Solid-liquid equilibrium phase diagrams for salt solutions
Transcript of Solid-liquid equilibrium phase diagrams for salt solutions
Solid-liquid equilibrium phase diagrams for salt solutions
Kaj Thomsen Associate Professor, Department of Chemical and Biochemical Engineering, Technical University of
Denmark [email protected]
Phase diagrams
• Phase Diagrams
– Solid-liquid equilibrium
– Vapor-liquid
– Liquid-liquid
• Focus on solid-liquid equilibrium phase diagrams
Calculated and experimental phase diagram
• If a good model is available, the phase diagram can be calculated at any temperature
• By comparing experimental and calculated phase diagrams, you can get an idea about how good the model is.
• Phase diagrams are good as visible tools to understand what is going on in a process – Operating lines for fractional crystallization
processes can be marked in phase diagrams
Prediction of phase diagram
• Not possible yet to predict what solid phases might form
• The types of solid phases are determined experimentally
• The standard state properties of solid phases can be determined from experimental phase equilibrium data
Phase Rule
• F = Number of degrees of freedom
• C = Number of independent components
• P = Number of phases
• Intensive variables of a system:
– Temperature,
– Pressure,
– C-1 mole fractions for each phase
• 2 + (C-1)*P intensive variables
Phase Rule
• Equilibrium equation for each component describing its distribution between two phases
• If two phases are present C equations can be written relating the concentrations in the two phases
• If P phases: C*(P - 1) equations
• F = 2 + (C-1)*P - C*(P-1) degrees of freedom
• F = 2 + CP – P – CP + C = C – P + 2
One component system: water
• One phase: F = 1 – 1 + 2 = 2 : T and P can be varied and the same phase continue to exist
• Two phases: F = 1 – 2 + 2 = 1: T or P can be varied and there is still equilibrium between the two phases
• Three phases: F = 1 – 3 + 2 = 0: T and P can not be chosen – Triple point, invariant point
Binary systems
• F = 2 – P + 2 : There can be up to 4 phases in equilibrium with each other in a binary system
• Solid – liquid equilibrium can be determined by thermal analysis:
– Known amounts of salt and water are mixed, the solution is cooled. At a certain temperature the cooling stops because crystallization starts
– Does not require that you visually observe that all solid is dissolved
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-40
-20
0
20
40
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80
100
0 10 20 30 40 50 60 70 80
Mass % CaCl2
Te
mp
era
ture
°C
Extended UNIQUACExperimentalSeries3
Ice
Ca
Cl2∙6
H2O
Ca
Cl2∙4
H2O
Ca
Cl2∙2
H2O
A
B
C
Binary diagram
• Eutectic point = invariant point
• Peritectic points
-40
-20
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60 70 80 90 100
Mass % MgSO4
Te
mp
era
ture
, °C
Extended UNIQUACExperimental
Mg
SO
4·6
H2O
Mg
SO
4·H
2O
Mg
SO
4·7
H2O
Mg
SO
4·1
2H
2O
Ice
Ternary phase diagrams
• F = 3 – P + 2 = 5 – P: up to 5 phases in equilibrium with each other
– 3 solid phases
– 1 liquid phase
– 1 vapor phase in invariant point
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-10 0 10 20 30 40 50 60 70 80 90 100 110
sa
lt f
racti
on
Calculated
Experimental
Temperature, °C
Mg
SO
4N
a2S
O4
3Na2SO4·MgSO4
Vanthoffite
Na2SO4·MgSO4·2.5H2O
Löweite
Na2SO4
Thenardite
Na2SO4·10H2O
Glauber salt
MgSO4·12H2O
MgSO4·7H2O
Epsom salt
MgSO4·6H2O
Hexahydrite
MgSO4·H2O
Kieserite
Na2SO4·MgSO4·4H2O
Bloedite
Ice
A
B
C
D
E
100
90
80
70
60
50
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30
20
10
0
0
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20
30
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50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100MgSO4
Na2SO4
H2O
T= 85.0°C
MgSO4·H2O
Kieserite
Na2SO4·MgSO4·2.5H2O
Löweite
3Na2SO4·MgSO4, Vanthoffite
AB
CD E
Salting out of NaCl by CaCl2
Salting out of NaCl by CaCl2
Schreinemakers method
Quaternary systems
• Systems with two anions and two cations
• Systems with three anions and one cation
• Systems with one anion and three cations
Jänecke coordinates
• For systems with 2 cations and 2 anions
• Equivalent fractions or charge fractions
• One axis for the two cations (0 – 1)
• One axis for anions (0 -1)
• Water content can be displayed
– By three dimensional plot
– By contour lines
– By marking the water content in the diagram
2.703.133.383.633.924.194.444.825.846.755.50
4.55 4.29 4.07 3.85 3.61 3.36 3.07 2.85 2.46 2.16 1.82
2.232.57
10.30
24.30 22.30 20.32 18.36 16.38 14.36 12.26 10.05 7.67 7.67 5.86
6.085.645.476.698.7610.6912.5414.3216.0817.8319.60
