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
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