DAT Organic Chemistry: Formal Charge and Common Arrow Errors

DAT High-Yield Concept

Conservation of Net Charge: The sum of formal charges across all reactants in a step must equal the sum of formal charges across all products.
Source-to-Sink Directionality: Curved arrows always start at an electron pair (lone pair or bond) and point toward an electron-deficient sink.
Strict Octet Rule for Period 2: Carbon, nitrogen, oxygen, and fluorine can never exceed 8 valence electrons (4 bonds / electron pairs). Pentavalent carbon ( $\ce{R5C}$ ) is strictly impossible.
Formal Charge Shifts: Forming a bond from a lone pair increases an atom's charge by +1; breaking a bond onto an atom as a lone pair decreases its charge by -1.

Formal Charge Formula:

\text{FC} = V - N - \frac{B}{2}

where

V

is valence electrons,

N

is non-bonding electrons (lone pair electrons), and

B

is bonding electrons.

1. Formal Charge Bookkeeping Across a Step

Formal charge tracks electron distribution across organic mechanism steps. Because chemical reactions redistribute valence electrons without creating or destroying them, total net charge is strictly conserved across every single elementary step.

When drawing curved arrows, formal charges shift predictably based on electron movement:

Lone pair to bond ( $\ce{:A + B -> A-B}$ ): Atom A shares a previously unshared pair. Its formal charge increases by +1 ( $\Delta \text{FC} = +1$ ).
Bond to lone pair ( $\ce{A-B -> A+ + :B-}$ ): Atom B receives full ownership of the bonding pair as a lone pair. Its formal charge decreases by -1 ( $\Delta \text{FC} = -1$ ).

Mechanism of an E1-reaction in organic chemistry. (Source: Matthias M. · Public domain · Wikimedia Commons)

Worked Example: Protonation of Dimethyl Ether

Starting Point: Neutral dimethyl ether ( $\ce{CH3OCH3}$ ) reacts with hydrogen chloride ( $\ce{HCl}$ ).

Step-by-Step Reasoning:

A lone pair on oxygen attacks $\ce{H+}$ in $\ce{H-Cl}$ , forming a new $\ce{O-H}$ bond. Oxygen goes from 2 bonds + 2 lone pairs ( $\text{FC} = 6 - 4 - 2 = 0$ ) to 3 bonds + 1 lone pair ( $\text{FC} = 6 - 2 - 3 = +1$ ).
The $\ce{H-Cl}$ $\sigma$ bond breaks onto chlorine as a lone pair. Chlorine goes from 1 bond + 3 lone pairs ( $\text{FC} = 7 - 6 - 1 = 0$ ) to 0 bonds + 4 lone pairs ( $\text{FC} = 7 - 8 - 0 = -1$ ).
Net Charge Check: Reactants ( $0 + 0 = 0$ ) = Products ( $+1 + (-1) = 0$ ). Charge is conserved.

DAT Exam Trap: Forgetting to assign a $+1$ charge to trivalent oxygen in $\ce{(CH3)2OH+}$ , leaving the product mixture falsely charged as $-1$ overall.

2. Common Invalid Arrow Errors

Curved arrows represent electron movement, not atom movement (a foundational topic detailed in dedicated lessons on electron flow). On the DAT, common arrow errors destroy mechanism validity:

Starting on a Positive Charge or Atom: Arrows must begin at an electron pair (lone pair or bond), never at a positive charge ( $+$ ) or an atomic symbol lacking drawn electrons.
Backward Directionality: Drawing an arrow from an electrophile (sink) to a nucleophile (source) reverses physical electron flow.
Omission of Leaving Group Arrows: Adding electrons to an atom that already has a full octet without breaking an existing bond violates valence rules.

Review the canonical valid and invalid arrow operations below:

Every curved arrow starts where electrons already are - a lone pair or a bond - and ends where they can be accepted. Drawing the arrow from the proton says the hydrogen brings electrons with it, which it does not. Landing an arrowhead on a carbon that already holds a full octet, with nothing prepared to leave, would give that carbon ten electrons. Arrows start at electrons, never at atoms that lack them.

