Strong and weak acids

A strong acid gives up essentially all of its protons to water; a weak acid gives up only a fraction, and that fraction is set by its acid dissociation constant, K_a. Hydrochloric acid at 0.1 mol/L has pH 1.00. Acetic acid at the same concentration has pH 2.88, because only 1.3 % of its molecules have released a proton at any moment. “Strong” and “weak” describe how willingly an acid parts with its proton, not how much acid is in the bottle.

This chapter is about that willingness: what it means for a molecule to be an acid, how one number captures its strength, and how to turn that number into a pH without the shortcuts that fail exactly when the question gets interesting.

What makes something an acid§

The modern answer is a sentence long: an acid is a proton donor and a base is a proton acceptor. Acid–base chemistry is the movement of a hydrogen nucleus from one molecule to another.

Here the acid HA donates a proton and water, acting as a base, accepts it. Read the reaction backwards and the roles swap: A⁻ can take a proton back, so it is a base, called the conjugate base of HA, and H₃O⁺ is the conjugate acid of water. Every acid–base reaction pairs two such couples, and the proton goes to whichever base holds it more tightly.

Arrhenius’s paper on dissociation^[1], Brønsted’s note on the concept of acids and bases^[2], Lowry’s paper “The uniqueness of hydrogen”^[3] and Lewis’s monograph on valence^[4] are all short and still readable. documented This site works in the Brønsted–Lowry picture, because pH is about protons and every reaction here takes place in water. The Lewis definition matters for metal ions and for organic chemistry, where an acid such as boron trifluoride has no proton to give.

Strong and weak§

Hydrogen chloride and acetic acid are both proton donors. The difference is in how the competition for the proton turns out. In water, HCl’s proton is held so weakly that essentially every molecule hands it to a water molecule. Acetic acid holds its proton more tightly than water does, so most molecules keep it.

The census at the top of the page makes the difference visible. It shows a thousand molecules of acid at equilibrium, colored by whether each has given up its proton.

At 0.1 M, 13 of every 1,000 acetic acid molecules are dissociated. Slide the concentration down and that number rises: 41 per thousand at 0.01 M, 124 at 0.001 M, and most of them below about 10⁻⁵ M. Now try boric acid at 0.1 M: fewer than one molecule in ten thousand. Try the hydrogen sulfate ion, HSO₄⁻, with pK_a 1.99: at 0.01 M it is 62 % dissociated, which is “weak” only by courtesy.

There is no sharp boundary between strong and weak. What chemists call strong acids (HCl, HBr, HI, HNO₃, HClO₄ and the first proton of H₂SO₄) are acids that donate to water so completely that the remaining undissociated fraction cannot be measured in dilute solution. In water they all look equally strong, because the strongest acid that can survive in water is H₃O⁺ itself: any stronger acid is converted into it. Chemists call this the levelling effect of the solvent; in a less basic solvent the same acids can be told apart^[5]. established

K_a and pK_a§

The equilibrium constant of reaction (2.1), with water’s concentration folded in, is the acid dissociation constant:

Like pH, pK_a is a logarithm, and it has a direct meaning on the pH scale: pK_a is the pH at which half the acid has given up its proton. Put [HA] = [A⁻] in (2.2) and the ratio cancels, leaving [H⁺] = K_a. Below that pH the acid form dominates; above it, the base form. A lower pK_a means a stronger acid, one that lets go of its proton even in quite acidic surroundings.

Equilibrium constants are measured quantities, and good values are hard to come by. Every pK_a on this site is the value selected by Goldberg, Kishore and Lennen of the US National Institute of Standards and Technology in their critical review of ionization data for buffers, which weighs the original measurements and reports thermodynamic values extrapolated to zero ionic strength at 25 °C^[6]:

The carbonic acid entry is worth a second look. Dissolved carbon dioxide mostly stays as CO₂(aq); only a small fraction becomes true H₂CO₃. The tabulated 6.351 is an “apparent” constant that treats the two together, which is what you want for any calculation that starts from dissolved CO₂.

