A curved arrow shows where a pair of electrons goes when bonds form or break. A mechanism is the step-by-step account of how a reaction happens, and every one in this course is drawn with these arrows.
Formal charge already drew one arrow, for ammonia taking a hydrogen ion. This page starts from that same reaction and builds the rules you need to draw and check any arrow.
One arrow, one pair of electrons
Ammonia's nitrogen has a lone pair. A hydrogen ion, H⁺, has no electrons at all, only an empty 1s orbital. When the two meet, the lone pair becomes a new N–H bond, and ammonia becomes the ammonium ion, NH₄⁺.
One curved arrow shows that change. Its tail sits on nitrogen's lone pair, where the electrons start. Its head points at the hydrogen, where they end up.
The charges check out. Nitrogen now has four bonds and no lone pair, so its formal charge is 5 − 0 − 4 = +1. The hydrogen shares a pair and is neutral. The +1 that came in on H⁺ now sits on nitrogen.
Drawing the arrow the other way, from H⁺ to nitrogen, is wrong, even though it would still show which atoms join. H⁺ has no electrons to give. An arrow follows electrons, not atoms.
That single arrow holds the whole idea. A curved arrow stands for two electrons moving together. The tail starts where the pair is now, and the head points to where the pair ends up.
So a tail can start in only two places: on a lone pair, or on a bond, which is a shared pair. A tail never starts on a bare atom, on a positive charge or on empty space, because none of those holds a pair to move.
One shortcut seems to break this rule, but does not. Lone pairs are often left off drawings, so chemists commonly start a tail at a drawn minus sign, such as the one on hydroxide, HO⁻. That works because a minus on an atom nearly always means a lone pair sits there too.
Borohydride, BH₄⁻, is the exception. Its boron carries the minus but has four bonds and no lone pair, so its arrows start on a B–H bond instead. Either way, the test is the same: name the pair of electrons the tail sits on. If you cannot, the arrow is wrong.
Where the head points tells you what forms. There are three cases, one per row in the figure below.
Head on another atom: a new bond. When the pair comes from elsewhere in the drawing, the head points at the atom the pair will bond to. Ammonia and H⁺ work this way. So does hydroxide bonding to a carbocation, a carbon with only three bonds and a positive charge.
Head on an atom of the same bond: a new lone pair. Here the pair starts as a bond, and the head points at one of that bond's own two atoms. The bond breaks, and that atom keeps both electrons as a lone pair.
Acetone's C=O shows it. The arrow moves the pair of the π bond (the second bond of the double bond) onto oxygen. Nothing new bonds. Oxygen gains a lone pair and a −1 charge, and carbon, now with three bonds, becomes +1.
That C=O arrow is one of the commonest in the course. In a reaction it usually works beside a second arrow, moving the π pair onto oxygen while another pair bonds to the carbon. Shown alone, it moves no atom and makes no new molecule, so the figure joins the two drawings with ↔ rather than a reaction arrow. The resonance section below explains this.
Head on the middle of a bond: a new π bond. A head drawn on the line between two atoms that are already bonded adds a second bond between them. Run the acetone arrow backwards to see it. A lone pair on the O⁻ moves into the C–O bond, the C=O double bond forms again, and both charges disappear.
When the target is already full: two arrows
In a real flask, a proton is almost never bare. It is bonded to something, as it is in hydrogen chloride, H–Cl, in H₃O⁺ or in sulfuric acid, H₂SO₄. So give ammonia H–Cl instead of H⁺.
Arrow 1 runs from nitrogen's lone pair to the hydrogen of H–Cl. On its own, it would give that hydrogen two bonds, and hydrogen can hold only one.
Arrow 2, drawn in the same step, fixes that. Its tail sits on the H–Cl bond and its head on chlorine. The bond breaks, and chlorine leaves with both electrons as the chloride ion, Cl⁻.
