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

Finding the Rate Law from Concentration -Time Data Given: Three Ways to Determine (-dC A /dt) from Concentration-Time Data (Graphical, Polynomial, Finite Difference, Non-Linear Least Squares Analysis)

Finding the Rate Law from Concentration -Time Data Given: Three Ways to Determine (-dC A /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 Data Given: Three Ways to Determine (-dC A /dt) from Concentration-Time Data (Graphical, Polynomial, Finite Difference, Non-Linear Least Squares Analysis) 1. Graphical 2. Polynomial (using Polymath) C A = a o + a 1 t + a 2 t 2 + a 3 t 3 +a 4 t 4 This method accentuates measurement error!

Finding the Rate Law from Concentration -Time Data Given: Three Ways to Determine (-dC A /dt) from Concentration-Time Data (Graphical, Polynomial, Finite Difference, Non-Linear Least Squares Analysis) 1. Graphical 2. Polynomial (using Polymath) C A = a o + a 1 t + a 2 t 2 + a 3 t 3 +a 4 t 4 3. Finite Difference 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 (r m ), and the calculated rate (r c ) 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 (r m ), and the calculated rate (r c ) is a minimum. That is we want to be a minimum. For concentration-time data, we can integrate the mole balance equation for - r A =kC A  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 (r m ), and the calculated rate (r c ) is a minimum. That is we want to be a minimum. For concentration-time data, we can integrate the mole balance equation for - r A =kC A  to obtain We find the values of  and k which minimize S 2 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