Furnish a proof that the concentration of true species i is maximum at composition xA* = ai/ (ai + bi), xB* = bi/(ai + bi) where ai and bi are given in Eqn. 15.1. [Hint: The Gibbs-Duhem equation is useful for relating derivatives of activity.] Show that the result for Z ^assoc is obtained by taking the appropriate derivative of A^assoc. Use the ESD equation to model the monomer, dimer, and trimer in the vapor and liquid phases of saturated water at 373 K, 473 K, and 573 K. How does the monomer fraction of saturated vapor change with respect to temperature? How does monomer fractions of saturated liquid change?

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