The enthalpy of mixing of a regular binary solution is given by   1 2 1 2 2 1 2 ( ) mix n n h rt n n n n              the entropy of mixing of real solution is the same as the entropy of mixing of ideal solution 1 2 1 2 1 2 1 2 ln ln mix n n s r n n n n n n                         where i i n n  and  is a constant. a. derive the expression for the relationship between chemical potential of a component in a regular binary solution as a function of mole fraction of the component in the solution, i. e. find , , ( ) i mix i pure    function b. derive the relationship between the fugacity of a component in a regular solution and the mole fraction. c. show that the relationship derived in part a obeys the gibbs duhem equation at constant p and t. d. apply the stability criteria to show that the mixture is a stable two-phase mixture for all   0 e. consider a situation at a concentration of 1 2 x x   0.5 . what is the minimum