10.7: Formal Charges (2024)

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    Learning Objectives
    • Compute formal charges for atoms in any Lewis structure
    • Use formal charges to identify the most reasonable Lewis structure for a given molecule

    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. To determine the best Lewis structure, we rely on the formal charges. In this section, we will first lear what is a formal charge. Then, we will learn how to use the formal charges rule to predict the best Lewis strucure.

    Calculating Formal Charge

    The formal charge of an atom in a molecule is the hypothetical charge the atom would have if we could redistribute the electrons in the bonds evenly between the atoms. 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.

    Thus, we calculate formal charge as follows:

    \[\textrm{formal charge = # valence shell electrons (free atom) − # lone pair electrons − }\dfrac{1}{2}\textrm{ # bonding electrons}\]

    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 \(\PageIndex{1}\): Calculating Formal Charge from Lewis Structures

    Assign formal charges to each atom in the interhalogen ion \(\ce{ICl4-}\).

    Solution

    We divide the bonding electron pairs equally for all \(\ce{I–Cl}\) bonds:

    10.7: Formal Charges (1)

    We assign lone pairs of electrons to their atoms. Each Cl atom now has seven electrons assigned to it, and the I atom has eight.

    Subtract this number from the number of valence electrons for the neutral atom:

    • I: 7 – 8 = –1
    • Cl: 7 – 7 = 0

    The sum of the formal charges of all the atoms equals –1, which is identical to the charge of the ion (–1).

    Exercise \(\PageIndex{1}\)

    Calculate the formal charge for each atom in the carbon monoxide molecule:

    10.7: Formal Charges (2)

    Answer

    C −1, O +1

      Example \(\PageIndex{2}\): Calculating Formal Charge from Lewis Structures

      Assign formal charges to each atom in the interhalogen molecule \(\ce{BrCl3}\).

      Solution

      Assign one of the electrons in each Br–Cl bond to the Br atom and one to the Cl atom in that bond:

      10.7: Formal Charges (3)

      Assign the lone pairs to their atom. Now each Cl atom has seven electrons and the Br atom has seven electrons.

      Subtract this number from the number of valence electrons for the neutral atom. This gives the formal charge:

      • Br: 7 – 7 = 0
      • Cl: 7 – 7 = 0

      All atoms in \(\ce{BrCl3}\) have a formal charge of zero, and the sum of the formal charges totals zero, as it must in a neutral molecule.

        Exercise \(\PageIndex{2}\)

        Determine the formal charge for each atom in \(\ce{NCl3}\).

        Answer

        N: 0; all three Cl atoms: 0

        10.7: Formal Charges (4)

        Lewis Structure of Charged Molecules: https://youtu.be/pTkziPtvMYU

        Using Formal Charge to Predict Molecular Structure

        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.

        Predicting Molecular Structure Guidelines
        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, \(\ce{CO2}\). 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:

        10.7: Formal Charges (5)

        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: \(\ce{CNS^{–}}\), \(\ce{NCS^{–}}\), or \(\ce{CSN^{–}}\). 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:

        10.7: Formal Charges (6)

        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 \(\PageIndex{3}\): 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?

        10.7: Formal Charges (7)

        Solution Determining formal charge yields the following:

        10.7: Formal Charges (8)

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

        10.7: Formal Charges (9)

        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.

        Exercise \(\PageIndex{3}\)

        Which is the most likely molecular structure for the nitrite (\(\ce{NO2-}\)) ion?

        10.7: Formal Charges (10)

        Answer

        \(\ce{ONO^{–}}\)

        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.

        Key Equations

        • \(\textrm{formal charge = # valence shell electrons (free atom) − # one pair electrons − }\dfrac{1}{2}\textrm{ # bonding electrons}\)

        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)
        10.7: Formal Charges (2024)
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