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pH Calculations

pH is a way of describing how acidic or alkaline a solution is. It refers to the concentration of H⁺(aq) and OH⁻(aq) ions present in a solution.

Acids release H⁺(aq) ions in solution. A highly acidic solution has a high concentration of H⁺(aq) ions.  The difference in concentration between H⁺(aq) ions in a highly acidic solution and H⁺(aq) ions in a weakly acidic solution can be very large. To refer to the actual concentration of H⁺(aq) ions in a solution would be very tiresome, and it could be very awkward with low concentrations. Vinegar, for example, has a typical concentration of H⁺(aq) ions of 0.001 mol dm.  Black coffee has a typical concentration of H⁺(aq) ions of 0.00001 mol dm.  

The pH scale makes referring to the concentration of H⁺(aq) ions easier as it is logarithmic. For students who aren’t budding mathematicians, this just means that we can refer to a large difference in numbers using a scale with smaller values.

The exact workings of logarithmic scales are not required for A-level chemistry, but a basic understanding can be very useful when trying to understand what pH tells us. The pH scale starts at zero (highly acidic), and this refers to a solution with a H⁺(aq) ion concentration of 1 mol dm.

In very simple terms, when the concentration of H⁺(aq) ions in a solution changes by a factor of ten, the pH changes by one.

For example, if the concentration of H⁺(aq) ions in a solution changes from 0.01 mol dm to 0.1 mol dm, the change in pH would be one. The H⁺ ion concentration has changed by a factor of ten.

The thing that gets confusing is when the concentration of H⁺ ions changes by larger factors. For every x 10 change in concentration, the pH will change by one. If the H⁺ ion concentration changes by x 100, then the pH will change by two. 100 = 10 x 10.

Remember, every time the concentration of H⁺ ions changes by a factor of 10, the pH changes by one. The concentration here has changed by a factor of ten twice (100 = 10 x 10), which means the pH will change by two.

This means a small change in pH can represent a very large change in H+ ion concentration.   

As pH is basically just a way of describing the concentration of H⁺ ions in a solution, to calculate it, we need to know the concentration of H⁺ ions present!

To do this, we use a logarithmic expression pH = - log10[H⁺]

This can re-arranged to give us the expression [H+] = 10

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