chemistry 163b multicomponent phase rule solution behavior ... · if the system is maintained at p...
TRANSCRIPT
1
Che
mis
try
163B
M
ultic
ompo
nent
Pha
se R
ule
Solu
tion
Beh
avio
rH
ando
ut
2
ph
ase r
ule
1 c
om
po
nen
t
f =3-
p
1 ph
ase:
T
,P v
ary
inde
pend
ently
2 ph
ases
pre
sent
: T
and
P co
vary
3 ph
ases
pre
sent
: fi
xed
T an
d P
3
mu
lti-
co
mp
on
en
t p
hase r
ule
•c
= nu
mbe
r of c
ompo
nent
s (m
olec
ular
spe
cies
)p=
num
ber o
f coe
xist
ing
phas
es•
inte
nsiv
eva
riabl
es re
quire
d to
spe
cify
sys
tem
T, P
, Xi(�
) (m
ole
fract
ion
of c
ompo
nent
iin
pha
se �
) •
tota
l var
iabl
es to
spe
cify
tota
l var
s=2
+ (c
-1) p
[2 fr
om T
,P; (
c-1)
inde
pend
ent m
ole
fract
ions
in e
ach
phas
e]•
tota
l res
trict
ions
for e
quili
briu
m
tota
l res
trict
ions
= c
(p-1
)[a
lread
y T,
P s
ame
in e
ach
phas
e]
•f =
tota
l var
iabl
es –
tota
l res
tric
tions
•f =
2 +
(c-
1) p
-c
(p-1
) =
2 +
c -
p
��1
()
()
()
()
pi
ii
ise
tth
en
(p-1
res
tric
tion
s fo
r ea
ch c
ompo
nen
t)
cp
tota
l re
stri
ctio
ns
for
c co
mpo
nen
ts
��
��
��
��
�
�
�
f =
2 +
c –
p f
=3-p
fo
r c=
1
4
ph
ase r
ule
an
d C
d-B
i p
hase d
iag
ram C
d (s
) +B
i (s)liq
uid
+ C
d(s)
liq+
Bi(s
)
liqui
d
•f=
2+c-
p•
c=2
(Bi,
Cd)
•f=
4-p
•se
t P=1
atm
•f re
aini
ng=3
-p•
varia
bles
:T,
� C
d in
liqu
idC
d (s
) +B
i (s)
P=
1 at
m
"� C
d "
�"� C
d "
�
5
Lis
ten
up
!!!
UN
DER
STA
ND
TH
E FO
LLO
WIN
G D
ISC
USS
ION
OF
THE
PHA
SE R
ULE
AN
D T
HIS
BIN
ARY
CO
MPO
NEN
T PH
ASE
D
IAG
RA
M
it m
ay b
e ve
ry g
ood
for y
our f
utur
eha
ppin
ess
6
ph
ase r
ule
an
d C
d-B
i p
hase d
iag
ram
Cd
(s) +
Bi (
s)
liqui
d
•f=
2+c-
p•
c=2
•f=
4-p
•se
t P=1
atm
•f re
aini
ng=3
-p•
varia
bles
:T,
� C
d
liqui
d,p=
1, f=
2T,
� cd
can
vary
solid
< 1
46
C,
p=2,
f=1
T ca
n va
ryno
te: C
d(s)
and
Bi(s
) are
pure
sol
ids,
not s
olut
ion
(allo
y),
scd
=1
s Bi=
1
" C
d "
�
m.p
. of p
ure
Bi=
m.p
. of p
ure
Cd=
271.
4ºC
321.
