Homework Assignment 1995 - 1 (Answers)

Problem 2

Carefully plot the data on semi-log graph paper (three-cycle) [Blue diamonds]. Draw a line 'through the data' (red 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. (In this data the points fall quite close to the line - don't expect this to happen all the time)

Semi-log Plot

From this plot we can estimate Cp0 from the intercept. Thus, Cp0 = 47.6 mg/L. From the slope of the line kel = 0.432 hr-1.

Since Dose = 500 mg and Cp0 = Dose/V then V = Dose/Cp0 = 500/48 L = 10.5 L.

t1/2 = ln2/kel = 0.693/0.432 = 1.61 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

47.6

-

0

1

30

38.8

38.8

2

20

25

63.8

6

3.8

47.6

111.4

12

0.26

12.2

123.6

-

0.6

124.2

Summary

Parameter

Value

Units

kel

0.432

hr-1

Cp0

47.6

mg/L

V

10.5

L

t1/2

1.61

hr

AUC

124.2

mg.hr/L