Chemical Reaction Engineering

Asynchronous Video Series Chapter 5:Finding the Rate Law

H. Scott Fogler, Ph.D.

AlgorithmConsider 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.)

AlgorithmConsider 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:

AlgorithmConsider 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:

AlgorithmConsider 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:

AlgorithmConsider 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 DataTaking the natural log of

Plotting the DataTaking the natural log of

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

Plotting the DataTaking 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 DataGiven:

Three Ways to Determine (-dCA/dt) from Concentration-Time Data (Graphical, Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

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time (s)0

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Finding the Rate Law from Concentration -Time DataGiven:

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!

Sheet1

time (s)0

Sheet2

Sheet3

Finding the Rate Law from Concentration -Time DataGiven:

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!

Sheet1

time (s)0

Sheet2

Sheet3

Finding the Rate Law from Concentration -Time DataGiven:

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 DifferenceThis method accentuates measurement error!

Sheet1

time (s)0

Sheet2

Sheet3

Curve FittingNon-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 FittingNon-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 FittingNon-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 ConstantZero Order First Order Second Order

Reaction Order and Rate ConstantZero Order First Order Second Order