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pH scale

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How do we measure acid/base?

We use a 14 point scale, called the pH scale, to measure the acidity/base level of a solution.

pH chart

Acids are defined by the amount of H+ ions floating in solution

The concentration of H+ ions varies a lot.

If we use a linear X and Y axis then we’d have to compress a huge range of into tiny regions of the graph.

Or, we could draw the data uncompressed, but then one of the axes would be huge. We’d need a 50 foot long sheet of paper.

Considerthis example from Math Bench. Has data for 600 animals. Can you see them all? On a linear scale, many points are very close to each other.

Let’s think about the size of most mammals. Are most small or big? How many different species of mice are there compared to, say, elephants?

Like most organisms, there are lots of species that are small and only a few that are big. In the case of our 600 mammals, about 95% are smaller than 15,000 grams.

That means that the vast majority of our 600 data points are smashed into that first little segment of the graph. It’s impossible to see whats going on.”

“Now look at the same graph with both axes scaled by factors of 10 (logarithmic axes)”  -> graph on the right

http://mathbench.umd.edu/modules/misc_scaling/page07.htm

“What a difference. There’s still lots of points to look at – but they are now spread evenly along both axes – so you can really see what’s going on across all six orders of magnitude in size.”

{quotes from Math Bench Biology Modules http://mathbench.umd.edu/modules/misc_scaling/page10.htm }

Here we can see a linear plot, and then the same plot transformed onto a log scale.

linear versus log scales

*If we use a log scale, we don’t have to use those huge ranges of H+ numbers (from billions, own to billionths. ) Now we just need to use the number in the exponent of the equations. Much simpler number system, and easy to graph.

pH scale examples
Adapted from “Creating the pH Scale – Teacher’s Guide”,  The WaterCAMPWS Center for Advanced Materials for Purification of Water with Systems, University of Illinois at Urbana-Champaign

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