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

After 9.0 hours

Step-by-step 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=(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=(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

`(m(t))/(m_0)=0.20`

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

`t=-(ln((m(t))/(m_0)))/(\lambda)=-(ln(0.20))/(0.178)=9.0 h`