Ionic Equilibrium - Strong Acids and Bases – A general relation for the pH of a strong acid.
The general problem of relating the pH of a strong acid solution to its analytical concentration will be presented below.
For a completely dissociated acid of analytical concentration C two equations for [H+] and [OH-] can be written:
The ion product of H2O [H+] [OH-] = kW (1)
and the proton condition [H+] = C + [OH-] (2)
From (2) [OH-] = [H+] – C (3)
From (1) and (3) ([H+]) ([H+] – C) = kW
Which is a quadratic function of [H+]:
[H+]2 - C[H+] -kW = 0 (4)
Solving (4) for C:
C = [H+] -kW / [H+] (5)
When [H+] is large compared to [OH-] the second term of (5) is negligible and it becomes:
[H+] = C (6)
In the opposite limit, where the concentration C is small compared to 10-7, the left-hand side of (5) is negligible, yielding:
[H+]2 = kW (7)
or pH = 7.
Note: Equation (5) (please see (6) also) tells us that the [H+] concentration will be the same as the nominal concentration of a strong acid as long as the solution is not very dilute. As the acid concentration falls below about 10-6 M equation (5) turns to (7) - [H+] approaches 10-7 M. The [H+] concentration can never fall below this value. This means that no amount of dilution can make the solution alkaline!
If we choose values of C (and therefore [H+]) and plot equation (5) for different values as shown in Fig. I.1 we get the graph shown below:
Plotting equation (5) instead of (4) is much easier – since (4) is a quadratic – and gives the same curve.
Therefore for strong acids:
[H+] = C where C is the initial concentration of the acid (6)
For worked examples please see the post “pH of a strong acid – Examples”
Relevant Posts - Relevant Videos
Chemical Equilibrium Calculations in Analytical Chemistry
pH of a strong acid – Examples
Strong Acids & Bases: pH Calculations involving mixtures of strong acids and bases
References
- David W. Oxtoby, H.P. Gillis, Alan Campion, “Principles of Modern Chemistry”, Sixth Edition, Thomson Brooks/Cole, 2008
- Steven S. Zumdahl, “Chemical Principles” 6th Edition, Houghton Mifflin Company, 2009
- Ralph H. Petrucci, “General Chemistry”, 3rd Edition, Macmillan Publishing Co., 1982
Key Terms
strong acid, strong base, pH calculation, [H+] concentration, pH, Kw, calculate the pH of a strong acid, calculate the pH of a strong base
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