7.4 Formal Charges and Resonance

Learning Objectives

By the end of this section, you will be able to:

  • Compute formal charges for atoms in any Lewis structure
  • Use formal charges to identify the most reasonable Lewis structure for a given molecule
  • Explain the concept of resonance and draw Lewis structures representing resonance forms for a given molecule

In the previous section, we discussed how to write Lewis structures for molecules and polyatomic ions. As we have seen, however, in some cases, there is seemingly more than one valid structure for a molecule. We can use the concept of formal charges to help us predict the most appropriate Lewis structure when more than one is reasonable.

Calculating Formal Charge

When we looked at the octet rule, we counted the total number of valence electrons around an atom.  In determining the formal charge of an atom, we are considering how many of the valence electrons around the atom are actually contributed by that atom.

The formal charge of an atom in a molecule is defined as the hypothetical charge the atom would have if we could redistribute the electrons in the bonds evenly between the atoms.  In other words, we are saying that an atom contributes one electron to every covalent bond it makes.  (We will see that this is not strictly true when we consider bond polarity later).  We will also count lone pairs of electrons as two electrons contributed by that atom.

So to calculate formal charge, we compare the number of valence electrons of a neutral atom and the number of valence electrons actually contributed by that atom.  If those counts are equal, i.e. the atom is contributing all of its valence electrons exactly, there is no formal charge.  Because electrons have a negative charge, an atom that contributes one more electron than the number of valence electrons has a formal charge of -1.

We can double-check formal charge calculations by determining the sum of the formal charges for the whole structure. The sum of the formal charges of all atoms in a molecule must be zero; the sum of the formal charges in an ion should equal the charge of the ion.

We must remember that the formal charge calculated for an atom is not the actual charge of the atom in the molecule. Formal charge is only a useful bookkeeping procedure; it does not indicate the presence of actual charges.

 

Example 7.6

Calculating Formal Charge from Lewis Structures:

Assign formal charges to each atom in the interhalogen ion ICl4.

Solution:

  1. First, draw the Lewis structure.
    A Lewis structure is shown. An iodine atom with two lone pairs of electrons is single bonded to four chlorine atoms, each of which has three lone pairs of electrons. Brackets surround the structure and there is a superscripted negative sign.
  2. From its position in the periodic table, we know that an iodine atom has 7 valence electrons.  In this structure, the I atom is contributing 8 electrons (4 x 1 for the four covalent bonds, and 2 x 2 for the electrons in the lone pairs).  So the iodine is contributing one extra electron, and its formal charge is -1.
  3. From its position in the periodic table, we know that a chlorine atom has 7 valence electrons.  In this structure, each Cl atom is contributing 7 electrons (1 x 1 for the covalent bond, and 3 x 2 for the electrons in the lone pairs).  Since these numbers are the same, the Cl atoms have no formal charge.
  4. Redraw the structure, showing the nonzero formal charges assigned to the appropriate atoms.

Now double-check; the sum of the formal charges of all the atoms equals –1, which is identical to the charge of the ion (–1).

 

Check Your Learning:
Assign the formal charge for each atom in the carbon monoxide molecule:

A Lewis structure is shown. A carbon atom with one lone pair of electrons is triple bonded to an oxygen with one lone pair of electrons.

Answer:

 

Example 7.7

Calculating Formal Charge from Lewis Structures:

Assign formal charges to each atom in the interhalogen molecule BrCl3.

Solution:

  1. First, draw the Lewis structure.
    A Lewis structure is shown. A bromine atom with two lone pairs of electrons is single bonded to three chlorine atoms, each of which has three lone pairs of electrons.
  2. From its position in the periodic table, we know that a bromine atom has 7 valence electrons.  In this structure, the Br atom is contributing 7 electrons (3 x 1 for the three covalent bonds, and 2 x 2 for the electrons in the lone pairs).  Since these numbers are the same, the Br atom has no formal charge.
  3. From its position in the periodic table, we know that a chlorine atom has 7 valence electrons.  In this structure, each Cl atom is contributing 7 electrons (1 x 1 for the covalent bond, and 3 x 2 for the electrons in the lone pairs).  Since these numbers are the same, the Cl atoms have no formal charge.
  4. As we found no formal charges, there is no need to update the structure!

All atoms in BrCl3 have a formal charge of zero, and the sum of the formal charges totals zero, as it must in a neutral molecule.

Check Your Learning:

Assign the formal charges for each atom in NCl3.

 

Answer:

No formal charges!

A Lewis structure is shown. A nitrogen atom with one lone pair of electrons is single bonded to three chlorine atoms, each of which has three lone pairs of electrons.

Using Formal Charge to Predict Molecular Structure

The arrangement of atoms in a molecule or ion is called its molecular structure. In many cases, following the steps for writing Lewis structures may lead to more than one possible molecular structure—different multiple bond and lone-pair electron placements or different arrangements of atoms, for instance. A few guidelines involving formal charge can be helpful in deciding which of the possible structures is most likely for a particular molecule or ion:

  1. A molecular structure in which all formal charges are zero is preferable to one in which some formal charges are not zero.
  2. If the Lewis structure must have nonzero formal charges, the arrangement with the smallest nonzero formal charges is preferable.
  3. Lewis structures are preferable when adjacent formal charges are zero or of the opposite sign.
  4. When we must choose among several Lewis structures with similar distributions of formal charges, the structure with the negative formal charges on the more electronegative atoms is preferable.

