Correct Use of Helmholtz and Gibbs Function Differences, δa and δg: The vant Hoff Reaction Box

Abstract

Helmholtz and Gibbs function (or energy) differences, δA and δG, are often invoked by their signs to describe conditions of spontaneity, nonspontaneity, and equilibrium in chemical reactions. While their differences are necessary conditions to establish these behaviors, they are insufficient because they do not apply to local situations where differential values, dA and dG, are appropriate. We here show that the differences are fully meaningful quantities, being important in examining overall reaction, such as in chemical synthesis, where dA and dG may be irrelevant. Interpretation of the differences is readily understood in terms of the vant Hoff reaction box in which reactants are converted to products, without reference to kinetics or mechanisms, and products are extracted as independent materials, each under their own specified conditions. This behavior can be attained in practical situations where a product can be extracted in a phase separate from the reactants, such as a single gas, an immiscible liquid, a precipitate, a new pure solid phase, or even in an electrochemical or fuel cell. This is illustrated in the case of the Haber-Bosch industrial process for the production of ammonia.