Computer calculations for binary electrolyte vapor-liquid equilibrium
by Gary Dale Nelson
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Chemical Engineering
Montana State University
© Copyright by Gary Dale Nelson (1969)
Abstract:
An investigation has been made into vapor-liquid equilibrium for binary monovalent electrolyte
systems. These electrolyte systems were treated as systems which deviate from nonelectrolyte behavior
due to their dissociation in the liquid phase. Corrections to this nonelectrolyte behavior were made in
fitting programs written to predict phase equilibrium for nonelectrolytes .
Improvements were made in the fitting programs for hydrochloric acid by considering the mole
fraction of undissociated electrolyte molecules in the liquid phase as the liquid phase solute
concentration. This undissociated molecule concentration was obtained from a concentration dependent
dissociation curve.
Slightly dissociating electrolytes such as ammonia seem to differ much less from nonelectrolyte
behavior than do highly dissociating electrolytes such as hydrochloric and hydrobromic acid. COMPUTER CALCULATIONS FOR BINARY
ELECTROLYTE VAPOR-LIQUID EQUILIBRIUM
by
GARY DALE NELSON
A t h e s i s s u b m i t t e d t o t he Gr a d u a t e
f u l f i l l m e n t o f the r e q u i r e me n t s
Faculty in p a r t i a l
f o r t he de g r e e
of
MASTER OF SCIENCE
in
Chemi cal
Engineering
MONTANA STATE UNIVERSITY
Bozeman, Mont ana
March 1969
[THESES
ill
ACKNOWLEDGMENT
T.he a u t h o r w i s h e s
to
who a s s i s t e d
hi m t o w a r d
particularly
wi shes
Sc h a e r f o r
his
and t he s t a f f
Center f o r
to
their
to
A c t Commi t t ee and t h e
University
investigation
and a s s i s t a n c e
cooperation
for
of
was b e i n g
Engineering
financial
carried
out.
Dr .
He
Mi c ha el
this
wo r k ,
Comput i ng
the pr ogr ess
t hank the N a t i o n a l
their
research.
throughout
University
during
Chemi cal
hi s
t he f o l l o w i n g :
t h e Mont ana S t a t e
He a I so w i s h e s
State
the c ompl et i o n
recognize
guidance
at
r e c o g n i z e and t hank, s e v e r a l .peo.pl e
of
this
wo r k .
Def ense E d u c a t i o n
staff
a t Mont ana
support while
this
i v
TABLE OF CONTENTS
Chapter
Page
VI TA
...................................... ....
'
.........................................................
Ti i
LI ST OF TABLES
............................................... ' .
- v
LI ST OF FIGURES
. . . . : ' .............................' .
................................. ....
INTRODUCTION
.
.
.
.
. . .
. ■
.................... ' .. .
.
III
■
STATEMENT OF THE PROBLEM
PROCEDURE
.
.
•V
.
.
.
I
.
’.
2
8
.........................................................................
22
Phase Mo l e c u l e s . . .'
................................................
. .
i
.............
S U M M A R Y .............................
Ap p e n d i x . A:
vi i
20
‘ RESULTS " ..........................................
APPENDIX '
•
................................
Undissociated Liquid
Excess Gi bbs. Ener gy
IV
yi
.
N o n e l e c t r o l y t e V a p o r - L i q u i d Equ i l i b r i u m
C h a r a c t e r i s t i c s of E l e c t r o l y t e Solutions
II
ii
ACKNOWLEDGMENT
.ABSTRACT
I
.
.' .
Derivations
t o Pr ogr ams
A p p e n d i x C: Dat a V .
LITERATURE CITED
29
43
......................... ' .
Appendix B: L i s t i n g
24
25
of
.
of
.
.
.
.
.
. .
45
Corrections
46
Program' s
.
.
. .
. . . . . .
.
.
. . . .
54
.
.............................■
61
68
V
LI ST OF TABLES
Table
I
C- I
C-II
Page
L i q u i d C o m p o s i t i o n s f o r HCl -HpO a t
I 9 . 95° C i n U n s y mm e t r i c C o n v e n t i o n
Binary
Vapor-Liquid
Physical
Properties
Equilibrium
of
. . . .
Dat a
Component s
.
.
. . . .
41
.
61
65
VI
LI ST OF FIGURES
Figure
1
Page
Vapor C o m p o s i t i o n s o f H CI - H9O Syst em a t
I 9 . 9 5 ° C u s i n g HVYFTW Pr ogr am f o r
Nonelectrolytes
.........................................................
3
D i s s o c i a t i o n C o n s t a n t o f HCl as a
F u n c t i o n o f T e mp e r a t u r e
......................................
11.
3
Ionization
........................
12
4
E x p e r i m e n t a l E q u i l i b r i u m Mol e F r a c t i o n s f o r
HCl -HgO Syst em a t I 9 . 95° C
.................................
14
Dependence o f HCl Vapor P r e s s u r e on
Concentration
..............................................................
16
Vapor C o m p o s i t i o n s
Two A t mo s p h e r e s
f o r NHg-H9O a t
.........................................................
30
Vapor C o m p o s i t i o n s f o r HF- H9O a t
One A t m o s p h e r e ..............................................................
31
2
5
6
7
of
Hydrochloric
Aci d
8.
Vapor
Composi t i ons f o r
HBr-HgO a t 5 4 . 5 ° C
9
Vapor
Composi t i ons f o r
HCl -HgO a t 19 . 95°C
10
Vapor
Composi t i ons f o r
HCl -HgO a t 7 5 0 C
11
Vapor
Composi t i ons f o r
HCl -HgO a t 5 5 . 2°C
12
.
.
33
.
34
.
.
37
.
.
38
Vapor C o m p o s i t i o n s f o r
HCl -HgO a t 1 . 0
A t m o s p h e r e ....................................................................... ..
39
vi i
ABSTRACT
An i n v e s t i g a t i o n has been made i nt o, v a p o r - 1 i qui d
e q u i l i b r i u m f o r b i n a r y mo n o v a l e n t e l e c t r o l y t e s y s t e ms .
These e l e c t r o l y t e syst ems wer e t r e a t e d as syst ems
wh i c h d e v i a t e f r o m n o n e l e c t r o l y t e b e h a v i o r due t o
t h e i r d i s s o c i a t i o n i n t h e l i q u i d phase.
Corrections
t o t h i s n o n e l e c t r o l y t e b e h a v i o r wer e made i n f i t t i n g
pr ogr ams w r i t t e n t o p r e d i c t phase e q u i l i b r i u m f o r
nonelectrolytes.
I mp r o v e me n t s wer e made i n t h e f i t t i n g pr ogr ams
f o r h y d r o c h l o r i c a c i d by c o n s i d e r i n g t he mol e f r a c t i o n
o f u n d i s s o c i a t e d e l e c t r o l y t e mo l e c ul es i n the l i q u i d
phase as t h e l i q u i d phase s o l u t e c o n c e n t r a t i o n . T h i s
u n d i s s o c i a t e d m o l e c u l e c o n c e n t r a t i o n was o b t a i n e d f r om
a c o n c e n t r a t i o n dependent d i s s o c i a t i o n cur v e.
S l i g h t l y d i s s o c i a t i n g e l e c t r o l y t e s such as
ammoni a seem t o d i f f e r much l e s s f r o m n o n e l e c t r o l y t e
b e h a v i o r t h a n do h i g h l y d i s s o c i a t i n g e l e c t r o l y t e s
such as h y d r o c h l o r i c and h y d r o b r o m i c a c i d .
I
I .
When d e s i g n i n g
tion,
it
is
for
experimental
able
for
to
data f o r
be d e s i r a b l e
binary
and h i g h e r
involved
in
physical
properties
First,
h o we v e r ,
binary
data
J.
only
using
fit
at
of
for
but
equilibrium
data,
dynami c f u n c t i o n s ,
calculate
have t o
certain
Thus
only
this
at
increased
it
woul d
at
wor k
for
component
s y s t e ms .
data.
the U n i v e r s i t y
of
such a met hod t o
no t
data w i t h
l ow or mo d e r a t e p r e s ­
in
for
t he f o r m o f
a series,
Mul t i component
component p r o p e r t i e s ,
correlations
avail­
to p r e d i c t
from b i n a r y
p r e d i c t mult icomponent
nonelectrolytes
Usi ng
the
be d e v i s e d
obtained
i n Comput er C a l c u l a t i o n s
Equilibria.
wo r k .
is
da t a f r o m b i n a r y
have d e v i s e d
They have p u b l i s h e d
pr ogr ams
Liquid
data
due t o
requiring
and c o - w o r k e r s
Berkeley,
binary
good a c c u r a c y
sures.
par amet er s
some
a met hod o f c a l c u l a t i n g m u l t i -
equilibrium
wou l d
is
b u t much l e s s
t he e x p e r i m e n t a l
a model
Ther e
syst ems
and e q u i l i b r i u m
M. P r a u s n i t z
California
order
distilla­
da t a on v a p o r - l i q u i d
involved.
syst ems,
t o have a v a i l a b l e
component v a p o r - l i q u i d
e q u i p me n t i n v o l v i n g
have a v a i l a b l e
t h e component s
ternary
difficulty
separation
necessary
equilibrium
INTRODUCTION
calculating
Va p o r -
binary
some t h e r m o ­
and t he r mody nami c , r e l a t i o n s , t h e pr ogr ams
p a r a m e t e r s wh i c h
ar e u s e f u l
for
predicting
I
-2multicomponent
good f i t
to
equilibrium
values.
nonelectrolyte
syst ems
results
for
the f i t
obtained
acid-water
calculate
certain
gr aph
all
s y s t e m.
Thus
vapor-liquid
represents
valid
report
hydrochloric
must be made.
concepts
is
its
of
fugacity
equilibrium.
using
either
the
each component
in
the
vapor
systems,
P r a u s n i t z 1 mono­
a c o mp u t e r
to modi f y those
program,
pr ogr ams t o
The f u g a c i t i e s
experimental
of
ideality
is
t h e mol e f r a c t i o n s
in
the
is
equal ; t o
liquid
t h e component s
ar e
is
be made-.
using
involved.
in
a n d , 2)
equal
at
calculated-
whi ch
ar e used t o do t he
need t o
reduced t o
o f t h e c omponent s
1.0,
phase
da t a o r c o r r e l a t i o n s
of
fugacities
the-- c o mp u t e r pr ogr ams w r i t t e n
phase when t he s y s t em i s
no a s s u m p t i o n s
syst em o r
into
vapor., phases
S i n c e c o mp u t e r s
the
Wh i l e
sum o f
good r e s u l t s .
of
electrolyte
to
Equilibrium
used i n
t h a t , I)
b o t h t h e ' .Li q u i d and t h e
to
pr ogr ams
and base e l e c t r o l y t e s , p a r t i c u l a r l y
Vapor-Liquid
- The b a s i c
the f u g a c i t y
f or ' a h y d r o c h l o r i c
t o summar i ze t h e r mo d y n a mi c .
an a t t e m p t
acid
poor
An exampl e o f
use t h e s e
for
nonelectrolytes
for
I,
give
acid.
Mbnelectrolytg
by P r a u s n i t z
Figure
equilibrium
represents
make t hem v a l i d
s y s t e m s.
in order to
an a t t e m p t
for
t e s t e d , they give
electrolyte
can be seen i n
modifications
functions
this
al most
Wh i l e t h e s e pr ogr ams
give
calculations
The c a l c u l a t i o n
properties
of - the '
Calculated
Mo I e
Fraction
-3-
Experimental
Figure
I.
Mol e
Fraction
Vapor C o m p o s i t i o n s
19 . 95°C u s i n g
o f HCl -HgO Syst em a t
HVYFTW Pr ogr am f o r
Nonelectrolytes.
