An important thing to notice is the integral rate laws

ln[reactant]t = -kt + ln[reactant]0

are in the form

y = mx + b

Experiments are performed to collect concentration and time data; the data is plotted

-if 1/conc vs time is linear then the reaction is 2nd order
and slope = k

-if ln(conc) vs time is linear then the reaction is 1st order

and slope = -k

Experiments are conducted to determine the rate law for the following reaction.

Data is collected under under pseudo zero order conditions for water; that is, the concentration of water is so high that the change in concentration is negligable. Therefore, the change in reaction rate caused by the change in the concentration of water is negligable too.

time
(minutes)
[phenyl acetate] M
ln[phenyl acetate]
1/[phenyl acetate]
0
0.55
-0.598
1.818
0.25
0.42
-0.868
2.381
0.5
0.31
-1.171
3.226
0.75
0.23
-1.470
4.348
1
0.17
-1.772
5.882
1.25
0.12
-2.120
8.333
1.5
0.086
-2.453
11.628

A plot of ln[phenyl acetate] vs time gives a straight line; so, the reaction is first order with respect to [phenyl acetate].