Now the charges. Nitrogen has 4 bonds and no lone pair: 5 − 0 − 4 = +1. Chlorine has no bonds and four lone pairs: 7 − 8 − 0 = −1. The charge going in is 0, and the charge coming out is +1 − 1 = 0. ✓
This two-arrow step is a proton transfer: a hydrogen ion moves from one molecule to another. The proton always comes from somewhere, so every proton transfer needs both arrows. The one-arrow version above is fine only when a question hands you H⁺ on its own.
Now run the same step with hydroxide, HO⁻, and ethanol, CH₃CH₂OH. This time hydroxide takes the hydrogen of ethanol's O–H.
Arrow 1 runs from a lone pair on the hydroxide oxygen to that hydrogen. Arrow 2 runs from the O–H bond onto ethanol's oxygen, which keeps the pair.
The hydroxide oxygen starts with one bond and three lone pairs (6 − 6 − 1 = −1). It ends with two bonds and two lone pairs (6 − 4 − 2 = 0), so it has become water.
Ethanol's oxygen starts with two bonds and two lone pairs, and is neutral. It ends with one bond and three lone pairs (6 − 6 − 1 = −1). That ion is ethoxide, an alkoxide: the anion left when an alcohol loses the hydrogen of its O–H. The −1 has moved from hydroxide to ethoxide, so the total is unchanged. ✓
Gaining a proton and losing one are the same step seen from its two sides. In both, the base, the molecule taking the proton, supplies the lone pair that bonds to the hydrogen. The atom the proton leaves keeps the old bonding pair.
Hydroxide can bond to carbon, too. Take bromomethane, CH₃Br. Bromine pulls the C–Br pair toward itself, so the carbon is δ+ and attracts the hydroxide's lone pair (Electronegativity explains the δ+).
Draw only the arrow from hydroxide to that carbon, and the carbon ends up with five bonds. Carbon cannot have five.
So a second arrow acts at the same moment. Its tail sits on the C–Br bond and its head on bromine. Bromine leaves with both electrons as the bromide ion, Br⁻. The new C–O bond forms as the C–Br bond breaks, so the carbon never has five full bonds. The products are methanol, CH₃OH, and bromide.
Chemists call this one-step swap an SN2 reaction. Substitution & Elimination covers it in full.
All three examples follow one rule. When a head points at an atom that is already full, such as a hydrogen with its one bond or a carbon with its four, a second arrow must break one of that atom's bonds at the same moment. One arrow makes a bond to the atom and the other breaks one of its bonds, and that pairing is the shape of most steps in a mechanism.
Four patterns
Every arrow so far fits one of four patterns, and most mechanisms in this course are built from these four in some order. Knowing them turns a new mechanism into steps you have drawn before. Faced with a reaction you have never seen, ask which pattern gets you one step closer to the product.
1. A lone pair makes a new bond to an electron-poor atom. One arrow runs from a lone pair, or from a π bond, to that atom. It can be an atom short of electrons, such as a carbocation or H⁺, or the δ+ end of a polar bond, such as the carbon of C–Br. Water bonding to a carbocation is an example. If the atom has an empty orbital and room, as a carbocation, H⁺ or BF₃ does, one arrow is the whole step. If it is already full, a second arrow must act beside it, as with bromomethane.
Chemists call the electron-rich partner that supplies the pair a nucleophile, and the electron-poor atom that receives it an electrophile. This pattern is called nucleophilic attack. How Reactions Happen treats both terms in full.
2. A bond breaks, and one atom keeps both electrons. One arrow runs from a bond onto one of its own two atoms. Take (CH₃)₃C–Br, a tertiary alkyl bromide. When its C–Br bond breaks this way, bromine leaves as Br⁻. The carbon, down to three bonds, becomes a carbocation. The charges balance: 0 goes in, and +1 and −1 come out.
The group that departs with the pair is called a leaving group. The tail sits on the C–Br bonding pair, which is as good a place for a tail as any lone pair. It is the first step of the SN1 and E1 reactions in Substitution & Elimination.