-4The v a p o r phase f u g a c i t y
its
mol e f r a c t i o n
f i V = y n-
by t h e
o f a component
is
related
to
following:
P
wher e
f ^
= v a p o r phase f u g a c i t y
y .
= v a p o r phase mol e f r a c t i o n
(j) •
= fugacity
P
of
component
i.
coefficient
= sy s t em p r e s s u r e .
The f u g a c i t y
is
actually
by t he f u g a c i t y
and f u g a c i t y
by B e a t t i e
coefficient
= partial
(16)
as a f u n c t i o n
just
gives
of
The l i q u i d
the
(in
an i d e a l
pressure).
a relation
an e q u a t i o n
of
phase f u g a c i t y
phase mol e f r a c t i o n
partial
according
pressure
s y s t e m,
corrected
<|>. = 1. 0
A t h e r mo d y n a mi c
for
t he f u g a c i t y
state
is
of
t he
a function
derivation
coefficient
v a p o r phase.
of
to the f o l l o w i n g
the
liquid
relation:
oL
T Yi
fi
wher e
f ^
I
x.
= liquid
phase f u g a c i t y
= liquid
phase mol e f r a c t i o n
= activity
f o oL= r e f e r e n c e
Ther e ar e t h u s
variable
state
the
Met hods wer e needed t o
and r e f e r e n c e
state
component
i
coefficient
fugacity.
t wo t h e r mo d y n a mi c
upon wh i c h
of
liquid
and one syst em
phase f u g a c i t y
calculate
fugacity
functions
the a c t i v i t y
using
only
is
dependent.
coefficient
syst em p r o p e r t i e s .
-5- .
The a c t i v i t y
coefficient
t h e r mo d y n a mi c
relation
of
The a c t i v i t y
a system.
must a l s o
satisfy
the
can be c a l c u l a t e d
involving
the
ity
Gi bbs
coefficient
a
free-energy
and mole, f r a c t i o n s
Gi bbs- Duhem e x p r e s s i o n ,
energy f u n c t i o n
is
excess Gi bbs
coefficients
M
E x . d I n Y- = 0 ( c o n s t a n t
i =I
1
1
The excess
using
t e m p e r a t u r e and p r e s s u r e )
used t o c a l c u l a t e
the a c t i v ­
the f o l l o w i n g
RT I n Y
d n T T , P ’.nj ^ j > i ^
wher e
= number o f mol es
nT
total
nT
excess
R
gas c o n s t a n t
Gi bbs
T
= temperature
P
= pressure.
including
Prausnitz
chose t o
Wi l son e q u a t i o n ,
to
these
two
t he, van La ar and Ma r g u l e s mo d e l s .
use a more r e c e n t l y
wh i c h
gave b e t t e r
d e v e l o p e d mo d e l ,
accuracy than
t he
any o f t he
ones.
The W i l s o n model
me t e r s
energy
have been p r o p o s e d as s o l u t i o n s
relations
previous
i
number o f mol es
gE
Many model s
of
bet ween s o l u t e
is
characterized
and s o l v e n t .
by i n t e r a c t i o n
para-
■
They ar e used as s o l u t i o n s
-6to
the
excess
E
Gi bbs
e n e r g y wh i c h
N
N
RT = % * i
The Wi l s o n
E
T" Yi
equation
N
is
defined
as
n.
= %
^
lny i
is
N
RT = 5 * i
i
ln
[ , ^ Ai j
J =I
xj ]
wher e
A1- j
= Wi l son
■ ^
Vi­
par amet er s
exp [ -
and
" ( A ^ j - A^ ^ ) i s
t erm c l o s e l y
an e m p i r i c a l l y
related
to
e n e r g y bet ween an i - j
By p e r f o r m i n g
energy,
t he
equations
coefficients
of
Prausnitz
ficient
indicated
is
uses
approaches
and an i - i
operation
for
or
I i m Y 1- = 1 . 0
in
energy
cohesive
p a i r . " ( 16)
on t h e excess
give
Gi bbs
the a c t i v i t y
syst em as s o l u t i o n s .
t he
by wh i c h
given
ar e a t . s u b c r i t i c a l
coefficient
1.0,
pair
t wo met hods
standardized
the a c t i v i t y
t he d i f f e r e n c e
ar e o b t a i n e d wh i c h
the- b i n a r y
component s. whi ch
det ermi ned
approaches
the a c t i v i t y
component .
conditions
in
coef­
For
the
syst em
1 . 0 as t h e mol e f r a c t i o n
-7If
a component
is
sup ercritica l, i.e.
is
h i g h e r t h a n t h e c o mp o n e n t ' s
activity
coefficient
fraction
approaches
is
the
critical
defined
to
syst em t e m p e r a t u r e
t e m p e r a t u r e , t hen t h e
ap p r o a c h u n i t y
as t he' mol e
z e r o , or
l i m i t Y 1- = 1 . 0
Xi -> 0
If
a supercritical
solute.
When b o t h component s
critical
tion
is
component e x i s t s , i t
they are t r e a t e d
used.
If
t h e component s
coefficients
one i s
ar e
for
in
in
t h e same and t he
u n s y mme t r i c
subcritical
for
supercritical
by P r i g o g i n e
shown by O ' C o n n e l l
and P r a u s n i t z
Tl .
Y 1*
lim it
symmet r i c
convention.
energy, while
Activity
by t he
the a c t i v i t y
ar e c a l c u l a t e d
and D e f a y .
( 1 3)
conven­
ar e c a l c u l a t e d
component s
a met hod d e v e l o p e d
ar e sub-
and one is' s u p e r c r i t i c a l
component s
above met hod f r o m t h e excess Gi bbs
coefficients
d e s i g n a t e d as t he
a binary mixture
subcritical
the
is
from
T h i s met hod i s
as
Yi
X 1- 0
wher e
Yi
■= a c t i v i t y
coefficient
in
s y mme t r i c
Yi * = a c t i v i t y
coefficient
in
u n s y mme t r i c c o n v e n t i o n .
The u n s y mme t r i c
convention
action
paramet er
solute
and 2 r e p r e s e n t s
also
= O, wher e I
convention
assumes t h a t
represents
the s u b c r i t i c a l
the
solvent..
the
inter­
supercritical
-8The second t h e r mo d y n a mi c f u n c t i o n
liquid
phase f u g a c i t y
conventions.
component
ture
the
is
that
pu r e l i q u i d
vapor at
of
in
the
is
component
in
set
the
ar e assumed t o
applicable
to
dissociates
together
dissociate
fugacity
of
by e q u a t i n g
t h e pu r e s a t u ­
state
fugacity
for
these
the He n r y ' s
constant
for
that
to
solvent.
fairly
component s
at
solutions
dissolved
to Henry's
Law, whi c h
l ow c o n c e n t r a t i o n s .
Solutions
by t h e p r e s e n c e
used i s
a polar
compound. , These
effects
present
in e l e c t r o l y t e
and non i d e a l i t y .
in the
solvent
on t h e
of
When t he
t he d e g r e e t o whi ch
bonds h o l d i n g
the
form p r i m a r i l y
in a polar
l ow c o n c e n t r a t i o n s
ar e c h a r a c t e r i z e d
is. d e p e n d e n t
whi ch
in
u n s y m m e t r i cal
n o n c o n d e n s a b l e component s
closely
Electrolyte
the
wh i c h t he
Thus t h e
and by t h e p o l a r i t y
Electrolytes
calculated
The r e f e r e n c e
such as c o n d u c t a n c e
is
s yst em t e m p e r a ­
present
p r o d u c e many o f
electrolyte
it
the
is
the
a condensabl e
ar e u s u a l l y
i o n s when t h e s o l v e n t
solutions
to
It
at
for
t he two
for
equal
of
Electrolyte
ions
pur e l i q u i d
pressure.
follow
Characteristics
of
fugacity
for
c o mp o n e n t s ,
used,
is
state
differently
t he
equilibrium.
solutions.
component s
is
the
fugacity
No n c o n d e n s a b l e
convention
calculated
The r e f e r e n c e
and a r e f e r e n c e
rated
is
characterizing
solvent
ionic
t h e mo l e c u l e
molecule.
bonds d i s s o l v e
s o l v e n t much more e a s i l y
and
t h a n t hose-
I
-9wh i c h
exist
as c o v a l e n t m o l e c u l e s .
Electrolytes
are c l a s s i f i e d
Tr u e e l e c t r o l y t e s
of s o lu tio n
may e x i s t
salt
exhibit
state,
lattice
i . e . , NaCl .
i n c l u d e most a c i d s
solution
Their
dissociation
mol ecul es
It
is
crystals
Potential
serve
is
dissociate,
molecules.
dissociate
and b a s e s ,
and do n o t
but
by d i s t i l l a t i o n .
to
these
Wat er
is
a particularly
molecul e
of
the
negative
dissociate
attached
If
the e l e c t r o l y t e
to
in
in
the
the
ion w i l l
water
it
exist
dissociates
solid
wh i c h
dissolved.
100% o f a l l
solution
as c o v a l e n t
w i t h wh i c h we ar e
pressure
and can t h u s
be
t he t er m e l e c t r o l y t e
good s o l v e n t
for
electrolytes
and i n
The c ha r ge
the e l e c t r o l y t e
bet ween o p p o s i t e l y
this
mi ght
attractive
dissociate
case o f an a c i d ,
case o f
the o t h e r
other
in
They
out of
o f the wat er mo l e cul e.
cause an a t t r a c t i o n
ions
i . e . , no t
a vapor
the wat e r mol ecul e
two m o l e c u l e s .
en oug h,
unless
out
compounds.
t he p o l a r i t y
in
dissociate
Hereafter
refer
p l a c e me n t
do n o t
electrolytes
separated
usual
electrolytes,
some r e ma i n
because t h e y e x e r t
because o f
groups.
solution.
their
as c o n d u c t o r s
concerned
will
in
in
not compl ete,
these
t wo p r i m a r y
conductance c h a r a c t e r i s t i c s
and c o m p l e t e l y
as i o n i c
into
a base.
as f o l l o w s :
into
in
is
great
positive
and
t he w a t e r mi g h t
One o f t h e
p o l a r molecul e
by i t s e l f .
or
force
c ha r g e d p a r t s
i o n s may become
t he s o l u t i o n
When an a c i d i s
and t h e
dissolved
in
- I O.
HA + H2O -> H3 O+ + A"
The amount o f
ionization
by a d i s s o c i a t i o n
is
defined
for
or d i s s o c i a t i o n
constant
the
for
the
occurring
reaction.
acid d i s s o c ia t i o n
is
Thi s
go v er n ed
constant
as:
aH3 O+ aA"
Kd i s s
aHA a H2O
wher e
a = activity
The a c t i v i t y
coefficient
is
related
in the
aB =
entity.
t h e mol e f r a c t i o n
by t h e a c t i v i t y
solution
o f a compound i s
and c o n c e n t r a t i o n
d e p e n d e n t on bot h
as shown i n
Figures
2 and 3
in water.
Si nce
electrolytes
exist
but . as c o v a l e n t m o l e c u l e s ,
c o v a l e n t mol ecul es
mol e f r a c t i o n
dissociation
constant
c h e mi c a l
..
temperature
HCl
to
the
particular
The d i s s o c i a t i o n
for
of
is
in
in
the
on t h e e l e c t r o l y t e
particularly
liquid
of
the p a r t i c u l a r
same f o r
all
dissociating
10.'
I O ' 4 t o 10" 5 .
as
The c o v a l e n t mo l e c u l e
by t he
electrolyte.
electrolytes
but
Hydrochloric
acid with
Th i s
is
de pendent
acid
is
a
a dissociation
Ammoni a and - h y d r o f l u o r i c
much we a k e r and have a d i s s o c i a t i o n
as i o n s
be p r e s e n t
phase may be d e t e r m i n e d
bond s t r e n g t h .
highly
c o n s t a n t o f about
t h e y must a l s o
the l i q u i d ' p h a s e .
constant
not the
i n t h e v a p o r phase n o t
constant
in
acid
t he
ar e
"
region of
Dissociation
Constant
( Xl 0
-11 -
T e mp e r a t u r e
Figure
2.
