Chapter 6
Law of Mass Action
Let us now consider the character of the material Nature
whose necessary results have been made available. . . for a final
cause.
(Aristotle)
6.1 Law of Mass Action Model
The law of mass action is a powerful concept that describes the average behavior of
a system that consists of many interacting parts such as molecules that react with
each other, or viruses that are passed along from a population of infected individuals to nonimmune ones. The law of mass action has been derived first for chemical
systems but subsequently found high use in epidemiology and ecology. In this
chapter, we will discuss the law of mass action in the context of a simple chemical
system. In later chapters, we will apply it to issues as diverse as enzyme–substrate
interactions, the spread of a disease, or the colonization of landscape patches.
Let us consider the case of oxygen O reacting with hydrogen molecules H to
form water H 2 O. The stock of each substance is given as a concentration, measured
in moles per cubic meter. For simplicity, we assume initial conditions of 200 moles
of hydrogen per cubic meter and 100 moles of oxygen atoms per cubic meter. Thus,
there is enough of each initial stock to just form 100 molecules of water. The
stochiometric equation for this reaction is
O þ 2H ! H 2 O
ð6:1Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_6,
© Springer International Publishing Switzerland 2014
65
Law of Mass Action
Let us now consider the character of the material Nature
whose necessary results have been made available. . . for a final
cause.
(Aristotle)
6.1 Law of Mass Action Model
The law of mass action is a powerful concept that describes the average behavior of
a system that consists of many interacting parts such as molecules that react with
each other, or viruses that are passed along from a population of infected individuals to nonimmune ones. The law of mass action has been derived first for chemical
systems but subsequently found high use in epidemiology and ecology. In this
chapter, we will discuss the law of mass action in the context of a simple chemical
system. In later chapters, we will apply it to issues as diverse as enzyme–substrate
interactions, the spread of a disease, or the colonization of landscape patches.
Let us consider the case of oxygen O reacting with hydrogen molecules H to
form water H 2 O. The stock of each substance is given as a concentration, measured
in moles per cubic meter. For simplicity, we assume initial conditions of 200 moles
of hydrogen per cubic meter and 100 moles of oxygen atoms per cubic meter. Thus,
there is enough of each initial stock to just form 100 molecules of water. The
stochiometric equation for this reaction is
O þ 2H ! H 2 O
ð6:1Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_6,
© Springer International Publishing Switzerland 2014
65