Doc Brown's Advanced A Level Chemistry Revision Notes

Theoretical–Physical Advanced Level Chemistry – Equilibria – Chemical Equilibrium Revision Notes PART 5.3

5.3 Definition of a strong acid, theory, examples and pH calculations of strong acids

What is a strong acid? How to calculate the pH of a strong acid solution given its concentration.

Chemical Equilibrium Notes Parts 5 & 6 Index



5.3 Definition, examples and pH calculations of strong acids

Note: H+(aq) = aqueous hydrogen ion = aqueous proton = oxonium ion = hydroxonium ion

  • 5.3.1 Definition and examples of STRONG ACIDS

    • Strong acids are highly ionised in water, in many cases approaching 100% dissociation into ions.

    • This means for the general reaction of an acid HX interacting in an acid–base manner with water ...

      • HX(aq) + H2O(l) ==> H3O+(aq) + X–(aq)

      • Ka = [H3O+(aq)] [X–(aq)]/[HX(aq)] (units are mol dm–3)

      • Ka the equilibrium constant for this reaction is called the acid dissociation/ionisation constant.

      • [H2O(l)] is considered constant and incorporated into Ka.

      • The high % of ionisation gives the maximum concentration of hydrogen ions and therefore the most acidic solution of lowest possible pH.

    • In 'strong acid' pH calculations, ionic dissociation is assumed to be 100% and in reality they have very large Ka values and very negative pKa values (pKa = –log(Ka/mol dm–3), compare Ka for weak acids e.g.

      • HCl Ka  ~107 pKa ~–7, HBr Ka  ~109 pKa ~–9, HI Ka  ~1010 pKa ~–10

      • The Ka is so high it is virtually 100% ionised and so the equilibrium sign is pointless and omitted.

      • Note the acid gets stronger down group 7 as the H–X bond enthalpy/strength decreases as the halogen atom gets bigger and the bond length increases.

      • These are all monobasic/monoprotic acids, meaning only one proton is available for transfer to a base, see HCl below, or the conjugate base of the acid can only accept one proton).

    • 5.3.1a: HCl(g) + H2O(l) ==> H3O+(aq) + Cl–(aq)

      • dissolving hydrogen chloride in water to form hydrochloric acid,

      • or more simply HCl(aq) ==> H+(aq) + Cl–(aq)

      • This has very high equilibrium constant Ka i.e. virtually 100% to the right.

      • The other gases, hydrogen bromide and hydrogen iodide similarly dissolve to form the very strong hydrobromic acid and hydriodic acid respectively.

      • However, hydrogen fluoride gas dissolves in water to form the relatively weak hydrofluoric acid (see 5.4.2d) in dilute solution.

    • 5.3.1b: HNO3(aq) + H2O(l) ==> H3O+(aq) + NO3–(aq)

      • or the dissociation of dilute nitric acid (monobasic/monoprotic) can be simply shown as

      • HNO3(aq) ==> H+(aq) + NO3–(aq)

      • Ka = 40, pKa = –1.4

    • 5.3.1c: H2SO4(l) + 2H2O(l) ==> 2H3O+(aq) + SO4(aq)

      • dissolving concentrated sulphuric acid in water to make dilute sulphuric acid (dibasic).

      • or more simply H2SO4(aq) ==> 2H+(aq) + SO4(aq)

      • Strictly speaking the ionization occurs in two stages since it is a dibasic/diprotic* acid

        1. H2SO4(aq) ==> H+(aq) + HSO4–(aq)

          • Ka1 is very high, pKa1 is very negative, when 1st conjugate base formed.

          • So the molecule of sulfuric acid is a VERY strong acid.

        2. HSO4–(aq) (c) doc b H+(aq) + SO4(aq)

          • Ka2 =  1.20 x 10–2 mol dm–3, pKa2 = 1.92, positive, when 2nd conjugate base formed.

          • Strictly speaking, ionisation 2. is incomplete, but is often ignored in AS–A2 level calculations.

