What is pH? Acids, bases and the pH scale, explained

pH is a number that says how acidic or basic a water-based solution is, by measuring how many hydrogen ions it contains. Pure water at 25 °C has a pH of 7, which is neutral. Lower numbers are acidic, like lemon juice at about 2; higher numbers are basic, also called alkaline, like bleach at about 12.5. The scale is logarithmic: each whole step means ten times more or fewer hydrogen ions.

In short

• pH is the negative logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺]. More hydrogen ions means a lower pH.
• Each step of 1 on the scale is a factor of 10, so pH 3 is ten times more acidic than pH 4 and a hundred times more than pH 5.
• An acid gives up hydrogen ions and a base takes them. Mixing the two neutralizes them into water.

What makes something an acid or a base?

The most widely used definition, proposed independently by Johannes Brønsted and Thomas Lowry in 1923, is about one particle: the hydrogen ion, H⁺, which is just a proton. An acid is a substance that gives away hydrogen ions, and a base is a substance that takes them. In water, a freed hydrogen ion doesn't float alone; it attaches to a water molecule to form H₃O⁺, but chemists usually just write H⁺.

When hydrogen chloride dissolves in water, nearly every molecule hands over its hydrogen ion, making hydrochloric acid, the acid in your stomach. When sodium hydroxide, lye, dissolves, it releases hydroxide ions, OH⁻, which grab hydrogen ions and turn them into water. Acids typically taste sour, which is why lemons and vinegar do, and bases feel slippery, like soapy water. Neither is a safe way to test anything in a lab.

Strength and concentration are different things, and mixing them up is a common error. A strong acid, such as hydrochloric acid, gives up almost all its hydrogen ions; a weak acid, such as the acetic acid in vinegar or the citric acid in lemons, gives up only a small fraction and keeps the rest. A very dilute strong acid can have a higher pH than a concentrated weak one.

How does the pH scale work?

Even pure water contains a few hydrogen ions, because a tiny fraction of water molecules split into H⁺ and OH⁻. At 25 °C the concentration of each is 10⁻⁷ moles per liter, one in about every 550 million water molecules. pH turns that awkward number into a simple one: take the power of ten and drop the minus sign. 10⁻⁷ gives pH 7.

The Danish chemist Søren Sørensen introduced the idea in 1909 at the Carlsberg Laboratory in Copenhagen, where controlling acidity mattered for studying proteins and brewing. The p is usually read as "power of," although Sørensen never said exactly what it stood for. Because pH is built on a logarithm, it squeezes a huge range of concentrations onto a short scale.

Substance	Approximate pH	Hydrogen ions compared with pure water
Battery acid	Below 1	Over a million times more
Stomach acid	1.5 to 3.5	About 3,000 to 300,000 times more
Lemon juice	About 2.2	About 60,000 times more
Black coffee	About 5	About 100 times more
Unpolluted rain	About 5.6	About 25 times more
Pure water at 25 °C	7	The same
Human blood	About 7.4	About 2.5 times fewer
Seawater	About 8.1	About 13 times fewer
Household ammonia	11 to 11.5	About 10,000 to 30,000 times fewer
Bleach	About 12.5	About 300,000 times fewer

Values for the common substances are typical figures from the reference article on pH; real samples vary. The scale is not strictly limited to 0 to 14: very concentrated acids can go below 0, and very concentrated bases above 14.

A worked example: why pH 3 is a hundred times more acidic than pH 5

Turn each pH back into a concentration of hydrogen ions, in moles per liter, by raising 10 to the power of minus the pH:

1. pH 5: 10⁻⁵ = 0.00001 moles per liter.
2. pH 4: 10⁻⁴ = 0.0001 moles per liter, ten times as many.
3. pH 3: 10⁻³ = 0.001 moles per liter, ten times as many again.
4. pH 3 compared with pH 5: 0.001 ÷ 0.00001 = 100.

