Organic Chemistry · An Overview of Organic Reactions

Using Curved Arrows in Polar Reaction Mechanisms

7 min read

On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

A is the chemist's way of drawing electron movement. Its tail starts where the electrons are (a lone pair or a bond) and its head points to where they end up (an atom or a bond). A represents an electron pair and is the arrow of polar reactions; a half-headed (fishhook) arrow represents a single electron and is reserved for radical reactions. Mastering them lets you read, predict, and check any polar mechanism — including the HBr–ethylene addition from the previous topic, powered by exactly three arrow pushes.

Why this matters

Every mechanism is shorthand for a sequence of curved arrows. Push arrows correctly and you can predict products, spot invalid mechanisms, and fix your own exam answers — most mechanism errors are arrow errors. The conventions encode physical reality: electrons move, atoms do not, and no second-row element (C, N, O, F) may exceed an octet. Curved arrows are the grammar of the subject; this topic teaches its rules.

The college version

Core Concepts

The two kinds of curved arrows

A full-headed curved arrow (solid triangular head) shows the movement of two electrons — a lone pair or a bond — and is used in all polar (ionic) mechanisms. A half-headed arrow, or fishhook (single barb), shows one electron and is used only for radical reactions, where bonds break homolytically and each fragment keeps one electron. Fishhook = radical chemistry; full head = polar chemistry.

Rule 1: Electrons move, atoms do not

The tail must begin at a source of electrons: a lone pair on an atom, a pi bond, or a sigma bond. The head points at the destination: an atom (forming a bond or lone pair) or a bond (breaking it). An arrow that starts on an atom with no lone pair, or that "jumps" from a positive charge, is invalid — positive charges cannot donate. Electrons are the only moving parts; nuclei simply adjust.

Rule 2: Respect the octet

For second-row elements (C, N, O, F), an arrow may never produce a species in which one of these atoms has more than eight valence electrons. If your arrow would give carbon five bonds, the mechanism is wrong. Heavier elements (P, S, halogens below F) can sometimes exceed an octet via d orbitals, but in standard organic mechanisms treat the second-row octet as a hard limit.

Rule 3: Keep track of charges and counts

Each arrow changes formal charges predictably. When a lone pair forms a bond, the donor loses the lone pair and gains a bond: its rises by +1. When a bond breaks so both electrons go to one atom, that atom gains a lone pair and loses a bond: its charge falls by −1. In short, an arrow from lone pair to bond makes the donor more positive; an arrow from bond to lone pair makes the recipient more negative. Total charge is conserved across each step.

Reading the HBr–ethylene mechanism as arrows

The addition of HBr to ethylene is three arrow pushes. Arrow 1: from the pi bond of CH₂=CH₂ to the hydrogen of H–Br, forming a new C–H bond. Arrow 2: from the H–Br sigma bond to bromine, breaking it heterolytically and giving a bromide lone pair. After these two, you have the ethyl cation and Br^-. Arrow 3: from a lone pair on Br^- to the carbocation carbon, forming the C–Br bond. Two arrows in, one arrow out is the classic rhythm of an addition.

Multiple arrows in one step

A step may show two or more arrows at once, as in step 1 above, where the pi-bond attack and the H–Br cleavage are simultaneous and concerted: as pi electrons move toward hydrogen, the H–Br electrons move toward bromine. This "push–pull" pattern appears throughout organic chemistry.

How It Works / Step-by-Step Process

Identify the : the lone pair or bond that will move (usually on a nucleophile or in a pi bond).
Identify the destination: the electron-poor atom or bond (a δ+ atom, carbocation, or bond to a leaving group).
Draw the arrow from source to destination: to form a bond, head at the atom; to break a bond, tail on the bond.
Recalculate new bonds, lone pairs, and formal charges.
Verify: no octet violations, total charge conserved, valences satisfied.

Common Confusions

Do not confuse	With	Difference
Full-headed arrow	Fishhook arrow	Full head = electron pair (polar); half head = one electron (radical). Mixing them is a classic error.
Arrow tail placement	Arrow head placement	The tail starts at the electrons (lone pair/bond); the head points at the destination. Reversing them reverses the mechanism.
"Arrow from positive to negative"	Arrow from electron-rich to electron-poor	Electrons flow from the electron-rich source (which may be neutral) toward the electron-poor site; the arrow does not connect charges directly.
Curved arrow	Equilibrium arrow	A curved arrow shows electron movement within a mechanism step; a double-headed equilibrium arrow shows forward and reverse reactions.

