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Unformatted text preview: 6.2. EQUILIBRIUM CONDITIONS 211 6.2 Equilibrium conditions For multicomponent mixtures undergoing multiple reactions, determining the equilibrium condition is more difficult. There are two primary approaches, both of which are essentially equivalent. The most straightforward method requires formal minimization of the Gibbs free energy of the mixture. It can be shown that this actually finds the equilibrium associated with all possible reactions . 6.2.1 Minimization of G via Lagrange multipliers Recall Eq. (4.395), dG | T,P 0. Recall also Eq. (4.397), G = N i =1 g i n i . Since i = g i = G n i vextendsingle vextendsingle vextendsingle P,T,n j , one also has G = N i =1 i n i . From Eq. (4.398), dG | T,P = N i =1 i dn i . Now one must also demand for a system coming to equilibrium that the element numbers are conserved. This can be achieved by requiring N summationdisplay i =1 li ( n io n i ) = 0 , l = 1 ,...,L. (6.51) Here recall n io is the initial number of moles of species...
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- Fall '11