Formal charge is a bookkeeping tool used in chemistry to determine the hypothetical distribution of electrons within a molecule or polyatomic ion. It provides a means for chemists to estimate the electrical charge that belongs to each individual atom, assuming the electrons in a bond are shared equally between the two atoms. This concept is instrumental in predicting the most stable molecular structure when multiple arrangements of atoms and electrons are possible. Calculating this charge helps standardize the way electron ownership is assigned within a covalent structure.
Understanding the Role of Formal Charge
Formal charge acts as a diagnostic tool for validating and selecting the most likely Lewis structure for a given molecule or ion. Because a single chemical formula can often be represented by several different Lewis structures, formal charge guidelines help determine the most stable representation. The sum of the formal charges on all atoms in a molecule must always equal the overall charge of the species; it must sum to zero for a neutral molecule or to the charge of the ion for a polyatomic ion.
The preferred Lewis structure is one where the formal charge on every atom is zero, or at least minimized to the smallest non-zero values possible. Structures with large formal charges, such as $+2$ or $-2$, are generally less favorable than those with only $+1$ or $-1$ charges. If non-zero formal charges are unavoidable, the negative formal charge should reside on the most electronegative atom. This arrangement is preferred because the more electronegative atom has a greater natural affinity for electrons, making the structure more energetically stable.
The Three Steps of Formal Charge Calculation
Calculating the formal charge for an atom within a Lewis structure is a three-step process that compares the atom’s valence electrons in its isolated state to the electrons assigned to it in the bonded structure.
Step 1: Determine Valence Electrons
The first step involves determining the number of valence electrons for the isolated, neutral atom, which is found by looking at the atom’s group number on the periodic table. For example, a carbon atom (Group 14) starts with four valence electrons, while an oxygen atom (Group 16) starts with six.
Step 2: Count Non-bonding Electrons
The second step requires counting the number of non-bonding electrons, also known as lone pair electrons, that are drawn on the atom in the Lewis structure. These electrons are not involved in any covalent bond and belong entirely to that specific atom.
Step 3: Count Half of Bonding Electrons
The third step is to count the number of bonding electrons associated with the atom and divide this number by two. Since a covalent bond is formed by two shared electrons, each bonded atom is assigned ownership of only one electron from every shared pair.
The formal charge is calculated using the formula: Formal Charge = (Valence Electrons) – (Non-bonding Electrons) – ($1/2$ Bonding Electrons). Applying this formula to a nitrogen atom, which starts with five valence electrons, has two non-bonding electrons, and shares six bonding electrons across three bonds, results in a formal charge of $5 – 2 – (6/2)$, which equals zero.
Applying the Calculation to Molecular Structures
The calculation process becomes useful when comparing potential structures for complex species, such as the carbon monoxide ($\text{CO}$) molecule. Carbon monoxide is a neutral molecule with a total of ten valence electrons. One common Lewis structure involves a triple bond between the carbon and oxygen atoms, with one lone pair on carbon and one lone pair on oxygen.
To assess this structure, the calculation is performed for each atom individually. For the carbon atom (4 valence electrons), it has two non-bonding electrons and six bonding electrons. The formal charge for carbon is $4 – 2 – (6/2)$, yielding $-1$. The oxygen atom (6 valence electrons) has two non-bonding electrons and shares six bonding electrons. The formal charge for oxygen is $6 – 2 – (6/2)$, resulting in $+1$.
Consider the carbonate ion ($\text{CO}_3^{2-}$), which has a total charge of $-2$. In the best Lewis structure, the central carbon atom forms one double bond and two single bonds to the surrounding oxygen atoms. The carbon atom has a formal charge of zero, calculated as $4 – 0 – (8/2)$. The oxygen atom with the double bond has a formal charge of zero ($6 – 4 – (4/2)$), while the two oxygen atoms with single bonds each have a formal charge of $-1$ ($6 – 6 – (2/2)$). The sum of these charges ($0 + 0 + (-1) + (-1)$) correctly equals the overall charge of the ion, $-2$.
Formal Charge Versus Oxidation State
Formal charge and oxidation state are both theoretical tools used in chemistry to track electrons, but they operate using fundamentally different assumptions about how electrons are shared in a bond. Formal charge assumes that all electrons in a covalent bond are shared equally between the two atoms, disregarding the relative electronegativity of the atoms involved. The calculation assigns one electron from each bond to each atom, effectively splitting the bonding electrons evenly.
Oxidation state, by contrast, operates on the opposite assumption: that the bonding electrons are not shared at all. Instead, it assumes that the electrons in a bond are completely transferred to the more electronegative atom. This method assigns all bonding electrons to the atom that pulls the hardest. Formal charge is useful for evaluating the stability of Lewis structures, while oxidation states are primarily used for tracking electron transfer in redox reactions.