Dissociation
Function
( 0C)
Constant
o f Temper at ur e.
o f HCl
as a
-12-
O
Figure
1.0
3.
2.0
3.0
Concentration
of
Ionization
Hydrochloric
of
4.0
HCl-Molarity
Acid
5.0
-13The d e v i a t i o n
from i d e a l i t y
rolyte,
hydrochloric
looking
at
acid,
F i g u r e 4.
hydrochloric
acid
solution
a noncondensable
acid
its
solution
is
non i d e a l i t y
bei ng
at
the
order
of
20 mm,
wh i c h woul d
l aw i f
the
effects.
of
point,
as a r e s u l t
of
hydrogen-chloride
a value
at m)
acid:
pressure
on t h e
the o r d e r
of
"At
is
of about
of
basis
a c i d wer e c o m p l e t e l y
(of
S i n c e t he
critical
hydrochloric
(41
particles
in ad ditio n
electrolyte
One e f f e c t
in
pr oduce l o n g - r a n g e
forces
exist
contain
its
( 19)
10 N,
o f the
7 . 6 at m.
pure
of
of
liquid
Raoult's
undissociatd
indicates
0. 3 p e r c e n t )
that
...
is
form o f c o v a l e n t . m o l e c u l e s . "
charged
i ons
component .
of
from vapor
20°
amount
Dissociation
other
except those
s o l u t e ...............Thi s" f i g u r e , . . . . . ,
an a p p r e c i a b l e
i n the
at
hydrochloric
and an i d e a l
from i d e a l i t y
Rob i n s on and St o k e s
contrast with
be e s t i m a t e d
hydrogen c h l o r i d e
does n o t
by
i d e a l , b u t t he
i s much f a r t h e r
c o mp o n e n t .
pressure
is
truly
19 . 9 5 ° C , and bel ow i t s
non i d e a l i t y
the p a r t i a l
is
s y s t em o b s e r v e d
apparently
elect­
may be o b s e r v e d
or s u p e r c r i t i c a l
a supercritical
discussed
in water,
No s o l u t i o n
t ha n any n o n e l e c t r o l y t e
i ng
o f one p a r t i c u l a r
to
is
solutions
electrostatic
These c ha r ge d p a r t i c l e s
interactions
van d e r Waal s and o t h e r
in
i n t wo
caused .by t he p r e s e n c e o f
solution.
commonl y p r e s e n t
results
solutions.
bet ween t h e
shorter
r ange
Mol e F r a c t i o n
in
Vapor Phase
-14-
0
.1
Mol e
F i g u r e 4.
for
Fraction
Exper i ment al
.2
in
Liquid
Phase
Equilibrium
H C l - H 2O Syst em a t
I 9. 95°C.
Mol e F r a c t i o n s
( 2)
The second e f f e c t
number o f
molecul e
solute
solute
particles
dissociates,
concentration
electrolyte
of
The r e s u l t
of
this
electrolyte,
solute.
In
function
of
concentration
concentration.
This
may be a : r e s u l t
of
for
in
at
hydrochloric
acid,
shown as a f u n c t i o n
curve
of
of .
shows
HCl
vapor p r e s s u r e
a finite
in
as a
s l o p e as i t
shoul d
l ow c o n c e n t r a t i o n s .
o f z e r o as i t
ap p r o a c h e s
The
z e r o HCl
two mol es- Of s o l u t e
'
in
e v e r y mol e d i s s o l v e d .
dissociate
into
more t h a n two
t h e r e may be many d i f f e r e n t
I o n s may a s s o c i a t e
other
Thus
i ons
of
valences
of
two or
solutions
in
addition
to
t he more common s i n g l e
wor k
t ha n
is
vapor-liquid
the p a r e n t mo l e c ul e
in
these
t h r e e may e x i s t
an i n i t i a l
pr obe
equilibrium,
only
into
ions
in s o l u t i o n
compl ex es
lyte
shown
dependence on t h e ^ c o n c e n t r a t i on s quar ed
solutions.
Since t h i s
is
The second c u r v e
the exi st ence- of
( HgSO^, H^PO^)
these
dissociated
increase
5 the f i r s t
shows
Law a t
S i n c e many e l e c t r o l y t e s
i ons
Thus t h e
the c o n c e n t r a t i o n
squared.
wer e t o obey H e n r y ' s
solution
of
zero c o n c e n t r a t i o n
has a s l o p e
is
Figure
t h e second c u r v e
curve
formed.
a completely
while
first
is
i n the
Ev e r y t i me a
in
solution
it
increase
wo u l d d o u b l e
as a f u n c t i o n
if
the
solution.
particle
vapor pr es s ur e
approaches
in
is
wher e t h e v a p o r p r e s s u r e o f
dissociating
concentration
present
another
solution.
by Denbi gh. ( 6 )
a highly
of d i s s o c i a t i o n
t o f or m
solutions.
in
some
valenced
t he f i e l d
single
present
valenced
of
ion.
electro­
i ons
-16-
-3
Figure
5.
Dependence o f HCl
Concentration
(6).
Vapor P r e s s u r e on
will
be c o n s i d e r e d .
s y s t e m.
is
Thi s
Hydrochloric
acid
monO:val en t y h i g h l y
on i t
will
is
reduce
of
non i d e a l ,
t h a n most o t h e r
primary
phenomena..
•and t h e
(8)
librium
tion
for
related
quantities
a met hod f o r
electrolytes
from the
free
a separation
function
for
of
predicting
Gi bbs
in
the
vi
as compar ed t o t h a t
needed f o r
its
this
of
f r o m t he s e
t he excess Gi bbs
for
V-,
.1
+v1~
and e mp l o y i n g
phases
t o Hal a t h e
as a means
excess
is:
nonelectrolytes
.n . RT I n y .
1
= t o t a l number o f
dissociation
equi­
energy f u n c ­
wher e
=
Hal a
However he does n o t
v a p o r and l i q u i d
According
study.
RT l n n ±
AG^ - n f g^ = S
1 ■
i =I
v1
t i me
electro
vap or- I i q u id
energy o f d i l u t i o n
an e l e c t r o l y t e
AG± = . ^ 1 n i
to or d e r i v e d
dissociation.
equilibrium.
energy f o r
and d i f f u s i o n
calculating
using
derived
equate f u g a c i t i e s
up t o
wor k has been done on phase e q u i l i b r i u m
t h e r mo d y n a mi c
has d e v i s e d
i n t e r e s t . because i t
solutions
conductivity
functions
Little
t he
electrolytes.
has been i n v o l v e d w i t h
and b a s i c
of
and more da t a a r e a v a i l a b l e
Most wor k done on e l e c t r o l y t e
lytes
t he c o m p l e x i t y
i ons
p r o d u c e d by
-18Y •± = ionic activity coefficient
(y i +
From t h i s
1+
function
the
ionic
activity
coefficient
can be
obtained
/ 9AG± \
v 3n
n 1 /yT , P , n i ( i / j )
If
a model
v . RT I n
i
Yi
wer e used wh i c h was a s o l u t i o n
t o t he
excess
Gi bbs
e n e r g y and s a t i s f i e d
t h e Gi bbs- Duhem e q u a t i o n ,
could
be used t o c a l c u l a t e
the
by means o f
that
unity
zero.
for
the l a s t
state
the a c t i v i t y
coefficient
similar
nonelectrolyte
The a c t i v i t y
determi ned
involving
to
it
Gi bbs
involves
a.system.
If
defined
the e l e c t r o l y t e
of
convention
a model
used
may be
or t h e o r e t i c a l l y
t h e above p r o c e d u r e
i s mo.re i n t e r e s t i n g
a met hod whi c h c o u l d
yield
a p pr o ac he s
approaches
an e l e c t r o l y t e
However ,
energy
such
noncondensables.
experi ment s
met hod.
grammed and one wh i c h w i l l
describing
coefficient
the e l e c t r o l y t e
containing
coefficient
t h e excess
of
is
t h e u n s y mme t r i c
by c o n d u c t i v i t y
wor k s i n c e
electrolytes
of
s y st ems
f r o m t h e De b y e- Huc k e l
this
for
as t h e c o n c e n t r a t i o n
is
activity
relation.
The s t a n d a r d
Thi s
ionic
it
physical
i n'
be p r o ­
p a r a me t e r s
wer e d e v e l o p e d wh i c h woul d
satisfy
ionic
t h e .,Gi bbs -Duhem e q u a t i o n
activity
equilibria
for
coefficients,
electrolytes.
it
and a c c u r a t e l y
predict
wou l d be v a l u a b l e .i n phase
II.
Although
equilibrium
this
STATEMENT OF THE PROBLEM
there
data f o r
met hod y i e l d s
s y s t e ms .
has been wor k done t o o b t a i n
nonelectrolyte
poor
results
to o b tai n
component syst ems
using
pr ogr ams
wh i c h
these
multicomponent
Hal a
( 8)
equilibrium
only
syst ems
has d e r i v e d
a met hod f o r
electrolyte
It
r i u m t h e r mo d y n a mi c s
functions
equat e f u g a c i t i e s
dynami c f u n c t i o n s
do t h i s .
in
no r e a l
electrolytes,
extremely
met hod
does n o t
attempt
for
this
t h e f or m o f
data
t he
for multidata.
Fitting
binary
syst ems
t he
objective
and r e l a t i o n s
and v a p o r
for
t he
t han t h a t
phase e q u i l i b ­
and does
not
phases.
has. been made t o summar i ze t h e r m o ­
as has been done f o r
represents
electrolytes
an i n i t i a l
attempt
Prausnitz w i l l
equilibrium
for
binary
syst ems
pr ogr ams
t he n a t t e m p t s
to obt ai n
nonto
be m o d i f i e d
such as h y d r o c h l o r i c
wer e a c c o m p l i s h e d
made t o use t h e s e f i t t i n g
vapor-liquid
good r e s u l t s
use many b a s i c
pr ogr ams' o f
vapor-liquid
obtaining
much d i f f e r e n t
electrolytes
report
non-ideal
is
t he- l i q u i d
The f i t t i n g
to p r e d i c t
for
syst ems w i t h
used by P r a u s n i t z .
Si nce
in
and can t h e n be used f o r
his
this
to e l e c t r o l y t e
equilibrium
par amet er s
good accuracy,
s y s t e ms .
for
tested
binary
but
If
when a p p l i e d
the e q u i l i b r i u m
a r e used t o o b t a i n
describe
syst ems
syst ems w i t h
P r a u s n i t z 1 wor k has been summar i zed
c o mp u t e r pr ogr ams
vapor-liquid
of
acid.
could
be
p a r a m e t e r s whi c h
-21 wou l d be used f o r
Thus
t he o b j e c t i v e s
following:
1.
of
this
s y s t e ms .
investigation
wer e t he
-
Make c o r r e c t i o n s
to
include
tion
2.
multi-component
on t h e t h e o r y
effects
characteristic
binary
to
predict
electrolyte
hydrochloric
acid.
nonelectrolytes
p r o d u c e d by e l e c t r o l y t e
of
electrolyte
Use t h e s e c o r r e c t i o n s ' t o
pr ogr ams
of
revise
vapor-liquid
dissdci
solutions.
Prausnitz'1 f i t t i n g
equilibrium
solutions, particularly'
for
III.
PROCEDURE
Ther e wer e t wo b a s i c met hods
an e f f o r t
to o b tai n
wou l d p r e d i c t
first
a correction
vapor-liquid
present
electrolyte
liquid
Gi bbs e n e r g y
as t h e s o l u t e
to
that
excess
fitting
of
The
covalent
of ■
t he e q u i l i b r i u m
Gi bbs
liquid
energy
excess
phase
pr opos ed
pr ogr ams wer e empl oyed
The f i r s t
subroutine
CALPHW used by P r a u s n i t z
pr ogr am was HVYFTW and i t s
t he symmet r i c c o n v e n t i o n .