Worked Example: Substitution on Chloromethane

Starting Point: Hydroxide ( $\ce{HO-}$ ) attacks chloromethane ( $\ce{CH3Cl}$ ) in an $\text{S}_\text{N}2$ step.

Step-by-Step Reasoning:

Arrow 1 originates at an oxygen lone pair on $\ce{HO-}$ and points to the electrophilic carbon.
Because carbon already has 8 valence electrons, a simultaneous second arrow must start at the $\ce{C-Cl}$ $\sigma$ bond and point to chlorine.

DAT Exam Trap: Drawing Arrow 1 while omitting Arrow 2 creates a pentavalent carbon intermediate ( $\ce{CH3(OH)Cl}$ ) with 10 valence electrons—a major DAT distractor.

3. Checking Octets After Every Arrow

To ensure valid mechanism steps, evaluate the electron count around every involved atom immediately after drawing an arrow:

Second-Row Maximum: Carbon, nitrogen, oxygen, and fluorine must have $\le 8$ valence electrons.
Incomplete Octets: Transient 6-electron intermediates like carbocations ( $\ce{R3C+}$ ) are valid in stepwise processes (e.g., $\text{S}_\text{N}1$ or $\text{E}1$ mechanisms).

Worked Example: Electrophilic Addition to Propene

Starting Point: Propene ( $\ce{CH3CH=CH2}$ ) reacts with $\ce{H+}$ .

Step-by-Step Reasoning:

An arrow starts at the $\ce{C=C}$ $\pi$ bond and points to $\ce{H+}$ .
$\ce{C1}$ gains the proton, forming a new $\ce{C-H}$ bond (4 bonds, 8 electrons).
$\ce{C2}$ loses its share of the $\pi$ pair, forming a secondary carbocation ( $\ce{CH3CH+CH3}$ , 3 bonds, 6 electrons). Neither carbon exceeds 8 electrons.

DAT Exam Trap: Drawing the arrow starting at $\ce{H+}$ and pointing to the double bond, or forming a 5-bonded carbon.

Mnemonic for Arrow Verification (S-O-A-C):

Source: Did the arrow start at an electron pair (lone pair or bond)?
Octet: Did any Period 2 atom exceed 8 electrons?
Alignment: Does the arrow point from nucleophile/base to electrophile/acid?
Charge: Is formal charge properly calculated and net charge conserved?

Concept Comparison

Feature	Valid Mechanism Step	Invalid DAT Distractor
Arrow Origin	Lone pair or $\sigma$ / $\pi$ bond	Positive charge label or non-bonded atom center
Arrow Destination	Electrophilic atom or adjacent bond site	Nucleophilic atom or filled orbital
Period 2 Valence	$\le 8$ valence electrons (e.g., $\ce{R3C+}$ , $\ce{R4C}$ )	10 valence electrons (e.g., pentavalent carbon $\ce{R5C}$ )
Charge Conservation	Sum of reactant charges = Sum of product charges	Unbalanced charges or unassigned formal charges

Critical Thinking Questions

If a neutral nitrogen atom forms a 4th covalent bond by donating its lone pair to a carbocation, what is the formal charge on nitrogen in the product, and what is the net charge of the system before and after?
Why is a single curved arrow sufficient to describe the cleavage of tert-butyl bromide into a tert-butyl carbocation and bromide, but two curved arrows are required when hydroxide attacks chloromethane?
A student draws an arrow from the oxygen lone pair of water to the carbon atom of acetone ( $\ce{(CH3)2C=O}$ ) without drawing a second arrow to the carbonyl oxygen. What rule is violated, and what intermediate structure is falsely produced?

References

Sources returned by Google Search grounding during lesson verification.

2.2: Formal Charges - Chemistry LibreTexts — chem.libretexts.org
Curved Arrows (for reactions) - Master Organic Chemistry — masterorganicchemistry.com

Formal Charge and Common Arrow Errors

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