Textbook Question Number F 25

[Ian_Lee_1E]

Practitioners of the branch of alternative medicine known as homeopathy claim that very dilute solutions of substances can have an effect. Is the claim plausible? To explore this question, suppose that you prepare a solution of a supposedly active substance, X, with a molar concentration of
0.10
mol⋅L
−1
. Then you dilute 10. mL of that solution by doubling the volume, doubling it again, and so on, for 90 doublings in all. How many molecules of X will be present in 10. mL of the final solution? Comment on the possible health benefits of the solution.

how do you solve this question?

[Melody Wu 2L]

This is actually G25, I believe.

So first, you want to find the molarity after the first dilution so
0.01mol/L x 0.01L = 0.001 mol X
0.001 mol X / 0.02 mL = 0.05M

Then, since you are repeating this process 90 times, it'll be
0.1M (0.5)^90 = 8.078 x 10^-29 mol/L

To find the number of molecules, you want to multiply by Avogadro's number to get 4.86z10^-5 molecules of X.
Since there is less than one molecule of the active substance "X," there are no health benefits.

[Natalie Do 3F]

This question is a very interesting application of unit analysis because it shows that even though moles are massive and consist of so many molecules, it is still a finite number and has practical implications as seen in this branch of "medicine"