          • So, H2SO4 is a strong acid but the first conjugate based formed, the hydrogensulfate ion, HSO4– is a weak acid!

      • *Dibasic/diprotic means a maximum of two protons per molecule are available for transfer to a base, or the 2nd conjugate base of the acid can accept two protons. (See section 5.1.3 for more examples)

    • See 5.3 for a brief comparison of selected weak/strong acid properties

  • 5.3.2 Calculating the pH of a strong acid

    • Calculation example 5.3.2a

      • (a) Calculate the hydrogen ion concentration and pH of a 0.25 mol dm–3 solution of hydrochloric acid.

        • HCl is monobasic/monoprotic acid, so [H+(aq)] = 0.25 mol dm–3

        • pH = –log(0.25) = 0.602

    • Calculation example 5.3.2b

      • (a) Calculate the hydrogen ion concentration and pH of a 1.5 mol dm–3 solution of sulphuric acid.

        • H2SO4 is dibasic/diprotic acid, so [H+(aq)] = 2 x 1.5 = 3.0 mol dm–3

          • This isn't strictly true, the 1st ionisation is 100%, but the ionisation of the hydrogensulphate ion to release the 2nd proton is not complete, but 100% ionisation is assumed at this academic level.

        • pH = –log(3.0) = –0.477

        • but in reality the ph will be higher (see above discussion on the double ionisation of sulphuric acid and the calculation in appendix 1 at the bottom of the page).

    • Calculation example 5.3.2c

      • Calculate the hydrogen ion concentration solution of hydrochloric acid of pH 1.2

      • [H+(aq)] = 10–pH = 10–1.2 = 0.0631 mol dm–3

    • –

Appendix 1. What is the real aqueous hydrogen ion concentration in dilute sulfuric acid?

e.g. take 0.500 molar H2SO4 (aq), if fully ionised, you would expect ...

the [H+(aq)] concentration to be 2 x 0.500 = 1.000 mol dm–3

and the pH to be –log10(1.000) = 0.00

BUT, what is the reality?

The 1st dissociation is complete: H2SO4(aq) ==> H+(aq) + HSO4–(aq)

and will provide an initial concentration of 0.500 mol dm–3 of hydrogen ions.

The 2nd ionisation HSO4–(aq) (c) doc b H+(aq) + SO4(aq) is not complete,

but will still provide further hydrogen ions, which can be calculated via a weak acid calculation using the equilibrium expression below

Ka2 =

[H+(aq)] [SO42–(aq)]

–––––––––––––––    =   1.20 x 10–2 mol dm–3


Prior to the 2nd ionisation, theoretically, the initial concentrations of hydrogensulfate ions and hydrogen ions will be equal, and both 0.500 mol dm–3.

On the 2nd ionisation, the hydrogensulfate ion will provide the extra hydrogen ions and the only sulfate ions, but in doing so, the hydrogensulfate ion is reduced.

If we call the 'equal' extra hydrogen ion concentration and the final sulfate ion concentration x, then the total hydrogen ion concentration is (0.5 + x) and the hydrogensulfate ion concentration is reduced to (0.5 – x)

1.20 x 10–2 =

     (0.5 + x) x


     (0.5 – x)

This gives the quadratic equation 0 = x2 + 0.512x – 0.006

On solving this using the quadratic equation formula, gives roots of –0.523 and +0.0114

Therefore x must be 0.0114 (the 'extra' H+), which then gives (0.5 + 0.0114) ...

a total hydrogen ion concentration [H+(aq)] of 0.511 mol dm–3, not 1.000 mol dm–3

and the real calculated pH = –log10(0.511) = 0.29, not pH 0.00 and significantly higher

You may think the extra hydrogen ion concentration is very low, but this is because the HSO4– ion is a weak acid AND the 2nd ionisation is actually heavily suppressed by the 1st ionisation – think Le Chatelier's equilibrium principle as regards the concentration effect.

To fully understand this calculation its handy to have studied the weak acid calculations page

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