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:

Differential Method

Taking the natural log of
The reaction order can be found from a ln-ln plot of:

Three Ways to Determine -dC_A/dt

1. Graphical

Methods for finding the slope of log-log and semi-log graph papers may be found here.

2. Polynomial (using Polymath)

C_A = a_o + a₁t + a₂t² + a₃t³ +a₄t⁴

3. Numerical

Finite Difference

Non-Linear Least-Squares Analysis

Generally want to be a minimum.

For concentration-time data,

Integral Method

We find the values of alpha and k which minimize S²

Finally we should also use the formula to plot reaction rate data in terms of concentration vs. time for 0, 1st, and 2nd order reactions.

Table CD5-1

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

                               

"What is Wrong with This Solution?" - Chapter 5

^* All chapter references are for the 3rd Edition of the text Elements of Chemical Reaction Engineering.

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