= 11.31. The excess Gibbs energy of a particular ternary liquid mixture is represented by the empirical expression, with parameters A12, A13, and A23 functions of T and P only: GE/RT = A12X] x2 + A13X1X3 + A23x2x3 = (a) Determine the implied expressions for In Yi, In 72, and in y3. (6) Verify that your results for part (a) satisfy the summability relation, Eq. (11.99). (c) For species 1 determine expressions (or values) for In Yi for the limiting cases: x = 0, x1 = 1, X2 = 0, and x3 = 0. What do these limiting cases represent