Suppose the (1) + (2) system exhibits liquid-liquid immiscibility. Suppose we are at a state where G₁/RT = 0.1 and G₂/RT = 0.3. The Gibbs energy of mixing quantifies the Gibbs energy of the mixture relative to the Gibbs energies of the pure components. Suppose the excess Gibbs energy for the (1) + (2) mixture is given by:

(a) Combine this with the Gibbs energy for ideal mixing to calculate the Gibbs energy of mixing across the composition range and plot the results against x₁ to illustrate that the system exhibits immiscibility.

(b) Draw a tangent to the humps to illustrate that the system is one phase at compositions greater than z₁ = 0.854 and less than z₁ = 0.145, but will split into two phases with compositions at any intermediate overall composition. Most systems with liquid-liquid immiscibility must be modeled with a more complex formula for excess Gibbs energy. The humps on the diagram are usually off-center, as in Fig. 14.3. The simple model used for the calculations here results in the symmetrical diagram.

(c) When a mixture splits into two phases, the over-all fractions (of total moles) of the two phases are found by the lever rule along the composition coordinate. Suppose 0.6 mol of (1) and 0.4 mol of (2) are mixed. Use the lever rule to calculate the total number of moles which would be found in each phase of the actual system. Designate the (1)-rich phase as the βphase.

(d) What is the value of the hypothetical Gibbs energy, (expressed as G / RT), of a mixture of 0.6 mol of (1) and 0.4 mol of (2) if the mixture were to remain as one phase? Calculate the Gibbs energy of the total system considering the phase split into two phases, and show that the Gibbs energy is less than the Gibbs energy of the single-phase system.

Transcribed Image Text:

GE/RT=2.5 X₁ X2