1 ºC
7
ph
ase r
ule
an
d C
d-B
i p
hase d
iag
ram
liqui
d +
Cd(
s)liq
+ B
i(s)
•f=
2+c-
p•
c=2
•f=
4-p
•se
t P=1
atm
•f re
aini
ng=3
-p•
varia
bles
:T,
� C
d
liqui
d +
Cd(
s),
p=2,
f=1
only
T o
r � cd
can
inde
pend
ently
vary
(i.e
.T
and
�cd
cova
ry)
just
app
ears
low
er T
tot
alC
d fi
xed
�C
d
Cd(
s) Cd(
s)
tota
l m
ole
fra
cti
on
Cd
8
ph
ase r
ule
an
d C
d-B
i p
hase d
iag
ram
(eu
tecti
c)
liqui
d +
Cd(
s)liq
+ B
i(s)
liqui
d +C
d(s)
+ B
i(s)
p=3,
f=0
T an
d �
cd
fixed
Cd(
s)ju
st a
ppea
rsB
i(s)
just
app
ears
eute
ctic
=con
stan
t fre
ezin
g co
mpo
sitio
n (m
ixtu
re)
T=14
6C
,�
Cd=
0.55
=0.3
9 w
t%C
d (s
) +B
i (s)
"� C
d "
�
f reai
ning
=3-p
9
ph
ase r
ule
an
d C
d-B
i p
hase d
iag
ram
(eu
tecti
c)
liqui
d +
Cd(
s)liq
+ B
i(s)
liqui
d +C
d(s)
+ B
i(s)
p=3,
f=0
T an
d �
cd
fixed
Cd(
s)ju
st a
ppea
rsB
i(s)
just
app
ears
eute
ctic
=con
stan
t fre
ezin
g co
mpo
sitio
n (m
ixtu
re)
T=14
6C
,�
Cd=
0.55
=0.3
9 w
t%C
d (s
) +B
i (s)
"� C
d "
�
f reai
ning
=3-p
10
no
t all s
olid
-so
lid
mix
ture
s f
orm
eu
tecti
cs
NaA
lSi 3O
8 +
CaA
l 2Si 2O
8C
u+
N
i
11
Idea
l Sol
utio
ns
12
Mol
ecul
ar B
asis
for
Ide
al S
ol’n
s.
�In
pur
e liq
uid
A, t
here
are
on
ly A
-Ain
tera
ctio
ns.
�In
pur
e liq
uid
B, th
ere
are
only
B-B
inte
ract
ions
.�
In so
lutio
ns o
f A a
nd B
, th
ere
are
A-B
inte
ract
ions
as
wel
l.�
�Hm
ixin
g= 0
mea
ns t
hat
all t
hree
in
tera
ctio
ns a
re o
f eq
ual
stre
ngth
.ht
tp://
clas
sweb
.gm
u.ed
u/sd
avis
/che
m33
1/en
gel9
x.pp
t
13
ideal so
luti
on
s
prop
ertie
s of
the
solu
tion
depe
nd o
nly
on th
e pr
oper
ties
ofco
mpo
nent
s in
bul
k (p
ure)
and
the
mol
e fra
ctio
ns o
f the
com
pone
nts.
for e
xam
ple
parti
al v
apor
pre
ssur
e of
com
pone
nts:
v v()
()
()
()
AA
A
BB
B
PX
P
PX
P
� �
� �
� �
vapo
r pr
essu
re o
f pur
e A
vapo
r pr
essu
re o
f pur
e B
��
��
1
vv
()
()
()
()
()
()
()
tota
lA
BA
AB
B
AA
AB
AA
BB
PP
PX
PX
P
XP
XP
XP
PP
��
��
��
�
�
�
�
�
��
��
��
�
mol
e fr
actio
n A
in li
quid
v()
()
•
()
()
()
()
()
ii
i
ii
ii
i
Pa
P
idea
la
non
idea
la
�
� ��
��
�
�
��
��
�
corr
ectio
nfo
r no
n-id
ealit
yac
tivity
HW
#55
linea
r P
tota
lvs
XA
(�)
14
liq �
�vap
Eq.
in B
inar
y M
ixtu
res
�Bo
th th
e liq
uid
and
the
vapo
r ph
ase
are
bina
ry
mix
ture
s of A
and
B.
�x
A, x
Bar
e th
e m
ole
frac
tions
in th
e liq
uid.
�y
A, y
Bar
e th
e m
ole
frac
tions
in th
e va
por.
