Approximate Chemical Concentration in parts per million (ppm)

Objective: To develop a rough simple means to calculate chemical concentration.

There are several means to describe the amount of chemical in a given amount of solution. Some of these are fairly complicated mathematically. The following is a rough approximation that is easy to do and is not all that far off from more detailed computations as long as the chemical volume is small relative to the solution volume.

If one pours a volume of chemical (V_c) into a volume of water (V_w) then there is a concentration ratio of chemical to solution given by

if the amount of chemical is very small relative to the amount of water then the concentration ratio is approximately

Concentration is often expressed by the numbers of parts per million of the chemical in the solution. An approximation to this is given by equating the concentration ratio to the number of parts per million (N).

Part per million is abbreviated with ppm.

The following calculator gives an approximate value for the resultant chemical concentration of a mixture from mixing a small amount of chemical into a much larger volume of water. The water volume should be at least 10 times larger than the chemical volume. First, select the units you want to use from the pull down menus. Then enter the values on the left side and the calculator will give the approximate chemical concentration of the mixture in part per million (ppm).

Example: What is the concentration of chemical in a pool if a coke can of it falls into a 30,000 gallon pool? A coke can contains 12 ounces. A gallon is 128 ounces so that the coke can is about 1/10 of a gallon. The concentration ratio is used to find N, the ppm of the chemical in the pool.

Solving this for N gives

The approximate concentration of the chemical in the pool when it has been well mixed is roughly 3 ppm.

The calculations with this method are often easier if you do not clear the ratios on a calculator but rearrange the numbers, 1,000,000 and all. Many of the zeros on the top and bottom will cancel then.

The concentration ratio can also be rearranged to give a prediction of the amount of chemical that is contained in a given volume of solution at N ppm. N ppm is always written as N/1,000,000 in calculations.

Volume Of Chemical=(Volume of Water)(Concentration)