LTFTXW and i t s
associated
treated
u n s y mme t r i c
in, t h e
ar e used t o c a l c u l a t e
convention
VI RI AL, . f o r
t h e gas m i x t u r e ;
syst ems
CAfXLW f o r
c.o'nven t i on .
coefficients
associated
treated
in
input
of
for
the
particu­
dat.a t o s u i t a b l e
calculating
m o l a r v o l u me s ;
component s
a l s o use t h e
t he- second v i r i a l
coefficients
t he
These ' s u b r o u t i n e s
Bot h pr ogr ams
RSTATE, f o r
and p a r t i a l
•the. f u g a c i t y
subroutine
converting
calculating
for
in
The second T i t t i ng pr ogr am was
activity
e mp l o y e d .
I NPUT, f o r
fugacities
in
calculate
research.
routines
electrolytes.
electrolytes.
Two d i f f e r e n t
lar
for
t h e mol e f r a c t i o n
used by P r a u s n i t z t o
in
P r a u s n T t z 1' program' s wh i c h
The second met hod was t o c o r r e c t - t h e
coefficients
by Hal a f o r
research
a s y s t em a t a g i v e n c o n c e n t r a t i o n
and use t h i s
phase.
activity
in
of
equilibrium
met hod was t o c a l c u l a t e
mol ecul es
used i n t h i s
coefficient
reference
PHIMIX f o r
t h e c o mp o n e n t s ,
sub­
f or m;
of
state
calculating
and LSQ wh i c h ’ i s
usea t o
obtain
a least
Seven d i f f e r e n t
data
sets
of
c o m p i l e d by Chu ( 2 ) ,
pr oposed f o r
this
solvent with
the
bromic,
all
squares
be used i n
can be used i n
hydrochloric
of
of
These
t he d a t a .
taken from e q u i l i b r i u m
wer e used
research.
sets
in
testing
ammoni a,
hydrochloric
acid.
LT FTVW.
its
a c i d was t h e
is
also
primary
a highly
degree.
more common t h a n t h a t
These d a t a c o u l d
i so t h e r ma l
electrolyte
dissociating,
hydrobromic
dat a
studied.
acid
nonideal
dissociate
Dat a on h y d r o c h l o r i c
for
hydro-
e x t r e me n o n i d e a l i t y ,
b u t ammoni a and h y d r o f l u o r i c
t o a much s m a l l e r
as t he
hydrofluoric,
but onl y
Because o f
t h e met hods
included water
t he HVYFTW p r o g r a m,
Hydr obr omi c a c i d
electrolyte,
da t a
electrolytes
and f o u r
fit
acid
acid
i s much
so h y d r o c h l o r i c
a c i d was s t u d i e d more e x t e n s i v e l y .
The d a t a
fluoric
acid
included
at
acid
These d a t a
physical
ar e
properties
I n maki ng
assumed t h a t
vapor
that
the mol ecul es
they
also
phase o f
of
at
19. 95°C,
included
one a t m . ,
hydro­
at
5 4 . 5°C., -
5 5 . 2 ° C , and
in Appendi x C al ong w i t h
other
t he c o m p o n e n t s ..
corrections
the
exist
t wo a t m o s p h e r e s ,
one a t m o s p h e r e , h y d r o b r o m i c a c i d
and h y d r o c h l o r i c
7 5 ° C.
ammoni a a t
to Pr a u sn i tz
phase m o l e c u l e s
have l i t t l e
ar e f a r
influence
as c o v a l e n t m o l e c u l e s
e l e c t r o l y t e s ' should
p r o g r a ms ,
in
be.similar
it
was
enough a p a r t
on each o t h e r .
Si nc e
v a p o r , the vapor .
in
behavior
to
that
-24■o f
nonelectrolytes.
Thus no changes wer e made i n
v a p o r phase f u g a c i t i e s
in
the
liquid
phase wer e
Undissociated
Liquid
Si nce o n l y
must be i n
phase.
great
this
equating
liquid
phase w i t h
solution
and n o t t h e
in
t he
should
of
3)
vapor,
in
shows t h a t
It
4,
mi ght
v a p o r phase f u g a c i t y ,
be c a l c u l a t e d T h e
wou l d b e . c o n s i d e r e d
solute.
dissociation
was t h o u g h t
with
that
increas­
be a r e s u l t
the
i ons
of
as. .a
of
phase. ' By
in
t he
vapor
present
phase
in
t he s o l v e n t
. .
of
undissociated
case t h e mol e f r a c t i o n
dissociation
The s u b r o u t i n e s
solve
as p a r t
they
the l i q u i d
mol ecul es
u n d i s s o c i a t e d mol ecul es
general
met hod o f
o f HCl
Figure
m o l e c u l e s was c a l c u l a t e d
wer e used t o
i n the
phase mol e f r a c t i o n
rolyte
rolyte.
exist
c o v a l e n t mol ecul es
(Figure
vapor
T h i s mol e f r a c t i o n
COVCAL u s i n g
research.
i n c o v a l e n t mol ecul es i n the l i q u i d
the f u g a c i t y
mol e f r a c t i o n
the
of
the
concentration.
mol e f r a c t i o n
increase
in
dissociation
increased
increase
ing l i q u i d
with
concentration
decreases w i t h
the
included
caused by d i s s o c i a t i o n
Phase M o l e c u l e s
equilibrium
of
effects
c o v a l e n t mol ecul es
The c u r v e o f
function
and o n l y
calculating '
by t wo me t h o d s . '
was c a l c u l a t e d
constants
for
phase e l e c t ­
In
t he
by s u b r o u t i n e
t he p a r t i c u l a r
CUBIC and QUAD f r om McCor mi ck
a cubic
calculation
liquid
equation
i s. o u t l i n e d
in
elect­
( 12)
t he c a l c u l a t i o n .
i n Ap p e n d i x A,, and t h e
Thi s
- 2 5's u b r o u t i n e s -are
used o n l y
tion
for
curve
straight
tion.
listed
hydrochloric
in
Figure
lines
3.
This
the di ss o c i a
c u r v e was- a p p r o x i m a t e d
fitted
by two
using a cubi c
eq u a ­
i n A p p e n d i x B.
used i n
consisted
by u s i n g
Gi bbs
excess
using
Ener gy
nonidealities
t h e excess
The second met hod was
solutions
and t h e n
is .outlined
The second met hod
coefficient
acid
This
initially
The met hod
Excess Gi bbs
i n Appendi x B .
of
calculating
t h e Wi l s o n
energy o f
Gi bbs
correcting
energy
is
the
equation
dilution
defined
for
electrolyte
ionic
activity
as a s o l u t i o n
to
as p r opo s ed by Hal a.
as:
N
£
- AG+ = E n . V1- RT I n Y1- +
and . i s
based on t h e c o m p l e t e d i s s o c i a t i o n
When t h e Wi l s o n
to
this,
the
excess
p a r a m e t e r s ^ar e
Gibbs.energy
k
N
-E n . v . RT.'.ln [ .E
i
1 1
j =l
A..
1J
differentiating
the f i r s t
mol es
of
an e x p r e s s i o n
ficient
of
i
i,
can be o b t a i n e d .
the
introduced
electrolyte
as a s o l u t i o n
becomes
After
component
of
x. +]
J~
expression with
for
re spect to
the a c t i v i t y
coef­
-26Then by p e r f o r m i n g
sion,
a similar
an e x p r e s s i o n
t h e Wi l s o n
v.
for
par amet er s
= v.
operation
the a c t i v i t y
is
on t h e second e x p r e s ­
coefficient
obtained.
(x i +
monoval ent
n.
J
i+
'i-
compl et e
J 1 / V 1-
i-
electrolyte
n.
1J +
nj + +nj - + n k
= mol es o f p o s i t i v e
of e l e c t r o l y t e
ion
p r o d u c e d per mol e
mol es o f n e g a t i v e
of e l e c t r o l y t e
i on
p r o d u c e d per mol e
n.
Jn,
by
paramet er
x . + = mol e f r a c t i o n o f component a f t e r
d i s s o c i a t i o n of sol ut e
Xj +
t er ms o f
+ v •+ = t o t a l number o f i o n s p r o d u c e d
compl et e d i s s o c i a t i o n
.^ . = Wi l s o n
for
in
= mol es o f s o l v e n t
electrolyte.
The r e s u l t i n g
electrolyte
expressions
and t h e
present
_,
for
solvent
activity
+A-
coefficients
v
x ? +A?-|
- 2 x ;,+ •
'■ " x 2± A01X-,- +Xn .
L21 I ± A2±
,
'I ± jM 2a 2±
2A12X1 ± " X1±
y 2± = BXpE- V1X
1± x I ±+Al 2 X2±
/ ( A2T x T ± + * 2 ± )
o f t he
are' : - ■
X-j + —2 x -t+A-i q
Y1± = e x p [ - x 2± x
p e r mol e, of :
^x I ±+Al 2X2±^
■2 x l ± A2 1 XI ± •
X2± A21x I ±+X2±
-27wher e
( I ) . refers
to e l e c t r o l y t e
(2)
to s o l v e n t
refers
This
operation
t h e s y mm e t r i c
in
binary.
as shown g i v e s
convention.
activity
The c a l c u l a t i o n
coefficients
procedure
in
is
shown i n A p p e n d i x A..
The a c t i v i t y
ar e c a l c u l a t e d
using
the
coefficients
t h e u n s y mme t r i c c o n v e n t i o n
f rom symmet r i c c o n v e n t i o n
following
Prausnitz
for
expression
activity
coefficients
as shown by O ' C o n n e l l
and
(13).
Il±
Iim
■±
Xl t * 0
wher e y-j
= activity
coefficient
The i n t e r a c t i o n
done by P r a u s n i t z
The r e s u l t i n g
convention
*
^li
u n s y mme t r i c
paramet er
as s umi ng
activity
little
was s e t
convention.
equal
solvent-solute
coefficients
for
to
z er o as
interaction
t he u n s y mme t r i c
are:
exp ( -Xw . X l ± ~2X- - - — - +
2± x I ±+A12X2±
Y2+ = e x p ( - v I x U
This
in
calculation
A p p e n d i x B as i t
1
is
2A12X1± _X1±
X1 ±+A] 2x 2±
2x 2 ±
vI
_
2
A1 2
vI
x I ±+Al 2 X2±
- . 2x 1 ± ) / x 2 ±
shown, in. A p p e n d i x A and. i s
appeared
i n t h e program. .
listed
in
-28Si n c e t h e a c t i v i t y
normalized
to approach
z e r o , they
should
The r e f e r e n c e
the
coefficient
unity
be t r e a t e d
state
fugacity
pr ogr am LTFTXW s h o u l d
these f e a t u r e s .
electrolytes
as t h e mol e f r a c t i o n
in
the
should
apply
wh i c h f i t
is
ap pr o ac he s
un s y mme t r i c c o n v e n t i o n .
be H e n r y ' s
because
Bot h c o n v e n t i o n s
t o o b t a i n mol e f r a c t i o n s
of
it
contains
wer e t e s t e d
the
constant,
data.
and
bot h
i n an e f f o r t
IV.
The o r i g i n a l
five
HCl
sets
data.
using
fitting
binary
data:
NH3 , HF,
symmet r i c c o n v e n t i o n
ar e shown i n
t h e u n s y mme t r i c
Figure
fitting
This
that
wou l d make t h e
chloric
acid.
correction
is
Hydrofluric
acid
in
dissociates
However ,
the f i t
much p o o r e r t h a n
obtained
for
excess
tions
Gi bbs
in
hydro­
no r e a l
only
slightly
of.their
more t han
dissociation
NH3..
