Determining the Spontaneity of Reactions

In our preliminary examples, we have assumed rather idealized cases where none of the products are present in the inlet. However, in some cases, products may be present and then the reaction direction may not be as we anticipate. We can look at the reaction thermodynamics in a slightly different way to determine the direction of the reaction under given compositions, T and P. Starting from Eqn. 17.10, we may add by weighting with the stoichiometric numbers, resulting in

The term  on the left side is called the Gibbs energy of reaction and is given the symbol ΔG_T. Note that this is a different term than the standard state Gibbs energy of reaction (the second term) that uses the superscript °. Thus, we can write,

A reaction with  is called exergonic and results in K_a > 1, and a reaction with  is called endergonic, resulting in K_a < 1. This provides an indication of whether the equilibrium favors products or reactants, but does not mean that reactions with small values of K_a cannot be conducted industrially. For example, Example 17.1 involved a small K_a (thus endergonic with ), yet the conversion of H₂ was 42%. The propensity for the reaction to go forward or backward depends instead on the Gibbs energy of reaction ΔG_T at the concentrations represented by the fugacity ratios. If the conditions provide ΔG_T < 0, then the Gibbs energy is lowered when the reaction proceeds in the forward direction. If we evaluate conditions and ΔG_T > 0, then the reaction goes in the reverse direction than what we have written. In either case, the concentrations adjust until the system reaches the equilibrium condition, ΔG_T = 0, and then Eqn. 17.12 applies. In summary, the direction a reaction proceeds is determined by ΔG_T, not by . Note when evaluating the fugacity term for determining spontaneity that the actual conditions are used, not the equilibrium conditions. At the feed conditions of Example 17.1, y_CH3OH = 0, which ensures ΔG_T < 0 at the feed conditions even though .