�p
A, p
Bar
e th
e pa
rtia
l pr
essu
res i
n th
e va
por.
http
://cl
assw
eb.g
mu.
edu/
sdav
is/c
hem
331/
enge
l9x.
ppt
15
ben
zen
e-t
olu
en
e,
qu
ite id
eal (
sim
ilar
to F
ig 9
.2 E
&R
) !!
http
://w
ww
.che
m.u
csb.
edu/
cour
sepa
ges/
06fa
ll/1C
-Wat
ts/d
l/Lec
ture
_Not
es/L
ectu
re16
.%20
11-8
-06C
ollig
ativ
e%20
Prop
ertie
s%20
Solu
tions
��
(
)to
tal
AA
BB
PX
PP
P�
��
��
�
16
Eth
yl A
ceta
te/A
ceti
c A
nhyd
ride
0
100
200
300
400
500
600
700
800 0.
00.
20.
40.
60.
81.
0
x eth
yl a
ceta
te
p /torr
http
://cl
assw
eb.g
mu.
edu/
sdav
is/c
hem
331/
enge
l9x.
ppt
(4 to
rr)
17
X(�
)vs X
(v)(n
ota
tio
n c
on
ven
tio
ns) (
)(
)
1
()
:
(&
)
solu
tion
AA
A
A
con
ven
tion
s
mol
eX
X
ER
mol
eX
�
v
frac
tion
liqu
id c
ompo
nent
A:
or
mos
t des
crip
tive
;
b
ut a
lso
X (s
lopp
y) a
nd x
frac
tion
gas
(vap
or) c
ompo
nent
A:
mos
t des
crip
tive
;
b
1(&
)E
Ru
t als
o y
[no
t ver
y d
escr
ipti
ve a
nd w
eird
??;
b
ut n
ote
for
E&
R H
W p
robs
]
18
X(�
)vs X
(v)
rela
te X
(�)vs X
(v)assu
min
g v
ap
or
is id
eal g
as
()
()
()
()
()
()
()
()
()
tota
lA
Bto
tal
AA
BB
AA
BB
AB
tota
lto
tal
tota
lto
tal
RT
PP
Pn
VR
TR
TP
nP
nV
V
Pn
Pn
Xan
dX
Pn
Pn
�
�
��
��
�
v
vv
vv
vv
vv
()
()
()
()
(&
')
AA
A
AA
AA
A
AA
AA
tota
lto
tal
PX
Por
PX
P
XP
PX
ER
sy
PP
��
�
�
��
��
��
�v H
W 7
pro
bs 5
0, 5
5 u
se E
&R
’s y
i
19
ideal so
luti
on
th
erm
od
yn
am
ics:
key i
deas
sim
ilar
to s
ec 6
.4 E
&R
vha
ve p
rove
n
sin
gle
com
pone
nt A
()
()
AA
��
�� 0
()
()
,
()
()
,,
i
i
jj
j
ii
TP
ii
dGS
dTV
dPdn
dGS
dTV
dPdn
ateq
uil
ibri
um
dGdn
��
�
��
�
� �
�
��
��
��
� �
�
��
00
i
ii
ii
ii
ii
ii
for
each
com
pon
ent
idn
dn
dndn
for
each
com
pon
ent
��
�
��
��
�
��
��
��
��
��
()
()
()
()
()
()
()
()
()
,
�
��
�
��v
vv
v
�ph
ase
icom
pone
nt
20
���������������
ho
w d
oes �
(v)re
late
to
X (�)
?
��
��
��
��
��
��
()
()
()
()
()
()
()
()
()
()
()
()
()
()
()
()
(,
,)
()
(,
,)
iii
ii
i
ii
i
ii
ii
ii
i
TP
XT
RT
lnP
T
f i
PX
P
TP
XT
RT
lnP
TR
Tln
X
�
�
�
�
�
�
�� �
��
�������
vv
vv
vv
vv
vv
��
�
�
��
��
?��
()
vi
T�
�
��
()
()
()
()
()
(,
,)
()
ii
ii
iT
PX
TR
Tln
X�
�
��
�v
v�
��
id
eal g
as;
id
eal s
olut
ion)
()
()
(1
1v i
ifo
rfo
r�
��
��
21
a lit
tle m
ore
of
ho
w d
oes �
(�)re
late
to
X (�)
?
