Formal ChargeCourse level: AP Chemistry

Expanded Octets and Formal Charge Trade-offs

What you'll be able to do: Decide when expanding an octet is justified and weigh the formal charge argument against the octet argument.

Best after: Choosing the Best Lewis Structure with Formal Charge, Exceptions to the Octet Rule

Introduction

Sulfate can be drawn with four single bonds or with two double bonds. Both appear in textbooks, and knowing why is the point of this lesson.

These are recommended, not required. You can start this lesson at any time.

Learning objectives

  • Identify central atoms that may expand their octet
  • Compare formal charges for octet and expanded octet structures
  • Explain the trade-off between minimising formal charge and keeping an octet
  • Write a justified answer that names the criterion used

The sulfate example

With four S-O single bonds, sulfur has an octet but carries a formal charge of +2 while each oxygen carries -1. Converting two of those bonds to double bonds gives sulfur twelve electrons and drops its formal charge to zero, leaving only two oxygens at -1.

Sulfate has 6 + 4(6) + 2 = 32 valence electrons. The all-single-bond drawing uses eight in bonds and twenty-four in oxygen lone pairs. In the two-double-bond drawing, twelve are in bonds and twenty in oxygen lone pairs: the budget is still thirty-two. Each new S=O component comes from an oxygen lone pair, not from additional electrons supplied to sulfur. The sulfur formal charge changes from +2 to 0 because its bond-order sum rises from four to six.

Two permitted sulfate Lewis conventions redistribute formal charge while keeping thirty-two electrons and total charge −2. Neither is a literal localized-bond measurement.
Both drawings account for all 32 valence electrons. They differ only in how the electrons are arranged.

The trade-off

An expanded Lewis drawing of sulfate can reduce formal-charge magnitudes; an all-single-bond drawing keeps an octet at sulfur. Neither drawing alone is the physical electron density. Modern bonding descriptions do not require literal d-orbital hybridization, and this does not uniquely certify one Lewis drawing or assign numerical resonance weights. Compare the bookkeeping conventions explicitly and follow the representation requested in the question.

Sulfate drawingElectrons around SFC on SO formal chargesNet charge
Four single S–O bonds8+2Four O at −1−2
Two S=O and two S–O bonds120Two O at 0; two at −1−2

Neither single drawing implies two permanent short S–O bonds and two permanent long ones in an isolated symmetric sulfate ion. A family of equivalent expanded-valence contributors distributes the double-bond positions. Those drawings remain a model; they do not by themselves determine a literal integer bond order or prove that sulfur uses d hybrids.

Sulfur dioxide

SO₂ with one single and one double bond gives sulfur +1 and the single bonded oxygen -1. Drawing both bonds double gives every atom a formal charge of zero at the cost of ten electrons on sulfur. The same argument applies, and the same two answers appear in different sources.

SO₂ has eighteen valence electrons. In the zero-formal-charge double/double drawing, the two S=O bonds use eight electrons, the oxygens' four lone pairs use eight, and one sulfur lone pair uses two. Sulfur therefore has ten surrounding electrons: four bonding pairs plus one lone pair. Omitting that sulfur lone pair would leave only sixteen electrons and give the wrong formal charge. In an octet-only drawing, one S=O and one S–O plus the sulfur lone pair gives +1 on S and −1 on the single-bonded O; there are two equivalent placements.

How to answer safely

Read the requested convention before drawing. If asked to minimize formal charges while allowing expanded octets, use that criterion; if an octet-only representation is requested, obey that constraint. Show total electrons, lone pairs and formal charges, with the sum equal to the ionic charge. Naming a criterion does not guarantee credit if the prompt requires a different convention.

Before answering, state whether the task requires an octet-only structure or allows expanded-valence drawings chosen to reduce formal-charge magnitudes. Then show lone pairs, local formal charges, bracket charge for ions, and the total electron count. Naming an alternative convention is useful explanation, but it does not override an explicit representation requested by a question.

This flexibility applies only to period 3 and heavier centres. A period 2 atom never gets the choice.

Use expanded valence as a permitted representation

P, S, Cl and heavier central atoms can appear with more than eight surrounding electrons in useful Lewis drawings. Ordinary C, N, O and F centers cannot use that bookkeeping shortcut. Period number therefore constrains which drawings are available; it does not require all compounds of period-3 elements to expand or justify adding extra bonds without checking the budget.

Modern descriptions of hypervalent bonding use delocalization and other orbital models rather than requiring literal occupation of d hybrids. The Lewis drawing remains useful for counting electrons and comparing representations. Keep that purpose separate from a claim about the exact physical distribution of bonding electrons.

Period and total valence electrons constrain what Lewis model is possible.

Key ideas

Rule
Who may expand

Only central atoms from period 3 downward, such as P, S, Cl, Br, I and Xe.

Key concept
Sulfate two ways

Four single bonds gives S at +2; two double bonds gives S at 0 with twelve electrons.

Rule
Name the criterion

State whether you are minimising formal charge or preserving the octet.

Definition
Charge separation

Having several nonzero formal charges within one species, which usually costs energy.

Equation
Formal charge

FC = V - N - B/2

    Worked examples

    Worked example 1

    Compare the two common Lewis structures of the sulfate ion SO₄ 2-.

    Try it first: Count the 32 valence electrons and try the all single bond structure first.

      0 of 3 steps revealed.

      Worked example 2

      Draw SO₂ so that all formal charges are zero, and state the cost.

      Try it first: Count the 18 valence electrons.

        0 of 3 steps revealed.

        Worked example 3

        Why can PF₅ be drawn with five P-F bonds while NF₅ is not a comparable ordinary molecule?

        Try it first: Compare the central atoms' periods and their valence-shell electron limits.

          0 of 3 steps revealed.

          Common mistakes

          Common mistakes and better checks
          MistakeWhy it's wrongCheck instead
          Expanding the octet of oxygen or nitrogen to zero the formal charges.Period 2 atoms cannot exceed eight electrons under any argument.Only expand a central atom in period 3 or below.
          Claiming one sulfate structure is simply wrong.Both are defensible depending on the criterion applied.Name the criterion in your answer.
          Adding double bonds without recounting the electron total.The valence budget is fixed, so a new bond must come from an existing lone pair.Recount bonding and non-bonding electrons after each change.

          Scroll horizontally if needed to read all columns.

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          What you should now know

          For period-3 and heavier central atoms, expanded-octet Lewis drawings may reduce formal charges, as in sulfate and SO₂. Strict-octet drawings use a different bookkeeping constraint. Neither alone is a measurement of bonding or proof of d-orbital hybridization. State the convention, show the electron count and charges, and satisfy the representation requested.

          • Expanded Lewis drawings can reduce formal-charge magnitudes on period-3 centers
          • Strict-octet and expanded-octet drawings use different bookkeeping conventions
          • Lewis drawings are not unique physical electron-density models
          • The ion’s total formal charge and electron count must be conserved
          • Follow the convention actually requested; naming a criterion alone does not guarantee credit

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          Sources and further reading

          • Chemistry 2e, Section 7.4: Formal Charges and Resonance
            OpenStax · Rice University · 7.4
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            Lesson-specific rights and provenance need review.

            The current online Chemistry 2e edition lists CC BY-NC-SA 4.0. The source version used for this lesson and its applicable rights remain unverified.

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