The letters pH stand half under water in a beaker, and the solution above them changes colour like a universal indicator, from red through yellow and green to blue and violet. A drop falls from the burette, a ring spreads across the surface, bubbles rise from the bottom, the stirrer turns, the bulb of the glass electrode glows. The meter in the corner shows a number, and the marker on the indicator strip below slides to the same square.
Quantity data sheet
chemistry and laboratory sheet 1/1 · rev. 2026-09Potential of hydrogen pH
Non-SI quantity · quantity: acidity of a solution, the dimensionless logarithm of hydrogen-ion activity
A logarithmic scale that has no unit
In 1909 the Danish chemist Søren Sørensen was studying, in the laboratory of the Carlsberg brewery, how enzymes depend on the acidity of the wort, and every day he wrote down concentrations such as 0.000 000 1 mole per litre. Tired of counting zeros, he proposed writing only the exponent with the minus sign removed, so that one ten-millionth became a plain seven, and ever since acidity has been measured by a number with no unit behind it.
The notation is convenient but treacherous: one step means a tenfold change, so a solution at pH 3 is not a third more acidic than one at pH 5 but a hundred times more, and two pH values can neither be added nor averaged. Mixing equal volumes of solutions at pH 2 and pH 4 gives not 3 but 2.30, because it is the concentrations that add up, and the logarithm is taken of the sum.
The sheet shows how pH behaves during a titration, why seven is neutral only at twenty-five degrees, and why the quantity every aquarium keeper measures still cannot be measured strictly without an agreement on what counts as the activity of a single ion.
Written with a lower-case p and a capital H, always in this order and without a space: pH, not PH or Ph, because the lower-case letter denotes an operation and the capital one a chemical element. The number follows the symbol, as with temperature in degrees: pH 7.40, and no unit is written after it.
pH is neither the concentration of an acid nor its strength: vinegar and hydrochloric acid of the same concentration give pH 2.9 and 1.0, while a buffer can contain a lot of acid and still show an almost neutral number. Do not confuse it with pKa either, which belongs to the acid itself and does not depend on how much of it is poured, whereas pH belongs to the solution.
01 · Definition
logarithm · activity · neutral pointThe potential of hydrogen, pH, is the negative decimal logarithm of the activity of hydrogen ions in a solution. Activity is dimensionless because it is measured relative to a standard concentration of one mole per litre, and so the logarithm is dimensionless too: pH is not measured in any unit, it is simply expressed as a number.
In dilute solutions activity almost coincides with concentration, and pH can then be calculated directly from moles per litre, whereas in strong solutions and seawater the ions interfere with one another and the difference between concentration and activity reaches tenths of a unit. Water itself slowly splits into hydrogen and hydroxide ions, the product of their activities at 25 °C is 10⁻¹⁴, and a solution in which there are equal amounts of both is called neutral, that is, pH 7.
The ionic product of water grows quickly with temperature, so the neutral point drops to 6.13 at boiling and rises to 7.47 at zero degrees; a solution at pH 7 is already slightly alkaline at 50 °C, even though the number is the same.
Two drops that recolour the beaker
On the left, titrant drips from a burette into a beaker holding 25 millilitres of solution; the liquid is coloured by universal indicator according to its current pH, and the meter in the corner shows the number. On the right the titration curve grows: the part already travelled is drawn as a thick line in the indicator colour, the rest as a thin grey dotted line, the horizontal dotted line is neutral pH 7, and the vertical one is the equivalence point, where exactly as much titrant has been added as the whole acid or base requires.
Mix pH 2 and pH 4 and you will not get three
A litre of solution at pH 2 holds one hundredth of a mole of hydrogen ions, and a litre at pH 4 holds one ten-thousandth, so after mixing two litres contain 0.0101 mole, that is 0.00505 per litre, which is pH 2.30. The acidic solution almost entirely determines the result, while the less acidic one adds only dilution, and so the mean pH of several samples, entered in a report as a simple average, always misrepresents the most acidic of them.
02 · Conversion
concentrations · substances · temperatureFrom the number on the meter to moles per litre
Enter pH, the concentration of hydrogen or hydroxide ions, or pOH, and the sheet will recalculate everything else, compare the solution with familiar substances and show where the neutral point lies at another temperature. The solution is the same in every tab; only what it is compared with changes.