Figure
The mol e, f r a c t i o n s
and no
t he c o r r e c t i o n s
for
o b t a i n e d from t he c o r r e c t e d
e n e r g y wer e wor se t h a n t h e u n c o r r e c t e d
calculating
7, was
s y mm e t r i c c o n v e n t i o n
and t h e change made by u s i n g
present
dissociating
ammoni a.
i mp r o v e me n t was made upon i n t r o d u c i n g
dissociation.
t he u n d i s s o c i a t e d
HF as shown i n
NH3 i n t h e
obtained
Thi s
HF and 1. 7 8 x I O - ^ f o r
for
dat a .
amount o f
wer e good enough t h a t
needed f o r
6.75 x I O- ^ f o r
fit
solution.
like
ammoni a as e v i d e n c e d by a c o mp a r i s o n
constants,
isothermal
t h e s ma l l
t h a n t h e more h i g h l y
These r e s u l t s
results
These
p r o g r a m. ■ The c l o s e
ammoni a under goes
probably
p r o g r a m.
because o n l y
ammoni a more n e a r l y
nonelectrolytes
good, f i t t i n g
of
da t a s e t was n o t used-
ammoni a sy s t em may be due t o
dissociation
r un w i t h
H B r , and t wo s e t s
fitting
6.
convention
can be us.ed i n . t h a t
for.the
pr ogr ams wer e i n i t i a l l y
The NH3 - H 3O syst em a t t a i n e d
the
results
in
of
RESULTS
calcula­
o n l y t he c o v a l e n t mo l e c u l e s
t h e mol e f r a c t i o n
made l i t t l e
■
-30-
O HVYFTW and HVYFTW
w i t h COVCAL
□ Excess Gi bbs
correction
0
.2
.4
.6
.8
y
J exper
Fi gur e 6.
Vapor Composi t i ons f o r
2 a t mospher e s .
NH^-HgO at
e n er g y
1. 0
-31-
y
■e x p e r
Figure
7.
Vapor C o m p o s i t i o n s
for
HF-HgO
-32difference.
this
The u n s y mme t r i c
d a t a was f o r . i s o b a r i c
H y d r e b r o mi c
acid
and t h e
acid
vapor
the o r i g i n a l
calculates
for
mol e f r a c t i o n .
properties
this.
so t h a t
in the
for
HCl , 10
centrations
of
zero
I
liquid
corrected
ex c e s s
Gi bbs
much t o o
constant
there
This
energy
high.
results
of
data
of
solute.
overcorrects.
o f HBr was u n a v a i l a b l e
gave v a p o r
phase c o n ­
of covalent
gave b e t t e r
These r e s u l t s
l o w.
results
shown i n
Figure
obtained
from t he
as l i q u i d
9.
It
is
involving
easily
theory
using
phase mol e f r a c t i o n
cur ve ar e t he
best.
The
but they
ar e Shown i n
Figure ■
,
t e s t e d most was t h a t
t he f o u r met hods
by
HVYFTW pr ogr am
:
The HCl
ar e l e s s
indicated
phase must have been t o o
s.
tion
t han
so t h e mol e f r a c t i o n
in the
wer e s t i l l
liquid
pr ogr am,
wh i c h ar e f a r
COVCAL a p p a r e n t l y
was us ed.
mol ecul es
fitting
if
based on mol e f r a c t i o n
The d i s s o c i a t i o n
hydrofluoric
values
The o r i g i n a l
subroutine
conditions.
convention
wou l d be e x p e c t e d
present
used because
much more t h a n
s y mme t r i c
Thi s
H o w e v e r , t h e use o f
isothermal
phase mol e f r a c t i o n
above e x p e r i m e n t a l .
c o v a l e n t mol ecul es
and no t
dissociates
uncorrected
HVYFTW, y i e l d s
convention wasn't
a t I 9 . 9 5 ° C.
The
t he HVYFTW pr ogr am ar e
seen t h a t
t he
results
-
the undissociated, e l e c t r o l y t e
calculated
These, r e s u l t s
f r o m t he
ar e s t i l l
dissocia­
in
error, but
'
show a g r e a t
i mp r o v e me n t o v e r
t h e o t h e r met hods
used.
. The
'
■
:
..
.
-
-33-
O
1
O
O
HVYFTW c a l c u l a t i o n
□
HVYFTW w i t h
e l e ctrolyte free
en e r g y c o r r e c t i o n
exper
Fi g u r e 8.
Vapor Composi t i ons
for
HBr-HpO at
5 4 . 5 ° C.
□G3
-34-
O
.2
.4
.6
.8
1. 0
y
^exper
Fi g u r e 9.
Vapor composi t i ons
f o r HCl-HgO a t
I 9 . 95°C.
i
■- 3 5 conditions
un der wh i c h t h i s
b y ' Cur t man
( 4 ) , but
obtained
from the
it
c u r v e was o b t a i n e d
was p r o b a b l y
excess
Gi bbs
at
25°C.
energy f o r
p r o p o s e d by Hal a and based on c o m p l e t e
electrolyte
since
yields
t he p o o r e s t
not d i s s o c i a t e
HBr w h i c h
greatly,
,The c a l c u l a t i o n
routine
the
second b e s t
of
(21).
that,
I)
zero
t h e a s s u mp t i o n s
wer e po or
latter
used
(activity
a s s u mp t i o n s
The mol e f r a c t i o n s
calculated
in
dissociation
fractions.
phase.
ammoni a,
did
2.5x10
a similar
by t h e s u b ­
'
should
n o t make a g r e a t
liquid
indicate
should
on e,
n o t be
or,
2)
t h e c o v a l e n t mol e f r a c t i o n
co' ef.f i c.i e.nts' ■= 1 . 0 0 ) .
However t h e s e
deal
of
difference.
phase c o v a l e n t m o l e c u l e s
were '
pr ogr am and gave v a l u e s , much l ess-
f r o m t he d i s s o c i a t i o n
not
does
constant,yielded
c o n s t a n t may be a po or way o f
It
wh i c h
an i mp r o v e me n t f o r
Thi s mi ght
of
obtained
in c a l c u la t i n g
of
seems s t r a n g e
b u t y i e l d e d mol e f r a c t i o n s
constant
( 1 8)
a separate
t han t hose o b t a i n e d
either.
the. v a p o r
Rob i n s on
t he
greatly.
was t r i e d
the d i s s o c i a t i o n
used a l t h o u g h
of
However a d i s s o c i a t i o n c o n s t a n t o f
7
2 . 5 x 10
as o b t a i n e d by Wynne-
t han
in
electrolytes
Thi s
uses a d i s s o c i a t i o n
The l a t t e r
t he near
The r e s u l t s
the c o v & l e n t mol ecul es
results.
. 24 was u s e d . r a t h e r
Jones
of
COVCAL, whi ch
for
and r e p r e s e n t e d
does- d i s s o c i a t e
not gi ven
dissociation
results.
t h i s , met hod gave good r e s u l t s
are
curve.
Thus t he
calculating
mol e
h,ave a dependence on c o n c e n t r a t i o n
-36The HCl
data a t
c u r v e as shown i n
predicted
Gi bbs
75°C was f i t
Figure
10.
v a l u e s much t o o
function
for
best
by t he d i s s o c i a t i o n
The o r i g i n a l
high.
electrolytes
The c o r r e c t i o n
predicted
higher
predicted
v a l u e s wh i c h wer e l ow b u t f a i r l y
tested
using
while
of
from the presence o f c o v a l e n t
phase u s i n g
the d i s s o c i a t i o n
t wo more HCl
good r e s u l t s
s y s t e ms .
as shown i n
for
t he
valid.
an e r r o r
of
fraction
range.
t he
temperature
this
set
11,
the
results
of
the
The d i s s o c i a t i o n
the
HCl
at
was t h e n
tested
5 5 . 2 ° C , gave f a i r l y
a t one
Figure
may n o t
have been
have been due t o
syst em o v e r
is
12.
pr ogr am c a l c u l a t i o n
t he
t h e mol e
not const ant
over a
as does t h e . d i s s o c i a t i o n
da t a may" have been o u t
speculation.
the l i q u i d -
but the second,
may a l s o
temperature
Some o f
for
during
r ange b u t v a r i e s
only
curve
and t he
t e m p e r a t u r e a t wh i c h
is
calculate
properties
in
wh i c h wer e v e r y l ow i n
These po or r e s u l t s
changing
the
to
Thi s
t he d i s s o c i a t i o n
s o l u t e mol ecul es
The f i r s t ,
developed
second d a t a
constant.
with
curve
consistent.
phase e q u i l i b r i u m
Figure
a t m o s p h e r e , gave r e s u l t s
Howev er ,
hi gh
. 24.
The met hod o f d e t e r m i n i n g
with
t oo
th.e d i s s o c i a t i o n
t h e COVCAL s u b r o u t i n e
t h e c o v a l e n t m o l e c u l e mol e f r a c t i o n
constant
u s i n g t he
values
except at
d a t a was n o t
concentrations
HVYFTW pr ogr am
of
t h e c u r v e was o b t a i n e d .
t h e r ange o f
However
-37-
O HVYFTW
□ E l e c t r o l y t i c Fr ee
Ener gy C o r r e c t i o n
O Usi ng D i s s o c i a t i o n
Cur ve
exper
Figure
10.
Vapor C o m p o s i t i o n s
for
H C l - H 9O a t
75°C.
-38-
O HVYFTW
D Usi ng D i s s o c i a t i o n
Cur ve
exper
Fi gur e
11.
Vapor Composi t i ons
f o r HCl - H9O at
5 5 . 2 ° C.
-39-
HVYFTW
□
Usi ng D i s s o c i a t i o n
Cur ve
calc
O
exper
Figure
12.
Vapor C o m p o s i t i o n s
for
HCl - H 9O a t
1 . 0 at m.
-40The HCl
convention
d a t a was used i n t t i e LTFTXW or u n s y mme t r i c
fitting
met hod wer e p o o r
wer e c o m p l e t e l y
tion,
wh i c h
is
dr opped f o r
or
it
p r o g r a m.
in a l l
cases
inconsistent
calculated
than
these poor r e s u l t s
is
Henry's
This
constant.
that
I . 00 .
t he
could
component g i v e n
mol e f r a c t i o n
of
fraction
is
very
wo u l d
indicate
lytes
should
the
of
the
liquid
One p o s s i b l e
data
easily
of
. 2.
is
out of
this
They
mol e f r a c ­
about
is
.04.
reference
explanation
the
for
r ange o f
da t a
I n t he exampl e o f a
nearly
in
d e c a n e , t he
100% f o r
The HCl
liquid
concentrations
be because t h e HCl
by P r a u s n i t z ,
vapor
l ow a t t h i s
that
for
I .
liquid-phase
experimental
supercritical
phase mol e f r a c t i o n s
as shown i n T a b l e
as t h e
up t o a mol e f r a c t i o n
N^ i n
obtained
and compar ed t o t he o r i g i n a l , even
some i n c r e a s i n g
became g r e a t e r
ranges
The r e s u l t s
vapor
liquid-
phase mol e
concentration.
state
fugacity
Th i s
for
be d e t e r m i n e d f r o m , t h e . pu r e s a t u r a t e d
electro­
v ap or
fugacity.
The s o l v e n t r s o l u t e
e q ual
to
zero
in
good a s s u m p t i o n
electrolytes.
the
for
u n s y mme t r i c
: The p r e s e n c e o f
No d i s s o c i a t i o n
<
to
test,this
parameter,
convention.
nonelectrolytes
c h a r g e s may make t h i s
lytes
interaction
bu t
no t
, was s e t
T h i s may be' a
necessarily
for
p o l a r m o l e c u l e s ' and i o n i c
a s s u mp t i o n
invalid.
c u r v e s wer e f o u n d f o r
c o v a l e n t molecul e
theory
the
other
.
electro'
•
as was done f o r
'
TABLE I
' LI QUI D COMPOSITIONS . FOR H C l - H 2O AT I 9 . 9 5 ° C IN UNSYMMETRIC CONVENTION
"
Experi­
ment al
. L'TFTXW,
.
