hydrometallurgyy-extractive metallurgyy.ppt

hydrometallurgy

1. MG – 4111
HYDRO-ELECTROMETALLURGY
Semester I, 2010/2011
DR. M. Zaki Mubarok
Department of Metallurgical Engineering,
Faculty of Mining and Petroleum Engineering (FTTM)-ITB
LECTURE NOTES

2. Course Outline
I.Introduction to Hydrometallurgy
II.Thermodynamic and Kinetic Aspects
in Hydrometallurgy
III.Leaching and Solid-Liquid Separation
IV.Solution Purification and Metals
Recovery Methods from Pregnant
Leach Solution

3. Course Outline
V.Leaching and Recovery of Metals and
Oxides Ores (Au, Ag, Zn, Al, Cu, Ni)
VI.Leaching and Recovery of Sulphide Ores
(Zn, Ni, Cu)
VII.Introduction to Electrometallurgy
VIII.Metals Production by Electrolysis in
Aqueous Solution
IX.Fused Salt Electrolysis

4. Literatures
1.Havlik,T., ”Hydrometallurgy: Principles and Applications,”
CRC publisher, 2008.
2.Habashi, F. ”A Textbook of Hydrometallurgy”, Metallurgie
Extractive, Quebec,1993
3.Norman L. Weiss, “SME Mineral Processing Handbook“,
Volume II, SME, 1985
4.Unit Processes in Extractive Metallurgy:
Hydrometallurgy, A Modular Tutorial Course of Montana
College of Mineral Science and Technology
5.Biswas, A.K. And Davenport, W.G., “ Extractive
Metallurgy of Copper”, Pergamon, Oxford, fourth edition,
2002

5. Literatures
6.Unit Processes in Extractive Metallurgy:
Electrometallurgy, A modular tutorial course of
Montana College of Mineral Science and
Technology
7.Yannopoulus, J.C,”The Extractive Metallurgy of
Gold”, Von Nostrand Reinhold, New York, 1991

6. Course Structure and
Mark Distribution
•Course Structure
–Lecture
–Tutorial
–Assignment and Lab Work
•Mark Distribution
–45% Midterm Exam
–45% Final Exam
–5% Assignment
–5% Lab Work
•Attendance: 70% minimum

7. CHAPTER I
INTRODUCTION TO HYDROMETALLURGY
Hydrometallurgy
Extraction, recovery and purification of metals,
through processes in aqueous solutions. Metals are
also recovered in the other forms such as oxides,
hydroxides.
Electrometallurgy
Recovery and purification of metals through
electrolytic processes by using electrical energy.

8. Hydrometallurgy Scope
•Traditionally, hydrometallurgy is emphasized for metals
extraction from ores.
•Hydrometallurgical processing may be used for the
following purposes:
Production of pure solutions from which high purity metals can be
produced by electrolysis, e.g., copper, zinc, nickel, gold, and silver.
Production of pure compounds which can be subsequently used for
producing the pure metals by other methods. For example, pure
alumina to produce smelter grade aluminium.
•However, hydrometallurgy principles can be applied to
a variety of areas such as metals recycling from scrap,
slag, sludge, anode slime, waste processing, etc.

9. Unit Processes in Hydrometallurgy
•In general, hydrometallurgy involves 2
(two) main steps:
1.Leaching
Selective dissolution of valuable metals from
ore.
2.Recovery
Selective precipitation of the desired metals from
a pregnant-leach solution.

10. General outline of hydrometallurgical
processes
Ore/concentrate
leaching
Solid-liquid separation
Solution purification
Precipitation
Pregnant Solution
Solid residu to waste
Leaching agentOxidant
Precipitant or
electric current
Pure compound Metals

11. •Commonly, solution purification is conducted prior to
metals recovery from the solution.
•Solution purification is aimed at obtaining a concentrated
solution from which valuable metals can be precipitated
in the next processes effectively
•Solution purification methods which are commonly used
are as follows:
–Adsorption by activated carbon
–Adsorption by ion exchange resins
–Solvent extraction (using organic solvents)
–Precipitation with metals (cementation)

12. Solution purification
•Solution purifications by adsorption with activated
carbon, ion exchange resins (IX) and solvent
extraction (SX) have the same unit operations,
namely:
–Loading, and
–Elution
•In the elution step, the adsorbers are usually
regenerated for another process cycle.

