Reaction Extrema: Extent of Reaction in General Chemistry

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 = −ni,0/νi. The symbol ξ̂i represents the reagent extremum for the chemical entity i; ni,0 represents the initial molar amount of entity i, and νi 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.