binary liquid systems handout
DESCRIPTION
Binary Liquid Systems HandoutTRANSCRIPT
11/29/2011
1
A. Completely miscible binary liquids
When C = 2,Intensive Variables: P, T, C1/C2
If T or P = kF = 3 – PIf T = k, P vs. CIf P = k, T vs. C
Phase Diagrams of
Binary Liquid Systems
Raoult’s LawFor each volatile component of an ideal mixture of liquids at constant T
Pi = χi Pi°T = k
P
A χB or YB B
PA
PB
P = (1–χB) PA° + χB PB°∴∴∴∴ PA = χA PA°
PB = χB PB°and
Since, Ptot = ΣPi
P = PA + PB
=χA PA° + χB PB°
= (1–χB) PA° + χB PB°
PB = χB PB°
PA = χA PA°
= (1 – χA)PA°
11/29/2011
2
For the vapor in equilibrium with the liquid
Pi = Yi Ptotal T = k
P
A χB or YB B
PA
PB
V
L
L + V
∴∴∴∴ PA = YA Ptotal
PB = YB Ptotal
and
For the vapor above the solution
YB =
(1–χB) PA° + χBPB°
χB PB°
Ideal Solutions
T = k
P
A χB or YB B
P°A
P°B
V
L
L + V
s v
A - - A = A - - B = B - - B1. IFA are completely balanced,
11/29/2011
3
Nonideal Solutions
1. A - - A ≈ A - - B ≈ B - - B
• closest to ideal behavior
•intermediate values of Psoln
• Intermediate values of Tsoln
T = k
P
A χB or YB B
P°A
P°B
V
L
L + V
s v
11/29/2011
4
P = k
T
A χB or YB B
TA
TB
V
L
L + V
s v
Temperature – Composition Diagram
P = k
T
A χB or YB B
TA
TB
V
L
L + V
f
Fractional distillation
d1 d2
11/29/2011
5
IFA are unbalanced
1. A - - A > A - - B < B - - B• Exhibits maximum vapor pressure• Exhibits minimum boiling point
T = k
P
A χB or YB B
P°A
P°BV
L
L + V
L
V
L + V
Vapor Pressure Diagram
Pmax
E
E: Azeotrope
11/29/2011
6
P = k
T
A χB or YB B
TA
TB
V
LL + V
L
V
L + V
Poling Point Diagram
Ef
Tmin
2. A - - A < A - - B > B - - B• Exhibits minimum vapor pressure• Exhibits maximum boiling point
11/29/2011
7
T = k
p
A χB or YB B
P°A
P°B
L
VL + V
V
L
L + V
Vapor Pressure Diagram
Cf
Pmin
P = k
T
A χB or YB B
TA
TBL
V
L + V
V
L
L + V
Boiling PointDiagram
Tmax
C
11/29/2011
8
Partially miscible liquid pairs
• Unbalanced strength of IFA at certain concentration range
A(l) B(l)
A in B
B in A
• Since only the liquid phase is involved, P = k
F = C – P + 1
= 2 – P + 1
= 3 – P
p = k
A B
composition, wt %
ccst
� A - - A > A - - B < B - - B
•1. Miscibility is enhanced by increase in T
Temp
cstmax
P = 1
P = 2
T1
x y
F = 3 – 1 = 2(T, %A / %B)
F = 1(T / %A / %B)
T2
x’ y’
11/29/2011
9
p = k
A B
composition, wt %
Material Balance
T
T1
x y
T2
x’ y’m
Consider a mixture of composition m kept at T1
x = comp. of A–rich layer
y = comp. of B–rich layer
wt of A–rich layer
wt of B–rich layer=
y – m
m – x
If mixture m is heated to T2
x’ = comp. of A–rich layer
y’ = comp. of A–rich layer
wt of A–rich layer
wt of B–rich layer=
y’ – m
m – x’
Tf
Tf = temp of complete miscibility
p = k
A B
composition, wt %
T
T1
x ym
If while T1 is kept constant, B is added to m until the composition of the mixture is m’
x = comp. of A–rich layer
y = comp. of B–rich layer
wt of A–rich layer
wt of B–rich layer=
y – m’
m’ – x
m’
11/29/2011
10
p = k
A B
composition, wt %
ccst
� A - - A < A - - B > B - - B
2. Miscibility is enhanced by decrease in T
Temp
cstmin
P = 1
P = 2
T1
x y
T2
x’ y’
p = k
A B
composition, wt %
Ccst,
� A - - A ≈ A - - B ≈ B - - B3. Miscibility is enhanced by increase or decrease in T
Temp
cstmin
P = 1
P = 2
T1
x y
T2
cstmax
Ccst’ y’
11/29/2011
11
PPA°
PB°
Completely immiscible liquid pairs
Patm
T Tb
For a pair of immiscible liquids at constant T
Ptotal = PAº + PBº
YA =PAº
Ptot
nA
nvap
YA /YB =PAº / Ptot
PBº / Ptot
=nA/nvap
nB/nvap
nA / nB = PAº / PBºwA / MA
wB / MB
= PAº / PBº
wA / wB = MAPAº / MBPBº
B
A
A + B
At the boiling pt. of the mixt.
PAº = vapor pressure of A
PBº = vapor pressure of B