Formal charge is a bookkeeping method used to track the theoretical distribution of electrons within a covalently bonded molecule. The calculated formal charge is a conceptual value, representing the charge an atom would possess under the strict assumption of equal sharing of all bonding electrons. This calculated number is not the same as the actual, partial charge an atom might carry due to differences in electronegativity in a real molecule.
Defining Formal Charge and Valence Electrons
The formal charge is the electric charge assigned to an atom in a molecule, assuming electrons in all chemical bonds are shared equally. This theoretical calculation helps evaluate the relative stability of different possible molecular arrangements, especially when multiple valid Lewis structures can be drawn. Before calculation, the number of valence electrons for the neutral atom must be established.
Valence electrons reside in the outermost electron shell and are the only electrons involved in forming chemical bonds. For main-group elements, the number of valence electrons is determined by the atom’s group number on the periodic table. The formal charge calculation compares this neutral count to the number of electrons associated with the atom within the bonded molecule.
The Calculation Formula
The determination of formal charge relies on subtracting the electrons associated with the atom in the molecule from the atom’s neutral valence electron count. The mathematical expression used to calculate this value is: Formal Charge = (Valence Electrons) – (Non-bonding Electrons) – (1/2 Bonding Electrons).
“Non-bonding Electrons” refers to electrons localized entirely on the atom as lone pairs. “Bonding Electrons” are those shared in the covalent bonds between atoms. This formula ensures the atom is credited with all of its own lone-pair electrons and exactly half of the electrons it shares with neighboring atoms.
Step-by-Step Calculation Example
Carbon Dioxide (\(\text{CO}_2\)) demonstrates this calculation method across all atoms. First, determine the total valence electrons: Carbon (4) plus two Oxygens (6 each) equals \(4 + 6 + 6 = 16\) valence electrons. The most stable Lewis structure places Carbon in the center, double-bonded to both Oxygen atoms.
To calculate the formal charge for the central Carbon atom, start with its neutral count of four valence electrons. In this \(\text{CO}_2\) structure, Carbon has zero non-bonding electrons. Since Carbon participates in two double bonds (eight bonding electrons), the calculation is \(4 – 0 – (1/2 \times 8)\), resulting in a formal charge of zero.
Next, calculate the formal charge for an Oxygen atom, starting with six valence electrons. Each Oxygen atom possesses two lone pairs, corresponding to four non-bonding electrons. The double bond connecting Oxygen to Carbon contains four bonding electrons.
Applying the formula gives \(6 – 4 – (1/2 \times 4)\), which simplifies to \(6 – 4 – 2\). This results in a formal charge of zero for each Oxygen atom. The sum of the formal charges on all atoms (\(0 + 0 + 0\)) equals the overall charge of the neutral \(\text{CO}_2\) molecule.
Interpreting Formal Charge Results
Formal charges help distinguish between different possible Lewis structures, especially resonance structures. The most plausible structure is the one that minimizes the magnitude of formal charges on all atoms. Structures where all atoms have a zero formal charge, like \(\text{CO}_2\), are preferred over those with large positive and negative charges.
If non-zero formal charges are unavoidable, the preferred structure places any negative formal charge on the atom with the greater intrinsic electronegativity (e.g., Oxygen or Nitrogen). Conversely, any positive formal charge should reside on the least electronegative atom. Adhering to these guidelines helps predict the most accurate electron arrangement.