Chemical Reaction Engineering

Asynchronous Video Series

Chapter 5:

Finding the Rate Law

H. Scott Fogler, Ph.D.

Algorithm

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.)

Algorithm

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:

Algorithm

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:

Algorithm

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:

Algorithm

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:

Plotting the Data

Taking the natural log of

Plotting the Data

Taking the natural log of

The reaction order can be found from a ln-ln plot of:

Plotting the Data

Taking the natural log of

The reaction order can be found from a ln-ln plot of:

Methods for finding the slope of log-log and semi-log graph papers may be found at http://www.physics.uoguelph.ca/tutorials/GLP.

Finding the Rate Law from Concentration -Time Data

Given:

Three Ways to Determine (-dCA/dt) from Concentration-Time Data (Graphical,

Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

time (s) 0 t1 t2 t3

concentration (mol/dm3) CAo CA1 CA2 CA3

Finding the Rate Law from Concentration -Time Data

Given:

Three Ways to Determine (-dCA/dt) from Concentration-Time Data (Graphical,

Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

1. Graphical

time (s) 0 t1 t2 t3

concentration (mol/dm3) CAo CA1 CA2 CA3

This method accentuates measurement error!

Finding the Rate Law from Concentration -Time Data

Given:

Three Ways to Determine (-dCA/dt) from Concentration-Time Data (Graphical,

Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

1. Graphical

2. Polynomial (using Polymath)

CA = ao + a1t + a2t2 + a3t

3 +a4t4

time (s) 0 t1 t2 t3

concentration (mol/dm3) CAo CA1 CA2 CA3

This method accentuates measurement error!

Finding the Rate Law from Concentration -Time Data

Given:

Three Ways to Determine (-dCA/dt) from Concentration-Time Data (Graphical,

Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

1. Graphical

2. Polynomial (using Polymath)

CA = ao + a1t + a2t2 + a3t

3 +a4t4

3. Finite Difference

time (s) 0 t1 t2 t3

concentration (mol/dm3) CAo CA1 CA2 CA3

€

dCdt

⎞ ⎠i

=C i +1 − C i−1

2Δt

This method accentuates measurement error!

Curve Fitting

Non-Linear Least-Squares Analysis (p. 252)

We want to find the parameter values (alpha, k, E) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is

a minimum.

Curve Fitting

Non-Linear Least-Squares Analysis (p. 252)

We want to find the parameter values (alpha, k, E) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is

a minimum.

That is we want to be a minimum.

For concentration-time data, we can integrate the mole balance equation for -rA=kCA

to obtain

Curve Fitting

Non-Linear Least-Squares Analysis (p. 252)

We want to find the parameter values (alpha, k, E) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is

a minimum.

That is we want to be a minimum.

For concentration-time data, we can integrate the mole balance equation for -rA=kCA

to obtain

We find the values of and k which minimize S2

Polymath will find the minimum for you. Thank you Polymath!

Reaction Order and Rate Constant

Zero Order First Order Second Order

Reaction Order and Rate Constant

Zero Order First Order Second Order