Solution Thermodynamics: Applications Chapter 12-Part III

Other models for GE/RT

Obtain activity coefficients from the one-parameter Margules equation

problem For methanol(1)/methyl acetate(2), the 1-parameter Margules equation gives a reasonable prediction of the activity coefficients, with A = 2.771 -0.00523 T. Vapor pressures as functions of T are known. T are in Kelvin. a) Calculate P and {yi} for T = 318.15K and x1 =0.25

Calculate P and {yi} given T = 318.15K and x1 =0.25 VLE, BUBL P calculation For i =1, 2 Calculate g1 and g2 at T and x1 =0.25 using Margules 1-parameter A(T) = 1.107 g1 = 1.864 g2 = 1.072 and calculate P = 73.5 kPa and y1 = 0.282

Calculate P and {xi} given T = 318.15K and y1 =0.60 VLE, DEW P calculation P1sat, P2sat, and A are the same as in the first part But, we don’t know xi, and g1, g2 are functions of x1, x2 For good initial guesses, solve the problem with Raoult’s law 1) Solution: P = 62.89 kPa x1 = 0.817 g1 = 1.038 g2 = 2.094 Evaluate g1, g2, and return to 1) until P converges

Calculate T and {yi} given P = 101.33 kPa and x1 =0.85 VLE, BUBL T calculation To obtain an initial T, get the saturation temperatures of both components (from Antoine) T1sat = 337.71; T2sat = 330.08 K Use a mole-fraction weighted average of these values to get T For that T calculate A, g1, g2 and a =P1sat/P2sat (1) Then calculate Get T from Antoine and return to (1) Once T converges, calculate y1

Calculate T and {xi} given P = 101.33 kPa and y1 =0.40 VLE, DEW T calculation Same P as in BUBLT calculation, saturation temperatures are the same, get weighted mole fraction average for initial T = 333.13 K Since we don’t know {xi} use Raoult’s law to initialize {gi} (1) At the initial T, evaluate A, P1sat, P2sat, a Calculate x1 = y1P/g1 P1sat Calculate g1, g2 New value of T from Antoine and return to (1) Once T converges, calculate x1

Find the azeotropic pressure and the azeotropic composition for T = 318.15 K Define the relative volatility How much is a12 at the azeotrope? Get a12 from the VLE equations

From the one-parameter Margules equation Calculate these values from the data at T = 318.15K This means that a12 is =1 at some point between x1 = 0 and x1 = 1

Double azeotrope

At the azeotrope, a12 = 1

The Van-Laar equation