13. Hydrometallurgy development
Hydrometallurgy is developed after pyrometallurgy.
Metals smelting has been practiced since thousands
years ago.
Hydrometallurgy was developed after the people
discovered acid and base solutions. However, modern
hydrometallurgy development is commonly associated
with the invention of Bayer Process for bauxite leaching
and cyanidation for gold extraction at the end of 19
th

century (1887).
One of important highlights of hydrometallurgy
development is uranium extraction (Manhattan Project)
aimed at nuclear weapon production in second world
war (1940‘s).

14. Important milestones in the development of
hydro-electrometallurgy
• Cementation & Aqua Regia Use - 8
th
Century
• Cyanidation - 1887
• Bayer Process - 1887
• Hall-Heroult Process - 1886, 1888
• Copper Electrowinning - 1912
• Zinc Electrolytic Process - 1916
• Manhattan Project (IX/SX) - 1940’s
• Biooxidation of Sulphide Concentrates - 1960’s
• Pressure Leaching
– Sherrit Gordon Nickel Process - 1954
– Pressure Acid Leaching of Ni Laterites - 1955
• Large Scale Copper SX/EW - 1960’s

15. Important milestones in the development of
hydro-electrometallurgy
• Carbon in Pulp (CIP)/Carbon in Leach (CIL)
for Gold Recovery - 1980’s
• Pressure Oxidation of Zinc Sulphides - 1981
• Two-Stage Zinc Pressure Leach - 1993
• Atmospheric Leaching of Zinc Sulphides
– Albion (1993), Outokumpu (1999)
Recent Developments:
• Skorpion Project (Anglo American) – 2003 (Zn from ZnS)
• Hydrozinc (TeckCominco) - 2004
• Inco’s Goro and Voisey Bay Projects - 2007
• Leaching of Chalcopyrite (CuFeS
2) Ores
Hydrocopper (Outokumpu)  Cu from sulfidic ores
•Atmospheric leaching of nickel laterite ore: 2008?

16. Hydrometallurgy vs. Pyrometallurgy
Hydrometalurgy Pyrometallurgy
Treat high grade
ore?
Less economic More economic
Treat low grade ore?Possible with
selective leaching
Unsuitable
Treat sulphide oreNo SO
2
; otherwise S
o

or SO
4
2-
are
generated
SO
2
generated (can
be converted to
H
2SO
4)
Separate similar
metal, such as Ni
and Co
Possible with certain
method
Not possible
Pollutant Waste water,
solid/slurry residues
Gases and dust
Reaction rates Slower Rapid

17. Hydrometallurgy vs. Pyrometallurgy
Hydrometalurgy Pyrometallurgy
Scale of operation?Possibly economic to
be done at small
scale operation and
expansion is easier
Unconomic at smale
scale operation
Capital cost Generally lower than
pyrometallurgy
Higher
Energy cost Lower Higher
Materials HandlingSlurry Easy to be
Pumped and
Transported
Handle Molten
Metal, Slag,
Matte
Residues Residues – Fine
and Less Stable
Slags – Coarse
and Stable

18. Thermodynamic and Kinetic
Aspects in Hydrometallurgy
CHAPTER II

19. Spontaneous Reaction, Equilibrium State
•As has been learned in basic engineering courses,
chemical reaction will spontaneously occur when the
Gibbs free (G) < 0.
G = G
o
+ RT ln K
G = 0  process is in equilibrium state
G
o
= standard Gibbs free energy
–R = ideal gas constant = 8,314 J/K.mol
–T = absolute temperature of the system (K)
–K = equilibrium constant
•Standard Gibbs free energy is determined at:
–Gaseous components partial pressure = 1 atm
–Temperature = 25
o
C (298 K)
–Ions activity = 1

20. Equilibrium Constant
•For reaction:
aA + bB  cC + dD


b
a
a
a
d
a
c
a
BA
DC
K ionconcentratA=]A[]A[γ=Aofactivity=A
a
→
X of pressure parsial=X whichin
,Xγ=X→Xofcomponent gaseous For
p
pa
 = activity coefficient of
component A

21. Nernst Equation
•Hydro-electrometallurgical processes often involve
electrochemical reactions.
•For electrochemical reaction
G = -nFE, G
o
= -nFE
o
, therefore
Kln
nF
RT
EE
o

In which,
E = potential for reduction-oxidation reaction
E
o
=standard potential for reduction-oxidation reaction
n = number of electron involved in the electrochemical reaction,
F = Faraday constant = 96485 Coulomb/mole of electron
Nernst Equation
• Spontaneous process  E > 0  G < 0

