Chemical Reaction Engineering Asynchronous Video Series

1
Chemical Reaction Engineering Asynchronous
Video Series

• Chapter 5
• Finding the Rate Law
• H. Scott Fogler, Ph.D.

2
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.)

3
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

4
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

5
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

6
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

7
Plotting the Data

• Taking the natural log of

8
Plotting the Data

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

9
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.
10
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)

11
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

This method accentuates measurement error!
12
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 a3t3 a4t4

This method accentuates measurement error!
13
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 a3t3 a4t4
• 3. Finite Difference

This method accentuates measurement error!
14
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.

15
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 -rAkCA? to obtain

16
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 -rAkCA? to obtain
• We find the values of ? and k which minimize S2

Polymath will find the minimum for you. Thank you
Polymath!
17
Reaction Order and Rate Constant

• Zero Order First Order
  Second Order

18
Reaction Order and Rate Constant

• Zero Order First Order
  Second Order