# Chemical Analysis

My dad (he is an Chemistry graduate so understands it all a lot better than me) put together this system calculate the volume of water which would neet changing.

Symbol | Description |
---|---|

a | Volume of water in aquarium (litre) |

b | Volume of water removed in bucket (litre) |

c | Concentration of contaminant (e.g. nitrate) in solution at the start |

n | Number of steps |

If we siphon off b litres of liquid from the aquarium, and replace this volume with b litres of clean water, the concentration of material in solution will be: *(a-b)c / a*

e.g. If our aquarium holds 360 litres, and the bucket has a capacity of 10 litres, then replacing the first 10l of water will reduce the concentration of contaminant by a factor of (360 – 10)/360. i.e. 0.9722

After two steps, the contaminant will be reduced by 0.9722 x 0.9722. i.e. 0.9452

After three steps, the contaminant will be reduced by 0.9722 x 0.9722 x 0.9722. i.e. 0.97223 or 0.9189.

After n steps, the contaminant will be reduced by a factor 0.9722n.

To find out how many steps it will take to halve the concentration of contaminant, we need to solve the following mathematical equation:

0.9722n = 0.5

n log 0.9722 = log 0.5

n = log 0.5 / log 0.9722

n = 24.6

Rounding up to a whole number, we arrive at 25 steps.

To conclude, using a 10 litre bucket on a 360 litre aquarium, we must replenish the volume that we remove 25 times to halve the concentration of a contaminant, such as nitrate.

Fish are able to tolerate the slow reduction in concentration in a large number of small steps. Removing and replacing half the water in an aquarium in one step would be too much of a shock to them.

The table below shows what percentage of the original concentration of contaminant is left after each step to empty and replenish.

Step | Concentration |
---|---|

1 | 97 % |

2 | 95 % |

3 | 92 % |

4 | 89 % |

5 | 87 % |

6 | 84 % |

7 | 82 % |

8 | 80 % |

9 | 78 % |

10 | 75 % |

11 | 73 % |

12 | 71 % |

13 | 69 % |

14 | 67 % |

15 | 66 % |

16 | 64 % |

17 | 62 % |

18 | 60 % |

19 | 59 % |

20 | 57 % |

21 | 55 % |

22 | 54 % |

23 | 52 % |

24 | 51 % |

25 | 49 % |