Acid-base equilibria and pH

Acids produce hydrogen ions, H^+, in water. Alkalis produce hydroxide ions, OH^-. When they react, the ions combine to make water, a neutralisation:

The pH scale measures acidity. Below 7 is acidic, 7 is neutral and above 7 is alkaline. A decrease of one pH unit means the hydrogen-ion concentration is ten times higher, so pH 2 is 100 times more acidic than pH 4.

pH is measured with universal indicator or, more accurately, a pH probe.

Strong and weak acids

• A strong acid (hydrochloric, nitric, sulfuric) is fully ionised in water.
• A weak acid (ethanoic, citric, carbonic) is only partly ionised: most molecules stay intact.

Strong and weak are not the same as concentrated and dilute. Concentration tells you how much acid is dissolved in a given volume; strength tells you how much of it has ionised. A dilute solution of a strong acid can have a lower pH than a concentrated solution of a weak acid.

Acids react with metals to give a salt and hydrogen, with bases to give a salt and water, and with carbonates to give a salt, water and carbon dioxide.

A Brønsted–Lowry acid is a proton donor; a base is a proton acceptor. Each acid has a conjugate base: \mathrm{CH_3COOH/CH_3COO^-}.

Strong acids dissociate fully, so 0.050 mol dm^{-3} HCl has pH 1.30. Water ionises slightly: K_\text{w} = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0\times10^{-14} mol^2 dm^{-6} at 298 K. For 0.10 mol dm^{-3} NaOH, [\mathrm{H^+}] = 10^{-13}, pH 13.0.

Weak acids

Assuming [\mathrm{H^+}] = [\mathrm{A^-}] and negligible dissociation, [\mathrm{H^+}] = \sqrt{K_\text{a}[\mathrm{HA}]}. For 0.10 mol dm^{-3} ethanoic acid (K_\text{a} = 1.7\times10^{-5}): [\mathrm{H^+}] = 1.3\times10^{-3}, pH 2.9.

Buffers

A buffer contains a weak acid and its conjugate base in similar amounts. Added H^+ is removed by \mathrm{A^-}; added OH^- is removed by HA. Its pH follows from K_\text{a}:

Blood is buffered mainly by \mathrm{H_2CO_3/HCO_3^-}.

Titration curves and indicators

• Strong acid–strong base: steep vertical section from about pH 3 to 11; equivalence at pH 7.
• Weak acid–strong base: equivalence above 7 (the conjugate base is basic); at half-neutralisation, pH = pK_\text{a}.
• Weak acid–weak base: no sharp jump; no indicator is suitable.

Choose an indicator whose colour change lies within the steep part: phenolphthalein (about 8–10) for weak acid–strong base, methyl orange (about 3–4.5) for strong acid–weak base.

Exact treatment

Approximate formulas fail for very dilute or relatively strong weak acids. A rigorous calculation combines:

• equilibrium expressions (K_\text{a}, K_\text{w});
• mass balance: c_\text{HA} = [\mathrm{HA}] + [\mathrm{A^-}];
• charge balance: [\mathrm{H^+}] = [\mathrm{A^-}] + [\mathrm{OH^-}].

Eliminating gives a cubic in [\mathrm{H^+}]. Checks: the "small dissociation" approximation holds if [\mathrm{H^+}]/c < 5\%, and water's contribution can be ignored unless [\mathrm{H^+}] approaches 10^{-6} mol dm^{-3}. This is why 1\times10^{-8} mol dm^{-3} HCl has pH just below 7, not 8.

For conjugate pairs, K_\text{a}K_\text{b} = K_\text{w}, so pK_\text{a} + pK_\text{b} = 14.00 at 298 K. K_\text{w} rises with temperature (autoionisation is endothermic): at 50 °C pure water has pH about 6.6 yet is still neutral, since [\mathrm{H^+}] = [\mathrm{OH^-}].

Henderson–Hasselbalch and buffer capacity

uses stoichiometric concentrations and fails when the buffer is very dilute or the acid fairly strong. Buffer capacity \beta = \mathrm{d}c_\text{base}/\mathrm{dpH} is greatest at pH = pK_\text{a} and scales with total buffer concentration; useful buffers operate within about one unit of pK_\text{a}.

Worked example. 0.10 mol dm^{-3} ethanoic acid with 0.15 mol dm^{-3} sodium ethanoate (pK_\text{a} 4.76): pH = 4.76 + log 1.5 = 4.94. Adding 0.01 mol dm^{-3} HCl converts ethanoate to acid: pH = 4.76 + log(0.14/0.11) = 4.86. The same amount of HCl added to pure water would give pH 2, a drop of five units.

Titration curves

For a weak acid titrated with strong base, four regions appear: the initial weak-acid pH; the buffer region, flattest at half-equivalence where pH = pK_\text{a} (the standard way to measure pK_\text{a}); equivalence, where the solution is just \mathrm{A^-} and \mathrm{pOH} = \tfrac{1}{2}(\mathrm{p}K_\text{b} - \log c); and excess base. Polyprotic acids such as phosphoric acid show separate steps when successive pK_\text{a} values differ by more than about 3 units.

Indicators and activities

An indicator is itself a weak acid HIn whose two forms differ in colour; the eye sees a change over roughly pK_\text{In} \pm 1. Strictly, pH = -\log a_{\mathrm{H^+}}, and in solutions of appreciable ionic strength activity coefficients shift apparent pK_\text{a} values by tenths of a unit, which matters for accurate buffer preparation.