E l e c . Gi bbs
Ener gy C o r r .
w i t h LTFTXW
COVCAL w i t h LTFTXW
ExperiCalculated
me n t a l
Covalent
Covalent
Diss-. Cur ve w i t h LTFTXW
Exper i
• Calculated
me nt al
- C o v a l en t
Covalent
. 0860
. 3723.
. 0475
. 0070
. 0062
.00
. 00
. 0978
.3801
. 0520
. 0062
. 0050
. 00
. 0129
.I I I 6 ■
. 5337
. 0483
. 0188
. 0123
. 00
. 0219
.6195".
. 0499
. 0243
. 01 54
. 00
. 0024
, 1413
. 6283
.0507.
. 0308
. 01 60
.0001
. 0306
' . I 747 ;
.091 9
. 1014
. .0431
. 0193
. 0008 .
. 0349
. 1950
. 5116
. 3327
. 0463
. 0203
. 0013 •
. 0354
..2240
2.2685
.0395.
. 0643
. 0464
. 01 24
. 0056
. 0754
. 3079
. 0338
. 1356
. I 585
2, 8 6 6 5
.0981
-2.8453
..1356
.
■
■
-42hydrochloric
conclusions
acid.
was a l s o
solutions
should
can be made a b o u t
show an i mp r o v e me n t
It
This
in
this
assumed t h a t
has no e f f e c t
met hod wher eas
equilibrium.
for
Actually
electrolytes
interaction
mol ecul es
vapor
is
in
in
this
theory although
equilibrium
calculations
the presence o f
i ons
on t h e p r o p e r t i e s
of
The i o n s wer e c o n s i d e r e d
in
be done b e f o r e any d e f i n i t e
as b e i n g
a part
they probably
t he
probably
theory with
lies
the
the s o l u t i o n
equilibrium.
solution
in
theory
act
of
it
for
di d
HCl .
i n the
t he s o l u t i o n .
the s o l v e n t
do p l a y a p a r t
i n the .
t o phase e q u i l i b r i u m
a combination
that
as- t h e
of
an i o n i c
the u n d i s s o c i a t e d
solute with
wh i c h t he
The r e s u l t s
electrolyte
following
1.
Slightly
from t h i s
investigation
equilibrium
in
dissociating
acid
seem t o
deviate
t h e s e syst ems
less
into
indicate
acid
equilibrium
be t r e a t e d
syst ems
and h y d r o c h l o r i c
lie
out o f the
calculations.
i n the
Neither
u n s y mme t r i c c o n v e n t i o n .
for
hydrochloric
a c i d wer e made by c o n s i d e r i n g
in
4.
in
the
in the l i q u i d
symmet r i c
The use o f
in c a l c u l a t i n g
va.por-liquid
Prausnitz
the
activity
no i mp r o v e me n t o v e r
the
acid.
shoul d
in
mol e f r a c t i o n
disso­
r ange o f
I mp r o v e me n t s
u n d i s s o c i a t e d mol ecul es
of non­
t h a n do such h i g h l y
3.
treated
t he
such as ammoni a
f r o m t he b e h a v i o r
as h y d r o b r o m i c
Hydrochloric
l aw i n
electrolytes
phase e q u i l i b r i u m
electrolytes
2.
tion
obtained
conclusions :
electrolytes
Henry's
SUMMARY
vapor-liquid
and h y d r o f l u o r i c
ciating
V.
pr ogr ams
equilibrium
calcula­
o n l y t he
phase as t h e s o l u t e
for
nonelectrolytes,
convention.
excess
Gi bbs
en e r g y f o r
coefficients
for
excess
en e r g y f o r
Gi bbs
electrolytes
electrolytes
yields
nonelectro­
lytes.
Thi s
of
wor k
vapor-liquid
is
only
an i n i t i a l
equilibrium
f r o m t h e more i d e a l
for
investigation
into
the f i e l d
e l e c t r o l y t e s , as a. d e v i a t i o n
nonelectrolytes.
Further
investigation
-44should
be made i n t o
theory
for
ionic
should
all
charges
also
the
u n d i s s o c i a t e d m o l e c u l e mol e f r a c t i o n
electrolytes.
in
solution
be s t u d i e d .
The e f f e c t
on t h e
of
electrolyte
t he p r e s e n c e o f
equilibrium
APPENDIX
APPENDIX A
DERIVATION OF CORRECTIONS TO PROGRAMS
C a l c u l a t i o n o f Cov a l e nt E l e c t r o l y t e Mol ecul e C o n c e n t r a t i o n i n
S-Q l u t i o n . ( Fr om I o n i c E q u i l i b r i u m : A Ma t h e ma t i c al Appr oach)
Dissociation
Reaction
HA +■ H2 O -»■ H3 O+ + A"
HA = e l e c t r o l y t e
H3 O
Reaction
I)
is
H . in
governed
Dissociation
(in
this
case an a c i d )
following.
by f o u r
equilibrium
constant
aA- a H+
and a = y [ C ]
aHA aH2O
wher e a = a c t i v i t y
Y = activity
[C]
= concentration
' Assume y = 1 . 0 0
' K Ka
2)
in a l l
LA ~ ] [ H+ ]
[ HA]
Wat er d i s s o c i a t i o n
Electrical
' [ H+ ]
constant
.
Neutrality
= [OH- ]
cases
■■
[ H + ] [ 0 H - ] ; =Vl-O"14
3)
coefficient
+ [A- ]
in S o l u ti o n
■
equations:
t
-474)
Electrolyte
C = [ HA]
concentration
r e ma i n s
constant
+ [A"j
wher e C = i n i t i a l e l e c t r o l y t e
dissociation
concentration
3a)
+
i n - 14
= [ H ] = —j-|| + j + [ A ]
(using
2)
la)
'
(using
4)
3a)
,
. [A ] = [H ]
(C-[A“ ])K a -
Substitute
3a)
into
[H+ ] ( [H+ ) -
[ H+ ] [ A “ ]
before
l n - 14
- — +j
la)
1 ^ )
.
Ka ( C - t H + ]
+
rearranging
[ H+ ] 3 + Ka [ H+ ] 2 This
cubic
e q u a t i o n wo u l d
from t h e . f i r s t
four
[OH"]
concentration
• IO -1 4 ZtH+ ] '
•
[ H * ] .
[H+ ]
-
U C l I O
t he n y i e l d
- Ka ( 1 0 " 1 4 ) = 0
a solution
equilibrium'equations
the c o v a l e n t mol ecul e
[A- ]
( KaC+ 1 0 " T 4 ) [ H + ]
[OH- ]
'
.
f o. r . [H + ] and
a solution
of
[HA],
was o b t a i n e d .
■;
'
-
' .
■
Ka
The pr ogr am used t o
B al ong w i t h
the
comput e t h i s
subroutines
val ue' i s
used t o
solve
included
i n Appendi x
the c u b i c
equation.
-48The mol e f r a c t i o n
(molarity)
was c o n v e r t e d
t o mol ar c o n c e n t r a t i o n
as f o l l o w s :
mol es X .
mol e f r a c t i o n
total
mol es
mol es X .
mol es
\ r ( qms/mt ) xl 0 0 0 -,
________ I = / _____
M. W.
J
l i t e r of
'total moles'L
solution
Molarity
mol es
X.
f r a c t i o n ) T t y j g ms / t ) )
T T t e r ------ = <m0,e
M.W.
Densities
-
( X 1 ) ( M . W . l ) + ( X 2 ) ( M. W. 2)
wer e t a k e n
from P e r r y ' s
Handbook and a s t r a i g h t
fairly
accurately
to
line
determine
straight
a least
This
lines.
squares
test
fitting,
pr ogr am y i e l d e d
(-3.3046
an e q u a t i o n
for
the
points
density.
U n d i s s o c i a t e d . HC1, Mo l e c u l e s
this,curve
Then i t
Engineer's
was dr awn t h r o u g h
C a l c u l a t i o n o f Mol e F r a c t i o n o f
Us i n g D i s s o c i a t i o n Cur ve
As an i n i t i a l
Chemi cal
.
was a p p r o x i m a t e d ' b y
was f i t t e d
by a cu.bi c e q u a t i o n
pr ogr am w r i t t e n
t he f o l l o w i n g
cubic
wher e x = m o l a r i t y
y = ionization
fraction
using
by R o b e r t J . Rober t as.
equation:
E - 04 ) x 3 + ( 1. 0 5 4 9 E - 0 2 ) x 2 - ( 1 561 3 )x
' +. . 95 53 7 - y
two
■
-49The e q u a t i o n
fit
t he data
X.
as f o l l o w s :
YCAL ( by c u r v e )
■
Error
. 01
. 98
.95381
2 . 6185E- 02
. 02
. 97
. 95226
I . 7744E- 02
. 03
.365
. 9507
I '. 4244E- 02
. 05
, .955
. 94759
7 . 4 0 5 2 E - 03
.1
.93
. 93987
-9.8672E-03
.2
.9
. 92457
-2.4568E-02
.3
. 88
. 90.948
-2 . 9 4 7 7 E-.02
.5
.86
. 87991
- I . 9907E- 02
I .0
. 82
. 80946
I . 0535E- 02
2.0
. 685
. 68267
2.3308E-03
3.0
.58
. 57301
6 . 9942E- 03
5.0
.4
■ .3971 4
2 . 8560E- 03
7.0
. 26
(interp.)
. 26602
-6.0171E-03
10.0
. 12
(interp.)
. 11851
I . 4 9 2 8 E- 03
Although these
the e n t i r e
for
t h is
range, i t
results
weren't
completely
was d e c i d e d t h a t
a c c u r a t e over
t h e y wer e c l o s e
enough
work .
T h i s . met hod was t h e n
t he mol e f r a c t i o n
mol e f r a c t i o n
of
of
HCl
pr ogr ammed and used i n
undissociated
in
solution.
mol ecul es
calculating
f rom the t o t a l ,
-50D e r i v a t i o n of Expression f o r A c t i v i t y C o e f f i c i e n t s
■Wi l s o n Mo d e l :
S y mme t r i c C o n v e n t i o n
Wi l s o n
equation
for
nonelectrolytes
N
gE E Z x . I n Yi =1 1
1
N
[ %
J=I
Pr opos ed W i l s o n e q u a t i o n
definition
N
Z
i = 1.
N
E Z
J=I
electrolytes
x ± V.
‘j ±
3- AG+\
Sni ' T , P , n ^ j
'j±
for
( Gi bbs
en e r g y
f r o m Hal a)
-gE =
.V-
Usi nq
N
RT I n Y . = Z x . ±
1i =1 1
\>.
]
_
i
RT I n Y i ±
= v . + + v . = t o t a l sum o f i o n s per m o l e c u l e
compl et e d i s s o c i a t i o n
(x
wher e
at
) 1/Vj
j +
[(
RT I n
1
nj +
1/ v .
