Reaction Extrema: Extent of Reaction in General Chemistry

Abstract

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.

Reversible Reactions: Extent of Reaction and Theoretical Yield

“…We use in this work the concept of fractional yield ( f ) which is related to the concept of extent of reaction. − The fractional yield ( f ) is the fraction of reactant which has reacted after time t elapsed since the start of the reaction. f max is a special (maximum) value; i.e., it is the fraction of individual reactant(s) which has been converted to product(s) at the time when reaction is completed or when the equilibrium state has been reached.…”

Reaction Extent and Mass Conservation(s)

“…To that quantity -which is the amount of reaction performed [13], and that can be found by variations in particle's (or mols) number of any species involved -it was given the name reaction extent. The reaction extent is a reaction-counter, and since its definition its meaning was clear: "how many complete reactions have taken place" [15]. Since n k is a quantity that changes through time, as much as ξ, both can be differentiated and integrated, according to proper boundaries in time:…”

Reviewing Some Crucial Concepts of Gibbs Energy in Chemical Equilibrium Using a Computer-Assisted, Guided-Problem-Solving Approach

“…These limits are specific for this chemical reaction and these initial amounts of reactants and products. Other numerical examples can be found in the work by Peckham, Levine, and Vandezande et al…”

“…These limits are specific for this chemical reaction and these initial amounts of reactants and products. Other numerical examples can be found in the work by Peckham, 31 Levine, 32 and Vandezande et al 33 Task 2: The Thermodynamic Model Now it is necessary to make a critical decision that completely determines the solution (ξ eq ) of the problem. The real chemical system (a gas mixture) must be approximately represented by means of a thermodynamic model.…”