handout14 - 4.14 Chemical Equilibrium and Chemical...

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4.14 Chemical Equilibrium and Chemical Potential AIM: Apply our knowledge of chemical potential to chemical reactions. Consider the following balanced chemical reaction α A + β B + . . . γ M + δ N + . . . , (4.185) where the Greek letters are stochiometric coefficients and the capital letters are reactants and products. By convention, we can write this in an abbreviated form as a sum over the molecule species i : - α A - β B - . . . + γ M + δ N + . . . = 0 (4.186) i ν i X i = 0 , (4.187) where the ν i are now negative ( positive ) for reactants ( products ). QUESTION: What determines the direction of the reaction, and the extent of the reaction? ANSWER: The change in Gibbs energy! We know how to calculate it at constant T and P for mixing: d G = i μ i d n i , (4.188) but here now the d n i are no longer zero; in addition, they are coupled by the stochiometry of the reaction. NOTE: The μ i will also change as the molar fraction of species i changes with the progress of the reaction. 4–59
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PROBLEM: We need to keep track of the amount of each species in the system depending on how far the reaction has progressed from left to right in Eq. 4.185. SOLUTION: Introduce a parameter ξ [ 0 . . .
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