A rule to remember: every pH unit is a tenfold change in concentration, every 0.3 units — a twofold one.
The converter treats activity as equal to concentration, which is true only for dilute solutions; in seawater, blood and strong acids the activity-coefficient correction shifts the answer by one or two tenths. The pH values for substances are typical, not normative: for lemon juice, coffee and rain they vary by up to half a unit from sample to sample.
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04 · Measuring instruments
paper · glass · platinum · buffersHow the hydrogen ion is caught
A rainbow on a strip
Universal indicator is a mixture of several dyes, each of which changes colour in its own narrow range, so that together they colour the whole scale from red to violet. The strip is dipped into the solution, the solution rises up the paper, and the colour is compared by eye with the printed chart; the accuracy is about one unit, but the answer is ready in a second and needs no instrument at all.
Glass that senses acid
A thin bulb of special glass swells at its surface, and hydrogen ions exchange with its hydrated layer, so that a potential difference appears between the inner and outer solutions. At 25 °C it changes by 59.16 millivolts for every pH unit, and on heating the slope increases, which is why a decent pH meter always measures temperature as well.
The zero of all electrochemistry
A platinum plate coated with spongy platinum black is bathed in hydrogen at a pressure of one bar, and an equilibrium is established on it between the gas and the hydrogen ions in the solution. Such an electrode is awkward and temperamental, but its potential follows the defining formula itself without intermediaries, and the primary buffers used to calibrate every glass electrode in the world are certified with it.
Three beakers before every measurement
A glass electrode ages, and its zero and slope drift, so before work the meter is checked against buffers of known pH, usually 4.01, 7.00 and 10.01 at 25 °C, and a new straight line is built from them. A meter without such a calibration shows a number with two decimals, but its second decimal is honest only until the electrode is moved into an unfamiliar solution.
05 · Writing rules
symbol before the number · no unit · with temperatureNumber after the symbol, no unit
The pH symbol is placed before the number, like the name of a scale, not after it like a unit, and the temperature at which a precise value was obtained is given next to it.
The first line on the right puts the symbol after the number, as if pH were a unit, the second writes a capital P, which means nothing in chemistry, and the third assigns moles per litre to the exponent, although moles live only in concentration. The fourth turns the logarithm into percentages, so that a drop of 0.3 looks modest, although there are half as many hydrogen ions, the fifth adds non-existent “units”, and the sixth averages logarithms where concentrations should be averaged.
06 · Neighbouring units
concentration · logarithm · amountUnder the logarithm of pH lies a concentration in moles per litre, the logarithm itself makes it a relative of the decibel, which likewise squeezes tens of orders into a short scale, and the mole remains the only SI unit through which pH is connected to the system at all.
The very concentration whose logarithm is taken, and the one in which you count how much acid has been poured.
Also a dimensionless logarithm, only of a power ratio and with a factor of ten.
Amount of substance, through which pH is connected to the International System of Units.
07 · Historical section
archive · from the brewery to IUPACHow the zeros became a scale
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Four steps that do not fit on one sheet
The height of each bar is the hydrogen-ion concentration on an ordinary, non-logarithmic scale, for pH 1, 2, 3 and 4. Each bar is ten times lower than the one before, and the fourth is already barely visible; the frame visits them in turn.
Sørensen chose the logarithm not for beauty but because otherwise the quantities he worked with would not fit on any paper: the seven steps from pH 1 to pH 7 would stretch a linear scale ten million times.
A quantity that cannot be measured without an agreement
The definition speaks of the activity of a single hydrogen ion, but thermodynamics can measure only products of activities of ions of opposite sign, because a solution is always electrically neutral and a single ion cannot be taken out of it. Strictly by definition, therefore, pH cannot be measured by any instrument; only a quantity in which the chloride ion enters together with hydrogen is accessible.
The gap is closed by convention: under the Bates–Guggenheim convention the activity coefficient of the chloride ion is calculated from a simple formula of solution theory, and then the Harned cell with hydrogen and silver–silver chloride electrodes and no liquid junction gives primary pH values for several reference buffers. All other measurements on Earth rest on these buffers through a chain of calibrations.
Thus every pH number contains, besides the measurement itself, an agreement as well, and two laboratories agree to hundredths of a unit not because they have measured the same nature but because they have adopted the same convention and calibrated against the same buffers.