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The pH scale
Skills to be tested
 Discuss the pH scale
 Point out the neat things about the pH scale.
 Tell the origin and the logic of of using the pH scale.
 Apply the same strategy for representing other types of quantities such as
pK_{a}, pK_{b}, pK_{w}.
The pH scale
From the simple definition of pH being the negative log of the
H^{+} ion concentration, [H^{+}],
pH =  log [H^{+}]
you already know the following:

This scale is convenient to use, because it converts some odd expressions
such as 1.23x10^{4} into a single number of 3.91.

This scale covers a very large range of [H^{+}], from 0.1 to
10^{14}. When [H^{+}] is high, we usually do not use
the pH value, but simply the [H^{+}].
For example, when [H^{+}] = 1.0, pH = 0. Because we seldom say
the pH is 0, and that is why you consider pH = 0 such an odd expression.
A pH = 0.30 is equivalent to a [H^{+}] of 2.0 M. Negative pH
values are only for academic exercises. Using the concentrations directly
conveys a better sense than the pH scales.

The pH scale expands the division between zero and 1 in a linear scale
or a compact scale into a large scale for comparison purpose.
In mathematics, you learned that there are infinit values between 0 and 1,
or between 0 and 0.1, or between 0 and 0.01 or between 0 and any small
value. Using a log scale certainly converts infinite small quantities
into infinite large quantities.

The nonlinearity of the pH scale in terms of [H^{+}] is easily
illustrated by looking at the corresponding values for pH between
0.1 and 0.9 as follows:
pH =  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9


[H^{+}] =  0.79  0.63  0.50  0.40  0.32  0.25  0.20  0.16  0.13



Because the negative log of [H^{+}] is used in the pH scale, the
pH scale usually have positive values. Furthermore, the larger the pH,
the smaller the [H^{+}].
Other Interesting Facts about the pH Scale
According to the Oxford Dictionary, the pH scale was originally introduced by
the Danish biochemist S.P.L. Sorensen in 1909 using the symbol p_{H}.
Other symbols such as p_{H} have been used in the past. The
letter p is derived from the German word potenz meaning
power or exponent of, in this case, 10.
You may argue that what have we learned by looking into historical origin
of the term? Well, the origin of concept is interesting in that we sometimes
need to develop concepts ourselves. A concept or tool becomes important
if many people find it convenient and elegant.
The reality is that many chemists have used the pH scale and the p scales
for many other quantities that they often take it for granted, without
realizing the logic behind their usages. For example, we have used the
pK_{a}, pK_{b}, pK_{w},
notations by analogy to the pH notations with out asking a question.
Now that you know the pH is an exponent, the following relationship is
obvious:
[H^{+}] = 10^{pH}
Confidence Building Questions