Homework Assignment 1995 - 1 (Answers)

Problem 2

Carefully plot the data on semi-log graph paper (two-cycle) [Blue squares]. Draw a line 'through the data' (red striped line).

Through the data means drawing the line so there are as many points above the line as below it. A visual averaging. A best-fit line. Don't pick two data points and draw the line through them. Draw the line through all the data points. An average fit.

Semi-log Plot

From this plot we can estimate Cp0 from the intercept. Thus, Cp0 = 18.6 mg/L. From the slope of the line kel = 0.144 hr-1.

Since Dose = 300 mg and Cp0 = Dose/V then V = Dose/Cp0 = 300/18.6 L = 16.1 L.

t1/2 = ln2/kel = 0.693/0.144 = 4.81 hr

For the AUC caclulation we need the time values, Cp values and the estimate of Cp0 and kel. Note last AUC segment is Cplast/kel.

Time (hr) Cp (mg/L) AUC (mg.hr/L) AUC (mg.hr/L)
0 18.6 - 0
1 15.7 17.1 17.1
2 13.8 14.8 31.9
6 8.3 44.2 76.1
12 3.2 34.5 110.9
- 22.2 132.8

Summary

Parameter Value Units
kel 0.144 hr-1
Cp0 18.6 mg/L
V 16.1 L
t1/2 4.81 hr
AUC 132.8 mg.hr/L