Reading and Interpreting Numbers on
Logarithmic Axes (lig)
Data values can be presented on a logarithmic
scale in two different formats.
- With one format, the raw numbers themselves are plotted against a logarithmic axis, such as that shown in the middle of the Washington Monument image. A similar logarithmic axis is found for the acetic acid titration plot shown below. The major intervals of the X-axis, indicated by the darker vertical lines in this figure, each correspond to one power of 10, e.g., 10-7, 10-6, etc. from left to right.
- With the second format, raw numbers are converted to their logarithmic values which are then plotted against a linear axis as illustrated by the X-axis of the acetic acid titration plot below.
Note that both graphs represent exactly the same data and they
are there quantitatively equivalent. However, each format
visually provides access to different types of information about
the titration. For example:
- To find the H+ ion concentration, [H+], at any level of saturation, the top profile is better because [H+] can be read directly off the X-axis. With the bottom profile, one must first read the logarithmic value from the X-axis and then calculate [H+] by converting this number to the negative of its antilogarithmic value.
- To find the pK of acetic acid -- i.e., the pH at 50% saturation (pK = 4.90) -- the bottom profile is better because this value can be read directly from the X-axis. With the top profile, one must first read the value for [H+] at 50% saturation from the X-axis -- i.e., 1.25 x 10-5 -- and then convert this number to the negative of its logarithmic value.
One additional advantage of the logarithmic
scale is that it retains the additivity of the exponents. This
concept is true for either X-axis format shown above and is
further illustrated by considering the properties
of a slide rule .
© Duane W.
Sears
Revised: August 10, 1998
![Acetic Acid Titration vs. [H+]](../images/acetic-acid-h.gif)
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