To see how these guidelines apply, let us consider some possible structures for carbon dioxide, CO2. We know from our previous discussion that the less electronegative atom typically occupies the central position, but formal charges allow us to understand why this occurs. We can draw three possibilities for the structure: carbon in the center and double bonds, carbon in the center with a single and triple bond, and oxygen in the center with double bonds:

Comparing the three formal charges, we can definitively identify the structure on the left as preferable because it has only formal charges of zero (Guideline 1).

As another example, the thiocyanate ion, an ion formed from a carbon atom, a nitrogen atom, and a sulfur atom, could have three different molecular structures: CNS, NCS, or CSN. The formal charges present in each of these molecular structures can help us pick the most likely arrangement of atoms. Possible Lewis structures and the formal charges for each of the three possible structures for the thiocyanate ion are shown here:

Note that the sum of the formal charges in each case is equal to the charge of the ion (–1). However, the first arrangement of atoms is preferred because it has the lowest number of atoms with nonzero formal charges (Guideline 2). Also, it places the least electronegative atom in the center, and the negative charge on the more electronegative element (Guideline 4).

 

Example 7.8

Using Formal Charge to Determine Molecular Structure:

Nitrous oxide, N2O, commonly known as laughing gas, is used as an anesthetic in minor surgeries, such as the routine extraction of wisdom teeth. Which is the likely structure for nitrous oxide?

Two Lewis structures are shown with the word “or” in between them. The left structure depicts a nitrogen atom with two lone pairs of electrons double bonded to a nitrogen that is double bonded to an oxygen with two lone pairs of electrons. The right structure shows a nitrogen atom with two lone pairs of electrons double bonded to an oxygen atom that is double bonded to a nitrogen atom with two lone pairs of electrons.

Solution:

Determining formal charge yields the following:

The structure with a terminal oxygen atom best satisfies the criteria for the most stable distribution of formal charge:

The number of atoms with formal charges are minimized (Guideline 2), and there is no formal charge larger than one (Guideline 2). This is again consistent with the preference for having the less electronegative atom in the central position.

Check Your Learning:

Which is the most likely molecular structure for the nitrite (NO2) ion?

Two Lewis structures are shown with the word “or” written between them. The left structure shows a nitrogen atom with two lone pairs of electrons double bonded to an oxygen atom with one lone pair of electrons that is single bonded to an oxygen atom with three lone pairs of electrons. Brackets surround this structure and there is a superscripted negative sign. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons that is single bonded to an oxygen with three lone pairs of electrons. Brackets surround this structure and there is a superscripted negative sign.

Answer:

ONO

Resonance

You may have noticed that the nitrite anion in Example 7.8 can have two possible structures with the atoms in the same positions. The electrons involved in the N–O double bond, however, are in different positions:

If nitrite ions do indeed contain a single and a double bond, we would expect for the two bond lengths to be different. A double bond between two atoms is shorter (and stronger) than a single bond between the same two atoms. Experiments show, however, that both N–O bonds in NO2 have the same strength and length, and are identical in all other properties.

It is not possible to write a single Lewis structure for NO2 in which nitrogen has an octet and both bonds are equivalent. Instead, we use the concept of resonance: if two or more Lewis structures with the same arrangement of atoms can be written for a molecule or ion, the actual distribution of electrons is an average of that shown by the various Lewis structures. The actual distribution of electrons in each of the nitrogen-oxygen bonds in NO2 is the average of a double bond and a single bond. We call the individual Lewis structures resonance forms. The actual electronic structure of the molecule (the average of the resonance forms) is called a resonance hybrid of the individual resonance forms. A double-headed arrow between Lewis structures indicates that they are resonance forms. Thus, the electronic structure of the NO2 ion is shown as:

We should remember that a molecule described as a resonance hybrid never possesses an electronic structure described by either resonance form. It does not fluctuate between resonance forms; rather, the actual electronic structure is always the average of that shown by all resonance forms. George Wheland, one of the pioneers of resonance theory, used a historical analogy to describe the relationship between resonance forms and resonance hybrids. A medieval traveler, having never before seen a rhinoceros, described it as a hybrid of a dragon and a unicorn because it had many properties in common with both. Just as a rhinoceros is neither a dragon sometimes nor a unicorn at other times, a resonance hybrid is neither of its resonance forms at any given time. Like a rhinoceros, it is a real entity that experimental evidence has shown to exist. It has some characteristics in common with its resonance forms, but the resonance forms themselves are convenient, imaginary images (like the unicorn and the dragon).

The carbonate anion, CO32-, provides a second example of resonance:

One oxygen atom must have a double bond to carbon to complete the octet on the central atom. All oxygen atoms, however, are equivalent, and the double bond could form from any one of the three atoms. This gives rise to three resonance forms of the carbonate ion. Because we can write three identical resonance structures, we know that the actual arrangement of electrons in the carbonate ion is the average of the three structures. Again, experiments show that all three C–O bonds are exactly the same.

Key Concepts and Summary

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).

 

Glossary

formal charge
charge that would result on an atom by taking the number of valence electrons on the neutral atom and subtracting the nonbonding electrons and the number of bonds (one-half of the bonding electrons)
molecular structure
arrangement of atoms in a molecule or ion
resonance
situation in which one Lewis structure is insufficient to describe the bonding in a molecule and the average of multiple structures is observed
resonance forms
two or more Lewis structures that have the same arrangement of atoms but different arrangements of electrons
resonance hybrid
average of the resonance forms shown by the individual Lewis structures

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