Minimization of the free enthalpy

Consider a batch reactor containing nj mol of constituent Cj (j = 1, 2. .. J). The constituent Cj contains ajj atoms of the element Ej (1 = 1,2. .. L). The reaction system contains bj moles of element Ej at the initial time. LAVOISIER S law indicates that these elements are conserved during the reaction  

The free enthalpy of the mixture of gases can be expressed as follows  

The problem here is a non-linear optimization one with constraints  

Taking equations (58) into account, the second term of L is equal to zero. The minimum 

The J + L equations with J variables nj and with L variables are solved by numerical methods. 

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Three main methods allow an equilibrium to be calculated the direct application of the law of mass action, the minimization of the free enthalpy of the system and the simulation of a kinetic model. This last approach has the advantage of providing the time necessary to reach equilibrium. 

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