A Simple Pollution Model

Purpose:

To model a simple chemical mixing problem.

Description:

A simple pollution model is created whereby a glass of 'clean' water becomes contaminated with ink. Ink is fed into a glass jar with an overflow valve at a consent rate. The water and ink are being continually mixed and the excess is allowed to drain out of the overflow valve so as to keep the amount of liquid in the glass jar constant. A differential equation modeling the process is derived and the solution is given. Students are asked to verify the solution and to graph it as a preliminary to the experiment.

The experiment consists of the students pouring the ink into the glass jar by hand. They collect data on how much ink is present by determining how clear the mixture is. Students are asked to write a report on their findings. This report will include:

• Graphs of the original MBL data, the regression analysis, and the overlay graphs showing the exponential fit.
• A very brief discussion of the experimental setup, the adequacy of the mathematical model and some error analysis
• A discussion of their thinking process in manipulating the data.

Materials Needed:

• Labtop computer with MBL software
• MBL light probe.
• 100 ml of bromocresol green solution (or bottle of ink).
• 25 ml of pH-7.
• One beaker.
• One glass jar with overflow valve.
• One laser (a flashlight will do).
• A magnetic stirrer.
• One clamp rod and several fork-clamps.

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