Final answer:
The student's question pertains to the calculation of excess Gibbs free energy, specifically in the context of a binary liquid mixture and how various expressions relating to Gibbs energy are combined to recover a given equation for the excess Gibbs free energy of the mixture.
Step-by-step explanation:
The question deals with the concept of Gibbs free energy which is a thermodynamic quantity used to predict the spontaneity of a process and understand the equilibrium of chemical reactions. Gibbs free energy, denoted by G, is a function of the enthalpy (H) and entropy (S) of a system and is defined by G = H - TS, where T represents the absolute temperature. The change in Gibbs free energy (ΔG) can be calculated for a reaction using the standard free energies of formation of reactants and products according to the equation ΔG° = ΣΔG°i (products) - ΣΔG°i (reactants).
To answer the student's specific question about the excess Gibbs free energy of a binary liquid mixture, the expression T = (−2.6 x1 − 1.8x2)x1x2 must be combined with the appropriate formulation of ΔG = ΔH - TΔS. The student is asking to show that, when the expressions for enthalpy and entropy are added in accordance with the Gibbs energy equation, the given equation for the excess Gibbs free energy of the mixture (Ge/RT) is recovered. This involves summing up the contributions of both components in the mixture by their mole fractions (x1 and x2) and enthalpy and entropy values.