Question

The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 81 minutes. Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.8 minutes later? g/mL. What will the concentration be 324 Round your answer to 2 significant digits. x 5 ?

Answer 1

Answer: 0.11 g/ml

Explanation:

Half-life = 81 minutes

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

$k=\frac{0.693}{81\text{minutes}}$

$k=0.008\text{minutes}^{-1}$

Now we have to calculate the age of the sample:

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  = 0.008\text{minutes}^{-1}[/tex]

t = time of decomposition = 324 minutes

a = let initial concentration of the reactant  = 1.8 g/ml

a - x = concentration after decay process  = ?

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

$324=\frac{2.303}{0.008}\log\frac{1.8}{a-x}$

$(a-x)=0.11g/ml$

Thus concentration after 324 minutes will be 0.11 g/ml.