solid/liquid systems
Post on 15-Jan-2016
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Solid/Liquid Systems
Phase Diagrams
Phase Rule
Lever Rule
LIQUID
SOLID
T
XB
LIQUID
SOLID
T
XB
START
FINISH
COOLING CURVE
time
T
liquidcools
solid formsand cools
solid cools
COOLING CURVE
time
T
liquidcools
solid formsand cools
solid cools
COOLING CURVE
How do I know its shape???
THE PHASE RULE
F = C + 2 - P
F = degrees of freedom ( How many variables? )
C = components
P = phases
P
100 KPa
T373K273K
Liquid
Gas
Solid
This is a one component system as it containsonly water. Therefore,
F = 1 + 2 P
= 3 P
P
100 KPa
T373K273K
Liquid
Gas
Solid
P = 1 F = 2Pressure & T varyindependantly
P
100 KPa
T373K273K
Liquid
Gas
Solid
On line P = 2F = 1 Pressureor T can vary
P
100 KPa
T373K273K
Liquid
Gas
Solid
At the triple pointP = 3 and F = 0Pressure and T are fixed.
LIQUID
SOLID
T
XB
This is a two component system as it containstwo different compounds. Therefore,
F = 2 + 2 P
= 4 P
I use up one degree of freedom by fixing thepressure.
F = 3 P
LIQUID
SOLID
T
XB
P = 1 F = 2T and XB vary.
P = 1 F = 2T and XB vary.
P = 2 F = 1
time
T
liquidcools
solid formsand cools
solid cools
COOLING CURVE
How do I know its shape???
time
T
liquidcools
solid formsand cools
solid cools
COOLING CURVE
The temperature can vary because the compositions can change.
LIQUID
SOLID
T
XB
A tie line
A tie line
At a given temperature, a tie line tells us what the compositions of the two phases are. It can also tell how much of each is present.
A tie line
At a given temperature, a tie line tells us what the compositions of the two phases are. It can also tell how much of each is present.
The compositions of the phases are deteremined from the ends of the line.
The amounts are determined from the Lever Rule.
Lever Rule
ff f
This is a tie line for system expressed in mass fraction.
f = mass fraction for whole system
f = mass fraction of the phase
f = mass fraction of the phase
Lever Rule
ff f
The system balances like a lever: m f f = m f f
m is the mass of the phase.
A bit more complicated?
The NaCl / NaBr system.
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
X
Y
Z
THREE TIE LINES:
X is pure NaCl Crystals in equilibrium with a solution of NaCl and NaBr. 50 mole % NaClY
Z
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
X
Y
Z
THREE TIE LINES:
X is pure NaCl Crystals in equilibrium with a solution of NaCl and NaBr.
Y is pure NaBr Crystals in equilibrium with a solution of NaCl and NaBr. 25 mole % NaClZ
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
X
Y
Z
THREE TIE LINES:
X is pure NaCl Crystals in equilibrium with a solution of NaCl and NaBr.
Y is pure NaBr Crystals in equilibrium with a solution of NaCl and NaBr. Z is pure NaCl crystals and pure NaBr crystals.
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
?
This point is called a EUTECTIC or minimum
melting point. 28 mole % NaCl at 731 o C.
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
TWO COOLING CURVES
X
Y
time
time
T
T
The T falls because 2 phases give degree of freedom.
The T is fixed because there are 3 phases and zero degrees of freedom.
(x)
(y)
NaBr / NaCl at 101 325 Pa
o C
800
760
720
.25 .50 .75
XNaCl
LIQUID
TWO COOLING CURVES
X
Y
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