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Why does the product (a•b), rather than the sum (a + b) appear in the Law of Mass Action? This is sometimes brought up to demonstrate how/why nonlinear terms arise in differential equations. The law of mass action states that The rate of a chemical reaction involving an interaction of two or more chemical species is proportional to the product of the concentrations of the given species.  This is NOT an assignment...I'm just curious and trying to understand mathematical relations better. Thanks!

Why does the product (a•b), rather than the sum (a + b) appear in the Law of Mass Action? This is sometimes brought up to demonstrate how/why nonlinear terms arise in differential equations. The law of mass action states that The rate of a chemical reaction involving an interaction of two or more chemical species is proportional to the product of the concentrations of the given species.  This is NOT an assignment...I'm just curious and trying to understand mathematical relations better. Thanks!

Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
2nd Edition
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Steven S. Zumdahl, Susan A. Zumdahl
Chapter12: Chemical Equilibrium
Section: Chapter Questions
Problem 1RQ: Characterize a system at chemical equilibrium with respect to each of the following a. the rates of...
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Why does the product (a•b), rather than the sum (a + b) appear in the Law of Mass Action?

This is sometimes brought up to demonstrate how/why nonlinear terms arise in differential equations. The law of mass action states that The rate of a chemical reaction involving an interaction of two or more chemical species is proportional to the product of the concentrations of the given species. 

This is NOT an assignment...I'm just curious and trying to understand mathematical relations better. Thanks!

In a chemical reaction, molecules of types A and B bind and react to form product P. Let a(t), b(t) denote the concentrations of A and B. These concentrations depend on time because the chemical reaction uses up both types in producing the product. The reaction only occurs when A and B molecules "collide" and stick to one another. Collisions occur randomly, but if concentrations are larger, more collisions take place, and the reaction is faster. If either the concentration a or b is doubled, then the reaction rate doubles. But if both a and b are doubled, then the reaction rate should be four times faster, based on the higher chances of collisions between A and B. The simplest assumption that captures this dependence is or rate of reaction x a. b rate of reaction = k.a.b
Transcribed Image Text:In a chemical reaction, molecules of types A and B bind and react to form product P. Let a(t), b(t) denote the concentrations of A and B. These concentrations depend on time because the chemical reaction uses up both types in producing the product. The reaction only occurs when A and B molecules "collide" and stick to one another. Collisions occur randomly, but if concentrations are larger, more collisions take place, and the reaction is faster. If either the concentration a or b is doubled, then the reaction rate doubles. But if both a and b are doubled, then the reaction rate should be four times faster, based on the higher chances of collisions between A and B. The simplest assumption that captures this dependence is or rate of reaction x a. b rate of reaction = k.a.b
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