3. Proton transfer. Two arrows, as in the ammonia and ethanol examples: a lone pair goes to the hydrogen, and the hydrogen's old bond goes onto the atom it leaves. They appear wherever a reaction runs with an acid (a source of H⁺) or a base present, and in such reactions many steps are nothing else. Brønsted acids/bases covers both.
4. A neighboring bond shifts. One arrow runs from a C–H or C–C bond on the carbon next to a carbocation, onto the positive carbon. The hydrogen or carbon group moves across with its bonding pair, and the positive charge moves to the carbon it left.
When a hydrogen moves, the step is a 1,2-hydride shift: a hydride is a hydrogen that travels with its pair of electrons, and 1,2 means it moves to the next carbon. When a carbon group moves, it is a 1,2-alkyl shift. Carbocations explains when a shift happens and why. For drawing arrows, the point is that a σ bond, a single bond, is a legal place for a tail.
Spotting invalid arrows
Four checks catch nearly every wrong arrow. The figure after them draws one mistake for each.
Does the tail start on electrons? An arrow that starts on a + sign is always wrong: a charge is not a pair of electrons. A carbocation's positive carbon has only six electrons and no lone pair, so it can only be where a head lands. This is the commonest beginner's mistake.
Does any atom end up with too many bonds? Hydrogen holds one bond. Carbon and nitrogen hold at most four, and oxygen at most three. If a product breaks one of these limits, a bond was formed without one being broken.
Does the charge balance? The total charge on the left must equal the total on the right, in every step. Work out the formal charges after each arrow until it becomes a habit.
Does the pair move from rich to poor? Electrons flow from an electron-rich site, such as a lone pair, a π bond or a negative charge, toward an electron-poor one. An arrow that moves a polar bond's own pair onto its δ+ atom is almost always backwards: the C=O pair goes onto oxygen, never onto carbon.
Arrows in resonance and arrows in a mechanism
Some molecules are described better by two or more drawings than by one. The drawings keep every atom in place and differ only in where the electrons sit. Each drawing is a resonance structure, and curved arrows show how to get from one to the next. Resonance, the next topic, explains why a molecule needs more than one.
Acetone's C=O arrow from the first section links two resonance structures: acetone and a drawing with C⁺ and O⁻. No atom moves and nothing new bonds; the arrow only changes where one pair is drawn. A double-headed arrow, ↔, goes between the two drawings.
In a mechanism, the same kind of arrow describes electrons really moving as one species becomes another. When hydroxide bonds to acetone's carbon, the π pair moves onto oxygen as the new C–O bond forms. A plain reaction arrow, →, goes between the structures.
The rules for drawing curved arrows are identical in both jobs, so everything on this page applies to resonance as well.
Fishhook arrows move one electron
Every arrow so far has a head with two barbs, one on each side of the tip, and moves two electrons. That covers nearly every reaction in this course. A fishhook arrow has a head with a single barb, and it moves just one electron.
Fishhooks belong to radical reactions. A radical is a species with a single unpaired electron, such as the methyl radical in Hybridization. Light can split the Cl–Cl bond evenly, sending one electron to each chlorine. Two fishhooks show that split, one toward each atom, and it is called homolytic cleavage.
Radical halogenation (in How Reactions Happen) and the radical addition of HBr to a C=C use fishhooks too. Learn to recognize a fishhook on sight; you will not draw one for SN1, SN2, E1 or E2, which all use full arrows.
What carries forward
Next comes Resonance, which uses these arrows to find every valid drawing of a molecule. After that, every mechanism from Substitution & Elimination onward is written with them.
When you meet a reaction you have never seen, start the same way each time. Find the electron-rich site, find the electron-poor site, and draw the arrow from the first to the second. Much of what looks like memorization in organic chemistry is this one skill, used on new molecules.