Question

Pharmacokinetics is the study of the rates of absorption and elimination of drugs by organisms. In most cases, elimination is slower than absorption and is a more important determinant of the availability of a drug for binding to its target. For example, consider the elimination of beta blockers used to treat hypertension. After intravenous administration, the concentration of residual drug in the blood plasma of a patient was monitored and the data are shown in the following table.

Time (min) 30 60 120 150 240 360 480

Conc (ng/cm3 ) 699 622 413 292 152 60 24

a) Is removal of the drug a first- or second-order process? b) Calculate the rate constant and half-life of the process. (A critical aspect of drug development is the optimization of the half-life of elimination, which must be long enough to allow the drugs to find and act on its target but not so long that harmful side effects become significant).

Answer 1

Graphical Method for Rate Order

The best way to identify fast and easy the rate of reaction AND the rate constant is via Graphical Method.

First, as the name implies, we need to graph all types of order (most common)

First = ln(C) vs. t

For first order

dC/dt = k*C^1

dC/dt = k*C

When developed:

dC/C = k*dt

ln(C) = ln(C0) - kt

if x axis is "time" then the slope is "-k", and y-intercept is initial concentration C0. y-axis if ln(C) (natural logarithm of concentration)

Second = 1/C vs. t

For Second order

dC/dt = k*C^2

When developed:

dC/C^2 = k*dt

1/C= 1/C0 + kt

if x axis is "time" then the slope is "k", and y-intercept is initial concentration C0. y-axis if 1/(C (inverse of concentration)

Cleary

the best fit for a straight line is:

FIRST ORDER

b)

the rate constant for first order:

slope = -k

slope = -0.0076

k = -(-0.0076)

k = 0.0076 1/min

For half life:

HL for ifrs torder:

HL = ln(2)/k

HL = ln(2)/(0.0076) = 91.203 min