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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.) .

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chemical reaction engineering asynchronous video series

Chemical Reaction EngineeringAsynchronous Video Series

Chapter 5:

Finding the Rate Law

H. Scott Fogler, Ph.D.

algorithm
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.)

algorithm1
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:

algorithm2
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:

algorithm3
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:

algorithm4
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
Plotting the Data

Taking the natural log of

plotting the data1
Plotting the Data

Taking the natural log of

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

plotting the data2
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
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)

finding the rate law from concentration time data1
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!

finding the rate law from concentration time data2
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!

finding the rate law from concentration time data3
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!

curve fitting
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 fitting1
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 fitting2
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
Reaction Order and Rate Constant

Zero OrderFirst OrderSecond Order

reaction order and rate constant1
Reaction Order and Rate Constant

Zero OrderFirst OrderSecond Order