The preparation of homeopathic "remedies" involves the repeated
dilution of solutions containing an active ingredient such as
arsenic trioxide (As2O3). Suppose one begins
with 73.0 g of arsenic trioxide dissolved in water, and repeatedly
dilutes the solution with pure water, each dilution reducing the
amount of arsenic trioxide in the solution by a factor of 100.
Assuming perfect mixing at each dilution, what is the maximum
number of dilutions one may perform such that at least one molecule
of arsenic trioxide remains in the diluted solution? For
comparison, homeopathic "remedies" are commonly diluted 15 or even
30 times.
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