Could you please help answering these questions please. Pharmacokinetics is the
ID: 946020 • Letter: C
Question
Could you please help answering these questions please.
Pharmacokinetics is the study of the rates of absorption and elimination of drugs by organisms. As an example, consider the elimination of/^-adrenergic blocking agents ('/^-blockers') used in the treatment of hypertension. After intravenous administration of a/^-blocker, the blood plasma of a patient was analyzed for remaining drug, and the data are shown below: t (min) 30 60 120 150 240 360 480 c(nM) 699 622 413 292 152 60 24 Inc(nM) 6.550 6.433 6.023 5.677 5.024 4.09 3.18 where c is the concentration of the drug measured at a time t after the injection. To see if the removal is a first-order process, the data is plotted. It is found that the plot is straight and can be fitted well to a linear function with a slope of -7.6 103 min 1 by least-squares method.Explanation / Answer
The integrated rate expression for first order reation is kt = ln [a/a-x] where k is the rate onstant, t is the time, a is the initial concentration, a-x is the concentration at time t.
When it is expanded we get the expression as
ln(a-x) = lna - kt
when a graph is plotted betweenln(a-x) [lnC in the given case] vs. time t , it is a straight line with negative slope of (-k) with an intercept of( ln a) on the Y- axis.
since the given graph exactly follows this pattern, we can say it is first order reaction
b) Since the slope of a first order reaction equals to -k (rate constant) ,
the rate constant of this reaction is 7.6x 10-3 min-1
c) For a first order reaction half life T = 0.693/ k and it is independent of initial concentration
thus T = 0.693/7.6x10-3 = 91.18 min
d) The time taken for 95% of the reaction(drug) to be removed is
t = 2.303/k [log a/a-x]
= 2.303/7.6 x10-3 log (100/5) = 394.24 min = 6.57 hr