) Vj + ( _ V
)Vj' l
nj + + n j - + n a
k refers
"j +
nJ
to
solvent
number o f mol es o f p o s i t i v e
d i s s o c i a t i o n mol ecul e
j
i ons
number o f mol es
j
ions.
of
negative
per
-51 For m o n o v a l e n t
( I ) , solvent
binary
as used i n
this
■2±
-
v-]
2n-| +n^
= 2, '
=
2n-j+n
.
v2 = I
- A G ^ ' = RT{ - n-j v -j I n [ A ]
-
e lectrolyte
(2)
X0 = [ ( ___ __________________ ) 1 ] V 2
2±
Vn-]+ n -] +H2 V J
■
research
o2 In
x 1± + A 12 x 2 ± ]
CA 2 -] x •] + + A 22 ^ 2 + 3 I
A 11
= RT{ -n-j V1 I n
- n2 In
r 9 ( - A 6 ± )' -1
L Sn1
JT , P , n 2
[ A 21
ni
= A 22 -
I
n Q-
L2n1+ n 2
12 . 2n1+ n 2J
2 ] ____.+
" P2 i } 2 n -j + n 2'
2 n -j + n-2 J
= RTf-V1
x 2±
xU
~
2 x 2±A12
x I ±+Al 2 X2±
x 2±A21~2 x 2±
A21X1±+X2±
v
I n [ x 1±+A] 2 x 2±
-52Thus
In
•1n [x-j ± +A-| £ x 2 + 1 vi
Yl±
- x
Differentiating
obtains
x
U
2 ± ~ 2 x x ±A 1 2
x ] ++A-, 2 x 2±
x 2+A21~2 x 2 ±
2± A21 x^ ++x
2±
with
respect
an e x p r e s s i o n
for
to
in
I n Y2+-
a s i m i l a r manne r ,
The r e s u l t s
one
f o r Y1+ and
Yg+ a r e :
Y1+ = e x p [ - X 2+
x I ± ~ 2 x 1±A12
x I ±+Al 2 X2±
- x
x
2±A21 ' 2 X 2 ±
2± A21x I±+X2±
] / ( X1 ++A1 2 X 2±)
2A12XI ± ~X1±
2 x I ± " A21X1i - x
Yg+ = GXpC-V1X1+ ^
2 ± A21X1±+ x 2±
I ±+Al 2 X2±
/ ( A21x I ±+ x 2 ± )
-53Un s y mme t r i c C o n v e n t i o n
Y1
—nr = I i m
. Y1
x i ->0
±
I i m Y1±
Xi ± + 0
as x-| + ->■ 0,
Limit
x 2+
I
Y1 + = C e x p ( Z - A 2 1 ) Z v 1I Z A 12
xH * 0
Setting
A21 "= 0 by a s s u m p t i o n o f weak i n t e r a c t i o n
Y1+ = e x p ( - x 2+
x I ± ~2 x l ± A1 2
x I ±+Al 2 X2±
Y2+ = GXpf - V1X1 +
2A1 2 X1±~x l ±
x I ±+Al 2 X2±
2x
2±
A1 2
Xl ± +Al 2 X2±
Pr ogr am L i s t i n g f o r S u b r o u t i n e COVCAL and O t h e r Pr ogr ams used i n
Coval ent Mol ecul e C o n c e n t r a t i o n from D i s s o c i a t i o n Constant
.
C
.C
C
C
C
.
OMEGA,
Y> SUMY,
HENRY,
-54-
S U B R O U T I N E CQVCAL
S U B R O U T I N E f o r C A L C U L A T I N G T H E . MOLE F R A C T I O N OF COV A L E N T
MOL ECUL ES' I N S O L U T I O N OF E L E C T R O L Y T E
REAL M W l M W S
OCBMMON T I T L E , NCOMPlf N L I G H T , N A C T C O, T C R I T , P C R I T , V C R l T ,
11 D E N T , VL I Q , C V L I Q , P S A T , C P S A T , C A C T C O , GAMMA, X , SUMX,
2 P , 'T, TOLD,
P H I , B, BMI X , VMI X , Z M I X , F , PREFER, NREFER,
3 C H E N R Y , V L I Q L , C V L I Q L , OMEGAH, D I P O L E ' , E T A , N C R l T
4 , V R A T I 0 , R T , R R T , D , WTMOLE
COMMBN A , X R , A Q , D E N A , 0 $ N B , D l S S K , M W i , M W 2 ' , X I
O D I MENS I ON T I T L E U S ) , T C R I T ( 5 , 5 ) , P C R I T ( 5 , 5 ) , V C R I T ( S ) ,
IBM EG A(S),IDENT( 5 , 4 ) , V L lQ ( S ) , C V L IQ (5 ,3 ) , PSAT(S),
E r P S A T ( 5 > 6 ) , c A c T c & ( 5 , 5 , 3 ) , C1AMMA. ( 5 ) , X ( - 5 ) , Y ( S " ) , P H I ( S ) ,
3 8 ( 5 , 5 ) , F ( 5 ) , P R E F E R ( 5 ) , NREFER( 1 0 ) , HENRY( 1 0 , 5 ) ,
4CHEN RY(1 0 , 5 , 2 ) , V L I Q L f 1 0 ' 5 ) , C V L I Q L ( 1 0 , 5 , 2 ) , OMEGAH(S),
C
C
Calculating
S D I P O L E ( 5 ) , E T A ( S ) , D ( 5 ) , WT M O L E ( 5 )
DIMENSION PARAM( 6 ) , D A T A ( 5 0 , 1 0 ) , P T ( 2 ) , P c A L ( S O )
DIMENSION A ( 4 ) , X R ( 3 ) , A 0 ( 3 ) , C M O L A R ( I ) , X I ( 2 ) , X X ( 3 )
D E N M I X s D E N S I T Y OF M I X T U R E AT C O M P O S I T I O N X ( I )
. . . . . .
AVGMWTs AVERAGE M - W 9 OF S O L U T I O N BASED ON C O M P O S I T I O N FACTOR .
C MB L A R s M O L A R I T Y . OF. E L E C T R O L Y T E S O L U T I O N C O N V E R T E D . FROM MOLE F R A C T I O N
MWl o M , W , OF S O L U T E ,
MWSsMW OF S O L V E N T
.C
DENMIX = DENAfXT I ) * DEN B .
A V GMWT s X f I ) * M W 1 + X ( 2 ) * M W 2
CMBLAR(I)
C
C
C
c
C
C
s
■
.
(X(l)*DENMl% *1000.)/AVGMW T'
A ( I ) ARE C O E F F I C I E N T S BF C U B j C E Q U Q T I O N USED I N S O L V I N G FOR
TED. M O L E C U L E S ,
D I S S K = A S S O C I A T I O N CONSTANT OF E L E C T R O L Y T E
ELECMs= c o n c e n t r a t i o n o f H f or o h = i o n
in
solution
C O N J M O e ■CONc
OF
C ONJ UGAT E
I ON
I N SOLUTION
ASSOCIA^
• AU )
A(2)
s IeOO
= DISSK
A{ 3) =■ f (DI SSK*CM8 UA R( D ■+ i « 0 E e l 4 )
A(4) a q ( D lS S K * l* 0 E - i4 )
I F { D I S S K « I « 0F- 04 ) 9 0 0 , 9 0 1 , 9 0 1
•
900
12
13
15
16
17
18
19
20
901
902
CALL C U B I C ( A , X X , X I ( 2 ) )
IF ( X X ( I ) ) 1 5 ,1 5 ,1 2
IF ( X I ( D )
15,13,15
EL ECMB @ X X ( I )
GO TQ 9 0 2
IF ( X X ( 2 ) ) 1 8 , 1 8 , 1 6
IF ( X I ( 2 ) )
18,17,18
ELECM8 e X X ( 2 )
6 9 TB 9 0 2
IF (X X ( 3 ) ) 3 0 , 3 0 , 1 9
IF ( X I ( 3 ) ) 3 0 , 2 0 , 3 0
ELECMe = X X ( 3 )
G S . T a 902
EL EC M G'« C M B L A R ( I )
C6NJM& g d » 0 E ^ 1 4 ) / E L E C M g
AMgLAR = E L E C M e ^ C e N U M e
. '36
30
'3 2
^ .
CSVMOL s ( E L E C M e ^ A M S L A R ) / 0. 1 SSK
X (I)
= <C8VM QL* AVG MWT )/(DENMI X * 1 0 0 0 » )
X (2)=1.0*X (1)
FSRMAT ( I IH NB R E S U L T )
GB TB 3 2 '
PRINT 36
RETURN • END
r> o n o
SUBROUTINE
C U B l C ( A 1, X R / X I )
■ S O L U T I O N OF C U B I C E Q U Q T I D N
A (j)*X **3 + A(2)*X **2 + A(3)*X**1
+ A(4>
s
O
.
DIMENSION
IPATH=S
EX
I , /3,
IF ( A ( 4 ) )
1004
A(4),
1006,
XR(3),
1004,
AQ(3)
1006
10Q6
X R (I) 5 0,
QO TQ 1 0 3 4
A2s A ( 1 ) * A ( 1 )
, ..
Q 8 (2 7 ,*A 2 *A (4 )« 9 i*A (l)*A (2 )*A (3 )
1008
I F (Q) 1 0 1 0 , ■1 0 0 8 /
Z=O'
G O T O 1032'
1014
+
2,*A (2)**3)/(54 ,*A 2*A (1))
'
1014
!PATH s I
'
P = ( 3 , * A ( 1 ) * A ( 3 ) , A ( 2 ) * A ( 2) : . ) / ( 9 , * A 2 )
ARG '=.• P * P-X-R -' 4- Q* Q- .
1016
I F- ( A R G ) 1 0 1 6 , - 1 0 1 8 , , 1 0 2 0
Z s ,2 .* S Q R T F ( ^ P ) *C 0 S F (ATANp(SQRTF( * A R G ) / Q ) / 3 , )
GD TO' 1 0 2 8
Z= * 2 a * Q * * E X
1018
1020
1022
1024
1026
I C28
1030
1032
.1034
Ge ' TQ 1 0 2 8
SARG = S Q R T F ( A R G )
:
I F ( P ) . 1 0 2 2 , 1 0 2 4 , 1026
Z= « ( 0 t S A R G ) * * E X H (Q ,S % R G )**E X
GD.TB 1028
Z s f(2 i*0 )**E X
GS Tc) 1 0 2 8 . .
Z = CSARG m Q ) * * E X " ( S A R G . + Q ) * * E X
GD , TQ ( 1 0 3 0 , 1 0 3 2 ) ,
IPATH ■
Z B «Z
XR(I)
= (3. *A(1)*Z A(2))/(3,*A(1))
AO(I) s A ( I )
-56-
1010 C =, o
A Q (.2)
s A ( 2) + X R ( I ) *A ( I )
s A (3) + XR(U*AQ(2)
c a l l - quad
( A Q, X R ( 2 ) , xR(3),xn
RETURN
END
AQ ( 3)
SO LUTIO N
BF
THE
(A
t
XRl',
QUADRATIC
A ( 1 ) * X * * 2 + A(S)-H-X + A( 3)
DIM ENSIO N
Xl
A (3)
s -A(2)/(2,*A(1X)
. ■ D I S C "= X U X l ™ A ( S ) V A ( I )
IF(DISc)
10,20,20
10 X2 B S Q R T F ( ^ D I S C )
'
■
XRl ; Xl ' ' '
XR2 = Xl
XI s X2
GO TO 30
20 X2 s S Q R T F ( D I S C )
- XRl * Xl + X2
XR2 = Xl « X2
XII 3 Oe
30 RETURNEND
XR2,
X I)
EQUATION!/
= Os
-57-
O OO O
SUBROUTINE Q U A D
Pr ogr am f or . C a l c u l a t i n g
D i s s o c i a t i o n Cur ve
Covalent Molecul e
Concentration
C
C
C
f r om
OOO
1ATED M6L' ECULES
C
C e VMQL
«. F R A C T I O N
QfT U N D I S S O C I A T E D
MOLECULES
c
DENMIX s DENA +- X( I ) ^DEHB.
AVGMWT' s X(1)*MW1 + X ( 2 )*m U2 .
XMOLAR s (X(1)*DENMIX*10&Q,)/AVGMWT .
...
