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Consortium for Mathematics and its Applications

Product ID: ILAP
Supplementary Print
Undergraduate

Getting the Salt Out (ILAP)

Author: Ethan Berkove, Thomas Hill, Scott Moor


When two water (or other solvent) volumes are separated by a semi-permeable membrane, water will flow from the side of low solute concentration to the side of high solute concentration. This is known as osmosis. The flow of solvent across the membrane may be stopped, or even reversed, by applying external pressure on the side of higher solute concentration. This process is called reverse osmosis. We will use van't Hoff's equation to model osmosis.

Physical Concepts Examined:
1. Osmotic pressure
2. Permeability
3. Desalination

Table of Contents:

SETTING THE SCENE

YOUR JOB

PART 1: NUMERICAL AND GRAPHICAL ANALYSES
Requirement 1
Requirement 2
Requirement 3
Requirement 4

PART 2: LET'S GET EXPLICIT
Requirement 5
Requirement 6

PART 3: WHAT DO YOU RECOMMEND?
Requirement 7

INSTRUCTOR'S SOLUTION

NOTES FOR THE INSTRUCTOR
Background on Reverse Osmosis
Notes on the Problem Solution
Pedagogical Advice

REFERENCES

ABOUT THE AUTHORS

©2003 by COMAP, Inc
The UMAP Journal 24.4
15 pages

Mathematics Topics:

Differential Equations

Application Areas:

Engineering & Construction , Physical Sciences , Chemistry, Engineering

Prerequisites:

Modeling with an ordinary differential equation with initial condition; Sketching a solution to a differential equation on its direction field; Solving an ordinary differential equation by separation of variables

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