Lesson 1 · 25 min

Proton transfer: acids, bases and pH

Acids donate protons, bases accept them — and water quietly does both. The logarithmic pH scale fits fourteen orders of magnitude onto one ruler.

In this lesson

Identify acids, bases, and conjugate pairs with the Brønsted–Lowry definition
Link $[\mathrm{H_3O^+}]$ and $[\mathrm{OH^-}]$ through the ion product of water, $K_\mathrm{w}$
Calculate pH and pOH, and read one pH unit as a tenfold change in concentration
Calculate the pH of strong acids and bases, and know when water’s own ionization matters

Stomach acid has a pH of about 1.5; blood must stay between 7.35 and 7.45 — a shift of 0.3 can be fatal; and over two centuries the surface ocean has fallen from about pH 8.2 to 8.1, which sounds tiny but means about 26 % more $\mathrm{H_3O^+}$ . Behind all these numbers is one event: protons moving from molecule to molecule.

Acids give protons, bases take them

In 1887 Arrhenius defined an acid as “a substance that produces H⁺ in water”. In 1923 Brønsted and Lowry gave a more general picture: an acid is a proton (H⁺) donor and a base is a proton acceptor. Every donation needs a recipient, so acid–base reactions always come in pairs:

\ce{HCl + H2O -> Cl- + H3O+}

\ce{NH3 + H2O <=> NH4+ + OH-}

What is left of an acid after it loses a proton is its conjugate base ( $\ce{HCl}$ → $\ce{Cl-}$ ); a base that gains a proton becomes its conjugate acid ( $\ce{NH3}$ → $\ce{NH4+}$ ). Water is the base in the first reaction and the acid in the second: a substance that can do both is amphiprotic.

Water transfers protons too

Predict first

In pure water at 25 °C, roughly how many water molecules are there for each $\ce{H3O+}$ ion?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

About 10 About ten thousand About 550 million None — pure water does not conduct

Protons also pass between two water molecules: $\ce{2H2O} \mathrel{\ce{<=>}} \ce{H3O+} + \ce{OH-}$ . The equilibrium lies far to the left; its constant is the ion product of water. Whatever else is dissolved, at 25 °C the product of $[\ce{H3O+}]$ and $[\ce{OH-}]$ stays $1.0\times10^{-14}$ : when one rises, the other must fall.

K_\mathrm{w} = [\mathrm{H_3O^+}][\mathrm{OH^-}] = 1.0\times10^{-14}\quad(25\ ^\circ\mathrm{C})

Strictly, activities; in dilute solution activity ≈ concentration (mol/L).

$K_\mathrm{w}$: ion product of water; increases with temperature
$[\mathrm{H_3O^+}]$: hydronium concentration, mol/L
$[\mathrm{OH^-}]$: hydroxide concentration, mol/L

pH: fourteen orders of magnitude on one ruler

In solution $[\ce{H3O+}]$ ranges from about 1 M down to $10^{-14}$ M. For convenience the Danish chemist Sørensen introduced a logarithmic scale in 1909:

\mathrm{pH} = -\lg[\mathrm{H_3O^+}],\qquad \mathrm{pOH} = -\lg[\mathrm{OH^-}],\qquad \mathrm{pH}+\mathrm{pOH}=14.00

Because of the minus sign, lower pH means more acidic, and each pH unit is a factor of ten in $[\ce{H3O+}]$ . Lemon juice at pH 3 is not “twice as acidic” as coffee at pH 6 — it has a thousand times more hydronium.

Exact charge balance · universal-indicator colour from spectra

pH bench

Concentration · 0.01 M

Hydrochloric acid

pH 2.00 acidic

[H₃O⁺]: 0.01 M
[OH⁻]: 1.00 × 10⁻¹² M
H₃O⁺ per OH⁻: 1.0 × 10¹⁰

pH scale (colours are the computed universal-indicator colours)

Typical measured ranges of everyday substances

Gastric juice
Lemon juice
Vinegar
Coffee
Clean rain
Blood
Seawater
Soapy water
Household ammonia
Bleach

Dilute hydrochloric acid from 0.1 M all the way to

10^{-7}

M: the pH stalls below 7 instead of “turning basic”. Then compare NaOH, ammonia, and sodium acetate at the same concentration. The tube colour is the computed universal-indicator colour.

Worked example

pH of strong acid and strong base solutions

Find the pH at 25 °C of (a) 0.020 M HCl and (b) 0.0050 M $\ce{Ba(OH)2}$ .

Concept check

Which pair is a conjugate acid–base pair?

\ce{HCl}

and

\ce{H2O}

\ce{NH4+}

and

\ce{NH3}

\ce{H3O+}

and

\ce{OH-}

\ce{H2SO4}

and

\ce{SO4^2-}

Try the calculation

A solution has pH 3.20 at 25 °C. What is its $[\ce{OH-}]$ in mol/L?

Try the calculation

Calculate the pH of 0.0025 M NaOH at 25 °C.

Key takeaways

Brønsted–Lowry: acids donate protons, bases accept them; a conjugate pair differs by one proton.
Water self-ionizes: $K_\mathrm{w} = [\ce{H3O+}][\ce{OH-}] = 1.0\times10^{-14}$ at 25 °C.
pH = −lg[H₃O⁺]; one pH unit is a tenfold change in concentration.
Strong acids and bases ionize completely, but at extreme dilution water’s contribution dominates and dilution never carries a solution past neutral.

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Data and references

D. C. Harris, Quantitative Chemical Analysis, 9th ed., W. H. Freeman (2016), Ch. 6 and 8; Appendix G.
R. P. Buck et al., “Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002)”, Pure Appl. Chem. 74, 2169–2200 (2002).
W. L. Marshall, E. U. Franck, “Ion product of water substance, 0–1000 °C”, J. Phys. Chem. Ref. Data 10, 295 (1981).
IPCC AR6 WG1 (2021), Ch. 5: surface-ocean pH decline since pre-industrial times.