. _
X 1.8N :'s (M,00033046)*(XM6LAR**3) + *010549*XM8LAR**2. B#l56l3*XMGLAR
!+,95537
COVMBL
X(I )
X ( 2)
m 1* 00 CBVMBL >
XIBN
DATA(J A -)
a 1,00 * X ( I )
I
Cn
CD
A ctivity Coefficient
for Electrolytes
C
C
Q
C
C
C
C
C
C
Calculation
in
Sy mme t r i c
SYMMETRIC CONVENTION A C T IV IT Y C O E F F IC IE N T
TO Be USED IN SUBROUTINE CALPHW
Convent i on
CALCULATION
FOR E L E C T R O L Y T E S
XD(I)
CORRECTED MOLE FRACTION
GAMMA(T) s A C T I V I T Y C O E F F I C I E N T
DI SNl s 2 , 0 0
XL AMD 3, s VRATIO * EXPF ( * C A C T C 0 ( 1 , 2 , 1 ) / R R T )
XLAMDB -B EXP'F- ( b CAc Tc 6 ( 2 / 1 ji 1 V R R T ) / V R A T IS
X D ( I ) 5 X ( I ) / ( U O +■ X ( I ) )
XD ( 2 > e X ( 2 ) / ( 1 * 0 + X ( I ) : )
XLDlR § X D ( I ) + XUAMDUXDi 2)
XLDRl s XD-(R) + XLAMD2*XD(I )
X L D l R l & 2 , * X L A MD 1 * X D ( I T f X D ( I )
XLDlRR * XD(2) » 2, * XD( E) * XLAMD1
XLB212. s XD(2)- *XLAMD2 T 2 * * X D ( 2 )
XL d R I I . g & * * X D ( I ) f XLAHD2*XD( I )
FACTl e . XD( I ) * X L D 1 2 2 / X L D l 2
FACT2 s ( X D ( 2 ) / D I S N 1 ) * ( % L D 2 1 2 / X L D 2 1 )
FACTS § ( D - I S N U X D ( I ) *.XLD12 1 ) / X L D I R
FAcT4 = ( X D ( 2 ) * X L D R l i ) / X L n 2 . 1
GAMMA(I) = E x P ( * F A C T l * F . A C f 2 ) / X L D l 2
=
A ctivity Coefficient
for Electrolytes
Calculation
i n Un s y mme t r i c
Convent i on
” 60**
C
:
C
UNSYMMETRI C CONVENTION ACTIVITY COEF CALC FOR ELECTROLYTES
C
TO BE USED IN SUBROUTINE CALXLW
C
C
DISN l ? NUMBER OF MOLECULES PRODUCED BY DISSOCIATION
C
XLAMDl♦ XLAMD2 = WILSON PARAMETERS FOR ELECTROLYTES,
XD(I) =
C - CORRECTED MOLE FRACTION
DISN l - 2 . 0 0
XLAMDl = VRATIO * EXPF (-CACTCOt1 , 2 , 1 )/RRT)
XD(I) = X ( I ) / ( 1 . 0 + X ( I ) )
XD ( 2 ) = X ( 2 ) / ( I • O + X ( D )
XL D 12 = X D ( I ) + XLAMDl-x-XD( 2 )
XL Dl 2 I ■'= 2 . * X L A MD 1 * X D ( 1 ) - X D ( 1 )
GAMMA(I) = E X P ( ( ( X D ( 2 ) * X L D 1 2 1 ) / X L D 1 2 ) + 2 , * X D (2> / D I SN I - 2VDISN1).
I * ( XLAMDl/ X L D l 2)
GAMMA!2) = EXP( -D I SN1*XD(I ) *XL D 12 I /XLD12 - 2 . * X D ( 1 ) ) / X D ( 2 )
APPENDIX C - DATA
TABLE C - I
BINARY VAPOR-LIQUID EQUI LI BRI UM DATA
Mol e % (A)
Liquid
(A)
(A)
Ammoni a
i n
Temp
°c ■
Vapor
(B)
Wat er
0.0
0.0
120.6
0. 1 5
I .5
I 20
2.9
29.0
HO
6.2
50.6
I 00
10.0
67.5
90
14 . 0
80.3
80
18.5
89.2
70
23.4
94.8
60
28.5
97.5
50 ■
33.7
98.4
40
Hydrofluoric
Pressure
mm Hg
Acid
(B)
I 520
Wat er
4.95
. 78
101.6
9.20
1. 8 3
10 2. 8
18.9
6. 4 2
10 6. 8
22.8
10 . 6
10 8. 4
27.9
17.8
■I I 0. 3
33.8
30.6
11 1. 7
' 34.4
32. 1
112.0
760
-62Mole
%
(A) in
Liquid
(A)
(A)
H ydro fluoric
Vapor
Acid
(B)
Temp
0C
Wat er
34.6
34.0
112. 1
35.8
35.7
112.3
36.7
38.6
112. 1
39.7
47.5
111.4
44.4
63.3
10 8. 7
50. 3
81 . 2
10 1. 7
52 . 3
86.2
98.9
56.0
92.2
90.9
58.2
96.9
86.6
61 .8
98.8
79.0
63.8
98.4
74.6
69 . 8
98.5
61 . 6
79.8
98.6
45 . I
88.0
99.0
33.5
Hydrobromi c Acid
(B)
2. 4
0.0
5. 4 5
0.0
Pressure
mm Hq
Wat er54.83
109. 7
99. 7
12.85
. 32
58 . 6
16 . 94
. 05
38 . 3
18.20
13.30
36.9
18.80
19.90
36.4
-63Mole
%
(A)
in
I emp
0C
Pressure
mm Hg
Liquid
Vapor
19.20
24.89
36.3
19.60
2 6 . 93
35.6
20.28
44.92
40.3
2 1 . 12
54.90
51 . 6
21 .38
65.63
53. 3
22.85
85.93
104.0.
25. 17
96.30
103. 1
'drochloric
Acid
(B)
Wat er
5. 11
0. 2 3
7.86
I . 08
23 6. 0
11.94
10.22
205. 3
12.50
13.13
203.6
12. 77
I 5 .v7 5
202.0
13.85
25 . 97
209.9
14. 63
36. 81
226.6
16 . 48
61.18
299. 2
17.94
76.92
42 7. 7
19.42
84.08
52 2. 2
19.82
85.84
• 561. 3
2. 5 3
0.0
5.20
0.0
75.9
19.95
26 4. 3
16 . 0
14.6
-64Mole
%
(A)
Liquid
in
Vapor
Temp
0C
Pr essur e
mm Hq
8.60
.51
12 . 3
9.78
I . 08
12.2
1 1 . 16
3. 21
10. 3
13 . 56
11.45
9. 3
14 . 13
16 . 17
9. 2
17 . 47
68.45
16. 1 .
19.50
88.85
38 . 5
22.40
97.90
14 5. 3
Hydrochloric
Acid
(B)
Wat er
2. 5 3
0.0
55 . 2
5.20
0. 7
8.60
0.83
89.9
9.78
I .97
84. 1
12.90
12.70
74. 1
13.40
16.14
. 74.0
14 . 13
23.40
76 . 3
1 5 . 14
34.65
86.5
16.76
58.38
111. 0
17. 47
70.50
I 45 . 8
I .0
0. 01
100.4
3.0
0.08
100. 79
114. 7
' 104. 7
760.
i
-65Mol e % ( A)
in
L i q u i d ________ Vapor
Temp
Pressure
°C____________ mm Hg
5.0
0. 31
10 1 . 5 5
10.0
4.78
104. 35
15.0
38.92
107.60 •
20.0
86.20
109.84
25.0
95 . 97
10 6 . 0 4
30.0
97 . 60
90.70
35.0
98.53
62.50
40.0
99.39
29.2
TABLE. C - I I
PHYSICAL PROPERTIES OF COMPONENTS
C r i t i c a l Properties
Phase Non i d e a l i t y
Tc , 0K
P ^ , at m.
and P a r a me t e r s
cc
c gmol
CO
. 133
324.6
82. 1
87.6
461.00
64.00
69.0 '
363.20
84.50
405.00
647.4
I 00.74
. 111. 3
72.5
218. 3
55.2
.
Characterizing
ajH .
Va p o r -
U 5Debye . n Compound
. 013
1.05
0. 3851 . . 013
I . 92
0. 0 6 7 2
. 013 '
0.80
0.250
. 010
1. 47
0 . 0 Hydr ogen
chloride
0 . 0 Hydr ogen
fluoride
0 . 0 Hydr ogen
br omi de
0 , 0 Ammoni a
0. 3 44
. . 010
1. 83
0 . 0 Wat er "
-66-
(Table C-II c o n t i n u e d )
C o n s t a n t s f o r t h e Vapor P r e s s u r e E q u a t i o n ( f r o m VAPFIT
Pr ogr am o f P r a u s n i t z )
C
I n P ( a t m) - C1 +
+ C4 T + C5 T 2 + Cg I n T
cI
C2
C3'
C4
C5
55; 9449130
-2958.5466 .
0.0
0. 01 71 6886
0.0
121. 4358521
-5606.8633
0.0
0.038559
0. 0
77. 8766174
-3907.2358
0.0
0. 0 1 8 7 5 1 4 5 7
0.0
17. 9889374
-3094.2170
0.0
70.4346943 -
-7362.6981
T e mp e r a t u r e
Dependence o f
T -j , ,0K
0. 006952085
Liquid
Mo l a r
- 8. 3 00 0
Hydr ogen
chloride
.-20.000
Hydr ogen
fluoride
- I I . 78995
Hydr ogen
br omi de
. 8999997
Ammoni a
- 9. 0000
Wat er
Vol ume
T 2 , °K
V2
c c / g mo l
T3 ’ ° K
273.15
39. 502
313. 15
. '_
--
cc/gmoI
0.0
- 0. 0 00 650 27
C6
■
Vg c c / g mo l
52 . 3 6 7
Hydr ogen
chloride
Hydr ogen
fluoride
■Hydrogen
' B r o mi de
Ammonia
213.. I
29. 869
293. 15
20. 2735 .
206.15
29. 213
273. 15
27. 113
28 8 . 6 5
28 , 19 2
310. 95
29.93
277.13
81. 348
29 8 . 1 5
83.229
323. 15
8 5 . 1 4 7 Wat er
--
-67-
( T a b l e C-II c o n t i n u e d )
D i s s o c i a t i o n c o n s t a n t s used i n
in.parentheses)
Ammoni a
Hydrofluoric
pr ogr am COVCAL ( r e f e r e n c e
1. 7 8 x 10
Acid
-5
(U-
6.75 x 10’
(I)
H y d r o b r o mi c A c i d
1 . 0 0 x 10'
(approximately
as HCI.)
Hydrochloric
2 . 5 x I O^
(8)
Acid
. 24
P a r t i a l m o l a r vol ume a t
acid (reference in
(no b a s i s i n
selection)
in fin ite dilution
parentheses)-
for
same
this
hydrochloric
2 9 8 . 1 5° C
1 7 . 8 2 c c / g mo l
( 7)
3 3 3 . 15 ° C
1 8 . 8 2 c c / g mo l
( used t h i s t o g e t pr ogr am
LTFTiXW t o ' r u n ; n o t a c t u a l
- vaIu e )
Equation f o r s o l u t i o n d e n s i t i e s ( wat er is s o l v e n t )
■ ( f r o m d e n s i t y d a t a i n P e r r y ' s C h e m i c a l - Engi n e e r i n g
Han d b o o k )
Densi ty. = A X + B
■
B
A
Ammoni a
Hydrofluoric
-
I . 00
Acid
1. 0 0
Hydr obr omi c Aci d
I . 00
Hydrochloric
I . 00
Acid
.373
.3.75..-
,
I . 30 .
. . 50
LITERATURE CITED
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"
Mc Co r mi c k , J . M. , M. G. S a l v a d o r i , Nu me r i c a l Met hods i n
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-
\
,
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v a p o r - liq u id e q u ilib r iu m
IMAMK AND addhbbk
W " 5 7 -g
337,
c o p
5