Formal charge Knowledge-Based Study

Study notes

1. What is Formal Charge?

   In covalent molecules and polyatomic ions, electrons are shared between atoms. However, electron sharing is not always completely symmetrical, and multiple valid Lewis electron dot structures can often be drawn for a single chemical species. Formal charge is a theoretical bookkeeping tool used by chemists to assign hypothetical electrical charges to individual atoms within a specific Lewis structure.

   It is important to remember that formal charge does not represent the actual, physical partial charge on an atom (which is determined by electronegativity differences and polar bonds). Instead, it assumes that all bonding electrons are shared equally between the bonded atoms, disregarding differences in electronegativity.

   Key Principles

   • The sum of the formal charges on all atoms in a neutral molecule must equal zero.
   • The sum of the formal charges on all atoms in a polyatomic ion must equal the overall net charge of the ion.

   How to Calculate Formal Charge

   To determine the formal charge ($\text{FC}$) of any atom in a Lewis structure, compare the number of valence electrons in the isolated, neutral atom with the number of valence electrons assigned to that atom in the structure.

   The standard formula is:

   $$\text{Formal Charge} = V - N - \frac{B}{2}$$

   Where:

   • $V$ = number of valence electrons of the neutral free atom (determined from its periodic table group).
   • $N$ = number of non-bonding valence electrons (each individual electron in lone pairs counts as 1).
   • $B$ = number of bonding electrons (each single covalent bond contains 2 shared electrons).

   A convenient shortcut is:

   $$\text{FC} = V - (\text{lone pair electrons}) - (\text{number of bonds})$$

   Example 1: Ozone ($O_3$)

   Consider the resonance structure of ozone: $O_{\text{terminal, 1}} = O_{\text{central}} - O_{\text{terminal, 2}}$.

   For oxygen, the neutral valence count is $V = 6$.

   • Double-bonded terminal oxygen: Has 2 lone pairs (4 non-bonding electrons) and 2 bonds.
     $\text{FC} = 6 - 4 - 2 = 0$
   • Central oxygen: Has 1 lone pair (2 non-bonding electrons) and 3 bonds (one double bond, one single bond).
     $\text{FC} = 6 - 2 - 3 = +1$
   • Single-bonded terminal oxygen: Has 3 lone pairs (6 non-bonding electrons) and 1 bond.
     $\text{FC} = 6 - 6 - 1 = -1$

   The sum of formal charges is $0 + (+1) + (-1) = 0$, matching the neutral charge of ozone.

   Example 2: Ammonium Ion ($[NH_4]^+$)

   In the ammonium ion, nitrogen forms 4 single covalent bonds with hydrogen atoms and possesses no lone pairs.

   • For Nitrogen ($V = 5$): $\text{FC} = 5 - 0 - 4 = +1$
   • For each Hydrogen ($V = 1$): $\text{FC} = 1 - 0 - 1 = 0$

   The sum of formal charges is $+1 + 4(0) = +1$, exactly equal to the charge of the polyatomic cation.

   Predicting the Most Stable Structure

   When multiple valid Lewis structures (nonequivalent resonance structures or isomers) can be drawn for a compound, formal charge helps determine the major contributor or most plausible structure using the following stability guidelines:

   1. Minimal Charges: A structure in which all formal charges are zero is generally more stable than one with non-zero formal charges. If non-zero charges are unavoidable, structures with smaller magnitudes of charge (such as $0$ and $\pm 1$) are favored over larger ones (such as $\pm 2$ or $\pm 3$).
   2. Electronegativity Agreement: Negative formal charges should preferably be located on the more electronegative atoms, while positive formal charges should reside on the less electronegative atoms.
   3. Charge Separation: Adjacent atoms bearing formal charges of the same sign represent an unfavorable, high-energy arrangement due to electrostatic repulsion.

   Application to the Thiocyanate Ion ($[SCN]^-$)

   Three valid Lewis arrangements exist for the connectivity $S-C-N$:

   • $[\,:\ddot{S}=C=\ddot{N}:\,]^-$ gives $\text{FC}(S) = 0$, $\text{FC}(C) = 0$, $\text{FC}(N) = -1$.
   • $[\,:\ddot{S}-C\equiv N:\,]^-$ gives $\text{FC}(S) = -1$, $\text{FC}(C) = 0$, $\text{FC}(N) = 0$.
   • $[\,:S\equiv C-\ddot{N}:^{\,3-}\,]^-$ gives $\text{FC}(S) = +1$, $\text{FC}(C) = 0$, $\text{FC}(N) = -2$.

   The third structure is eliminated due to higher magnitudes of formal charge. Between the first two, nitrogen is more electronegative than sulfur, making the structure placing the $-1$ formal charge on nitrogen ($S=C=N^-$) the major contributor.