7.5 Formal Charges

In a Lewis structure, formal charges can be assigned to each atom by treating each bond as if one-half of the electrons are assigned to each atom. These hypothetical formal charges are a guide to determining the most appropriate Lewis structure. A structure in which the formal charges are as close to zero as possible is preferred. Resonance occurs in cases where two or more Lewis structures with identical arrangements of atoms but different distributions of electrons can be written. The actual distribution of electrons (the resonance hybrid) is an average of the distribution indicated by the individual Lewis structures (the resonance forms).

Although the total number of valence electrons in a molecule is easily calculated, there is not aways a simple and unambiguous way of determining how many reside in a particular bond or as non-bonding pairs on a particular atom. For example, one can write valid Lewis octet structures for carbon monoxide showing either a double or triple bond between the two atoms, depending on how many nonbonding pairs are placed on each: C::O::: and :C:::O: (see Problem Example 3 below). The choice between structures such as these is usually easy to make on the principle that the more electronegative atom tends to surround itself with the greater number of electrons. In cases where the distinction between competing structures is not all that clear, an arbitrarily-calculated quantity known as the formal charge can often serve as a guide.

The formal charge on an atom is the electric charge it would have if all bonding electrons were shared equally with its bonded neighbors.

How to calculate the formal charge on an atom in a molecule

The formal charge on an atom is calculated by the following formula:

Figure 7.61 Formal Charge calculation

The core charge referred to in this diagram is the electric charge the atom would have if all its valence electrons were removed. In simple cases, the formal charge can be worked out visually directly from the Lewis structure, as is illustrated farther on.

Another way of saying this is that formal charge results when we take the number of valence electrons of a neutral atom, subtract the nonbonding electrons, and then subtract the number of bonds connected to that atom in the Lewis structure.

Key Equation to calculate formal charge as follows:

formal charge=#valence shell electrons (free atom)−#lone pair electrons−12#bonding electrons

So Knowing the formal charge on a particular atom in a structure is an important part of keeping track of the electrons and is important for establishing and predicting the reactivity. The formal charge on an atom in a molecule reflects the electron count associated with the atom compared to the isolated neutral atom.

Figure 7.62 Sulfuric Acid H₂SO₄

Ref: commons.wikimedia.org

Problem Example 1

Find the formal charges of all the atoms in the sulfuric acid structure shown here.

Solution: The atoms here are hydrogen, sulfur, and double- and single-bonded oxygens. Remember that a double bond is made up of two electron-pairs.

hydrogen: FC = 1 – 0 – 1 = 0
sulfur: FC = 6 – 0 – 6 = 0
hydroxyl oxygen: FC = 6 – 4 – 2 = 0
double-bonded oxygen: FC = 6 – 4 – 2 = 0

Using formal charge to select the best Lewis structure

The general rule for choosing between alternative structures is that the one involving the smallest formal charges is most favored, although the following example shows that this is not always the case.

Problem Example 2

Write out some structures for carbon monoxide CO, both those that do and do not obey the octet rule, and select the “best” on the basis of the formal charges.

Solution:

Structure that obeys the octet rule:

a) For :C:::O:   Carbon: 4 – 2 – 3 = –1; Oxygen: 6 – 2 – 3 = +1

Structures that do not obey the octet rule (for carbon):

b) For :C:O:::  Carbon: 4 – 2 – 1 = +1; Oxygen: 6 – 6 – 1 = –1

c) For :C::O::  Carbon: 4 – 2 –2 = 0; Oxygen: 6 – 4 – 2 = 0

Comment: All three structures are acceptable (because the formal charges add up to zero for this neutral molecule) and contribute to the overall structure of carbon monoxide, although not equally. Both experiment and more advanced models show that the triple-bonded form (a) predominates. Formal charge, which is no more than a bookeeping scheme for electrons, is by itself unable to predict this fact.

In a species such as the thiocyanate ion SCN^— (below) in which two structures having the same minimal formal charges can be written, we would expect the one in which the negative charge is on the more electronegative atom to predominate.

Figure 7.63 Formal Charge

Ref: commons.wikimedia.org

The electrons in the structures of the top row are the valence electrons for each atom; an additional electron (purple) completes the nitrogen octet in this negative ion. The electrons in the bottom row are divided equally between the bonded atoms; the difference between these numbers and those above gives the formal charges.

Formal charge can also help answer the question “where is the charge located?” that is frequently asked about polyatomic ions. Thus by writing out the Lewis structure for the ammonium ion NH₄⁺, you should be able to convince yourself that the nitrogen atom has a formal charge of +1 and each of the hydrogens has 0, so we can say that the positive charge is localized on the central atom.

How oxidation numbers are assigned

This is another arbitrary way of characterizing atoms in molecules. In contrast to formal charge, in which the electrons in a bond are assumed to be shared equally, oxidation number is the electric charge an atom would have if the bonding electrons were assigned exclusively to the more electronegative atom. Oxidation number serves mainly as a tool for keeping track of electrons in reactions in which they are exhanged between reactants, and for characterizing the “combining power” of an atom in a molecule or ion.

The following diagram compares the way electrons are assigned to atoms in calculating formal charge and oxidation number in carbon monoxide.

Figure 7.64 Formal Charge  vs. Oxidation Number

Ref: commons.wikimedia.org

Calculating Formal Charge

Reference: https://youtu.be/J03H472fAKI?t=75

Practice Example #3: , let’s calculate the formal charge on the atoms in ammonia (NH₃) whose Lewis structure is as follows:

Figure 7.65 Ammonia NH₃

Ref: commons.wikimedia.org

A neutral nitrogen atom has five valence electrons (it is in group 15). From the Lewis structure, the nitrogen atom in ammonia has one lone pair and three bonds with hydrogen atoms. Substituting into Equation 2.3.1, we obtain

 Formal Charge of N = (5 valence e-) – (2 lone pair e-) – (1/2 x 6 bond pair e-) = 0

A neutral hydrogen atom has one valence electron. Each hydrogen atom in the molecule has no non-bonding electrons and one bond. Using Equation 2.3.1 to calculate the formal charge on hydrogen, we obtain

Formal Charge of H = (1 valence e-) – (0 lone pair e-) – (1/2 x 2 bond pair e-) = 0

The sum of the formal charges of each atom must be equal to the overall charge of the molecule or ion.  In this example, the nitrogen and each hydrogen has a formal charge of zero. When summed the overall charge is zero, which is consistent with the overall neutral charge of the NH₃ molecule.

Typically, the structure with the most formal charges of zero on atoms is the more stable Lewis structure. In cases where there MUST be positive or negative formal charges on various atoms, the most stable structures generally have negative formal charges on the more electronegative atoms and positive formal charges on the less electronegative atoms. The next example further demonstrates how to calculate formal charges for polyatomic ions.

Reference: https://www.youtube.com/watch?v=vOFAPlq4y_k

Reference: https://www.youtube.com/watch?v=C2l-76VP8s0

Reference: https://youtu.be/vOFAPlq4y_k