Acids and Bases

Two words get used as though they mean the same thing, and almost nothing in this topic makes sense until they come apart.

Strong describes the substance: how completely it gives up protons when it dissolves. Concentrated describes the solution: how much of the substance is dissolved in a given volume.

They are independent. A very dilute solution of a strong acid and a very concentrated solution of a weak acid are different things, and either can turn out to be the more acidic depending on the numbers. Hydrofluoric acid is a weak acid by this definition — it does not fully dissociate — and it is also one of the more dangerous substances in a chemistry laboratory. Weak is not a synonym for mild.

Three definitions, each broader than the last

Courses present three definitions of an acid, usually without saying how they relate. They are not rival theories. Each was introduced because the previous one could not describe something real, and each contains the one before it.

Arrhenius, 1884. An acid produces H⁺ ions in water; a base produces OH⁻ ions. This works for hydrochloric acid and sodium hydroxide and fails immediately for ammonia, which is unquestionably a base and contains no hydroxide at all. It is also restricted to water as a solvent.

Brønsted and Lowry, 1923. An acid is a proton donor and a base is a proton acceptor. Ammonia now qualifies, because it accepts a proton to become NH₄⁺. So does a reaction between ammonia gas and hydrogen chloride gas, with no solvent present anywhere. Johannes Brønsted in Copenhagen and Thomas Lowry in England published this independently within months of each other, which is why it carries both names.

Lewis, 1923. An acid is an electron-pair acceptor and a base is an electron-pair donor. This drops the requirement for a proton entirely. Boron trifluoride has an incomplete octet and accepts a lone pair from ammonia to form a stable adduct — a textbook acid–base reaction in which no hydrogen moves at all.

Every Brønsted acid is also a Lewis acid; the reverse is not true. When a question says "acid" without qualification, it almost always means Brønsted–Lowry, which is the definition that covers the widest range of chemistry while still being easy to apply.

Conjugate pairs, and water on both sides

The Brønsted view makes every acid–base reaction a transfer with two sides, and each side has a partner.

When HCl donates a proton it becomes Cl⁻. Those two are a conjugate pair — species differing by exactly one H⁺. HCl is the acid, Cl⁻ its conjugate base. On the other side, water accepts the proton to become H₃O⁺, so water is the base and H₃O⁺ is its conjugate acid.

A general rule falls out of this and is worth holding on to: the stronger the acid, the weaker its conjugate base. Hydrochloric acid gives up its proton so readily that chloride has essentially no tendency to take one back, which is why chloride solutions are neutral. Acetic acid gives up its proton reluctantly, and acetate is correspondingly a noticeable base.

Water appears on both sides of that description because it can do either job — donate a proton to become OH⁻, or accept one to become H₃O⁺. Species that can do both are amphiprotic; hydrogencarbonate and hydrogensulfate behave the same way. The broader term amphoteric covers anything that can act as either an acid or a base, including oxides like aluminum oxide and zinc oxide that have no protons to trade.

The logarithm, worked in both directions

pH is defined as the negative base-10 logarithm of the hydrogen ion concentration:

pH = −log₁₀[H₃O⁺]

Because it is logarithmic, each whole unit is a factor of ten. A solution at pH 3 has a hundred times the hydrogen ion concentration of one at pH 5, not 1.67 times.

Forward, round numbers. A 0.01 M solution of a strong acid dissociates completely, so [H₃O⁺] = 0.01 = 10⁻², and pH = 2.

Forward, awkward numbers. If [H₃O⁺] = 4.5 × 10⁻⁴:

pH = −log(4.5 × 10⁻⁴) = 4 − log 4.5 = 4 − 0.65 = 3.35

Splitting the logarithm like that is worth practising, because it gives you a sense of where the answer should land before the calculator confirms it. Any concentration between 10⁻⁴ and 10⁻³ must give a pH between 3 and 4.

Backwards. Given pH 5.6, the concentration is 10⁻⁵·⁶ = 2.5 × 10⁻⁶ M. Note that the concentration is not a round number when the pH is — the round numbers live on the logarithmic side.

The companion scale, pOH, is defined the same way from hydroxide concentration. For a 0.001 M strong base, [OH⁻] = 10⁻³, so pOH = 3 and pH = 11.

