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_i, B_i, and C_i. Raoult’s 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 ; ... ; y_N) in the first bubble that 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 line for identification of the problem and a row that has entries for the given pressure and an estimate of the system temperature. Be sure to label these variables and show the units in which each is expressed. Adjacent columns should be headed Species, p^∗_i ; x_i ; p_i ; and y_i : Values of vapor pressures at the estimated temperature should be calculated using the physical property database in APEx, and Raoult’s law should be used to determine partial pressures. The final row in the table should have the sums of the vapor mole fractions and partial pressures. Place a convergence function f(T) = P - Σp_i below the table so that Goal Seek can be used to vary the estimated T until f(T) = 0. Test the spreadsheet by calculating the bubble-point temperature for a liquid mixture containing 22.6 mole% benzene, 22.6% ethylbenzene, 22.3% toluene, and the balance styrene at pressures of 250 mm Hg, 760 mm Hg, and 7500 mm Hg. Identify any concerns you may have about the calculated results. 

(c) It is determined that instead of styrene, the balance of the above mixture in Part (b) is propylbenzene. Upon entering the name “propylbenzene” in the APEx AntoineP estimator, you probably get the error message #VALUE!, which means that this substance is not in the APEx database. Poling et al. provide constants for the vapor pressure of propylbenzene corresponding to the following expression of the Antoine equation: 

where A = 4.07664, B = 1491.8, and C = 207..25; the correlation is valid over the range 324 K– 461 K. Modify the spreadsheet to incorporate this expression, and estimate the bubble-point temperature of the mixture at a pressure of 760 mm Hg.

Transcribed Image Text:

log1op (bar) = A - B/[T(°C)+ C],