��
()
()
()
()
(,
,)
()
ii
ii
TP
XT
RT
lnX
��
�
�v
v�
�
solu
tion �
vapo
r co
mpo
nent
s in
equ
ilibr
ium
at T
v(
)(
)i
i�
��
��
�
v(
)(
)(
)(
)(
,,
)(
,,
)i
ii
iT
PX
TP
X�
��
��
�
pure
liqu
id �
pure
vap
orco
mpo
nent
s in
equ
ilibr
ium
at T
we
get
��
()
()
()
()
(,
,)
()
ii
ii
TP
XT
RT
lnX
��
�
��
��
�id
eal s
olut
ion
��
()
()
()
()
()
(,
,)
()
ii
ii
iT
PX
TR
Tln
X a i
��
�
��
��
�����
��
�co
rrec
ted
for
noni
deal
ity
22
Idea
l Sol
utio
ns
I.T
he
pa
rtia
l m
ola
r v
olu
me
of
ea
ch
co
mp
on
en
t in
so
luti
on
is
th
e
sa
me
as
its
mo
lar
vo
lum
e in
pu
re liq
uid
an
d t
hu
s t
he
vo
lum
e
of
the
so
luti
on
is
th
e a
dd
itiv
e v
olu
me
of
the
pu
re c
om
po
ne
nts
II.
Th
e e
nth
alp
y o
f m
ixin
g is
ze
ro:
III.
Th
e f
ree
en
erg
y o
f m
ixin
g is
:
IV.
Th
e e
ntr
op
y o
f m
ixin
g is
:
ln�
��
�m
ixk
kk
Gn
RT
X
ln�
��
��
�� �
�m
ixm
ixm
ixk
kk
HG
Sn
RX
T0m
ixH
��
ii
VV
��
�i
ii
Vn
V��
from
:http
://sw
itkes
.che
mis
try.
ucsc
.edu
/teac
hing
/CH
EM
163B
/Win
ter1
3/ha
ndou
ts_W
13.h
tml
Ha
nd
ou
t #
49
23
Lis
ten
up
!!!
UN
DER
STA
ND
TH
E FO
LLO
WIN
G D
ISC
USS
ION
OF
THE
PHA
SE R
ULE
AN
D T
HIS
BIN
ARY
CO
MPO
NEN
T PH
ASE
D
IAG
RA
M
it m
ay b
e ve
ry g
ood
for y
our f
utur
eha
ppin
ess
24
T v
s X
(P
=1 a
tm)
for
so
luti
on
-vap
or
eq
uilib
riu
m T
OLU
ENE
+ B
ENZE
NE
tolu
ene
(b.p
.=38
3.78
) +
benz
ene
(b.p
.=35
3.25
)
tol+
ben
(sol
utio
n)[f r
emai
ning
=2]
tol+
ben
(vap
or)
[f rem
aini
ng=2
]
so
luti
on
co
mp
osit
ion
vap
or
co
mp
osit
ion
25
T v
s X
(P
=1 a
tm)
for
so
luti
on
-vap
or
eq
uilib
riu
m T
OLU
ENE
+ B
ENZE
NE
tolu
ene
(b.p
.=38
3.78
) +
benz
ene
(b.p
.=35
3.25
)
tol+
ben
(sol
utio
n)[f r
emai
ning
=2]
tol+
ben
(vap
or)
[f rem
aini
ng=2
]
065
()
.be
nz�
�a
solu
tion
of X
at T
=35
7K
is a
liqu
id
83v
at T
~36
2K th
e so
luto
n is
in
equ
ilibr
ium
wit
h va
por
()
.be
nz�
�
v
if th
e sy
stem
is m
aint
aine
d
at P
1 at
m a
nd T
is r
aise
d
to 3
65K
, liq
uid
will
eva
pora
te
unt
il =
0.53
and
=0
.74
()
()
tota
l
benz
benz
�
��
�
� � �
065.
tota
lbe
nz�
�
�0
65v
abov
e T
=38
9.6K
the
syst
em is
all
vapo
r w
ith
()
.be
nz�
�
)to
tal
that
boi
ls a
t ~36
2K (P
=1a
tm�
liqui
dva
por
tota
l
vapo
rco
mpo
sitio
n
solu
tion
com
posi
tion
26
fracti
on
al d
isti
llati
on
http
://w
ww.