22. Chemical reactions usually
perform in leaching processes
•Dissolution by acid
–Example: ZnO
(s) + 2H
+
→ Zn
2+
(aq) + H
2O
(l)
•Dissolution by base
–Example: Al
2O
3(s) + 2OH
-
→ 2AlO
2
-
(aq) + H
2O
(l)
•Dissolution by complex ion formation
Example: CuO
(s) + 2NH
4
+
(aq) + 2NH
3(aq) →
Cu(NH
3)
4
2+
(aq) + H
2O
(l)

23. •Dissolution by oxidation
–Ex: CuS
(s)
+ 2Fe
3+
→ Cu
2+
(aq)
+ 2Fe
2+
+ S
o
(s)
Other oxidators: O
2, ClO
-
, ClO
3
-
, MnO
4
-
, HNO
3, H
2O
2,
Cl
2
•Dissolution by reduction mechanism
–Ex: MnO
2(s)
+ SO
2(aq)
→ Mn
2+
(aq)
+ SO
4
2-
(aq)
Chemical reactions usually
perform in leaching processes

24. Correlation of free energy (G)
and heat (enthalphy = H)
G = H - TS
G
o
= H
o
- TS
o
Cp = heat capacity at constant pressure (J/molK)
Where possible, processes are designed to be autothermal →
maintain constant temperature by the heat given by the reaction
∆H
o
= Standard enthalpy (kJ/mol)
∆G
o
= Standard entropy (kJ/mol)
∆G
o
(reaction) = ∆G
o
(products) - ∆G
o
(reactants)
∆H
o
(reaction) = ∆H
o
(products) - ∆H
o
(reactants)
∆S
o
(reaction) = ∆S
o
(products) - ∆S
o
(reactants)
∫
T
298
p298T
dTC+H=HΔΔ

25. Calc. example 1
•Find K for each reaction using
a) Standard free energy data
b) Standard electrode potential data

26. Calc. Example 2
a) What is the electrode potential of the
Ni
2+
/Ni reaction in sulphate solution at 25°C
at a Ni
2+
concentration of 0.005 M (assumption:
activity of Ni
2+
is equal to its molar concentration)
b) At what pH is H
2 at 10 atm at equilibrium
with this solution and pure nickel?
Ni
2+
+ 2 e = Ni E° = -0.26 V
2H
+
+ 2 e = H
2 E° = 0.00 V

27. Pourbaix Diagram
•Pourbaix Diagram = Potensial (E
h) – pH
Diagram.
•The diagram represents thermodynamic
equilibrium of metal, ions, hydroxides (or,
oxides) in aqueous solution at certain
temperature (isothermal).
•The boundary of stability regions of metal, ion,
hydroxides (or oxides) are equilibrium lines.
•Does not reflect reaction kinetics.

28. Pourbaix Diagram
•Three possible types of equilibrium lines:
–Horizontal
–Vertical
–Slope
•Variations in ion activities are plotted as
contours/dashed lines
•Horizontal Line: for equilibrium reactions
that are independent of pH.

29. Horizontal Line
•Example:
Fe
3+
+ e = Fe
2+
E
o
= 0.77 V
R = 8.314 J/Kmol, T = 298 K, F = 96500 C/mol e
-
, n = 1 mol e
-
+3a
+2Feo
Fe
a
ln
nF
RT
E=E -
If all ion concentrations are assumed to be equal to
their molar concentrations  10
-6
M.
[ ]
[ ]
+2
+3
o
Fe
Fe
ln
nF
RT
E=E -
[ ]
[ ]
[ ]
[ ]
77,0=E
Fe
Fe
log0592,077,0=E
Fe
Fe
ln
96500x2
298x314,8
77,0=E
+3
+2
+3
+2
-
-

30. Vertical Line
•Reactions do not involve electron → n = 0, no
potensial , the equilibrium depends only on pH.
•Example:
Fe
2
O
3
+ 6H
+
= 2Fe
3+
+ 3H
2
O
[]
[]
--a
++a
OHlog)OH(glo=pOH
pOH14=HlogHglo=pH
-≈-
--≈-
For certain Fe
3+
concentration we can determine the
equilibrium pH for the above reaction.
K = [Fe
3+
]
2
/[H
-
]
6

31. Slope Line
•For reactions that depend both on potensial
(E
h) dan pH.
•Example:
If all ion concentrations are assumed to be equal to
their molar concentrations  10
-6
M.

