**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.

- Acidity is determined by the concentration of H
- 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 = - log

_{10}[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 = - log _{10}[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 | -log_{10}(1) |
0 |

0.1 | -log_{10}(0.1) |
1 |

0.01 | -log_{10}(0.01) |
2 |

0.001 | -log_{10}(0.001) |
3 |

0.0001 | -log_{10}(0.0001) |
4 |

0.00001 | -log_{10}(0.00001) |
5 |

0.000001 | -log_{10}(0.000001) |
6 |

0.0000001 | -log_{10}(0.0000001) |
7 |

0.00000001 | -log_{10}(0.00000001) |
8 |

0.000000001 | -log_{10}(0.000000001) |
9 |

0.0000000001 | -log_{10}(0.0000000001) |
10 |

0.00000000001 | -log_{10}(0.00000000001) |
11 |

0.000000000001 | -log_{10}(0.000000000001) |
12 |

0.0000000000001 | -log_{10}(0.0000000000001) |
13 |

0.00000000000001 | -log_{10}(0.00000000000001) |
14 |