Eli explains

The same idea, in plain words

Explain it like I’m 10

A curved arrow is like a delivery route drawn on a map: it starts at the house where the electrons live (a lone pair or a bond) and points to the house where they're going. A full arrow delivers a pair of electrons together, while a fishhook arrow delivers them one at a time. Electrons are the only things that travel — the atoms just stay put and react to whoever shows up.

Worked example

Example 1: Arrow-by-arrow analysis of HBr addition to ethylene

Step 1: Draw arrow 1 from the pi bond of CH₂=CH₂ to the hydrogen of H–Br, and arrow 2 from the H–Br sigma bond to bromine. Read the result: the pi bond is now a C–H bond, the H–Br bond is gone, bromine has gained a lone pair and a −1 formal charge, and the carbon that lost the pi electrons has a +1 charge. Products: CH₃CH₂⁺ and Br^-. Charge check: neutral reactants give +1 and −1 — conserved. Octet check: no atom exceeds eight electrons.

Step 2: Draw arrow 3 from a lone pair on Br^- to the carbocation carbon. The result: a new C–Br bond, the bromide loses its lone pair and charge, and the carbocation carbon gains two electrons, becoming neutral. Products: CH₃CH₂Br. Charge check: +1 and −1 cancel — conserved. The mechanism is complete and valid.

Example 2: Testing an invalid arrow

A student proposes that the ethyl cation forms by an arrow drawn from the positive carbon of a "carbocation-like" intermediate to the bromine of HBr. Is this valid? No. The tail must start at an electron source, and a positively charged carbon has no lone pair or bond to donate — its empty p orbital is a sink, not a source. The correct arrow starts on the pi bond and points to hydrogen. Classic exam trap: arrows start at electrons, never at positive charges or empty orbitals.

Key takeaways

Full-headed arrow = two electrons (polar); half-headed fishhook = one electron (radical).
Tail starts at an electron source (lone pair, pi bond, sigma bond) — never at a positive charge or empty orbital; head points at the destination.
Second-row atoms (C, N, O, F) may never exceed an octet; an arrow that breaks this rule is invalid.
Lone pair → bond raises the donor's formal charge by +1; bond → lone pair lowers the recipient's by −1; total charge conserved.
The HBr–ethylene addition is three arrows: pi bond → H; H–Br bond → Br; Br^- lone pair → carbocation carbon.
Arrows drawn correctly force the product and the charges — arrow-pushing is predictive, not decoration.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

What is the difference between a full-headed curved arrow and a , and when is each used?
Show answer
A full-headed arrow shows a two-electron movement and is used in polar reactions; a fishhook (half-headed) arrow shows a one-electron movement and is used in radical reactions.
Where must the tail of a curved arrow always start?
Show answer
At an electron source: a lone pair, a pi bond, or a sigma bond. It can never start at a positive charge or an empty orbital.
After arrow 1 and arrow 2 in the HBr–ethylene mechanism, what two species exist, and what are their charges?
Show answer
The ethyl cation CH₃CH₂⁺ (+1) and the bromide ion Br^- (−1); the charges cancel, conserving total charge.
Why is an arrow drawn from a carbocation carbon to a nucleophile invalid?
Show answer
The carbocation carbon is electron-poor with no lone pair or available bond to donate; an arrow tail must start at an electron source. The correct arrow starts on the nucleophile's electrons.
When a lone pair forms a new bond, what happens to the donating atom's formal charge?
Show answer
Its formal charge rises by +1: the atom loses the lone pair but gains a bond (e.g., neutral oxygen becomes +1 after donating a lone pair).

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsKey vocabulary · Related

Key vocabulary

curved arrow: A drawn arrow whose tail marks where electrons start and whose head marks where they go.
full-headed arrow: A curved arrow with a solid head, representing a two-electron (electron-pair) movement.
fishhook arrow: A curved arrow with a single barb, representing a one-electron movement.
electron source: A lone pair or a bond that supplies the moving electrons.
octet rule: Second-row elements are stable with eight valence electrons and may not exceed eight.
formal charge: The charge an atom would have if bonding electrons were shared equally.

Sources & references

openstax.org — Organic Chemistry

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.