- Acids and alkalis — pH and neutralisation · coming soon
- Covalent bonds — sharing electrons
- What is dynamic equilibrium
- pH — the hydrogen ion concentration scale
- Buffer solutions
- Acid-base equilibria — Ka and Kb · coming soon
A base with no hydroxide in it
Ammonia, NH₃, is a gas that dissolves very well in water. Its solution turns red litmus paper blue, and it neutralises acids. It is also used in some household cleaners. So ammonia is a base.
But look at its formula. There is no OH⁻ in NH₃. The first definition of a base most students meet says that a base gives hydroxide ions. So how can ammonia be a base?
Here is a second puzzle. Open a bottle of concentrated hydrochloric acid next to a bottle of concentrated ammonia solution. A white smoke forms in the air between them, where the two gases meet:
That looks exactly like an acid neutralising a base. Yet there is no water, no H⁺(aq) and no OH⁻(aq) anywhere in it.
Chemists solved these puzzles by changing the definition of an acid and a base, twice. This lecture follows those two changes, and shows why each new definition kept the old one inside it.
The first definition: Arrhenius
In his doctoral thesis of 1884, the Swedish chemist Svante Arrhenius argued that many substances break up into ions when they dissolve in water. His examiners were not impressed, and gave the thesis a low grade. He developed the theory fully in 1887, and in 1903 it won him the Nobel Prize in Chemistry. From it came the first precise definitions of acids and bases.
An acid is a substance that produces hydrogen ions, H⁺(aq), when it dissolves in water.
A base is a substance that produces hydroxide ions, OH⁻(aq), when it dissolves in water.
So hydrochloric acid is HCl(aq) giving H⁺(aq) and Cl⁻(aq), and sodium hydroxide gives Na⁺(aq) and OH⁻(aq). Neutralisation is then one simple reaction, whichever acid and base you use:
This explained a great deal at once. It explained why all acids share properties: they all contain the same ion. It also explained why neutralisation releases about the same energy whichever strong acid and alkali you use.
There is one correction to make. A hydrogen atom is one proton and one electron. Take the electron away, and H⁺ is a bare proton, tens of thousands of times smaller than an atom. Something that small, with a full positive charge, cannot float about freely in water. It attaches at once to a lone pair on a water molecule, forming the hydronium ion, H₃O⁺ (also called the oxonium ion):
Writing H⁺(aq) is a useful short form, and you will see it often. But the particle really present is H₃O⁺(aq).
The Arrhenius definition has two limits. It works only in water. And it cannot call ammonia a base, because ammonia contains no hydroxide.
The second definition: Brønsted–Lowry
In 1923, the Danish chemist Johannes Brønsted and the English chemist Thomas Lowry each published the same new idea, independently. Look again at the HCl equation above. The HCl did not just "produce H⁺". It handed a proton to a water molecule. The water took it. An acid–base reaction, they said, is the transfer of a proton from one particle to another.
An acid is a proton donor: a particle that gives away H⁺.
A base is a proton acceptor: a particle that takes H⁺.
Now ammonia makes sense. When it dissolves, a few of its molecules take a proton from water:
Ammonia accepts the proton, so it is the base. Water gives the proton, so here water is the acid. The OH⁻ in the solution was never inside the ammonia. It is what is left of a water molecule after it has lost a proton. The ⇌ arrow matters: this is an equilibrium, and only a small fraction of the ammonia molecules have taken a proton at any moment.
The white smoke is now explained too. In the gas, an HCl molecule gives its proton straight to an NH₃ molecule. The NH₄⁺ and Cl⁻ ions formed make solid ammonium chloride. No water is needed, because the definition is about the proton, not the solvent.
That is it. That is the whole idea. An acid is not a substance that contains something. It is a particle that gives a proton to another particle that takes it. An acid can only act as an acid when a base is there to receive the proton.
Conjugate pairs
Every proton transfer can run backwards. In the ammonia equation, NH₄⁺ can give its proton back, so NH₄⁺ is an acid. OH⁻ can take a proton, so OH⁻ is a base. Each reaction therefore contains two acids and two bases, linked in pairs.
A conjugate acid–base pair is two particles that differ by exactly one H⁺. When an acid gives away its proton, what is left is its conjugate base. When a base takes a proton, it becomes its conjugate acid. In the ammonia reaction:
- NH₃ (base) and NH₄⁺ (its conjugate acid): they differ by one H⁺.
- H₂O (acid) and OH⁻ (its conjugate base): they differ by one H⁺.
To find the pairs in any equation, look for two particles that differ by a single proton, one on each side of the arrow. One member of each pair has the extra H⁺.
