Textbook question G25

[Aaina 2D]

Could someone please explain this question?

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.

I know we would have to use the dilution equation, but how do you calculate it for 90 doublings?

[sophie esherick 3H]

Hi! You don't have to calculate all 90 doublings but rather you will have to think about what diluting a solution many times would do to the amount of moles in the original solution and how that would affect the amount of active X in a small 10mL sample.

[Natalie Do 3F]

In the end with all the doubling, you are trying to find out if the number of molecules can even be spread out so thin across all the dilutions. If you find that there will be some samples with literally a fraction of (aka zero) molecules of the active ingredient, then you know the medication will be ineffective.