Consider a binary liquid mixture for which the excess Gibbs energy is given by GEIRT = Ax1x2 (x1 + 2x2). What is the minimum value of A for which liquid/liquid equilibrium is possible?

Prompt/Given Information: Consider a reversible isothermal expansion of vapor benzene at 450 K from 1 to 0.1 MPa. Assume that the PVT behavior of benzene obeys van der Waals equation of state.                                      P = (RT)/(V - b) - a/V2            for benzene: a = 1884514 (cm6 * MPa)/mol2 and                                  b = 119.47 cm3/mol For your convenience, at 450 K and 0.1 MPa the volume of vapor benzene is 37025 cm3/mol, and at 450 K and 1 MPa it is 3312.4 cm3/mol. R = 8.314 (MPa*cm3)/(mol*K). Note: 1 cm3*MPa/mol = 1 J/mol   Question: What is the change of internal energy? What would be the change of internal energy if the gas was ideal?

Question: A vapor/liquid experiment for the carbon disulfide(1) + chloroform(2) system has provided the following data at 298 K: P1sat = 46.85 kPa, P2sat = 27.3 kPa, x1 = 0.2, y1 = 0.363, and P = 34.98 kPa. Estimate the dew pressure at 298 K and y1 = 0.6, using the Van Laar equation. Request: Can you please help me with creating an algorithm to solve this problem. This is related to Thermodynamics by the way. Thank you!

PLEASE ANSWER AS SOON AS POSSIBLE. I NEED THE ANSWER IN 1 HOUR.

please don't use graph to solve

This problem is (12.24) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

Prompt/Given Information: Consider a reversible isothermal expansion of vapor benzene at 450 K from 1 to 0.1 MPa. Assume that the PVT behavior of benzene obeys van der Waals equation of state.                                      P = (RT)/(V - b) - a/V2            for benzene: a = 1884514 (cm6 * MPa)/mol2 and                                  b = 119.47 cm3/mol For your convenience, at 450 K and 1 MPa the volume of vapor benzene is 3312.4 cm3/mol, and at 450 K and 0.1 MPa it is 37025 cm3/mol. R = 8.314 (MPa*cm3)/(mol*K). Note: 1 cm3*MPa/mol = 1 J/mol   Question: Calculate the work done to the system? Calculate the work for the system if the gas was ideal?