Nearly 100 years ago de Donder introduced
the term “extent
of reaction”, ξ. We build on that work by defining the
concept of reagent extrema for an arbitrary chemical reaction, aA + bB ⇄ yY + zZ. The central equation is ξ̂i =
−n
i,0/ν
i
. The symbol ξ̂
i
represents the reagent extremum for the chemical entity i; n
i,0 represents
the initial molar amount of entity i, and ν
i
is its stoichiometric number, which is positive
for products and negative for reactants. A reagent extremum exists
for each reactant and each product; those of reactants are zero or
positive, and the least positive of these is the reaction extremum
to the right, ξmax; those of products are zero or
negative, and the least negative is the reaction extremum to the left,
ξmin. These two boundary values, called reaction
extrema, indicate the maximum extent to which the reaction can progress
in the forward or reverse direction, respectively. The ξmax and ξmin values are an important pedagogical
tool for a quantitative understanding of chemical reaction stoichiometry.
A graphical presentation in which the amounts of reagents are depicted
versus extent of reaction is useful for helping general chemistry
students understand intuitively the extent to which chemical reactions
can progress. The Supporting Information includes a student handout, a student exercise, and a Web-enhanced
object, Reaction Progress, which can be used to help
students understand the concept of extent of reaction and reaction
extrema.