Acids, Bases & pH

From lemon juice to soap: the pH scale

Junior level — plain language, no maths

Some things are acids - lemon juice, vinegar, the fizz in cola, the acid churning in your stomach. Their opposites are bases (or alkalis) - soap, baking soda, bleach, oven cleaner. The pH scale is just a ruler from 0 to 14 that says how acidic or how basic something is. Low numbers (0-6) are acids, 7 is neutral (pure water), and high numbers (8-14) are bases. Battery acid sits near 0, drain cleaner near 14, and most everyday things fall somewhere in between.

The clever way to tell them apart is with an indicator - a dye that changes colour with pH. Universal indicator runs through a whole rainbow: red for a strong acid, through orange and yellow, green at neutral, then blue and purple for bases. Litmus paper is the simple version - red in acid, blue in base - and red cabbage juice pulls off the very same trick in your kitchen.

Mix an acid and a base and they cancel each other out, a reaction called neutralisation. The base tames the acid and the acid tames the base, meeting near the middle at neutral and usually leaving behind water and a salt. It's why an antacid tablet soothes a sour stomach, why gardeners add lime to over-acidic soil, and why a dab of baking soda takes the sting out of an acidic wasp bite.

pH, the logarithm of acidity

Student level — the core equations

Acidity comes down to a single ion: the hydrogen ion \(H^+\) (really the hydronium \(H_3O^+\)). The more \(H^+\) floating in a solution, the more acidic it is. But those concentrations span an enormous range - from about \(1\) mol/L down to \(10^{-14}\) - so we compress them with a logarithm: \(\text{pH} = -\log_{10}[H^+]\). Each whole step is therefore a tenfold change in \(H^+\): pH 3 is ten times more acidic than pH 4 and a hundred times more than pH 5.

Water itself quietly splits into \(H^+\) and \(OH^-\), and their product is fixed: \([H^+][OH^-] = 10^{-14}\) at 25 °C. In pure water the two are equal at \(10^{-7}\), giving pH 7 - neutral. Add acid and \(H^+\) rises while \(OH^-\) falls to keep the product constant; add base and the reverse happens. That is why the acid and base scales are two halves of one ruler: \(\text{pH} + \text{pOH} = 14\).

Strong acids (HCl, \(H_2SO_4\)) dissociate completely, so their pH follows straight from concentration. Weak acids (acetic, carbonic) only partly ionise, governed by an equilibrium constant \(K_a\), so they sit at a higher pH than a strong acid of the same concentration. Neutralisation, \(H^+ + OH^- \to H_2O\), is the basis of titration: adding measured base to an acid until the equivalence point, where the pH leaps through neutral in one sharp step.

Equilibria, buffers, and titration curves

Scholar level — full mathematical depth

01Brønsted-Lowry and beyond

An acid is a proton donor and a base a proton acceptor, and every acid has a conjugate base left behind when it gives up its proton. The Lewis picture generalizes further, to donors and acceptors of electron pairs. Strength is captured by the acid dissociation constant \(K_a\), and chemists rank acids by \(pK_a = -\log_{10} K_a\): the smaller the \(pK_a\), the stronger the acid.

02The Henderson-Hasselbalch equation

For a weak acid mixed with its conjugate base, the pH is \(\text{pH} = pK_a + \log_{10}\dfrac{[A^-]}{[HA]}\). When the two are equal - the half-neutralised point - the log vanishes and \(\text{pH} = pK_a\) exactly. This is both the flat, well-buffered middle of a titration curve and the standard way to measure a weak acid's strength.

03Buffers

A mixture of a weak acid and its conjugate base resists changes in pH: any added \(H^+\) or \(OH^-\) is mopped up by the pair. Blood's bicarbonate buffer, \(H_2CO_3/HCO_3^-\), is why arterial pH barely stirs despite the acid your metabolism dumps into it. A buffer works best near \(\text{pH} = pK_a\), where the two partners are in balance.

04Titration curves

Plot pH against added titrant and you get the signature S-curve: a gentle buffered stretch, a near-vertical jump at the equivalence point, then a plateau. For a strong acid with a strong base the equivalence point lands at pH 7; for a weak acid it shifts above 7, because the salt's conjugate base hydrolyses. The steepness of that jump is exactly what lets a single-colour indicator mark the endpoint.

05What "neutral" really means

Neutral means \([H^+] = [OH^-]\), not necessarily pH 7. Because \(K_w\) grows with temperature, water self-ionises more when hot: neutral water at 50 °C has pH ≈ 6.6 - still perfectly neutral, because \(OH^-\) has risen to match. pH 7 is only the neutral point at 25 °C.