So two steps on the scale is a factor of 100, three steps a factor of 1,000. Running the other way: take 1 liter of a strong acid at pH 2 and add 9 liters of water. The hydrogen ions are now spread through 10 liters, a tenth as concentrated, and the pH rises to 3. To reach pH 4 you would need to dilute it tenfold again, to 100 liters. Weak acids such as lemon juice change less on dilution, because they release more of their held-back hydrogen ions as the solution thins out.

Small-looking changes can be large. According to NOAA, the average pH of the surface ocean has fallen by about 0.1 since the industrial revolution began, to around 8.1, as seawater absorbs carbon dioxide from the air. Since 10 to the power 0.1 is about 1.26, that drop means roughly 30 percent more hydrogen ions. The ocean is still basic, but it has moved toward acid, which makes it harder for corals and shellfish to build their skeletons and shells. This is one of the consequences of climate change.

What happens when an acid meets a base?

They neutralize each other. The hydrogen ions from the acid and the hydroxide ions from the base combine into water: H⁺ + OH⁻ → H₂O. Mix hydrochloric acid with sodium hydroxide in the right amounts and you get salt water: HCl + NaOH → NaCl + H₂O. It is a chemical reaction that gives off heat, about 57 kilojoules for every mole of water formed between a strong acid and a strong base, because the water formed sits at lower energy than the separated ions did.

Neutralization is everyday chemistry. An antacid tablet uses a mild base, such as calcium carbonate, to neutralize excess stomach acid. Gardeners spread lime on acidic soil. Baking soda, a base, reacts with acidic buttermilk or vinegar to release the carbon dioxide bubbles that make a cake rise.

How do living things handle pH?

Life is very sensitive to it. Each enzyme works best in a particular pH range: pepsin, which breaks down protein in the stomach, works best in strong acid, while most enzymes in the blood and cells need conditions near neutral. Too far from that range and their shapes, and so their functions, fall apart.

The body holds its blood within a narrow range, with arterial blood normally at a pH of about 7.38 to 7.42, according to MedlinePlus. Buffers in the blood, chiefly the bicarbonate system, soak up excess acid or base; the lungs adjust by breathing out more or less carbon dioxide, which forms acid in water; and the kidneys excrete acid or base over hours and days. Keeping steady conditions like this is called homeostasis.

What about alkaline diets?

This note explains chemistry; it isn't medical advice. Food can change the pH of urine, but in a healthy person it does not meaningfully change the pH of blood, which the body regulates tightly. A 2016 systematic review in BMJ Open found almost no research on alkaline diets or alkaline water and cancer, and concluded that promoting them to the public for cancer prevention or treatment is not justified.

How is pH measured?

Two ways are common. Indicators are dyes that change color with pH: litmus paper turns red in acid and blue in base, and universal indicator paper shows a rainbow of colors across the scale. The juice of red cabbage works as a homemade indicator. For precise work, a pH meter uses a glass electrode that develops a small voltage depending on the hydrogen ions around it, about 59 millivolts per pH unit at 25 °C.

One subtlety: neutral is pH 7 only at 25 °C. Water splits into ions more readily when it is hot, so at 100 °C neutral water has a pH of about 6.1, even though it is no more acidic than before, because it still holds equal amounts of H⁺ and OH⁻.

Check yourself

• Without looking back, explain why a solution at pH 2 has a thousand times more hydrogen ions than one at pH 5.
• What is the difference between a strong acid and a concentrated one?
• Why did a drop of only 0.1 in the ocean's pH amount to about 30 percent more hydrogen ions?

Sources

• pH and pOH — OpenStax, Chemistry 2e
• Ocean acidification — National Oceanic and Atmospheric Administration
• Blood gases — MedlinePlus, U.S. National Library of Medicine
• Systematic review of the association between dietary acid load, alkaline water and cancer — Fenton and Huang, BMJ Open, 2016
• PH — Wikipedia