Theories of Acids and Bases – pH of Acidic and Alkaline Solutions (Senior 6 Chemistry) | Ganzaa

pH of Acidic and Alkaline Solutions

Lessons

Senior 6 · Chemistry

pH of Acidic and Alkaline Solutions

5 lessons

Lesson 1 of 5

Theories of Acids and Bases

25 min

A base with no hydroxide in it

Acidic soils hold back crops in many parts of Rwanda, and farmers treat them with agricultural lime (ishwagara). In June 2024, for example, farmers in Gatsibo District were trained to apply a finely ground lime. Agricultural lime is mostly calcium carbonate. It contains no hydroxide ions, yet it removes acid from the soil:

$\mathrm{CaCO_3(s) + 2H^{+}(aq) \rightarrow Ca^{2+}(aq) + CO_2(g) + H_2O(l)}$

A second puzzle: open a bottle of concentrated ammonia solution next to a bottle of concentrated hydrochloric acid and a white smoke forms in the air between them, although no water is involved: $\mathrm{NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)}$ . Is ammonia gas a base? Is the carbonate ion? The answer depends on which definition of "acid" and "base" you use. This lesson compares the three definitions chemists use, each wider than the one before.

Definition

Arrhenius acid: a substance that produces hydrogen ions, $\mathrm{H^{+}(aq)}$ , in water. Arrhenius base: a substance that produces hydroxide ions, $\mathrm{OH^{-}(aq)}$ , in water. Example: HCl is an acid and NaOH a base.

Oxonium (hydronium) ion, $\mathrm{H_3O^{+}}$ : a proton bonded to a water molecule. A bare $\mathrm{H^{+}}$ never exists in water; $\mathrm{H^{+}(aq)}$ is shorthand for $\mathrm{H_3O^{+}(aq)}$ .

Brønsted–Lowry acid: a proton ( $\mathrm{H^{+}}$ ) donor. Brønsted–Lowry base: a proton acceptor. Example: in $\mathrm{NH_3 + HCl \rightarrow NH_4^{+} + Cl^{-}}$ , HCl is the acid and $\mathrm{NH_3}$ the base.

Conjugate acid–base pair: two species that differ by exactly one proton. Example: $\mathrm{NH_4^{+}}$ is the conjugate acid of $\mathrm{NH_3}$ ; $\mathrm{Cl^{-}}$ is the conjugate base of HCl.

Amphoteric (amphiprotic) species: one that can act as an acid or as a base. Example: $\mathrm{H_2O}$ , $\mathrm{HCO_3^{-}}$ .

Lewis acid: an electron-pair acceptor. Lewis base: an electron-pair donor. Example: in $\mathrm{BF_3 + NH_3 \rightarrow F_3B{\leftarrow}NH_3}$ , $\mathrm{BF_3}$ is the Lewis acid and $\mathrm{NH_3}$ the Lewis base.

1. The Arrhenius theory

In the 1880s the Swedish chemist Svante Arrhenius explained the conductivity of acid and alkali solutions by ions. An acid such as nitric acid ionises in water, $\mathrm{HNO_3(aq) \rightarrow H^{+}(aq) + NO_3^{-}(aq)}$ ; a base such as sodium hydroxide releases hydroxide ions; and neutralisation is simply

$\mathrm{H^{+}(aq) + OH^{-}(aq) \rightarrow H_2O(l)}$

The theory works well for aqueous acids and alkalis, but it has three limits: it applies only in water; it cannot call ammonia or the carbonate ion a base, since neither contains OH; and it cannot describe the gas-phase reaction of $\mathrm{NH_3}$ with HCl.

2. The Brønsted–Lowry theory

In 1923 Johannes Brønsted in Denmark and Thomas Lowry in England, working independently, defined acids and bases by proton transfer. An acid–base reaction always involves two conjugate pairs (Figure 1.1).

Figure 1.1: Proton transfer from ethanoic acid to water, with the two conjugate pairs.

Reaction	Acid (proton donor)	Base (proton acceptor)
$\mathrm{HCl(aq) + H_2O(l) \rightarrow H_3O^{+}(aq) + Cl^{-}(aq)}$	HCl	$\mathrm{H_2O}$
$\mathrm{NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^{+}(aq) + OH^{-}(aq)}$	$\mathrm{H_2O}$	$\mathrm{NH_3}$
$\mathrm{CO_3^{2-}(aq) + 2H_3O^{+}(aq) \rightarrow CO_2(g) + 3H_2O(l)}$	$\mathrm{H_3O^{+}}$	$\mathrm{CO_3^{2-}}$
$\mathrm{NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)}$	HCl	$\mathrm{NH_3}$

Water is a base in the first reaction and an acid in the second: it is amphoteric. So is the hydrogencarbonate ion: $\mathrm{HCO_3^{-} + H_3O^{+} \rightarrow H_2CO_3 + H_2O}$ (base), and $\mathrm{HCO_3^{-} + OH^{-} \rightarrow CO_3^{2-} + H_2O}$ (acid).