32. Water stability region (dotted lines)
•Upper boundary line
•Lower boundary line
 At pO
2
= 1 atm
 At pH
2
= 1 atm

33. E
h-pH diagram of Fe-H
2O system at 25°C

34. E
h-pH Diagram of Zn-H
2O System at 25
o
C.

35. E
h
-pH Diagram of Cu-H
2
O System at 25
o
C.

36. Application of E
h – pH diagram in
hydrometallurgy
•Predicting potential leaching behaviour
for certain mineral system
•Predicting the possibility of metals ion
precipitation at the purification of
pregnant-leach solution

37. Application of E
h
– pH diagram in hydrometallurgy
Fe(OH)
3
or Fe
2
O
3
can be precipitated from Fe
3+
at lower
pH than the precipitation of Zn
2+
to Zn(OH)
2
or ZnO.
Fe
2+
have to be oxidized to Fe
3+
to gain lower pH value for
Fe(OH)
3
precipitation.

38. Pourbaix Diagram can be constructed at various
temperature for more than two systems
E
h
-pH diagram of Zn-S-H
2
O system at 25
o
C

39. Diagram Pourbaix in Presence of Complex Ion
•Example: Au-H
2
O system with the presence of cyanide (CN
-
) ion (case
of gold cyanidation leaching)
•Equilibrium of Au
3+
/Au
mol/KJ433
)Au(G)Au(GG
)1(Aue3Au
3
f
0
f
00
3





Standard reduction potential for Reaction 1:
V5.1
965003
10433
nF
G
E
30
0







40. •Equilibrium reaction of O
2/H
2O
E
o
= 1.23 V.
Therefore, Au
3+
ions are not stable in water and readily reduced to Au
by oxidation of H
2O to O
2 (the opposite of Reaction 2). In the other
word, gold can not be oxidized (dissolved) in water only with the
presence O
2.
OH2=e4+H4+O
2
+
2
O2H/2O
Au/
+3
Au
22
+3
E>E
23.1= OH/O
5.1= Au/Au
(2)

41. Potensial – pH diagram of Au–H
2
O system without
the presence of complexing agent

42. With the presence of CN
-
,

Au
3+
forms STABLE
COMPLEX of “aurocyanide“ (Au(CN)
2
-
) and the
potential-pH diagram for Au changes significantly as
follow:

E
h
-pH Diagram of Au-CN-
H
2
O system at 25
o
C for [Au]
= 10
-4
M and [CN
-
] = 10
-3
M

43. •By the presence of cyanide ions,
Au
+
+ e = AuE = 1.69 – 0.0591 log [Au
+
]
Au
+
+ 2CN
-
= Au(CN)
2
-
(K = 2 x 10
38
)
Au(CN)
2
-
+ e = Au + 2CN
-
...........................(3)
In comparison to the first reaction that has E
o
of 1.69 V,
Reaction (3) has much lower E
o
at -0.57 V.
Dissolution of Au is limited by the following equilibrium of
Reaction (3).
•During cyanidation leaching, dissolved oxygen is required to
oxidize Au prior to the formation of stable complex of
Au(CN)
2
-
.
   


2
2
/log0591.0log0591.069.1 CNAuCNKE
aa

44.  Interactions in Electrolyte Solution
Two types of interactions in electrolyte:
-Ion-ion interaction, and
-ion-solvent interaction
Knowledge of interaction in electrolyte solution is
important because the interactions affect solvation
effects, diffusion, conductivity, ionic strength and
activity coefficients of ions in solution.
Interactions in electrolyte solution influence the
transport properties of ions in solution.

45.  Ionic Strength and Activity Coefficient
-Ionic strength (I), expresses the ionic concentration
that includes the effects of ionic charge.
-Ionic strength (I) is defined as follow:
-It is found that activity coefficient, electrical
conductivity and the rates of ionic reactions are all
the functions of ionic strength.

i
iizcI
2
2
1
in which c
i
= concentration of ion i in molar (mol/L)
and z
i = the charge of ion i.