wpb
scho
olho
use.
btin
tern
et.c
o.uk
/pag
e12/
gifs
/Fra
cDis
tRed
.gif
27
fracti
on
al d
isti
llati
on
[T
bp
vs (
Xb
en
ze
ne)s
olu
tio
n]
bp
•va
pbe
nbe
nzen
e•
ben
(�H
)P
(T)
11
•ln
=--
1atm
RT
(T)
��
��
��
��
��
��
!
vap
ben
•be
nbp
vap
tol
•to
lbp
(�H
)1
1-
-•
RT
(T)
benz
ene
(�H
)1
1-
-•
RT
(T)
tolu
ene
P(T
)•
=e
1a
tm
P
vapo
r pr
essu
re o
f ben
zene
at T
vapo
r pr
essu
re o
f tol
uene
at
(T
T)
•=e
1a
tm
��
��
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benz
ene
tolu
ene
solu
tion
•so
lutio
n•
benz
ene
benz
ene
tolu
ene
tolu
ene
•in
idea
l sol
utio
n P
(T)=
XP
(T) a
nd P
(T)=
XP
(T)
benz
ene
benz
ene
benz
ene
tolu
ene
solu
tion
•so
lutio
nso
lutio
n•
solu
tion
benz
ene
bpto
luen
ebp
•at
boili
ng P
+ P
= 1
atm
1atm
=XP
(T)+
(1-X
)P(T
)
�
benz
ene
solu
tion
solu
tion
bp•
for
agi
ven
Xso
lve
for
T
(or
bette
rha
veM
athe
mat
ica
solv
eequ
atio
ns
se
e ha
ndou
t #50
)
��
lnso
bpbe
nzen
eT
X
28
fracti
on
al d
isti
llati
on
[T
bp
vs (
Xb
en
ze
ne)v
ap
or ]
ln
ln
()
()
sinc
e1
soso
lutio
nbe
nbe
nbp
vapo
rbe
nzen
ebe
nzen
eto
tal
tota
l
vapo
rso
solu
tion
benz
ene
ben
ben
bp
solu
tion
tota
lbp
solu
tion
bp
XP
TP
XP
P
XX
PT
Pat
mat
T
getT
from
equa
tions
onpr
evio
ussl
ide
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vapo
rbp
benz
ene
TX
29
Fra
cti
on
al D
isti
lati
on
so
luti
on
co
mp
osit
ion
vap
or
co
mp
osit
ion
I.�st
art w
ith 5
0-50
mix
ture
�T b
p �
366
II.�
vapo
r Xv be
nzen
e �.
72
III.
�co
nden
se X
soln
benz
ene �.
72�T b
p�35
9.5
IV. �
evap
orat
e �
vapo
r Xv be
nzen
e �.
88
V.
etc
, ...
VI.
app
roac
hes
Xbe
nzen
e=1
I
II
III
IV
botto
m o
f col
umn
(war
mer
)
top
of c
olum
n (c
oole
r)
30
azeo
tro
pe (
no
n-i
deal
so
luti
on
)
•fra
ctio
nal d
istil
latio
n le
ads
to c
onst
ant
boilin
g az
eotro
pe in
vap
or
•and
(in
pot
afte
r az
eotr
ope
boils
off)
•(X
A) in
itial
> (X
A) a
zeot
rope
pure
A
•(X
A) in
itial
< (X
A) a
zeot
rope
pur
e B
http
://w
ww.
solv
ent--
recy
clin
g.co
m/a
zeot
rope
_1.h
tml
31
fracti
on
al d
isti
llati
on
http
://ho
me.
att.n
et/~
cat6
a/im
ages
/fuel
s_06
.gif
32
Vap
or
Dif
fusio
n C
rysta
l G
row
th
33
Vap
or
Dif
fusio
n C
rysta
l G
row
th
http
://sc
ienc
e.na
sa.g
ov/s
sl/m
sad/
pcg/
#HA
RD
WA
RE
End
of L
ectu
re
34