electron pairs, is that it has two sets of non-equivalent sites -- three equatorial sites and two axial sites. These are shown on the right.
The question which is raised by the non-equivalent sites is illustrated by SF4, a molecule which has four bonding pairs and one unshared pair. Where does the unshared pair go? Is it equatorial or is it axial? Although this is not obvious, it turns out that the unshared pair(s) are always equatorial. Thus SF4, with its equatorial unshared pair, is considered to resemble a see saw. Similarly IF3, with its two unshared pairs and three bonding pairs is said to be “t-shaped,” while XeF2 is linear.
see-saw t-shaped linear
A complete table of possible electron arrangements along with the associated shapes is given below.
Table II. Shapes Predicted by VSEPR Theory
9. Multiple Bonds – Sigma and Pi Bonding
As was mentioned previously, a multiple bond counts the same as a single bond when determining molecular shapes. This is because the multiple bond is composed of two different types of bonds – referred to as sigma and pi.
It was previously stated that covalent bonds result from the sharing of electron pairs. But bonds can also be described as the result of overlapping atomic orbitals. It is the way in which the orbitals overlap which determines whether the bond is sigma or pi.A sigma bond lies on the internuclear axis. All single bonds and one of the bonds in a multiple bond are sigma. A pi bond lies off the internuclear axis and is generally made from overlapping p orbitals.
A sigma bond A sigma and a pi bond
Between any two adjacent atoms we can form a pi bond in the plane of the paper and another pi bond perpendicular to the plane of the paper. That’s all! So two carbon atoms can be held together by, at most, one sigma bond and two pi bonds. The bond order can be no higher than three. Note also that the pi bond drawn above consists of two overlapping lobes above the plane of the molecule and two lobes overlapping below the plane. This is one bond, not two.
It also can now be said that the reason a multiple bond counts only for one in VSEPR calculations is that the pi bonds are equally distant from all of the sigma bonds. The pi bonds don’t repel one electron pair more than another. They don’t “take up space.”
10. Hybridization
How is it possible for electrons in p orbitals, which are at right angles to each other, to make structures with as many different bond angles as we have seen? The answer is that bonding does not involve simple s and p orbitals; it involves orbitals which are mixtures -- or hybrids -- of s and p orbitals.
Consider methane, CH4. Carbon, the central atom, has an electron configuration of 1s2 2s2 2p2.
The four orbitals available for bonding are the 2s and the three 2p orbitals. But instead of using two different types of orbitals, these are combined to give four identical orbitals, each of which is part s and part p. Since the orbitals are one part “s” and three parts “p,” they are called sp3 hybrids (a superscript of “1” is assumed over the “s.”) The superscripts in the hybrid orbital designations come from the number of orbitals used to make them and the sum of the superscripts gives the number of hybrid orbitals.For the molecules which we will study, the number of sigma orbitals (sigma bonds plus unshared electron pairs) determines the hybridization, just as it determines the arrangement of electron pairs. This is summarized in Table III.
Table III. Orbital Hybridizations
Orbitals / Arrangement of Orbitals / Hybridization2 / Linear / Sp
3 / Trigonal / sp2
4 / Tetrahedral / sp3
5 / Trigonal Bipyramidal / dsp3
6 / Octahedral / d2sp3
11. Molecules with More than an Octet
Structures in which the central atom has 5 or even 6 pairs of electrons have been frequently discussed. Clearly they violate the octet rule. Why does this happen and, more importantly, how can we predict when it will happen?
As can be seen in Table III, molecules which exceed the octet rule use d orbitals. Cases in which an atom exceeds an octet involve a fairly heavy atom in which the energy of the valence electrons is at least close to the energy of the d orbitals. Thus sulfur, even though it has no d electrons in its ground state, has d orbitals (3d) which are close to the energy of its outer (3p) electrons. However the outer electrons of oxygen (2s and 2p) are much lower in energy than the 3d orbitals. Oxygen, therefore, is unable to exceed the octet rule.