46. Ionic Strength for unit concentration in molal
-Remember, molality = moles of solute in 1 kg
solvent. Molality can be converted to molality by the
following correlation:
in which M
i
= the molar mass of each solute in
kg/mol (not in g/mol), c
i
= molarity of solute i, and 
is the density of the solution in kg/m
3
(=g/L)
-In dilute solutions, c
i
 0.001m
i

o
(in which 
o
=
density of pure solvent).
∑
ii
i
i
Mc-ρ001.0
c
=m

47. Ionic Strength for unit concentration in molal
-Therefore for dilute solution,
If the solvent is water at 25
o
C (density  1000 kg/m
3
),
then:
∑ zρm001.0
2
1
=∑zc
2
1
=I
2
ioi
i
2
ii
∑
2
ii
o
zm
2
ρ001.0
=I
∑
i
2
iizm
2
1
≈I
Similar form with ionic
strength in molarity

48. - Molar activity coefficient can be converted to molal
activity coefficient by the following correlation:)




mM
f
s

1
for salt, or


mM
f
s
i
i


1
for single ion.
in which  = total moles of ion formed during
complete dissociation, m = ionic molality and M
s
=
molecular weight of solvent (kg/mol).

49. Activity and Activity Coefficient,
DEBYE-HUCKEL LAW
-Debye Huckel Law correlates the activity coefficient (f
i , 
i)
with ionic strength (I).
-Forms of Debye-Huckel equations depend on
concentration of solution and the unit concentration used.
-For dilute solution at 25
o
C and I given in molar (M),
-The above equations are known as LIMITING DEBYE
HUCKEL LAW.
I-zz51159.0=flog
+±
Izf
ii
2
51159.0log
for single ion, and
for salt.

50. The limitation of LIMITING Debye-Huckel Equation
•The D-H Limiting Law is called a ”limiting” law
because it becomes increasingly accurate as the limit
of infinite dilution is approached.
•Up to concentrations of about 0.01m THE LIMITING
D-H LAW gives reasonable values, but at higher
concentrations the calculated activity coefficient
become inaccurate (high %error compared to the
values determined experimentally).

51. Debye-Huckel Law for Concentrated
Solution
-For concentrated solution (> 0.01 molal), Limiting
Law D-H is modified by considering the ionic size
parameter:
IBa
IzzA
f





1
log
-in which A and B are constants that depend on the
kind of solvent and temperature, a = ion size
parameter.
- For aqueous solution at 25
o
C, A = 0.51159 and B =
3.2914 x 10
9
meter.

52. ACTIVITY AND MEAN ACTIVITY
-Molar activity and molar activity of a single ion i is
determined as follow:
-For 1 mole of M
+
A
-
salt that dissociates to 
+
mol of
M
z+
and 
-
mole of A
z-

iii
ma
M
+A
- 

+
M
z+
+ 
-
A
z-

 =

+
+

-
iii
Cfaand

53. Mean molal activity coefficient can be determined by
the following correlation:
 



/1




Mean molality,
 


/1




 mmm
Thus, mean molal activity,
ma
 

mm



/1




Note that m
  m
ACTIVITY AND MEAN ACTIVITY

54. Exercise: 1
1. Determine the molar activity coefficient of Ca
2+
at 25
o
C using
relevant Debye Huckel Equation in the following solution:
a.0.0004 mole of HCl and 0.0002 mole of CaCl
2 in one liter solution
b.0.004 mole of HCl and 0.002 mole of CaCl
2 in one liter solution
c.0.4 mole of HCl and 0.2 mole of CaCl
2 in one liter solution
Ion size parameter for Ca
2+
= 0.4 nm.

55. Exercise 2:
2.The stoichiometric mean activity coefficient at 25
o
C
of the sulphuric acid in a mixture of 1.5 molal
sodium sulphate (Na
2
SO
4
) + 2 molal H
2
SO
4
is
0.1041. If the second dissociation constant, K
2
, for
sulphuric acid is 0.0102 and the pH of the solution is
–0.671, calculate:
a)the molal activity of H
2
SO
4
b)the molal activity of SO
4
2-
c)the molal activity of HSO
4
-
d)the mean activity

of H
2
SO
4

56. Exercise:3
1 gram FeCl
2, 1 gram NiCl
2 and 1 gram of HCl are added to 200 ml of
deaerated water. Platinum electrodes are used to deliver electrical current so
that the electrolysis performs. The anodic and cathodic current density are
1000 A/m
2
. The following are the reactions and E
o
(in the reduction direction)
that may occur:
Fe
2+
+ 2e = FeE
o
= -0,277 V
Ni
2+
+ 2e = NiE
o
= -0,250 V
2H
+
+ 2e = H
2
E
o
= 0 V
Cl
2 + 2e = 2Cl
-
E
o
=

1,359 V
a) Calculate molar activity coefficients of the cations and anion contained in
the solution (use the Finite Size of Debye Huckel Limiting Law)
b) Calculate the activity of the cations and anion contained in the solution
c) Determine the half cell potential of the above reactions
d) Which pair of redox (reduction –oxidation reaction) that would occur
(based on the calculation of c)

57. Exercise: 3 (cont.)
e) What would be the cell voltage of the reaction d
Data: Atomic weight Fe = 55.8, Ni = 58.7, Cl = 35.5, H =1
Ion size parameter in nm : Fe
2+
= Ni
2+
= 0.6, H
+
= 0.9, Cl
-
= 0.3
H
2 overpotential = 0.28 V
Cl
2
overpotential = 0.03 V
Ohmic overpotential = 0.25 V.

