Kinetomycin is dissolved into 400ml of a saline/dextrose solution. The amounts o

Question

Kinetomycin is dissolved into 400ml of a saline/dextrose solution. The amounts of drug in a serial samples obtained over a period of 10 hours are presented below:

Time (hr) 2, 4, 6, 8, 10

Amount (mg) 38.0, 21.9, 10.1, 5.41, 2.39

1. What is the initial amount of the drug added to the solution?

2. Determine the rate constant of the degradation process.

3. What is the half-life of degradation?

4. What is the initial concentration of the drug in solution?

5. Estimate the amount of drug at 1 hour.

6. At what time the amount of drug reaches 0.4 mg?

7. Use equations and the first two sampling data at 2 and 4 hour to estimate the rate constant of the degradation process and the initial amount of the drug added to the solution. Why are these data different than from those estimated in question 1?

Explanation / Answer

the degradation has to be verified for 1st order kinetics

for 1st order reaction, lnCA= lnCAO-Kt, CAO= initial concentration (t=0), CA= concentration at any time t

the plot of lnCA vs t gives a straight line whose slope gives rate constant K and intercept gives lnCAO. The plot is shown below

from the plot

1.at t=0 lnCAO= 4.398 ( intercept), CAO= 81.288 mg

2.K= 0.346/hr. Rate constant

3. for 1st order reaction, half ilfe =0.693/K =0.693/0.346 hr=2.00 hr

4. initial concentration = 81.288/400 mg/ml =0.20322 mg/ml

5. from lnCA= -0.346*t+4.398

at t=1hr, lnCA= 4.398-0.346=4.052, CA= 57.51 mg

6. given CA=0.4mg, lnCA= ln(0.4)= -0.92= 4.398-0.346t

0.346t= 4.398+0.92, t= 15.4 hr

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