Example 3.2.1:
Crystal violet reacts with hydroxide to convert the dye to a colorless form:

CV⁺ + OH^- -> CVOH
purple colorless

The time course, measured as the absorbance of the solution at 590 nm, is given below for an initial crystal violet concentration of 1.2x10^-5 M and a hydroxide concentration of 0.0300 M. The long-time absorbance is 0.040. Determine the order of the reaction and the rate constant.

t (min) 0 1 3 5 7 9 11 13 15
A 1.200 0.905 0.526 0.317 0.200 0.133 0.094 0.071 0.058

Method: Do a fit based on the absorbance directly using non-linear curve fitting:

t (min) A
0 1.200
1 0.905
3 0.526
5 0.317
7 0.200
9 0.133
11 0.094
13 0.071
15 0.058

or a fit to the transformed data:

t (min) A A - A_oo ln(A - A_oo) 1/(A - A_oo)
0 1.200 1.160 0.148 0.862
1 0.905 0.865 -0.146 1.157
3 0.526 0.486 -0.722 2.059
5 0.317 0.277 -1.282 3.604
7 0.200 0.160 -1.833 6.250
9 0.133 0.093 -2.376 10.760
11 0.094 0.054 -2.926 18.649
13 0.071 0.031 -3.484 32.593
15 0.058 0.018 -4.041 56.876

t (min)	0	1	3	5	7	9	11	13	15
A	1.200	0.905	0.526	0.317	0.200	0.133	0.094	0.071	0.058

t (min)	A	A - A_oo	ln(A - A_oo)	1/(A - A_oo)
0	1.200	1.160	0.148	0.862
1	0.905	0.865	-0.146	1.157
3	0.526	0.486	-0.722	2.059
5	0.317	0.277	-1.282	3.604
7	0.200	0.160	-1.833	6.250
9	0.133	0.093	-2.376	10.760
11	0.094	0.054	-2.926	18.649
13	0.071	0.031	-3.484	32.593
15	0.058	0.018	-4.041	56.876