Gibbs Phase Rule for Chemically Reacting Systems and Independent Reactions

Gibbs Phase Rule for Chemically Reacting Systems and Independent Reactions 

Say we have a system in which the species undergo chemical reaction by rearranging their bonds to minimize the total Gibbs energy and obtain equilibrium. While we have identified the significant species at play and their phases, we do not know what the reaction mechanism is. In fact, there may be many simultaneous reactions that describe these molecular rearrangements. We may be concerned with questions about how to set up the chemical reaction equilibrium problem, such as What equations should I use to describe the reactions and How do I know if I have included enough reactions  

It turns out that as far as the thermodynamic calculations go, we do not need to pick the actual reactions that the real system undergoes we are free to choose any set of independent reactions we can think up. As we have seen many times, hypothetical paths can often be convenient for calculating thermodynamic properties. Since the chemical reaction equilibria calculation is based on a thermodynamic property—Gibbs energy— it should not surprise us that it does not depend on the specific reaction path used. 

A set of chemical reactions is termed independent if we are unable to write any reaction in the set as a linear combination of the other reactions. Equilibrium calculations or energy balances on reacting systems should only be performed on sets of independent reactions. Additionally, it does not matter what set of reactions we consider, as long as we consider the largest number of linearly independent chemical reactions possible for the species present. 

The number of independent chemical reactions we need to specify can be obtained by using the Gibbs phase rule for reacting systems. The phase rule for reacting systems is obtained by counting the total number of variables in the system and making sure we have the same number of independent equations. It is accomphshed in much the same way we accounted for variables for nonreacting systems in Example 6.17. 

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