Question

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Concentration ! 5. How many half-lives (t) would it take for 99.9% of any initial concentration of a drug to decompose? Assume first-order kinetics.

Answer 1

Initial concentration C0= 100 mg X 0.999= 99.9 mg (as 99.9 % of initial concentration is to be decomposed)

Remaining or the final concentration C= 100 mg X 0.001= 0.1 mg (as 99.9 % is decomposed and remaing is 0.1% of 100 mg)

As first order kinetics is involved in the decomposition,

Hence time taken will be t= {2.3 (Log C - Log C0) (t1/2)}/ -k

t= {2.3 (log 0.1- log 99.9)}/ -0.693

t= 9.96 t 1/2

Means almost 10 half lives will be required to decompose 99.9% of initial concentration of the given drug.