Vapor Liquid Equilibrium
At low to moderate P
yi P = xig i Pi
sat
 Raoult’s Law for Adults (RLA)
 Solve for 4 cases
 Bubble Pressure (know T and xi)
 Dew Pressure (know T and yi)
 Bubble Temp. (know P and xi)
 Dew Temp. (know P and yi)
All Algorithms
 List out equations (unknowns=eqs)
 List out what you know and what you
don’t know
 Keep track of what you know, what
you don’t know, and WHAT YOU
HAVE A VALUE FOR
 Iterate until you converge
Bubble P Algorithm
 Assume binary initially
 What are my equations, what do
I know, and what do I don’t
know?
Bubble P Algorithm
yi P = xig i Pi
 For each component:
 No matter what:
åx
i
=1
sat
åy =1
i
 What do I know?
T, xi ,g i (T, xi ), Pi (T )
 Activity model for activity coefficient
 Antoine’s Eq for saturation pressure
sat
 What do I not know? (P, yi)
Bubble P algorithm
 3 equations, 3 unknowns
yi P = xig i Pi
sat
åy =1
i
xig i Pi sat
yi =
P
xig i Pi sat
sat
y
=
1
=
Þ
P
=
x
g
P
åi
å P
åiii
xig i Pi sat
yi =
P
Dew P Algorithm
 Assume binary initially
 What are my equations, what do
I know, and what do I don’t
know?
Dew P Algorithm
yi P = xig i Pi
 For each component:
 No matter what:
åx
i
=1
åy =1
i
 What do I know?

sat
T , yi , Pi (T )
 What do I not know?
sat
xi ,g i (T , xi ), P
Dew P algorithm
 3 equations, 3 unknowns, BUT
can’t solve analytically
 Must be iterative
yi P = xig i Pi
sat
xi = ?
é A 2ù
å xi = 1 y1P = x P exp êë RT x2 úû
sat
1 1
 Let’s GUESS for activity
coefficient
Dew P algorithm
 Set it to 1.0
 Represents an ideal solution
 Look at list, what do I know, what
do I not know, and what do I
have values for?
yi P = xig i Pi
sat
åx
i
=1
yi P
xi =
g i Pi sat
Dew P algorithm
 Similar to Bubble P
yP
1
y
åx = 1 = åg P Þ P = åg P
i
i
i
sat
i i
sat
ÞP=
i i
1
yi
å g P sat
i i
¹å
g i Pi sat
yi
 3 ?’s (know/unknown/have?)
yi P
xi =
g i Pi sat
g i (T , xi )
Does xi
Change?
1
yi
=å
P
g i Pi sat
é A 2ù
g 1 (T , xi ) = exp ê
x2 ú
ë RT û
Bubble T Algorithm
 Assume binary initially
 What are my equations
 My 3 Variable equations
Bubble T Algorithm
yi P = xig i Pi
 For each component:
 No matter what:
åx
i
=1
sat
åy =1
i
 What do I know?

xi , P
 What do I not know?
T, yi ,g i (T, xi ),Pi sat (T )
Bubble T algorithm
 3 equations, 3 unknowns, BUT
can’t solve analytically
 Must be iterative
 Same Reasoning as for Dew P
 Re-ask my 3 ?’s
 Let’s GUESS for T
 Antoine’s Eq
Bi
=
- Ci
Ai - ln P
Ti
sat
T
guess
= å xiTi
sat
Bubble T Algorithm
 Ask my 3 ?’s again
 Get Psat and Activity Coefficients
 Use algebra after REASKING 3?’s
xig i Pi
yi P = xig i Pi
å yi = 1 yi = P
xig i Pi sat
å yi = 1 = å P
sat
sat
 SHOULD be 1, but is it?
 Use as a weighting factor
Bubble T Algorithm
 Weighting Factor
 Adjust a variable? (unknown, but have
value for)
 Want it to get to get an updated thing of
the FIRST thing I guessed (??)
sat
1
1* P
P1satnew
=
P
sat
x
g
P
åiii
* P1sat
P * P1satold
B1
new
=
T =
- C1
satold
satnew
A1 - ln P1
å xig i Pi
Bubble T algorithm
 I have T, what is NEXT thing I got a
value for?
 Get Psat and Activity Coefficient
 What I am still missing though?
xig i Pi
yi =
P
sat
 What is the last thing to be “guessed”
 Temperature
Bubble T algorithm
 Similar to Dew P
satnew
1
P
P * P1satold
=
satold
x
g
P
åiii
T new =
Does T
Change?
Pi sat , g i
xig i Pi sat
yi =
P
B1
- C1
satnew
A1 - ln P1
Dew T Algorithm
 Assume binary initially
 What are my equations
 My 3 Variable equations
Dew T Algorithm
yi P = xig i Pi
 For each component:
 No matter what:
åx
i
=1
sat
åy =1
i
 What do I know?

yi , P
 What do I not know?
T, xi ,g i (T, xi ), Pi sat (T )
Bubble T algorithm
 3 equations, 3 unknowns, BUT
can’t solve analytically
 Re-ask my 3 ?’s
 Let’s GUESS for T
 Antoine’s Eq
Bi
=
- Ci
Ai - ln P
Ti
sat
T
guess
= å yiTi
sat
Dew T Algorithm
 Ask my 3 ?’s again
 Get Psat
 Set Activity Coefficients = 1.0
 Ideal Solutions
 Similar reasoning as Bubble T
åy =1
yP
åx = 1 = åg P
yi P = xig i Pi
sat
i
i
i
yi P
xi =
sat
g i Pi
sat
i i
 Use as a weighting factor
Dew T Algorithm
 Weighting Factor
yi P
yi
sat
satnew
satold
1* P = å
* P1 P1
= P1 På
sat
satold
g i Pi
g i Pi
B1
new
T =
- C1
satnew
A1 - ln P1
sat
1
 Now have T, what can I update
 Psat, still need xi for gamma
yi P
xi =
g i Pi sat
Dew T algorithm
 I have values for all, what did I
guess FIRST
 Activity Coefficient
 Start the cycle (but dual as activity
coefficient is function of T and xi)
Dew T algorithm
 Similar to Dew P
Get new T via
weighting factor
and Antoine’s
Get Psat
and xi
g i (T , xi )
Does T
Change?
Does xi
Change?
Summary
 Decide what you know, what you
don’t know, and what you have
values for
 In terms of updating, update what you
have values for in order
 Equations
 RLA
 Summation of mole fraction = 1.0