The preparation of homeopathic \"remedies\" involves the repeateddilution of sol

Question

The preparation of homeopathic "remedies" involves the repeateddilution of solutions containing an active ingredient such asarsenic trioxide (As2O3). Suppose one beginswith 55.0 g of arsenic trioxide dissolved in water, and repeatedlydilutes the solution with pure water, each dilution reducing theamount of arsenic trioxide in the solution by a factor of 100.Assuming perfect mixing at each dilution, what is the maximumnumber of dilutions one may perform such that at least one moleculeof arsenic trioxide remains in the diluted solution? Forcomparison, homeopathic "remedies" are commonly diluted 15 or even30 times.

Explanation / Answer

Molecular weight of A2O3 = 198 (Handbookof Chem & Physics) N = 6.02 * 10E23 * 55 / 198 = 1.67 * 10E23 molecules ofarsenic trioxide in 55 grams (1 / 100)n * 1.67 * 10E23 < 1 1.67 * 10E23 < 100n log 1.67 * 10E23 < n log 100 n > log 1.67 * 10E23 / log 100 = 11.6 So no more than 11 dilutions can be made log 1.67 * 10E23 < n log 100 n > log 1.67 * 10E23 / log 100 = 11.6 So no more than 11 dilutions can be made

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