A 3.00-kg batch of a synthetic mixture containing a new antibiotic drug was prep

Question

A 3.00-kg batch of a synthetic mixture containing a new antibiotic drug was prepared in a "pilot plant" operation. The crude product was analyzed by IDA. A spike of exactly 8.25 mg of pure radiolabeled antibiotic having an activity of 8600 dpm was added to a 10.0-g sample of the crude product. After thorough mixing, a sample of pure antibiotic was extracted from the spike-sample mixture in low chemical yield. A 50.0-mg portion of this pure fraction was counted and yielded an activity of 230 dpm. Calculate the percent by mass of the antibiotic in the crude product.

Explanation / Answer

Crude sample = 3 kg = 3000 g

8.25 mg = 0.00825 g of pure radiolabelled antibiotic has activity 8600 dpm

Added to 10 g sample

acitvity of radionulceide in 10 g sample = 0.00825 x 8600/10.00825 = 7.09 dpm

50 mg = 0.05 g of this fraction gave a signal of 230 dpm

pure nucleide sample signal = 7.09 x 0.050/10.00825 = 0.0354 dpm

Signal for the antibiotic in sample = 229.96 dpm

concentration of antibiotic in fraction = 230 x 8.25/8600 = 0.22 mg

concentration of antibiotic in crude = 13.2 g

percent by mass of antibiotic in the crude product = (13.2g/3000g) x 100 = 0.44%

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