58. Kinetics in Hydrometallurgy
•Kinetics in hydrometallurgy deals with the kinetics of
leaching, adsorption and precipitation
•Studying of leaching kinetics is done for the establishment
of the rate expression that can be used in design,
optimization and control of metallurgical operations.
•The parameters that need to be estabished:
–Numerical value of the rate constant
–Order of reaction
–Rate determining step
–Activation energy

59. Leaching Kinetics
•Consider the dissolution of a metal oxide, MO, with
an acid by the following reaction:
•The reaction rates for this leaching system can be
given by
MO
(s) + 2H
+
(aq)  M
2+
(aq) + H
20
(aq)
dt
dC
=
dt
dC
=r
or
dt
dC
2
1
=
dt
dC
=r
O2H+2
M
P
+
HMO
R
--

60. Leaching Kinetics
•For general example if a chemical reaction involves A
and B as reactants and C and D as products, the
stoichiometric reaction can be written as follows:
where
a, b, c, and d = stoichiometric coefficients of species A,
B, C, and D, respectively
k
1, k
2 = reaction coefficients in the forward and
reverse directions, respectively
dD+cCbB+aA
1k
2
k
⇔ (1)

61. Leaching Kinetics
•The rate expression of this stoichiometric reaction
can be written in a more general way:
where
C
A, C
B, C
c, and C
D are concentrations of species A, B,
C, and D, respectively and m, n, p, q are orders of
reaction.
q
D
p
C2
m
B
n
A1
DCBA
CCkCCk=
dt
dC
d
1
=
dt
dC
c
1
=
dt
dC
b
1
=
dt
dC
a
1
--- (2)

62. Leaching Kinetics
•However, if the reaction given in Eq. 1 is irreversible, as in most
leaching systems, Eq. 2 is reduced to the following form:
where k
1
’
= k
1
x a.

m
B
n
A
'
1
A
m
B
n
A1
A
CCk=
dt
dC
or
CCk=
dt
dC
a
1
-
-

63. •For this system, the rate constant, k
1', and the orders of
reaction, n and m, should be determined with the aid of
leaching experimental data.
•The rate expression given in the above equations can be
further reduced if the reaction is carried out in such a way
that the concentration of A is kept constant.
•For such situations, the rate expression is reduced to:
where k
1
”
=k
1
’
x C
A
n
. It should be noted that the rate
constant and the order of reaction are constant as
long as the temperature of the system is maintained
constant.
m
B1
A
Ck=
dt
dC ″
-

64. •Consider the dissolution of zinc in acidic medium:
Zn
(s) + 2H
+
(aq) → Zn
2+
(aq) + H
2(g)
•For the above reaction, the rate of disappearance of H
+

ion is directly related to the rate of appearance of Zn
2+
ion;
thus,
n
H
n
H
m
Zn
+
H
+2
Zn
kC=CCk′=
dt
dC
2
1
=
dt
dC
-

65. •If concentration of zinc metals is assumed to be constant and C
H is further
abbreviated generally as C
A
, then the equation can be written as follow:
•The order of reaction, n, can be any real number (0, 1, 2, 1.3, etc.).
•When n = 0, the reaction is referred to as “zero order” with respect to the
concentration of A.
where C
A
o
represents the concentration of A at t = 0, and X
A
represents
the fractional conversion, i.e., X
A
= [ (C
A
o
— C
A
)/ C
A
o
].
n
A
A
kC=
dt
dC
-
0
A
A
kC=
dt
dC
-
t
C
k
=Xor
kt=dtk=CC=dC
o
A
A
t
0
o
AA
AC
o
A
C
A
∫∫ --

66. •If the plot of X
A versus t gives a straight line, the zero-
order assumption is consistent with experimental
observations and the k value can be obtained from the
slope of the plot.
•When n = 1, the reaction is first order with respect to the
concentration of A:
A
A
kC=
dt
dC
-
k/C
A
o
X
A
time

67. ( )
kt
AA
o
A
A
t
0
AC
o
A
C
A
A
e-1=Xorkt-=X-1ln
kt-=
C
C
ln
kt-=dtk=
C
dC
-
∫∫ -
k
time
ln (1 - X
A)

68. For second order reaction,
ktC=
X1
X
kt-=
C
1
C
1
kt-=dtk=
C
dC
o
A
A
A
o
AA
t
0
AC
o
A
C
2
A
A
-
-
-∫∫
k
time
X
A
(1 - X
A) C
A
o
k
If the second-order assumption is valid, we obtain a
straight line from a plot of X
A/(1 - X
A) versus t, and the
rate constant can be determined from the slope of the
plot.

