Vernier Software and Technology
Vernier Software & Technology

Titration Curves: An Application of the Logistic Function

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:

y = \frac{A}  {{1 + {B^{x - C}}}} + D

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 features the following Vernier sensors and equipment.

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Standards Correlations

See all standards correlations for Real-World Math with Vernier »

Real-World Math with Vernier

See other experiments from the lab book.

1Walk the Line - Straight Line Distance Graphs
2Making Cents of Math: Linear Relationship between Weight and Quantity
3Pool Plunge - Linear Relationship between Water Depth and Pressure
4Funnel Volumes - Volume and Weight
5Keep It Bottled Up - Rates of Pressure Increase
6Mix It Up - Mixing Liquids of Different Temperatures
7Spring Thing - Newton's Second Law
8Stretch It to the Limit - The Linear Force Relation for a Rubber Band
9What Goes Up - Position and Time for a Cart on a Ramp
10That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
11Walk This Way - Definition of Rate
12Velocity Test - Interpreting Graphs
13From Here to There - Applications of the Distance Formula
14Under Pressure - The Inverse Relationship between Pressure and Volume
15Light at A Distance - Distance and Intensity
16Chill Out: How Hot Objects Cool
17Charging Up, Charging Down - Charging a Capacitor
18Bounce Back - The Pattern of Rebound Heights
19Sour Chemistry - The Exponential pH Change
20Swinging Ellipses - Plotting an Ellipse
21Lights Out! - Periodic Phenomena
22Tic, Toc: Pendulum Motion
23Stay Tuned: Sound Waveform Models
24Up And Down: Damped Harmonic Motion
25How Tall? Describing Data with Statistical Plots
26And Now, the Weather - Describing Data with Statistics
27Meet You at the Intersection: Solving a System of Linear Equations
28Titration Curves: An Application of the Logistic Function
29Clock Design: Period and Length of a Simple Pendulum
30Graph It in Pieces: Piecewise Defined Functions
31Stepping to the Greatest Integer: The Greatest Integer Function
32Crawling Around: Parametric Plots

Activity 28 from Real-World Math with Vernier Lab Book

<i>Real-World Math with Vernier</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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