The Bronsted-Lowry theory

Result

The Bronsted-Lowry theory

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Statement

Acids and bases as proton donors and acceptors.

Why it matters

The Arrhenius definition of an acid (a substance producing \(\text{H}^+\) in water) and a base (producing \(\text{OH}^-\) in water) works well enough for simple aqueous cases but cannot explain why, for example, ammonia acts as a base in water despite containing no hydroxide ion at all, or how acid-base chemistry works in a non-aqueous solvent altogether. The Bronsted-Lowry theory resolves this by redefining acids and bases functionally, as proton donors and proton acceptors respectively, a definition that applies equally well in water, in any other solvent, or with no solvent present at all.

This proton-transfer framework is the foundation the rest of this unit builds on directly: water-autoionisation-ph's definition of pH rests on water acting simultaneously as both a weak acid and a weak base (amphoterism, a direct Bronsted-Lowry concept), and henderson-hasselbalch, titration-curves, and polyprotic-acids all describe, in increasing detail, the quantitative consequences of exactly the proton-transfer equilibria defined here.

Hypotheses

Acid-base behaviour is defined entirely by the transfer of a proton (\(\text{H}^+\)) from one species to another, not by reference to any particular solvent or to hydroxide ion specifically.This deliberately generalises beyond the Arrhenius definition's reliance on water and hydroxide ion; a Bronsted-Lowry acid-base reaction is fundamentally just \(\text{HA}+\text{B}\rightleftharpoons\text{A}^-+\text{HB}^+\), a proton moving from one species to another, regardless of what solvent (if any) the reaction occurs in. Every Bronsted-Lowry acid, on losing a proton, generates a corresponding conjugate base; every base, on gaining a proton, generates a corresponding conjugate acid.This conjugate-pair structure is not incidental but central to the theory's whole logic: because every proton-transfer reaction necessarily runs in both directions to some extent (it is a genuine chemical equilibrium), both the forward acid/base pair and the reverse conjugate base/acid pair must be tracked simultaneously to describe the system correctly. A species can be amphoteric — capable of acting as either a Bronsted-Lowry acid or a Bronsted-Lowry base depending on what it reacts with. Water is the paradigm example: it donates a proton to a sufficiently strong base, and accepts a proton from a sufficiently strong acid, and it is precisely this dual behaviour, applied to water reacting with itself, that underlies water's own autoionisation (water-autoionisation-ph).

Proof

\text{HA} + \text{B} \rightleftharpoons \text{A}^- + \text{HB}^+

Any Bronsted-Lowry acid-base reaction is, at its core, exactly this single proton-transfer step: \(\text{HA}\) (the acid) donates a proton to \(\text{B}\) (the base), generating \(\text{A}^-\) (the conjugate base of \(\text{HA}\)) and \(\text{HB}^+\) (the conjugate acid of \(\text{B}\)). A

\text{HA and A}^-\text{ form one conjugate acid-base pair; B and HB}^+\text{ form a second.}

Each species in the reaction is paired with the species it becomes upon losing or gaining exactly one proton; identifying both conjugate pairs is the standard first step in analysing any Bronsted-Lowry reaction, since the equilibrium position depends on the relative strengths of the two acids and two bases involved. A

\text{The equilibrium of Step 1 favours the side with the weaker acid and weaker base.}

Because a stronger acid gives up its proton more readily than a weaker one, and a stronger base accepts a proton more readily than a weaker one, a proton-transfer equilibrium is driven toward forming the weaker acid and weaker base of the two conjugate pairs present — the thermodynamically more stable, less reactive combination. A

K_a = \frac{[\text{A}^-][\text{H}_3\text{O}^+]}{[\text{HA}]}

Applying Step 1 specifically to an acid \(\text{HA}\) donating a proton to water (itself acting as the base, per the Hypotheses' amphoterism point) gives the standard acid dissociation equilibrium and its associated equilibrium constant \(K_a\), quantifying exactly how strongly, on average, \(\text{HA}\) favours donating its proton. A

Result

\text{Acid: proton donor} \qquad \text{Base: proton acceptor} \qquad \text{HA}+\text{B}\rightleftharpoons\text{A}^-+\text{HB}^+

Reading. Acid-base chemistry is redefined entirely in terms of proton transfer between a conjugate acid-base pair and a conjugate base-acid pair, freeing the concept from any dependence on water or hydroxide ion specifically.

Scope. Applies in any solvent, or with no solvent at all, wherever a proton can be transferred between species; does not, by itself, describe acid-base behaviour that does not involve proton transfer at all (the broader Lewis definition, based on electron-pair donation and acceptance, is needed for those cases).

Corollaries & converses

Every Bronsted-Lowry acid has exactly one conjugate base, and vice versa; a strong acid necessarily has a very weak conjugate base (Step 3), which is why the conjugate bases of strong acids like \(\text{HCl}\) are essentially non-basic in water.
henderson-hasselbalch's buffer equation is a direct, quantitative consequence of the conjugate acid-base pair structure established here: a buffer specifically exploits the presence of both members of one conjugate pair simultaneously in solution.
Converse: given the measured equilibrium position of a proton-transfer reaction (which side is favoured), one can directly rank the relative strengths of the two acids (or two bases) involved, without needing to measure either \(K_a\) independently (Step 3, run in reverse).

