Drug X has an expiration date that is 1.5 years after the date it was manufactur

Question

Drug X has an expiration date that is 1.5 years after the date it was manufactured. Drug X decomposes following the reaction below. Assume the decompostion follows first order kinetics. Y is not toxic but Z is somewhat toxic. An average human should not ingest more that 2.8 mg of Z at a given time.

x----->Y + 2Z

1) A bottle contains pills of X that were manufactured 5.00 years ago. The drug is analyzed and it is found that 95.0% of X has not decomposed. What is the half life for the decomposition of X?

2)One of the pills contains 10.0mg of X. The molecular weight of X is 245g/mol. The molecular weight of Z is 91.0g. How long will it take for enough X to decompose so as to produce 2.8 mg of Z?

Explanation / Answer

a) k=1/5 * ln(100/95)

t1/2 = (ln2)/k = 67.6 years

b) ans= 46.12 years

solution ---

moles of X =10/245000

moles of Z= 2.8/91000

moles of X required for this Z =(1/2) * moles of Z =1.5385*10^-5

X remains = 10/245000 - 1.5385*10^-5

t =1/k * ln(A0/A)=   46 .12 years

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