Immediately following an intravenous injection

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

Immediately following an intravenous injection, the concentration

C(t)

of a certain drug in the bloodstream (in mg L

^{-1}

) is assumed to satisfy

\dfrac{dC}{dt}=kC

for

t\ge 0

, with

t

measured in hours. Blood samples reveal that

C(0.5)=12.0

mg L

^{-1}

and

C(4)=5.00

mg L

^{-1}

. Therapeutic effectiveness requires the concentration to remain above

2.00

mg L

^{-1}

. (a) Derive an expression for

C(t)

and use the data to determine the exact value of the decay constant

k

. Show all algebraic steps leading to

k

. (b) Using your value of

k

, calculate the initial concentration

C_0=C(0)

immediately after injection. (c) Determine the time

t_{\text{th}}

(in hours, accurate to two decimal places) at which the drug concentration will drop to the therapeutic threshold of

2.00

mg L

^{-1}

. Justify the units of your answer.