Fails without

Assume a base must contain hydroxide ion, per the older Arrhenius definition: a substance like ammonia, containing no hydroxide, is still a genuine Bronsted-Lowry base, since it accepts a proton directly (Hypotheses, first point); restricting "base" to hydroxide-containing species alone misses this and many other important cases.
Ignore that proton transfer is a genuine equilibrium, treating it as one-directional: the reverse reaction still occurs to some extent, and the equilibrium position (not simply "does it react") depends on the relative strengths of both conjugate pairs present (Step 3), not on the forward reaction in isolation.

Common errors

Assuming a Bronsted-Lowry base must contain hydroxide ion, carrying over the narrower Arrhenius definition; ammonia, a classic Bronsted-Lowry base, contains no hydroxide and instead accepts a proton directly onto its lone pair.
Confusing a conjugate acid-base pair (species differing by exactly one proton, Step 2) with an arbitrary acid and base appearing on opposite sides of a reaction, which need not be conjugates of one another at all.
Forgetting that conjugate acid-base strength is inversely related (Step 3): a stronger acid always has a weaker conjugate base, never a stronger one.
Treating a proton-transfer reaction as going to completion in one direction, rather than as a genuine equilibrium whose position depends on the relative strengths of both conjugate pairs present.

Discussion

Johannes Nicolaus Brønsted and Thomas Martin Lowry independently proposed this proton-transfer definition in 1923, generalising the earlier, narrower Arrhenius picture. The same year, Gilbert N. Lewis proposed a still broader definition based on electron-pair donation and acceptance rather than proton transfer specifically, which subsumes the Bronsted-Lowry definition as a special case (every Bronsted-Lowry acid-base reaction is also a Lewis acid-base reaction, though the converse is not true, since some Lewis acid-base reactions, such as \(\text{BF}_3\) accepting an electron pair from ammonia, involve no proton transfer at all).

Common misconception: that a substance's identity alone fixes whether it acts as an acid or a base. In the Bronsted-Lowry framework, whether a given species acts as an acid or a base can depend entirely on what it is reacting with — water accepts a proton from a strong acid (acting as a base) but donates a proton to a strong base (acting as an acid), an amphoteric behaviour that only makes sense once acid/base identity is understood as relational, not absolute.

Worked examples

\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-

Ammonia has no hydroxide ion in its own formula, yet is a classic weak base: it accepts a proton directly from water, which here acts as the Bronsted-Lowry acid, generating the ammonium ion (ammonia's conjugate acid) and hydroxide (water's conjugate base). A

\text{Conjugate pairs: NH}_4^+/\text{NH}_3 \quad\text{and}\quad \text{H}_2\text{O}/\text{OH}^-

Identifying both conjugate pairs explicitly (Step 2 of the Proof) clarifies that this reaction is not fundamentally different in kind from any other Bronsted-Lowry proton transfer, despite ammonia containing no hydroxide of its own, precisely the generalisation the Arrhenius definition could not accommodate. A

\text{Ammonia is a Bronsted-Lowry base by accepting a proton from water, generating OH}^-\text{ as a product, not as a constituent}

Reading. Basic behaviour does not require a substance to already contain hydroxide ion; it only requires the substance to be able to accept a proton from whatever acid (here, water itself) is present.

Scope. The same logic explains the basicity of many nitrogen-containing organic compounds (amines) in water, none of which contain hydroxide ion in their own structure.

Problems

Identify the Bronsted-Lowry acid, base, conjugate acid, and conjugate base in the reaction \(\text{HF} + \text{H}_2\text{O} \rightleftharpoons \text{F}^- + \text{H}_3\text{O}^+\).
Solution
\(\text{HF}\) is the acid (donates a proton); \(\text{H}_2\text{O}\) is the base (accepts the proton); \(\text{F}^-\) is the conjugate base of \(\text{HF}\); \(\text{H}_3\text{O}^+\) is the conjugate acid of \(\text{H}_2\text{O}\).
In the reaction \(\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 + \text{OH}^-\), bicarbonate acts as a Bronsted-Lowry base. In a separate reaction, \(\text{HCO}_3^- + \text{OH}^- \rightleftharpoons \text{CO}_3^{2-} + \text{H}_2\text{O}\), it acts as an acid. What property of bicarbonate does this illustrate?
Solution
This illustrates amphoterism (the Hypotheses' third point): bicarbonate is capable of acting as either a proton donor or a proton acceptor depending on what it reacts with — donating a proton to the strong base hydroxide in the second reaction, but accepting a proton from water (itself normally a weak acid toward bicarbonate) in the first.
Explain, using Step 3, why the reaction \(\text{HCl}+\text{F}^-\rightleftharpoons\text{Cl}^-+\text{HF}\) lies essentially entirely to the right (favouring products), given that \(\text{HCl}\) is a strong acid and \(\text{HF}\) is only a weak acid.
Solution
By Step 3, a proton-transfer equilibrium favours forming the weaker acid and weaker base. Since \(\text{HCl}\) (a strong acid) is a far stronger acid than \(\text{HF}\) (a weak acid), and correspondingly \(\text{Cl}^-\) is a far weaker base than \(\text{F}^-\), the equilibrium strongly favours the side containing the weaker acid (\(\text{HF}\)) and weaker base (\(\text{Cl}^-\)) — i.e., the product side — driving the reaction essentially to completion toward \(\text{Cl}^-\) and \(\text{HF}\).