Home > 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 H_{2}O [H^{+}] [OH^{-}] = k_{W} (1)

and the proton condition [H^{+}] = C + [OH^{-}] (2)

From (2) [OH^{-}] = [H^{+}] – C (3)

From (1) and (3) ([H^{+}]) ([H^{+}] – C) = k_{W}

Which is a quadratic function of [H^{+}]:

[H^{+}]^{2} - C[H^{+}] -k_{W} = 0 (4)

Solving (4) for C:

C = [H^{+}] -k_{W} / [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} = k_{W} (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**,

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