Reference no: EM13929211

The simulation of this problem A liquid mixture contains N components (N may be any number from 2 to 10) at pressure P(mm Hg). The mole fraction of the ith component is xi (i = 1. 2...., N), and the vapor pressure of that component is given by the Antoine equation with constants A,, B,, and Ci. Raoults law may be applied to each component.

(a) Write the equations you would use to calculate the bubble-point temperature of the mixture, ending with an equation of the form f (T) = 0. (The value of T that satisfies this equation is the bubble-point temperature.)

Then write the equations for the component mole fractions (y1, y2,... , yN) in the first bubble chat forms, assuming that the temperature is now known.

(b) Prepare a spreadsheet to perform the calculations of part (a). The spreadsheet should include a title tine and two tables: the first table should contain the Antoine-equation constants and the total pressure, and the second should contain columns for the liquid-phase mole fractions, guessed values of the bubble-point temperature, any intermediate quantities generated in the bubble-point calculation (such as vapor pressures at the guessed temperatures), the function f(T), and the values of the vapor-phase mole fractions. Enter the values of Ai, Bi, Ci, P, and x, for each species in the mixture, assume a value of T. and enter formulas for the other variables in the spreadsheet including f. Then determine the bubble-point temperature by using the goal seek tool (or simple trial and error) to find the value of T for which f = 0.

Test your program by calculating the bubble-point temperatures and vapor compositions for liquids at 760 mm Hg containing (i) 22.6 mole% benzene, 44.3 mole% ethylbenzene, and the balance toluene;

(ii) 44.3 mole% benzene, 22.6% ethylbenzene, and the balance toluene: and

(iii) 22.6 mole% benzene, 22.6% ethylbenzene, and the balance toluene

Briefly explain why the variations in bubble-point temperature for these three cases make sense.

(c) Write a computer program to perform the calculations of part (b), and test it using the same three cases.

To calculate the bubble-point temperature, evaluate f for the first guessed value of T, and then vary T in increments of ± 5°C until the value of f changes sign from its initial value.

Use the two values of T for which the corresponding values of f bracket 0 as the starting point for a regula-falsi method calculation (Appendix A.2c), stopping when |f(T)| < 1.0="" x="">