Formal Charge and Determining Preferred Lewis Structures
What Is Formal Charge?
Formal charge
Formal charge is a theoretical concept that assigns a charge to each atom in a molecule or ion. It assumes that bonding electrons are shared equally between the bonded atoms.
The formula for calculating formal charge is:
$$
\text{Formal Charge (FC)} = \text{VE} - (\text{NBE} + \frac{1}{2} \text{BE})
$$ where:
- VE = Number of valence electrons the atom has in its free (unbonded) state.
- NBE = Number of non-bonding (lone pair) electrons assigned to the atom.
- BE = Number of bonding electrons assigned to the atom (count all electrons in bonds directly attached to the atom).
Formal charge is a useful tool to evaluate which Lewis structure is most likely to represent a molecule's actual bonding arrangement.
Steps to Calculate Formal Charge
- Draw the Lewis Structure: Ensure all valence electrons are accounted for, and aim to satisfy the octet rule wherever possible.
- Assign Electrons to Atoms:
- Lone pair electrons belong entirely to the atom they are on.
- Bonding electrons are split equally between the two atoms in the bond.
- Apply the Formula: Use the formal charge formula for each atom in the structure.
- Sum the Formal Charges: The total formal charge of the molecule or ion must equal its overall charge.
Deduce the formal charge in water.
Solution
Step 1: Draw the Lewis Structure
Water consists of two single bonds between oxygen and hydrogen, with two lone pairs on the oxygen atom.
Step 2: Assign Electrons
- Oxygen: It has 4 lone pair electrons and 4 bonding electrons (2 from each bond).
- Hydrogen: Each has 0 lone pair electrons and 2 bonding electrons (1 from the bond with oxygen).
Step 3: Calculate Formal Charges
- Oxygen: $ \text{FC} = 6 - (4 + \frac{1}{2} \times 4) = 6 - 6 = 0 $
- Each Hydrogen: $ \text{FC} = 1 - (0 + \frac{1}{2} \times 2) = 1 - 1 = 0 $
Step 4: Verify the Total
The total formal charge is $ 0 + 0 + 0 = 0 $, which matches the neutral charge of the water molecule.
- The sum of all formal charges in a molecule must equal its overall charge.
- If it doesn't, recheck your Lewis structure and calculations.
Choose the preferred structure of sulfate ion ($ \text{SO}_4^{2-} $) based on the formal charges.
Solution
Step 1: Draw Possible Lewis Structures
Two common Lewis structures for $ \text{SO}_4^{2-} $ are:
- All single bonds between sulfur and oxygen, with three lone pairs on each oxygen.
- Two double bonds between sulfur and oxygen, and two single bonds with oxygen atoms carrying lone pairs.
Step 2: Calculate Formal Charges
- Structure 1 (All Single Bonds):
- Sulfur: $ \text{FC} = 6 - (0 + \frac{1}{2} \times 8) = 6 - 4 = +2 $
- Each Oxygen: $ \text{FC} = 6 - (6 + \frac{1}{2} \times 2) = 6 - 7 = -1 $
- The total formal charge is $ +2 + (-1 \times 4) = -2 $, consistent with the ion's charge.
- Structure 2 (Two Double Bonds):
- Sulfur: $ \text{FC} = 6 - (0 + \frac{1}{2} \times 12) = 6 - 6 = 0 $
- Oxygen (doubly bonded): $ \text{FC} = 6 - (4 + \frac{1}{2} \times 4) = 6 - 6 = 0 $
- Oxygen (singly bonded): $ \text{FC} = 6 - (6 + \frac{1}{2} \times 2) = 6 - 7 = -1 $
- The total formal charge is $ 0 + (0 \times 2) + (-1 \times 2) = -2 $.
Step 3: Choose the Preferred Structure
- Structure 2 is preferred because:
- It minimizes the formal charges (closer to zero).
- Negative charges are placed on the more electronegative oxygen atoms.
- The range of formal charges is smaller ($ 0 $ to $ -1 $) compared to Structure 1 ($ +2 $ to $ -1 $).
- One common mistake is assuming that a structure with all single bonds is always preferred.
- Minimizing formal charges is a better indicator of stability.
Assumptions in Formal Charge vs. Oxidation States
- While formal charge assumes equal sharing of bonding electrons, oxidation states assume that the more electronegative atom "owns" all the bonding electrons.
- This leads to different conclusions:
- Formal Charge: Predicts the most stable Lewis structure and reflects electron distribution in covalent bonding.
- Oxidation State: Reflects hypothetical charges if all bonds were ionic, useful for redox reactions.
In $ \text{SO}_4^{2-} $:
- Formal Charge: Assigns $ 0 $ to sulfur and $ -1 $ to oxygen (in the preferred structure).
- Oxidation State: Assigns $ +6 $ to sulfur and $ -2 $ to oxygen
Formal charge focuses on individual atoms within a structure, while oxidation state applies to the entire molecule or ion.
- Draw the Lewis structures for $ \text{CO}_2 $ and $ \text{NO}_3^- $. Calculate the formal charges for each atom and identify the preferred structure.
- Compare the formal charge and oxidation state of nitrogen in $ \text{NH}_4^+ $ and $ \text{NO}_2^- $.
- Consider the molecule $ \text{ClO}_3^- $. Draw two possible Lewis structures and use formal charge to determine which is preferred.
