Video Tutorial pH Calculations

Quick Notes pH Calculations

• pH (potential of hydrogen) is a scale used to show how acidic or alkaline a solution is.
• Acidity is determined by the concentration of H+(aq)ions in a solution, meaning pH is a way of describing the H+(aq)concentration in a solution.
• The pH scale is logarithmic, meaning a change in pH value of one refers to a change in concentration of H+(aq)ions by a factor of 10. It can be calculated using:

pH = - log10[H+]

[H+] = 10-pH

• pH of 0 means a solution has a H+(aq)ion concentration of 1 mol dm-3.
• pH of 1 means a solution has a H+(aq)ion concentration of 0.1 mol dm-3.

Full Notes pH Calculations

pH is a way of describing how acidic or alkaline a solution is. It refers to the concentration of H+(aq) ions present in a solution. The larger the value of pH, the less acidic the solution.

Acids release H+(aq)ions in solution. A highly acidic solution has a high concentration of H+(aq)ions.

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 H+(aq)concentration of 0.001 mol dm-3. Black coffee has a typical H+(aq)concentration of 0.00001 mol dm-3.

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 range of numbers using a scale with smaller values.

The exact workings of logarithmic scales aren’t 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 and this refers to a solution with a H+(aq)ion concentration of 1 mol dm-3. When the concentration of H+(aq)ions in a solution changes by a factor of ten, the pH value changes by one.

If H+ ion concentration is increasing by a factor of ten, the pH will decrease by one. If H+ ion concentration is decreasing by a factor of ten, the pH will increase by one. This is why there is a negative (-) sign in the pH expression, see below.

For example, if the concentration of H+(aq)ions in a solution changes from 0.01 mol dm-3 to 0.1 mol dm-3, the H+ ion concentration has increased by a factor of ten. This means the pH would decrease by one.

The thing that gets confusing is when the concentration of H+ ions changes by larger factors. 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-pH

Below is a table showing how pH changes with H+ concentration.

H+ ion concentration (in mol dm-3) pH expression pH
1 -log10(1) 0
0.1 -log10(0.1) 1
0.01 -log10(0.01) 2
0.001 -log10(0.001) 3
0.0001 -log10(0.0001) 4
0.00001 -log10(0.00001) 5
0.000001 -log10(0.000001) 6
0.0000001 -log10(0.0000001) 7
0.00000001 -log10(0.00000001) 8
0.000000001 -log10(0.000000001) 9
0.0000000001 -log10(0.0000000001) 10
0.00000000001 -log10(0.00000000001) 11
0.000000000001 -log10(0.000000000001) 12
0.0000000000001 -log10(0.0000000000001) 13
0.00000000000001 -log10(0.00000000000001) 14