Question

What is the half-life of a pharmaceutical if the initial dose is 500 mg and only 31 mg remains after 6 hours?

a. 2.0 hours
b. 1.5 hours
c. No right choice.

Answer 1

`\large \boxed{\text{b. 1.5 h}}`

Step-by-step explanation:

1. Calculate the rate constant

The integrated rate law for first order decay is

`\ln \left ((A_(0))/(A_(t))\right ) = kt`

where

A₀ and A_t are the amounts at t = 0 and t

k is the rate constant

`\begin{array}{rcl}\ln \left ((500)/(31)\right) & = & k * 6\\\\\ln 16.1 & = & 6k\\2.78& =& 6k\\k & = & (2.78)/(6)\\\\& = & 0.463 \text{ h}^(-1)\\\end{array}`

2. Calculate the half-life

`t_{(1)/(2)} = (\ln2)/(k) = \frac{\ln2}{\text{0.463  h}^(-1)} = \textbf{1.5 h}\\\\ \text{The half-life is $\large \boxed{\textbf{1.5 h}}$}`