69. Temperature Effect on the Reaction Rate
(Arrhenius Law)
Reaction rate increases markedly with increasing
temperature. It has been found empirically that
temperature affects the rate constant in the manner
shown in the following equation:
RT/
a
Eo
ek=k
-
T
1
R303.2
E
klog=klog
T
1
R
E
kln=kln
ao
ao
-
-
where E
a is the activation energy and k° is a constant
known as the frequency factor, frequently assumed to
be independent of temperature.

70. Modeling of heterogenous reaction
kinetics
•Heterogenous reaction between solid and fluid in
hydrometallurgical processes is frequently modelled with
“shrinking core“ model.
•If we select a model we must accept its rate equation, and vice
versa.
•If a model corresponds closely to what really takes place, then its
rate expression will closely predict and describe the actual
kinetics;
•If a model differ widely from reality, then its kinetic expressions
will be useless.
•Detailed of modeling and relevant kinetics equations for various
rate determining steps can be found in previous course
(Metallurgical Kinetics).

71. •For determination of E
a, number of experiments, at least at
three or four different temperatures are needed, with all
other variables being kept constant. The next step is to
calculate the rate constant for each temperature as
discussed previously.
•A plot of In k versus 1/T yields a straight line from which the
activation energy, E
a, can be determined
•Activation energy value can be used to predict the rate
determining step of the reaction:
•E
a
= 40 – 80 kJ/mol: process is controlled by surface chemical
reaction
•E
a
= 8 – 20 kJ/mol: process is controlled by diffusion to and from the
surface

72. Mass Transfer in Solution
•For hydrometallurgical system, mass transfer of
component i in solution frequently consists of a
molecular diffusion term, migration term, and convective
diffusion term, as indicated in the following expression:
VC+FCμzCD=N
iiiiiii
Φ∇-∇-
where
N
i= flux of i, C
i = concentration of i, D
i = diffusion coefficient of i
C
i
= concentration gradient of i, z
i
= valence of the specified ion,
µ
i
= ionic mobility, F = the Faraday constant, Ф = electrical
potential gradient, and V = net velocity of the fluid of the system

73. First and Second Fick’s Law of Diffusion
•If N
i consists of the molecular diffusion term only,
•Dimensionless Parameter for Convection Calculation
iii CD-=N ∇
)lawseconds'Fick(0=CD+
t
C
i
2
i
i
∇
∂
∂
(Fick's first law)





















ii
D
LV
D
LV
where µ = the viscosity of the
fluid, ρ = the density of the
fluid

74. Dimensionless Parameter for
Convection Calculation
•The parameter LV/D
i is known as the Peclet number and can be
separated into two other parameters: Lvρ/µ that known as the
Reynolds number, and µ/ρD
i is the Schmidt number.
•Peclet number is regarded as a measure of the role of
convection against diffusion,
•For most hydrometallurgical systems, the Schmidt number is on
the order of 1,000 because the diffusivity of ions and kinematic
viscosity of water are, respectively, on the order of 10
-5
cm
2
/s
and 10
-2
cm
2
/s.
( ) diffusionmolecular
diffusionconvective
=
L/C∇D
VC∇
=
D
LV
ii
i
i

75. •Therefore, if the Reynolds number is greater than 10
-3
,
the Peclet number is greater than 1, and consequently,
convective diffusion is more dominating than molecular
diffusion in such systems.
Mass Transfer Coefficients for Convective Diffusion
•For systems with large Peclet numbers, it is frequently
assumed that there is a diffusion boundary layer at some
distance from the solid surface. For such systems, it is
quite common to write the mass flux from the bulk
solution to the solid surface as follows:
N
i = k
m (C
b - C
s)

76. where
N
i
= mass flux of species i
k
m = mass transfer coefficient, in cm/s
C
b = concentration of species i in the bulk solution, in mol/cm
3