The theory also links the strength of an acid to its partner. A strong acid such as HCl gives up its proton completely, so its conjugate base, $\mathrm{Cl^{-}}$ , has almost no tendency to take a proton back. A weak acid such as ethanoic acid holds its proton more tightly, so its conjugate base, ethanoate, is a noticeably stronger base. Lessons 3 and 4 put numbers on this.

3. The Lewis theory

Also in 1923, the American chemist Gilbert N. Lewis looked at the electrons instead of the proton. A base has a lone pair; an acid accepts that pair to form a dative (coordinate) bond. Every Brønsted–Lowry base is a Lewis base, because it uses a lone pair to accept $\mathrm{H^{+}}$ , but many Lewis acids contain no hydrogen at all:

$\mathrm{BF_3 + NH_3 \rightarrow F_3B{\leftarrow}NH_3}$ : boron has only six outer electrons and accepts the lone pair of nitrogen.
$\mathrm{AlCl_3 + Cl^{-} \rightarrow AlCl_4^{-}}$ : the reason aluminium chloride works as a catalyst in Friedel–Crafts reactions (Unit 3).
$\mathrm{Cu^{2+} + 4NH_3 \rightarrow [Cu(NH_3)_4]^{2+}}$ : every complex ion (Unit 1) is a Lewis acid–base adduct, with the ligands as Lewis bases.

Theory	Acid	Base	Main limitation
Arrhenius	gives $\mathrm{H^{+}}$ in water	gives $\mathrm{OH^{-}}$ in water	water only; misses $\mathrm{NH_3}$ , $\mathrm{CO_3^{2-}}$
Brønsted–Lowry	proton donor	proton acceptor	misses acids with no H, e.g. $\mathrm{BF_3}$
Lewis	electron-pair acceptor	electron-pair donor	so wide that it gives no simple scale of strength

Worked example

Problem. Identify the Brønsted–Lowry acid and base on the left, and the two conjugate pairs, in: (a) $\mathrm{HNO_3 + H_2O \rightarrow H_3O^{+} + NO_3^{-}}$ ; (b) $\mathrm{NH_4^{+} + OH^{-} \rightleftharpoons NH_3 + H_2O}$ ; (c) $\mathrm{HSO_4^{-} + CO_3^{2-} \rightleftharpoons SO_4^{2-} + HCO_3^{-}}$ .

Solution. Find the species that loses $\mathrm{H^{+}}$ (the acid) and the one that gains it (the base). Each then appears on the right as its conjugate partner.

	Acid	Base	Pairs (acid / conjugate base)
(a)	$\mathrm{HNO_3}$	$\mathrm{H_2O}$	$\mathrm{HNO_3/NO_3^{-}}$ and $\mathrm{H_3O^{+}/H_2O}$
(b)	$\mathrm{NH_4^{+}}$	$\mathrm{OH^{-}}$	$\mathrm{NH_4^{+}/NH_3}$ and $\mathrm{H_2O/OH^{-}}$
(c)	$\mathrm{HSO_4^{-}}$	$\mathrm{CO_3^{2-}}$	$\mathrm{HSO_4^{-}/SO_4^{2-}}$ and $\mathrm{HCO_3^{-}/CO_3^{2-}}$

Answer: as in the table. Check each pair: the two members differ by exactly one $\mathrm{H^{+}}$ and by one unit of charge.

Worked example

Problem. Classify each reaction as Arrhenius, Brønsted–Lowry and/or Lewis acid–base, and explain: (a) $\mathrm{KOH(aq) + HCl(aq) \rightarrow KCl(aq) + H_2O(l)}$ ; (b) $\mathrm{CaCO_3(s) + 2H^{+}(aq) \rightarrow Ca^{2+}(aq) + CO_2(g) + H_2O(l)}$ ; (c) $\mathrm{BF_3 + F^{-} \rightarrow BF_4^{-}}$ .

Solution.

(a) HCl gives $\mathrm{H^{+}}$ and KOH gives $\mathrm{OH^{-}}$ in water: Arrhenius. $\mathrm{H^{+}}$ passes to $\mathrm{OH^{-}}$ : Brønsted–Lowry. $\mathrm{OH^{-}}$ donates a lone pair to $\mathrm{H^{+}}$ : Lewis. All three.
(b) The carbonate ion accepts protons, so it is a Brønsted–Lowry base (and therefore also a Lewis base), but not an Arrhenius base, because it does not release $\mathrm{OH^{-}}$ .
(c) No proton moves. $\mathrm{F^{-}}$ donates a lone pair to boron, which has an empty orbital: Lewis only.

Answer: (a) all three theories; (b) Brønsted–Lowry and Lewis; (c) Lewis only. Each theory includes everything in the one before it.

Warning

Common mistakes

Writing a conjugate pair that differs by two protons, e.g. $\mathrm{H_2SO_4/SO_4^{2-}}$ . The conjugate base of $\mathrm{H_2SO_4}$ is $\mathrm{HSO_4^{-}}$ .
Forgetting the charge: removing $\mathrm{H^{+}}$ lowers the charge by one; adding $\mathrm{H^{+}}$ raises it by one.
Confusing strong with concentrated. Strength is how completely an acid ionises; concentration is how much of it is in each $\mathrm{dm^{3}}$ . A dilute solution of a strong acid is still a strong acid.

