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Can someone explain to me how this is the correct answer. Please show all work.

ID: 985915 • Letter: C

Question

Can someone explain to me how this is the correct answer. Please show all work.

Cocaine is a chiral compound and, therefore, could exist as a pair of enantiomers. The levorotatory isomer occurs naturally and is physiologically active, whereas the dextrorotatory isomer does not occur naturally and is physiologically inactive. Pure natural cocaine has an [ab25 of-16. The cocaine Rusty, the friendly neighborhood drug dealer, sells, which he swears to be of the finest quality, has a [ab25 of +8 . What is the percent composition of the physiologically active enantiomer in the cocaine Rusty sells, assuming that it is mixture of the two enantiomers of cocaine? 25% 50% 67% 75% none of the above

Explanation / Answer

active cocine = x

fraction of inactive cocaine = 1 - x

hence

-16 x + 16 (1-x) = +8

-16 x + 16 -16 x = 8

32 x = 8

x = 8/ 32

x = 1/4 fraction

so

active cocain = 1/4 % = 25 %