Question

The drug propanolol, which is used as an anxiolytic (relieves anxiety) has a half-life of 3.9 h. How long does it take for 80% of a dose of propanolol to be eliminated?

Answer 1

Answer:

After 9.0 hours

Explanation:

Using the decay equation, we can write the amount of drug propanol after time t as:

$m(t)=m_0 e^{-\lambda t}$ (1)

where

m(t) is the mass left at time t

$m_0$ is the initial mass of the substance

$\lambda$ is the decay constant

t is the time

The decay constant is related to the half-life of the substance as follows:

$\lambda=\frac{ln2}{t_{1/2}}$

where $t_{1/2}$ is the half-life.

Here we have

$t_{1/2}=3.9 h$

So the decay constant is

$\lambda=\frac{ln 2}{3.9}=0.178 h^{-1}$

We want to find the time t after which the dose is 80% of the initial dose is eliminated, so the time t after which 20% of drug is left, so

$\frac{m(t)}{m_0}=0.20$

Substituting eq(1) and solving for t, we find:

$t=-\frac{ln(\frac{m(t)}{m_0})}{\lambda}=-\frac{ln(0.20)}{0.178}=9.0 h$