Tip

To find conjugate pairs fast, line up the formulas that look alike: $\mathrm{HSO_4^{-}}$ with $\mathrm{SO_4^{2-}}$ , $\mathrm{CO_3^{2-}}$ with $\mathrm{HCO_3^{-}}$ . The member with the extra H is the acid. For Lewis questions, draw the lone pair and the empty orbital: the arrow of the dative bond always points from the base to the acid.

Richard Louie Chemistry Lectures: Arrhenius, Brønsted–Lowry and Lewis theories of acids and bases. Watch how each definition widens the one before, and practise picking out the proton donor, the proton acceptor and the electron-pair donor in each example.

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Practice

Define an acid and a base according to (a) Arrhenius; (b) Brønsted–Lowry; (c) Lewis.
Write the formula of the conjugate base of: (a) $\mathrm{H_2SO_4}$ ; (b) $\mathrm{HCO_3^{-}}$ ; (c) $\mathrm{NH_4^{+}}$ ; and the conjugate acid of: (d) $\mathrm{NH_3}$ ; (e) $\mathrm{HPO_4^{2-}}$ ; (f) $\mathrm{H_2O}$ .
Identify the acid, the base and the two conjugate pairs in $\mathrm{CH_3NH_2 + H_2O \rightleftharpoons CH_3NH_3^{+} + OH^{-}}$ .
Write two equations showing that the dihydrogenphosphate ion, $\mathrm{H_2PO_4^{-}}$ , is amphoteric.
Explain why ammonia is a base in the Brønsted–Lowry theory but not, strictly, in the Arrhenius theory.
Explain, with a diagram of the bonding, why aluminium chloride is a Lewis acid in $\mathrm{AlCl_3 + Cl^{-} \rightarrow AlCl_4^{-}}$ .
A farmer says: "Lime cannot be a base, because the bag says calcium carbonate, not calcium hydroxide." Evaluate this statement using two acid–base theories.

Show answersHide answers

(a) Acid gives $\mathrm{H^{+}}$ in water, base gives $\mathrm{OH^{-}}$ in water; (b) acid is a proton donor, base a proton acceptor; (c) acid is an electron-pair acceptor, base an electron-pair donor.
(a) $\mathrm{HSO_4^{-}}$ ; (b) $\mathrm{CO_3^{2-}}$ ; (c) $\mathrm{NH_3}$ ; (d) $\mathrm{NH_4^{+}}$ ; (e) $\mathrm{H_2PO_4^{-}}$ ; (f) $\mathrm{H_3O^{+}}$ .
Base: $\mathrm{CH_3NH_2}$ ; acid: $\mathrm{H_2O}$ . Pairs: $\mathrm{CH_3NH_3^{+}/CH_3NH_2}$ and $\mathrm{H_2O/OH^{-}}$ .
As an acid: $\mathrm{H_2PO_4^{-} + OH^{-} \rightarrow HPO_4^{2-} + H_2O}$ . As a base: $\mathrm{H_2PO_4^{-} + H_3O^{+} \rightarrow H_3PO_4 + H_2O}$ .
$\mathrm{NH_3}$ accepts a proton (from water or HCl), so it is a Brønsted–Lowry base. It contains no hydroxide; the $\mathrm{OH^{-}}$ in ammonia solution comes from water, which gives up a proton. Arrhenius's definition (a substance that releases its own $\mathrm{OH^{-}}$ ) does not strictly fit.
Aluminium in $\mathrm{AlCl_3}$ has only six electrons in its outer shell and an empty orbital. A chloride ion donates a lone pair into it, forming a dative bond and the tetrahedral $\mathrm{AlCl_4^{-}}$ ion. Accepting an electron pair makes $\mathrm{AlCl_3}$ a Lewis acid.
Wrong under the wider theories. By Arrhenius, carbonate is not a base because it has no $\mathrm{OH^{-}}$ . By Brønsted–Lowry, $\mathrm{CO_3^{2-}}$ accepts protons from the soil acid (forming $\mathrm{HCO_3^{-}}$ , then $\mathrm{CO_2}$ and water), so it is a base; by Lewis, it donates lone pairs to $\mathrm{H^{+}}$ . The lime does neutralise the acid, so the Brønsted–Lowry view fits the facts better.

Sources and credits

Lime training in Gatsibo District: Enhancing soil health in Rwanda: What's lime got to do with it?, International Institute of Tropical Agriculture (IITA), 2024.
Image: Spreading lime at Aghnahoo - geograph.org.uk - 6126367.jpg by Kenneth Allen, via Wikimedia Commons, licensed under CC BY-SA 2.0.
Video: Arrhenius, Bronsted-Lowry, & Lewis Theories of Acids & Bases, Richard Louie Chemistry Lectures, embedded from YouTube.
The text, diagram, tables, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1A base with no hydroxide in it

21. The Arrhenius theory

32. The Brønsted–Lowry theory

43. The Lewis theory

A base with no hydroxide in it

1. The Arrhenius theory

2. The Brønsted–Lowry theory

3. The Lewis theory