21.39 18.54 16.96 15.41 13.87 12.33 10.77 9.18 7.52 5.74 5.04
5.154.614.575.296.677.929.1210.4211.7413.0714.42
15.79 14.13 13.01 11.91 10.83 9.74 8.64 7.50 6.30 4.99 4.03
4.013.323.424.515.706.797.838.849.8310.8311.84
12.87 11.22 9.41 8.53 7.65 6.77 5.86 4.91 3.87 2.70
2.501.482.073.103.964.755.516.256.997.738.48
9.26 7.06 6.43 5.83 5.24 4.65 4.07 3.47 2.85
0.00
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0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SO42-
Anion charge fraction NO3-
Moles of water per mole of ions given at grid intersections
K+
Ca
tio
n c
ha
rge
fra
ctio
n
Na
+
K2SO4
NaK3(SO4)2
Na2SO4 Na2SO4•10H2O NaNO3•Na2SO4•H2O
NaNO3
KNO3
Three anions, one cation 0
10
20
30
40
50
60
70
80
90
100
100
90
80
70
60
50
40
30
20
10
0
73.3
71.771.8
69.970.071.0
67.867.969.872.4
65.465.568.571.172.9
62.662.767.169.871.672.9
59.360.265.568.370.271.572.6
55.158.463.966.768.670.071.171.9
49.656.662.165.066.968.369.470.371.0
48.654.760.363.265.166.567.668.569.269.9
47.352.858.361.263.164.565.566.467.167.868.3
0 10 20 30 40 50 60 70 80 90 100
NaNO3
Na2SO4
NaCl
T= 50.0°C Mass percent water given at
grid intersections
Na2SO4
NaCl
NaNO3
NaNO3·Na2SO4·H2O
0
10
20
30
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50
60
70
80
90
100
100
90
80
70
60
50
40
30
20
10
0
70.2
67.968.4
65.265.866.2
66.762.763.366.2
70.665.264.966.468.2
73.269.165.768.768.869.2
74.871.667.369.370.870.269.4
75.673.069.671.271.671.970.969.3
76.873.670.473.174.273.972.170.872.0
79.076.373.074.676.076.375.773.671.674.3
80.878.575.875.877.478.178.077.174.974.076.2
0 10 20 30 40 50 60 70 80 90 100
K2SO4
Li2SO4
Na2SO4
T= 100.0°C Mass percent water given at
grid intersections
NaK3(SO4)2
K2SO4Li2SO4·K2SO4Li2SO4
Na2SO4·Li2SO4 2Li2SO4·Na2SO4·K2SO4
Na2SO4
One anion, three cations
Quinary systems
• Phase diagrams for systems with 5 ions
• Can be shown as surfaces saturated with two salts
– Relevant for describing salt deposits with large NaCl content
– Can be used for separating the quinary system into ternary systems
Quinary system,
all points sat. with
NaCl
61.78 67.07 67.55 70.45 70.47 70.27 70.04 69.99 70.25 70.37 70.44
70.1370.0269.8469.5069.1469.2769.3168.9766.1266.0765.35
66.41 65.58 65.62 67.27 67.98 68.13 68.11 69.03 69.44 69.67 69.83
69.5269.3369.0468.5767.5566.8066.4365.8865.1065.7667.02
67.03 65.86 66.13 66.54 66.52 66.35 67.08 68.12 68.65 68.99 69.22
68.9368.6668.2767.6966.6066.6666.7766.7566.3965.7766.85
66.62 65.63 66.43 66.80 66.87 66.81 66.68 67.26 67.90 68.33 68.64
68.3568.0067.5366.8466.8066.8866.9066.7866.3765.4866.39
66.18 65.33 66.27 66.73 66.88 66.91 66.86 66.78 67.17 67.68 68.06
67.7867.3766.8166.8366.8966.9066.8466.6566.1565.2065.98
65.81 65.08 66.02 66.56 66.79 66.88 66.90 66.87 66.81 67.05 67.50
0.00
0.10
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0.90
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Mg
++
Ca
tio
n C
ha
rge
fra
ctio
n
K+
Cl- Anion Charge fraction SO4--
T= 55.0°C
NaCl + Na2SO4
NaCl + KCl
NaCl + NaK3(SO4)2
NaCl + K2SO4·MgSO4·4H2O
NaCl + KCl·MgSO4·3H2O
NaCl + KCl·MgCl2·H2O
NaC
l + M
gSO
4·6
H2O
Mass % water given at grid intersections
Quinary system
all points sat. with
NaCl
1.17 3.41 5.02 12.72 16.04 18.08 19.52 20.95 22.46 23.41 24.08
24.223.5622.6721.2819.3717.8815.7812.395.764.332.97
5.13 5.78 7.46 11.93 15.45 17.62 19.16 21.58 22.87 23.71 24.32
24.4423.8623.0621.8619.6617.2714.9912.29.158.097.82
10.19 10.5 12.79 15.24 16.89 18.14 20.18 22.13 23.25 24.01 24.56
24.6824.1523.4322.3820.6319.6618.6117.2215.1612.5612.23
13.97 14.31 16.86 18.63 19.83 20.73 21.47 22.62 23.6 24.29 24.8
24.9124.4223.7722.8522.221.5520.7519.718.1415.7815.45
16.71 17.04 19.15 20.54 21.48 22.19 22.77 23.26 23.94 24.56 25.02
25.1324.6924.123.6823.2422.7122.0721.2219.9818.1117.79
18.72 19.04 20.67 21.8 22.57 23.15 23.63 24.04 24.39 24.82 25.24
0.00
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0.30
0.40
0.50
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0.70
0.80
0.90
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Mg
++
Ca
tio
n C
ha
rge
fra
ctio
n
K+
Cl- Anion Charge fraction SO4--
T= 55.0°C
Mass % NaCl given at grid intersections
NaCl + Na2SO4
NaCl + KCl
NaCl + NaK3(SO4)2
NaCl + K2SO4·MgSO4·4H2O
NaCl + KCl·MgSO4·3H2O
NaC
l + K
Cl·
Mg
Cl 2
·6H
2O
NaCl + MgSO4·H2O
Multicomponent systems
• Increasing complexity of phase diagrams with increasing number of components
• Phase diagrams can give a visual understanding of the process
• With an accurate thermodynamic model, separation processes can be optimized
– Input: composition and temperature of stream
– Output: composition of solid and liquid phase