Neutral is only pH 7 at 25 °C

Water dissociates very slightly on its own, and the product of the two ion concentrations is a constant:

Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴

which is where pH + pOH = 14 comes from, and where the value 7 for neutrality comes from — neutral means the two concentrations are equal, so each is √(10⁻¹⁴) = 10⁻⁷.

That value of Kw applies at 25 °C and nowhere else. Dissociation is endothermic, so heating water increases it. At 100 °C, Kw is 5.1 × 10⁻¹³, which makes the neutral point:

[H₃O⁺] = √(5.1 × 10⁻¹³) = 7.2 × 10⁻⁷, so pH = 6.14

Pure water at 100 °C has a pH of about 6.14 and is perfectly neutral, because its hydroxide concentration is identical to its hydrogen ion concentration. It is not acidic. At 0 °C the same calculation gives a neutral pH of about 7.47.

So "pH 7 is neutral" is a statement about room temperature that textbooks present as a definition. The definition is that neutral means equal concentrations of the two ions; 7 is merely the number that produces at 25 °C.

Below zero and above fourteen

The scale is routinely drawn as running from 0 to 14, with ticks at the ends as though those were limits. They are not.

pH is just a logarithm, and nothing stops the concentration exceeding 1 M. Concentrated hydrochloric acid at about 12 M has a hydrogen ion concentration above 1, so its logarithm is positive and its pH is around −1. Very concentrated alkalis go above 14 by the same argument.

The 0-to-14 range is simply where most dilute aqueous solutions fall. It is a description of common cases, not a boundary.

Why the second proton is a hundred thousand times harder

Acids with more than one removable proton — polyprotic acids — do not release them all at once, and the successive dissociations get dramatically weaker.

Phosphoric acid has three, with pKa values of 2.15, 7.20 and 12.35. Each step is roughly a hundred thousand times harder than the one before.

The reason is electrostatic. Removing the first proton leaves H₂PO₄⁻, and pulling a second positive proton away from a species that is now negatively charged is much more difficult. Removing the third from a 2− ion is harder still.

The practical consequence is that in most solutions, only the first dissociation matters. Treating phosphoric acid as though all three protons were available will give an answer wrong by orders of magnitude.

Strength, quantified

Weak acids are described by their acid dissociation constant, Ka. Acetic acid's is 1.8 × 10⁻⁵, and the contrast with a strong acid at identical concentration is stark.

A 0.1 M solution of a strong acid gives [H₃O⁺] = 0.1, so pH = 1.

For 0.1 M acetic acid, the standard approximation gives:

[H₃O⁺] = √(Ka × C) = √(1.8 × 10⁻⁵ × 0.1) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³
pH = 2.87

Same concentration, and nearly two pH units apart — the strong acid solution has about 75 times the hydrogen ion concentration. That gap is what "strength" means, and it is why the distinction from concentration matters arithmetically rather than just semantically.

Six acids are conventionally treated as strong: hydrochloric, hydrobromic, hydroiodic, nitric, perchloric, and sulfuric in its first dissociation only. Everything else is weak to some degree.

The trap: adding acid can never make water alkaline

Here is a question that catches out people who have learned the formula and not the chemistry. What is the pH of 10⁻⁸ M hydrochloric acid?

The formula says pH = 8. That answer is impossible: it claims that adding an acid to pure water made the water alkaline.

The error is ignoring the water. At this dilution the acid contributes less hydrogen ion than water's own dissociation does, and both sources have to be counted. Solving properly, with the requirement that the product of the ion concentrations still equals Kw, gives [H₃O⁺] = 1.05 × 10⁻⁷ and a pH of 6.98 — very slightly acidic, which is exactly what adding a trace of acid to water ought to do.

The general lesson: the simple pH formula assumes the acid dominates water's own contribution. Below about 10⁻⁶ M that assumption fails, and any answer on the wrong side of 7 is telling you so.

Neutralisation, on paper

An acid and a base give a salt and water. Hydrochloric acid with sodium hydroxide gives sodium chloride and water, and once the spectator ions are removed the net ionic equation is:

H⁺(aq) + OH⁻(aq) → H₂O(l)

There is a striking piece of evidence that this really is the whole reaction. The enthalpy change for neutralising any strong acid with any strong base is close to −57.3 kJ per mole of water formed, whichever acid and base are chosen. The identity of the spectator ions makes no measurable difference, because they take no part.

Weak acids give a smaller figure, and the shortfall is the energy consumed in dissociating the acid — which is a direct measurement of how much the weak acid was holding on to its proton.