Concepts: acids, bases and pH

Equilibrium24 min readLesson 4 of 8

4.1 Acids and bases: three definitions The earliest definition is practical: an acid turns blue litmus red and neutralises a base, while a base does the opposite. Arrhenius added the ionic picture: an acid gives hydrogen ions in water and a base gives hydroxide ions. Bronsted and Lowry gave the definition that chemists use most often: an acid is a proton donor and a base is a proton acceptor. Every acid has a conjugate base, the species left after losing a proton, and every base has a conjugate acid. A stronger acid gives away its proton more readily, and its conjugate base is weaker. Hydrogen chloride is a strong acid in water because the chloride ion is a weak base. Acetic acid is a weak acid because the acetate ion is a stronger base and can take the proton back. This inverse relation between acid strength and conjugate base strength explains why strong acids have weak conjugate bases. Lewis gave the broadest definition: an acid is an electron pair acceptor and a base is an electron pair donor. This definition covers reactions without any proton, such as boron trifluoride accepting a pair from ammonia. 4.2 Autoionisation of water Pure water conducts electricity very slightly because a small fraction of its molecules transfer a proton to another molecule. The equilibrium constant for this process is the ionic product of water, and its value at 298 K makes the concentration of hydrogen and hydroxide ions each 10^-7 mol L^-1 in pure water.

2 H_{2} O ⇌ H_{3} O^{+} + O H^{-} K_{w} = [H^{+}] [O H^{-}] = 1.0 \times 1 0^{- 14} at 298 K

Autoionisation of water and the ionic product

The product of the two concentrations is constant at a given temperature, so adding acid increases the hydrogen ion concentration and decreases the hydroxide ion concentration in such a way that the product stays at 10^-14. The temperature matters because the autoionisation is endothermic; at a higher temperature Kw is larger. 4.3 pH and pOH The hydrogen ion concentration covers many orders of magnitude, so it is written on a logarithmic scale. The pH is the negative logarithm of the hydrogen ion concentration on a base ten scale, and pOH is defined the same way for hydroxide.

p H = - lo g_{10} [H^{+}] pO H = - lo g_{10} [O H^{-}] p H + pO H = 14

pH, pOH and their relation at 298 K

The pH scale is useful because it compresses a huge range into small numbers. Pure water has pH 7 at 298 K. A solution with pH below 7 is acidic and one above 7 is basic. A change of one pH unit means a tenfold change in hydrogen ion concentration, so pH 3 is ten times more acidic than pH 4. 4.4 Strong acids and bases A strong acid is essentially completely ionised in water. Hydrochloric, nitric and sulphuric acids are the common examples. For a monobasic strong acid of concentration c, the hydrogen ion concentration equals c, so the pH is minus log c. A strong base behaves the same way: for sodium hydroxide of concentration c, the hydroxide concentration equals c, and pH is 14 plus log c. Acids such as sulphuric acid are diprotic. The first ionisation is complete but the second is not, so the second proton contributes only partially to the hydrogen ion concentration. 4.5 Weak acids and weak bases A weak acid is only partly ionised, so an equilibrium is set up between the undissociated acid, the hydrogen ion and the conjugate base. The acid dissociation constant Ka measures the strength of the acid, and the degree of dissociation depends on both Ka and the concentration.

K_{a} = \frac{[ H ^{+} ] [ A ^{-} ]}{[ H A ]} [H^{+}] \approx K_{a} c

Weak acid equilibrium and the approximate hydrogen ion concentration

The square root formula is valid when the degree of dissociation is small, typically below about five percent. In that case the undissociated concentration is nearly equal to the original concentration. When the acid is stronger or more dilute, the exact quadratic treatment is needed. The degree of dissociation can be written in terms of the hydrogen ion and the concentration, and it rises as the solution is diluted. Weak bases behave in mirror image. A base B accepts a proton from water to give its conjugate acid and hydroxide ion, and the base dissociation constant Kb measures its strength. For a weak base the hydroxide concentration is approximately the square root of Kb times c, and pOH follows from that.

K_{b} = \frac{[ B H ^{+} ] [ O H ^{-} ]}{[ B ]} K_{a} K_{b} = K_{w}

Weak base equilibrium and the relation between Ka and Kb

The product relation is useful because it gives the conjugate acid strength from the base strength and the other way round. A weak base has a moderately strong conjugate acid, and a very weak base has a strong conjugate acid. Ammonium ion is the conjugate acid of ammonia and behaves as a weak acid in water, which is why solutions of ammonium chloride are acidic. 4.6 Relative strengths and structure The strength of an acid depends on the stability of the conjugate base. A conjugate base is stabilised when the negative charge is spread over several atoms by resonance, when the atom bearing the charge is larger and more polarisable, and when electron-withdrawing groups pull charge density away. This is why acetic acid is much stronger than ethanol and why trichloroacetic acid is stronger than acetic acid: the halogen atoms withdraw electron density and stabilise the anion.

Common mistake

Do not confuse strength with concentration. A dilute solution of hydrochloric acid is still a strong acid, because all its molecules are ionised; a concentrated solution of acetic acid is still a weak acid, because most of its molecules remain unionised. Strength is a property of the acid, concentration is a property of the solution.