In HCl(g) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq), a student pairs HCl with H₃O⁺, "because they are both acids". What is wrong?
Show the answer
Members of a conjugate pair differ by exactly one H⁺. HCl and H₃O⁺ do not: one contains chlorine and the other oxygen. HCl loses a proton to become Cl⁻, so HCl and Cl⁻ are a pair. H₂O gains a proton to become H₃O⁺, so H₂O and H₃O⁺ are the other pair. Each pair has one acid and one base. Two acids can never be a conjugate pair.
Now find the mistake in this working.
The reaction is CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO⁻(aq) + H₃O⁺(aq). One line of this working is wrong. Tap the line you think is wrong. Every line has an explanation.
The working for the conjugate pairs in CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO⁻(aq) + H₃O⁺(aq), with the mistake marked and corrected:
- Line 1. CH₃COOH gives a proton to H₂O, so CH₃COOH is the acid. (Correct.)
- Line 2. H₂O takes the proton, so H₂O is the base. (Correct.)
- Line 3. CH₃COOH and H₃O⁺ are one conjugate pair. The mistake: they do not differ by one H⁺. CH₃COOH pairs with CH₃COO⁻.
- Line 4. H₂O and CH₃COO⁻ are the other pair. (This follows from the mistake. H₂O pairs with H₃O⁺.)
- Line 5. Each pair should contain one acid and one base. (Correct, and lines 3 and 4 fail this test: line 3 pairs two acids.)
The one-proton test catches every wrong pairing. Use it every time: if the two formulas do not differ by exactly one H⁺, they are not a pair.
Water, both ways round
Water was the acid in the ammonia reaction and the base in the HCl reaction. A particle that can either give or take a proton is called amphiprotic. To give a proton, it needs a hydrogen it can lose. To take one, it needs a lone pair. Water has both. The hydrogencarbonate ion, HCO₃⁻, is another example:
You will also meet the word amphoteric. It is broader: an amphoteric substance reacts with both acids and bases, whether or not it does so by passing protons. Aluminium oxide is amphoteric. It contains no hydrogen at all, so it cannot be amphiprotic. Every amphiprotic particle is amphoteric, but not the other way round.
The third definition: Lewis
Look closely at what a Brønsted–Lowry base does when it takes a proton. Ammonia's nitrogen has a lone pair of electrons. The bare proton has no electrons at all. The new N–H bond in NH₄⁺ is made from the nitrogen's lone pair. So the base's real job is to supply a pair of electrons.
The American chemist Gilbert N. Lewis saw this. In 1923, the same year as Brønsted and Lowry, he defined acids and bases by electron pairs instead of protons.
A Lewis base is an electron-pair donor.
A Lewis acid is an electron-pair acceptor.
Now reactions with no proton at all become acid–base reactions. The classic example is boron trifluoride, BF₃, with ammonia. Boron has only three outer electrons, and it uses all of them in its three B–F bonds. So boron has only six electrons around it, and room for two more. The lone pair on ammonia's nitrogen fills that space.
A covalent bond in which both shared electrons come from the same atom is called a dative covalent bond, or a co-ordinate bond. Once formed, it is just like any other covalent bond. The arrow only records where the electrons came from. BF₃ accepts the pair, so it is the Lewis acid. NH₃ donates it, so it is the Lewis base. No proton moves.
Lewis theory also covers metal ions. A silver ion has empty orbitals, and in ammonia solution each Ag⁺ takes lone pairs from two NH₃ molecules: Ag⁺(aq) + 2NH₃(aq) → [Ag(NH₃)₂]⁺(aq). Here Ag⁺ is the Lewis acid.
How the three fit together
Each definition kept the old one inside it. Every Arrhenius reaction in water is a proton transfer, so it is also a Brønsted–Lowry reaction. Every proton transfer uses a base's lone pair to bond to the proton, so it is also a Lewis reaction. The new definitions did not throw the old ones away. They widened the circle.
For bases, the nesting is exact. An Arrhenius base supplies OH⁻, which is a proton acceptor. And every proton acceptor uses a lone pair, so it is a Lewis base. For acids, take care with the words. HCl is a Brønsted–Lowry acid because it donates a proton. In Lewis's terms, though, the electron-pair acceptor is the proton itself, H⁺, not the HCl molecule. So it is better to say that every Brønsted–Lowry reaction is a Lewis reaction, than that every Brønsted–Lowry acid is a Lewis acid.
Sort the reactions below by the oldest definition that already calls them acid–base reactions.
For each reaction, choose the oldest definition that already counts it as an acid–base reaction. Choose a card, then choose a box.