C
s
= concentration of species i at the solid surface, in mol/cm
3
•Because the units of measure of k
m
are the same as those of (D/), where 
is the diffusion boundary layer thickness, k
m
, is often substituted by this ratio.
Therefore,
•The diffusion boundary layer thickness is often estimated by the
relationship k
m = D/δ, provided k
m is known.( )
sbi
CC
δ
D
N -=

77. Mass Transfer from or to a Flat Plate.
•The mass transfer coefficient for a flat plate where fluid is
flowing over the plate at a velocity V
0 has been well
documented.
•The mass transfer coefficient for such a system can be
estimated from first principles and has the following form:
where
D = the diffusivity of the diffusing species
v = the kinematic viscosity of the fluid
L = the length of the plate
62/1
0
2/1-6/1-3/2
m
10<ReForVLD664.0=k ν

78. Rotating Disk.
•Although it is not a practical geometry, because the
mathematical representation of the system is exact and
follows very closely to the experimental data, a rotating
disk is frequently used to determine the mass flux and the
mass transfer coefficient.
•The mass transfer coefficient for this system is as follow
•The equation is valid for the Reynolds number, r
2
ω/ν is
less than 10
5
, where r and ω are, respectively, the radius
and the angular velocity of the disk.
2/16/1-3/2
m D62.0=k ων

79. Particulate System
•It has been demonstrated that the mass transfer
coefficient for particulate systems can be given by the
following equation:
where d = the diameter of the particle, V
t = the slip
velocity, which is often assumed to be the terminal
velocity of the specified particle.
3/26/1-2/1-2/1
tm
DdV6.0+
d
D2
=k ν

80. •The terminal velocity of a particle can be
calculated using the following equation depending
on the Reynolds number of the system, which is
defined by dV
tρ/μ, where ρ is the density of the
fluid:
where ρ
s is the density of the particle. The
preceding equation is often referred to as the
Stokes' equation and is valid as long as the
Reynolds number is less than 1.
( )
μ
ρρ
9
g-r2
=V
s
2
t

81. When the Reynolds number is between 1 and
700, the following equations are used:
( )
( )
2
s
3
2/1
A
t
3
-gd4
=K
55.5-Klog4.0+66.00.5=A
10
d
=V
μ
ρρρ
ρ
μ
where g is the gravitational coefficient.

82. •A cementation reaction, Zn + Cu
2+
→ Cu + Zn
2+
,
is taking place at the surface of a zinc plate of
10 cm x 10 cm area.
•Feed flowing parallel to the plate at a velocity of
1 m/s contains copper at 1 mo/dm
3
.
•Suppose we want to estimate the rate of
deposition assuming that the mass transfer of
Cu
2+
to the zinc plate is rate determining step.
The diffusivity of Cu
2+
is 7.2x10
-6
cm
2
/s, and the
kinematic viscosity of water is 0.01 cm
2
/s.
Example 1:

83. where
S = the surface area of the plate
N
cu
2+
= the number of moles of Cu
2+
ion
Cu
b
2+
= the concentration of Cu
2+
in the bulk
Cu
s
2+
= the concentration of CU
2+
at the
interface
k
m
= 0.664 (7.2 x 10
-6
)
2/3
(0.01)
-1/6
(10)
-1/2
(100)
1/2
= 0.664 x 3.7 x 10
-4
x 2.15 x 0.316 x 10
= 1.7 x 10
-3
cm/s.
( )
+2
bm
+2
s
+2
bm
+2
Cu
Cuk=Cu-Cuk=
dt
dN
S
1

84. Therefore,
Example 2:
•Consider the situation from the previous example,
except that instead of a zinc plate, zinc particles 100 µm
in diameter are suspended in a 1 mol/dm
3
Cu
2+
solution.
Suppose we want to estimate the rate of deposition of
Cu
2+
(Note that the density of Zn is 7.14 g/cm
3
.)
5
23
10
01.0
10100
Re
./7.1000,1107.1
1 2






and
scmmol
dt
dN
S
Cu

85. For particulate,
 
 
 58.210/58.210Re
/58.210
,
412.055.53.80log4.066.05
3.80
103
114.7101.09814
22
412.0
2/1
4
3









scmV
Therefore
A
K
t

86.  
scmmol
dt
dN
S
k
Finally
scm
k
resultaAs
Cu
m
m
./19.9000,11019.9
1
,
/1019.9
1075.71044.1
102.701.001.058.26.0
01.0
102.72
,
23
3
33
3/2
66/12/12/1
6
2











