Exercise No: 08 Date: 24/10/2016
VAPOR LIQUID EQUILIBRIUM CALCULATIONS (Antoine Equation)
AIM
To create a T- x-y phase diagram for mixtures of benzene and toluene, where T is temperature, x is the mole fraction of benzene in the liquid, and y is the mole fraction of benzene in the vapor. A horizontal line drawn for a given T gives the compositions of liquid and vapor in equilibrium at that T. Such diagrams are very ve ry useful for distillation calculations. PROBLEM STATEMENT
Given below are five equations relating seven variables: x , T, pa*, p b* , pa , p b, and y. 1090
Log1o ∗ = 6.841_
(1)
197.1+
Log1o ∗ = 7.136_
1457
231.8+
(2)
Pa = x ∗
(3)
P b= (1-x)∗
(4)
y =
+
(5)
Equation (1) and (2) are Antoine equations for benzene (a) and toluene (b), respectively.
These give the vapor pressure pi* in Torr (mm Hg) of the pure liquid i (= a or b) versus temperature T in0C. Here, xa is the mole fraction of benzene in the liquid, ya is its mole fraction in the vapor, and pi is the partial pressure of i( = a or b ). Equations 3 and 4 come from assuming an ideal liquid mixture, which is approximately true for benzene and toluene. Using these equations, you will create T- x- y graph for benzene-toluene mixtures at 1 atm. This graph will show the mole fraction ya of benzene in the vapor corresponding to equilibrium with liquid of mole fraction xa at temperature T required to give a total pressure of 760 Torr.
ALGORITHM STEP 1:
Create an Excel Spread sheet giving T and y versus x for P = 760 Torr.
STEP 2:
Enter the values for the Antoine constants from equations 1 and 2.
STEP 3:
In Column A enter values for x from 0 to 1 by increments of 0.1
STEP 4:
Leave Column B blank for values of T.
STEP 5:
In Column C calculate Pa* using the Antoine equation, the constants for benzene, and the temperature in column B.
STEP 6:
Create the equations in column C for benzene which is Pa* in C11 - type = 10^ ( $B $7-$C$7/($B11+$D$7), then drag this down to copy in to the other cells.
STEP 7:
In column D calculate p b* using the Antoine equation, the constants for toluene, and the temperature in column B.
STEP 8:
In column E calculate P = pa + p b using columns C&D and equations 3&4.
STEP 9:
In column F use Equation 5 to calculate values of y.
STEP 10:
Use goal seek to find the temperature required to give 1 atm with pure toluene (x=0). Click on E11 then data, What-If-Analysis, Goal seek. In the Goal seek window, set cell E11 to value 760 by changing cell B11, OK.
STEP 11:
Use Goal Seek row to row to calculate T required to give P = 760 Torr (1 atm). This will automatically fill in the correct values in all columns.
STEP 12:
Use the results in the spread sheet to create a graph, with x and y on the horizontal (X) axis and T on the vertical (Y) axis.
RESULT
Thus we have prepared a Microsoft excel spread sheet for the vapor liquid equilibrium as shown in the report.