This table gives the oldest definition that counts each reaction as an acid–base reaction.
| Reaction | Oldest definition |
|---|---|
| HCl dissolves in water, giving H₃O⁺(aq) and Cl⁻(aq). | Arrhenius |
| NaOH dissolves in water, giving Na⁺(aq) and OH⁻(aq). | Arrhenius |
| H⁺(aq) + OH⁻(aq) → H₂O(l) | Arrhenius |
| NH₃ dissolves in water, and the solution turns red litmus blue. | Brønsted–Lowry |
| NH₃(g) + HCl(g) → NH₄Cl(s), with no water present. | Brønsted–Lowry |
| HCO₃⁻(aq) + H₃O⁺(aq) → H₂CO₃(aq) + H₂O(l) | Brønsted–Lowry |
| BF₃(g) + NH₃(g) → F₃B←NH₃(s) | Lewis |
| Ag⁺(aq) + 2NH₃(aq) → [Ag(NH₃)₂]⁺(aq) | Lewis |
Use the narrowest definition that does the job. In water, chemists mostly use Brønsted–Lowry language, because it handles ammonia and conjugate pairs. They reach for Lewis when no proton is involved.
Worked examples
Identify the acid, the base and the two conjugate pairs in HNO₃(aq) + H₂O(l) → H₃O⁺(aq) + NO₃⁻(aq).
Think first. Find which particle loses a proton and which gains one.
HNO₃ loses a proton and becomes NO₃⁻, so HNO₃ is the acid. H₂O gains a proton and becomes H₃O⁺, so H₂O is the base. The pairs are HNO₃ / NO₃⁻ and H₃O⁺ / H₂O.
Check. Each pair differs by one H⁺, and each contains one acid and one base. ✓ The charges balance: 0 + 0 on the left, +1 and −1 on the right. ✓
Write the conjugate base of H₂SO₄ and of NH₄⁺. Write the conjugate acid of CO₃²⁻ and of H₂O.
Think first. Conjugate base: take away one H⁺, so one H fewer and the charge goes down by one. Conjugate acid: add one H⁺, so one H more and the charge goes up by one.
H₂SO₄ → HSO₄⁻. NH₄⁺ → NH₃. CO₃²⁻ → HCO₃⁻. H₂O → H₃O⁺.
Check. In each case, the hydrogen count changes by one and the charge changes by one in the same direction. ✓ Notice that HSO₄⁻ and HCO₃⁻ can each lose another proton too, so both are amphiprotic.
Carbon dioxide reacts with hydroxide ions: CO₂(aq) + OH⁻(aq) → HCO₃⁻(aq). Explain why this is an acid–base reaction, and say which definition you need.
Think first. Does a proton move? If not, look for a lone pair.
No proton moves: the H in HCO₃⁻ was already part of the OH⁻. Instead, a lone pair on the oxygen of OH⁻ forms a new bond to the carbon of CO₂. OH⁻ donates the pair, so it is the Lewis base. CO₂ accepts it, so it is the Lewis acid. Only the Lewis definition counts this as acid–base.
Check. Atoms: 1 C, 3 O and 1 H on each side. Charge: −1 on each side. ✓ This also explains a familiar fact: carbon dioxide is called an "acidic oxide" although it contains no hydrogen.
Three traps
That is only the Arrhenius definition. Ammonia, the carbonate ion and the hydrogencarbonate ion are bases because they accept protons. The OH⁻ in ammonia solution comes from water, not from the ammonia.
A conjugate pair differs by exactly one H⁺: HCl with Cl⁻, never HCl with H₃O⁺. If your two formulas contain different atoms, or are both acids, the pairing is wrong.
For Arrhenius and Brønsted–Lowry, yes. For Lewis, no: BF₃, CO₂ and Ag⁺ are Lewis acids with no hydrogen at all. Say which definition you are using.
Work each one on paper first. Open a hint only when you are stuck.
-
Identify the acid, the base and both conjugate pairs: HF(aq) + NH₃(aq) → NH₄⁺(aq) + F⁻(aq).
Hint 1
Which particle on the left has a hydrogen it loses?
Hint 2
HF loses H⁺ and becomes F⁻. What does NH₃ become?
Full answer
HF gives the proton, so it is the acid. NH₃ takes it, so it is the base. Pairs: HF / F⁻ and NH₄⁺ / NH₃. Check: each pair differs by one H⁺, and each has one acid and one base. ✓
-
Write the conjugate base of HSO₄⁻ and of H₂O, and the conjugate acid of OH⁻ and of NH₃.
Hint 1
Conjugate base: remove one H⁺. Conjugate acid: add one H⁺.
Hint 2
Removing H⁺ lowers the charge by one; adding H⁺ raises it by one.
