Consider the following reaction that occurs in a constant volume batch reactor: (We will withdraw samples and record the concentration of A as a function of time.)
Mole Balance: 

Rate Law: 

Stoichiometry: 

Combine: 
Integral Method  top 
We could integrate the combined mole balance and rate law to plot reaction rate data in terms of
concentration vs. time for 0, 1st, and 2nd order reactions.
Table CD51 Derivation Equations used to
Plot 0, 1st, and 2nd order reactions.
These types of plots are usually used to determine the values k for runs at various
temperatures and then used to determine the activation energy.
Zero Order  First Order  Second Order 
If the data do not fall on a straight line for α=0,1, or 2 such as α=2;
then we should stop guessing reaction orders and proceed to either the differential method of analysis or to regression.
Differential Method (p. 224232)  top 
Taking the natural log of 

The reaction order can be found from a lnln plot of: 

Methods for finding the slope of loglog and semilog graph papers may be found at http://www.physics.uoguelph.ca/tutorials/GLP/.
However, we are usually given concentration as a function of time from batch
reactor experiments.
time (s)  0  t_{1}  t_{2}  t_{3} 
concentration (mol/dm^{3})  C_{Ao}  C_{A1}  C_{A2}  C_{A3} 
2A. Graphical
This method accentuates measurement error!
2B. Polynomial (using Polymath)
C_{A} = a_{o} + a_{1}t + a_{2}t^{2} + a_{3}t^{3} +a_{4}t^{4}
2C. Finite Difference
NonLinear LeastSquares Analysis (p. 252)  top 
That is we want to be a minimum.
time (s)  0  t_{1}  t_{2}  t_{3} 
concentration (mol/dm^{3})  C_{Ao}  C_{A1}  C_{A2}  C_{A3} 
For concentrationtime data, the measured parameter P has concentration C_{A}. We can integrate the combined mole balance equation and rate law
to obtain
We now guess k and alpha and calculate each C_{ACi} at the times shown in the above table and then compare it with the measured concentration by taking the difference and squaring it.
We then sum up the differences for all the data points.
We continue to guess k and alpha until we find the values of alpha and k which minimize S^{2} (actually we let the computer find these values.)
^{*} All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .