Ionic Equilibrium - Strong Acids and Bases – A general relation for the pH of a strong acid. | Chemistry Net

# Ionic Equilibrium - Strong Acids and Bases – A general relation for the pH of a strong acid.

Ionic Equilibrium - Strong Acids and Bases – A general relation for the pH of a strong acid.

# 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

Acid and base strengths

pH of a strong acid – Examples

Strong Acids & Bases: pH Calculations involving mixtures of strong acids and bases

References

1. David W. Oxtoby, H.P. Gillis, Alan Campion, “Principles of Modern Chemistry”, Sixth Edition, Thomson Brooks/Cole, 2008
2. Steven S. Zumdahl, “Chemical Principles”  6th Edition, Houghton Mifflin Company, 2009
3. 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