Full answer
HSO₄⁻ → SO₄²⁻. H₂O → OH⁻. OH⁻ → H₂O. NH₃ → NH₄⁺. Check: OH⁻ and H₂O appear in both lists, as a pair, because water is amphiprotic. ✓
-
For each reaction, say which is the oldest definition that counts it as an acid–base reaction, and name the acid and the base. (a) KOH(aq) + HNO₃(aq) → KNO₃(aq) + H₂O(l). (b) AlCl₃ + Cl⁻ → AlCl₄⁻, in a solvent other than water. (c) NH₄⁺ + NH₂⁻ → 2NH₃, in liquid ammonia as the solvent.
Hint 1
Ask, in order: is it H⁺ and OH⁻ in water? Does a proton move? Is a lone pair shared?
Hint 2
In (b), aluminium has only six outer electrons in AlCl₃, like boron in BF₃. In (c), which particle loses a proton, and is there any water?
Full answer
(a) Arrhenius: HNO₃ gives H⁺(aq), KOH gives OH⁻(aq), and they form water. (b) Lewis: no proton moves. Cl⁻ donates a lone pair (Lewis base) to aluminium in AlCl₃ (Lewis acid). (c) Brønsted–Lowry: a proton moves from NH₄⁺ (the acid) to NH₂⁻ (the base), and there is no water at all. Check (c): NH₄⁺ loses a proton to become NH₃, and NH₂⁻ gains one to become NH₃. The pairs are NH₄⁺ / NH₃ and NH₃ / NH₂⁻, each differing by one H⁺. ✓ Liquid ammonia behaves like water here, with NH₄⁺ in the role of H₃O⁺ and NH₂⁻ in the role of OH⁻.
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A stretch. The dihydrogenphosphate ion, H₂PO₄⁻, is amphiprotic. (a) Write an equation for it acting as an acid with OH⁻, and one for it acting as a base with H₃O⁺. (b) Water can also react with itself: one water molecule gives a proton to another. Write the equation, and identify both conjugate pairs. (c) Why can this happen with water but not with methane, CH₄?
Hint 1
As an acid, H₂PO₄⁻ loses H⁺ to become HPO₄²⁻. As a base, it gains H⁺ to become H₃PO₄.
Hint 2
For (c), list what a particle needs to give a proton, and what it needs to take one.
Full answer
(a) H₂PO₄⁻(aq) + OH⁻(aq) → HPO₄²⁻(aq) + H₂O(l). H₂PO₄⁻(aq) + H₃O⁺(aq) → H₃PO₄(aq) + H₂O(l). (b) H₂O(l) + H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq). The pairs are H₂O / OH⁻ (the molecule that gave the proton) and H₃O⁺ / H₂O (the one that took it). (c) Taking a proton needs a lone pair. Water's oxygen has two lone pairs, and its O–H bonds are polar, so a proton can leave one molecule and join another. Methane's carbon has no lone pair, and its C–H bonds are almost non-polar, so it neither takes nor gives protons in water. Check (a): each equation balances in atoms and in charge. ✓ The reaction in (b) happens in only a tiny fraction of water molecules, and the next lecture uses it to build the pH scale.
Arrhenius's thesis of 1884 was nearly failed, and it was later the basis of a Nobel Prize. The Brønsted–Lowry and Lewis definitions both appeared in 1923. None of the three definitions was "wrong". Each was a tool that worked for the reactions it was made for, and each new one kept the old one as a special case. (Sources: Encyclopedia.com, "Arrhenius, Svante August"; Britannica, "The Brønsted–Lowry definition"; W. B. Jensen, Chemical Reviews, 1978.)
Science often grows this way. A definition is widened when a real example will not fit it: ammonia without hydroxide, a neutralisation without water, a reaction without a proton. When you meet a definition, ask what it was built to explain, and where it stops. Lewis acids and bases go on to explain how metal ions hold molecules around them, how many catalysts work, and how enzymes speed up reactions in living cells.
- An Arrhenius acid gives H⁺(aq) and a base gives OH⁻(aq) in water, and the H⁺(aq) is really the hydronium ion, H₃O⁺.
- A Brønsted–Lowry acid is a proton donor and a base is a proton acceptor, so acid–base reactions can happen without water and without OH⁻.
- A conjugate acid–base pair differs by exactly one H⁺, and every proton transfer contains two such pairs.
- An amphiprotic particle, such as H₂O or HCO₃⁻, can either give or take a proton, while "amphoteric" is the broader word for reacting with both acids and bases.
- A Lewis base donates an electron pair and a Lewis acid accepts one, often forming a dative covalent bond, so reactions such as BF₃ with NH₃ count as acid–base reactions.