3.31 This problem involves computing the liquid-vapor Pxy diagram from the two parameter Margulies model. In this model, the activity coefficients are given by ln1=1x22+1x23 and ln2=2x12+2x13 The parameters and are already in dimensionless form in units of RT and are restricted to have the values i=A+3(1)i+1B and i=4(1)iB For this problem, we will use A=1 and B=0.3. This is sufficiently non-ideal to exhibit an azeotrope but not so bad that you will also get liquid-liquid phase separation. Recall from thermodynamics that the equilibrium is given by x11P1sat=y1P and x22P2sat=y2P where we have assumed an ideal vapor phase. For this problem, let's assume the saturation pressures are P1sat=1100mmHg and P2sat=800mmHg. The ultimate goal is to plot the Pxy diagram, but we are going to lead you through the problem in steps to make it easier. (b) Write a MATLAB program that implements Newton-Raphson to compute the equilibrium compositions. It is easiest to do this with four unknowns x=12x1y1 to avoid having to take very complicated derivatives. What is the residual vector and Jacobian needed for Newton-Raphson? Show that your answer from part (a) gives a very small value of R and compute the condition number of the Jacobian with the answer from part (a) using MATLAB's function cond. What does this mean for implementing Newton-Raphson? You do not need to execute the while loop here if you can answer the previous question without an "experiment" - you can make it not execute by giving it a very loose tolerance value. (c) Now write a MATLAB program that uses the results so far to make the Pxy diagram. You already have a big hint; the azeotrope is a turning point so you will need to make the diagram in two pieces, one before the turning point and one after. Your program should produce the Pxy diagram