Titration Curves: An Application of the Logistic Function
Recommended for grades 9–12.
Introduction
Think about how cold germs spread through a school. One person comes to class with a cold and infects other students. At first, the disease spreads slowly, but as more students catch cold and spread it to other classmates, the disease spreads more rapidly. The rate of infection slows down again when most students are infected and there is no one left at school to infect. The maximum number of students in the school who can contract the disease is the number of students in the school.
A logistic function is often used to model this type of situation. The logistic function is an exponential function, but it contains a ratio and offset which make its behavior interesting. The formula for a logistic function is:
In this activity, you will add base to an acid and use a logistic function to model the data and locate the equivalence point.
Objectives
- Record pH versus base volume data for an acid-base titration.
- Manually model the titration curve using a logistic function.
- Describe the role of each parameter in the logistic function.
Sensors and Equipment
This activity requires each of the following Vernier sensors and equipment (unless otherwise noted):
Additional Requirements
You may also need an interface and software for data collection. What do I need for data collection?
Download Experiment Preview
The student-version preview includes:
- Step-by-step instructions for computer-based data collection
- List of materials and equipment
Note: The experiment preview of the computer edition does not include essential teacher information, safety tips, or sample data. Instructions for Logger Pro and other software (such as LabQuest App or TI handheld software, where available) are on the CD that accompanies the book. We strongly recommend that you purchase the book before performing experiments.
Standards Correlations
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Included in the Lab Book
Vernier lab books include a CD with word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.