Question

A drug decomposes by a first order mechanism, with a half-life of 5.00 years. Calculate how long it will take for 80% of the drug to decompose

Answer 1

Answer : The time taken for the decomposition of drug will be 11.6 years.

Explanation :

Half-life = 5.00 years

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{5.00}$

$k=0.139\text{ years}^{-1}$

Now we have to calculate the time taken.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = time taken = ?

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process = 100 - 80 = 20 g

Now put all the given values in above equation, we get

$t=\frac{2.303}{0.139}\log\frac{100}{20}$

$t=11.6\text{ years}$

Therefore, the time taken for the decomposition of drug will be 11.6 years.