Three ways to compute the pH of a weak acid§

Suppose you dissolve acetic acid at a formal concentration C. How much of it dissociates? Call [H⁺] = x. If water’s own ionization can be ignored, every H⁺ came with one A⁻, so [A⁻] = x and [HA] = C − x. Then

That is a quadratic in x, and it has an exact solution. Most textbooks go one step further and say: if the acid is weak, x is small compared with C, so drop it from the denominator. Then x = √(K_aC) and pH = ½(pK_a − log C). For 0.1 M acetic acid this gives 2.878 against the exact 2.881, which is excellent.

Each simplification throws away a term. The exact treatment keeps them all. Write down everything that must be true at equilibrium: the two equilibrium constants (K_a and K_w), the mass balance (C = [HA] + [A⁻]) and the charge balance ([H⁺] = [A⁻] + [OH⁻]). Eliminate everything except [H⁺] = h and you get a cubic^[7]:

The figure above solves the cubic numerically and shows all three answers. Try lowering the concentration of acetic acid. The square-root shortcut is within 0.01 of the exact pH down to about 0.01 M, where 4 % of the acid has dissociated; at 10⁻⁵ M it is wrong by 0.27, because now most of the acid is dissociated and “x ≪ C” is false. The quadratic stays good much longer, but below a few times 10⁻⁷ M it fails too, for the other reason: water is now supplying a large share of the hydrogen ions. Only the cubic is right everywhere. The common textbook guide, that an approximation is acceptable if it changes the answer by less than about 5 %, is a choice about tolerable error rather than a law^[7]; the figure lets you see exactly how large the error is.

What dilution does to a weak acid§

The left panel shows two slopes. A strong acid’s pH rises one unit for every tenfold dilution. A weak acid’s rises about half a unit, because diluting it pushes reaction (2.1) to the right: with fewer ions around to recombine, a larger share of the molecules stays dissociated. This is Ostwald’s dilution law, and the right panel shows it directly: percent dissociation climbs toward 100 % as the acid is diluted. At very low concentrations both curves bend toward neutral, for the same reason as in Chapter 1, and the distinction between strong and weak disappears: a weak acid diluted far enough is completely dissociated, and it still cannot make water more acidic than its own small amount allows.

This is the practical meaning of “weak”. A weak acid keeps most of its protons in reserve. That reserve is exactly what makes weak acids useful as buffers, as Chapter 4 shows.

Weak bases§

Everything above runs in reverse for bases. Ammonia takes a proton from water, NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, and its strength can be given as a base constant K_b. It is simpler to describe a base by the pK_a of its conjugate acid, because the two are tied together by water:

For ammonium pK_a = 9.245, so ammonia’s pK_b is 13.994 − 9.245 = 4.749, almost a mirror image of acetic acid. The exact pH of 0.1 M ammonia is 11.12, and 1.3 % of it is protonated: the same fraction as acetic acid at the same concentration, mirrored around neutral. A strong conjugate base belongs to a weak acid, and the conjugate base of a strong acid, such as chloride, is so weak a base that it does nothing measurable to pH.

Acids with more than one proton§

Phosphoric acid can give up three protons, one after another, with pK_as of 2.15, 7.20 and 12.35. Carbonic acid gives up two; citric acid three. Each step is its own equilibrium, and at any pH the acid is spread across its forms. The fractions follow from the same constants: for a diprotic acid, the fraction in the fully protonated form is h²/(h² + K₁h + K₁K₂), and the others follow the same pattern.

Two patterns are worth taking away. Between two pK_as that are far apart, one intermediate form takes over almost completely: at pH 4.67, halfway between phosphoric acid’s first two pK_as, more than 99 % of the phosphate is H₂PO₄⁻. When pK_as are close together, as for citric acid (3.13, 4.76, 6.40), several forms coexist over the whole range, and no single form ever dominates cleanly. That difference decides whether a titration of such an acid shows one jump or several, which is the subject of Chapter 3.