Formal charge is used in chemistry to analyze the distribution of electrons within a molecule or polyatomic ion, especially when represented by a Lewis structure. This concept assigns a hypothetical charge to each atom in a covalently bonded system, calculated assuming that the electrons in every chemical bond are shared equally between the two bonded atoms. The primary purpose of determining formal charge is to predict the most plausible and stable structure among several possible Lewis structures for a given chemical species. Applying this calculation guides the selection of the most accurate molecular representation.
Why Formal Charge Matters
Formal charge evaluates and validates different ways a molecule’s atoms can be connected and how its electrons are arranged. Since multiple valid Lewis structures often satisfy the octet rule, formal charge provides guidelines for choosing the structure that best represents the true electron distribution.
The most stable Lewis structure is generally the one where the formal charges on all atoms are minimized, ideally resulting in zero charge for every atom. Structures with the smallest magnitude of formal charges are preferred, as minimal charge separation suggests greater stability. If non-zero charges are unavoidable, the preferred structure places any negative formal charge on the most electronegative atom. Conversely, any positive formal charge should reside on the least electronegative atom.
Defining the Components for Calculation
Calculating the formal charge requires three components. The first is the number of Valence Electrons (VE), which is the count of electrons the atom possesses in its neutral state, determined by the atom’s group number on the periodic table.
The second component is the count of Non-bonding Electrons (NBE), which are electrons not involved in any bonds, typically existing as lone pairs on the atom. The third component is the number of Bonding Electrons (BE), which are the electrons shared in covalent bonds.
The calculation assumes equal sharing of bonding electrons, so only half of the total shared electrons are assigned to the atom of interest. The formal charge formula is:
Formal Charge = (VE) – (NBE) – (1/2 BE)
This equation is applied individually to every atom. The sum of all individual formal charges must equal the overall charge of the molecule or ion, serving as a critical check.
Step-by-Step Application and Worked Examples
The process of determining the formal charge for an atom begins with creating a complete Lewis structure for the molecule or ion being studied. The diagram must explicitly show all bonding pairs and lone pairs of electrons for every atom.
The first step for any specific atom is to determine its Valence Electron (VE) count from the periodic table. Next, count the Non-bonding Electrons (NBE), which are represented by the lone pairs surrounding the atom in the Lewis structure. Following this, the Bonding Electrons (BE) are counted, which are the total number of electrons in all the covalent bonds connected to that atom. A single bond counts as two bonding electrons, a double bond as four, and a triple bond as six.
Finally, these three values are substituted into the formula: Formal Charge = (VE) – (NBE) – (1/2 BE) to find the theoretical charge for that specific atom. This systematic approach is repeated for every atom in the structure.
Carbon Dioxide (\(\text{CO}_2\)) Example
Two primary Lewis structures are possible for carbon dioxide. The preferred structure is \(\text{O}=\text{C}=\text{O}\), where the central carbon is double-bonded to each oxygen atom.
For the central Carbon atom: it has 4 Valence Electrons (VE=4), 0 Non-bonding Electrons (NBE=0), and 8 total Bonding Electrons (BE=8). The formal charge is \(4 – 0 – (1/2 8) = 0\).
For the two Oxygen atoms: each has 6 Valence Electrons (VE=6), 4 Non-bonding Electrons (NBE=4), and 4 total Bonding Electrons (BE=4). The formal charge for each oxygen is \(6 – 4 – (1/2 4) = 0\). Since all formal charges are zero, this structure is the most stable representation.
A less preferred structure, \(\text{O}\equiv\text{C}-\text{O}\), has non-zero charges. The triple-bonded oxygen has a formal charge of \(+1\), and the single-bonded oxygen has a formal charge of \(-1\). Because the first structure has zero formal charges on all atoms, it is favored over the structure with non-zero charges.
Nitrate Ion (\(\text{NO}_3^-\)) Example
The nitrate ion (\(\text{NO}_3^-\)) is a polyatomic ion that demonstrates the use of formal charge in resonance structures. The common Lewis structure involves a central nitrogen atom with a double bond to one oxygen and single bonds to the other two oxygen atoms. The total charge on the ion is \(-1\), meaning the sum of all formal charges must equal \(-1\).
For the central Nitrogen atom: VE=5, NBE=0, BE=8. The formal charge is \(5 – 0 – (1/2 8) = +1\).
For the Oxygen atom with the double bond: VE=6, NBE=4, BE=4. The formal charge is \(6 – 4 – (1/2 4) = 0\).
For the two Oxygen atoms with single bonds: VE=6, NBE=6, BE=2. The formal charge for each is \(6 – 6 – (1/2 2) = -1\).
The total formal charge is \((+1) + 0 + (-1) + (-1) = -1\), which matches the overall ion charge. Since the unavoidable negative charge resides on the highly electronegative oxygen atoms, this arrangement is considered chemically appropriate for the ion.