Question

If in cup 1 you have a 40,000 ppm of a solution and you transfer one drop from cup 1 to cup 2 and add 9 drops of

water. You continue this process for the next two cups, how many ppm do you have in cup 4? (please help this is so confusing.)

Answer 1

The dilution ration is 1÷10 (1 drop of concentrated solution in 10 drops of diluted solution).

If we do that 4 times we repeat the same dilution with the same dilution ratio of 1÷10 (numerically is 0,1). Therefore we can multiply the solution ratio by itself 4 times.

0,1⁴ = 10^-4

This means that we end up with a solution which concentration is 10^-4 times the beginning concentration. Therefore the final concentration is

40 000 ppm × 10^-4 = 4ppm

PS: we can do this because we have the same unit of measurement for the volumes of both the concentrated solution and the diluted one (drops)