HYDROMETALLURGY

Theory and Practice

Copper Course Workbook

Fundamentals

H-1,+1-259-253

1.0079

1

Hydrogen

Li+1181

1347

6.941

3

Lithium

Na+198

883

22.990

11

Sodium

K+164

774

39.098

19

Potassium

Rb+139

688

85.468

37

Rubidium

Cs+128

678

132.91

55

Cesium

Fr+127

677

223.02*

87

Francium

Be+2

12782970

9.0122

4

Beryllium

Mg+2649

1090

24.305

12

Magnesium

Ca+2839

1484

40.078

20

Calcium

Sr+2769

1384

87.62

38

Strontium

Ba+2725

1640

137.33

56

Barium

Ra+2700

1140

226.03*

88

Radium

Sc+3

15412831

44.956

21

Scandium

Y+3

15413338

88.906

39

Yttrium

La+3

9213457

138.91

57

Lanthanum

Ac+3

10503200

227.03*

89

Actinium

Ti+3,416603287

47.88

22

Titanium

Zr+4

18524377

91.224

40

Zirconium

Hf+4

22274602

178.49

72

Hafnium

V+2,3,4,5

18903380

50.942

23

Vanadium

Nb+3,524684742

92.906

41

Niobium

Ta+5

29965425

180.95

73

Tantalum

Cr+2,3,6

18572672

51.996

24

Chromium

Unq261*

104*

UnnilquadiumUnp

262*

105#

UnnilpentiumUnh

263*

106

UnnilhexiumUns

262*

107

Unnilseptium

108

Une266*

109

Unnilennium

Mo+2,3,4,5,6

18572672

95.94

42

Molybdenum

W+2,3,4,5,6

34105660

183.85

74

Tungsten

Mn+2,3,4,6,7

12441962

54.938

25

Manganese

Tc+7

21724877

98.906*

43

Technicium

Re+2,4,7

31805627

186.2

75

Rhenium

Fe+2,3,6

15352750

55.847

26

Iron

Ru+3,4,8

23103900

101.07

44

Ruthenium

Os+2,3,4,6,8

30455027

190.2

76

Osmium

Co+2,315352750

58.933

27

CobaltNi

+2,315352750

58.69

28

Nickel

Rh+1,2,3,4

19663727

102.91

45

Rhodium

Ir+1,2,3,4,6

24104130

192.22

77

Iridium

Pd+2,415523140

106.42

46

Palladium

Pt+2,417723827

195.08

78

Platinum

Cu+1,210832567

63.546

29

Copper

Ag+1,2962

2212

107.87

47

Silver

Au+1,310642807

196.97

79

Gold

Zn+2420907

65.39

30

Zinc

Cd+2321765

112.41

48

Cadmium

Hg+1,2-38.8357

200.59

80

Mercury

Al+3660

2467

26.982

13

Aluminium

B+3

20792550

10.811

5

BoronC

-4,+2,433674827

12.011

6

CarbonN

-3,+2,3,4,1-210-196

14.007

7

NitrogenO

-2,-1-218-183

15.999

8

OxygenF

-1-220-188

18.998

9

FluorineNe

0-249-246

20.179

10

Neon

He0

-272-269

4.0026

2

Helium

Si+4

14102355

28.086

14

Silicon

Ga+330

2403

69.723

31

GalliumGe

+4937

2830

72.61

32

Germanium

In+3157

2080

114.82

49

IndiumSn

+2,4232

2270

118.71

50

Tin

Tl+1,3157

2080

204.38

81

ThalliumPb

+2,4328

1740

207.2

82

Lead

P-3,+3,5

44280

30.974

15

Phosphorus

As-3,+3,5

817613

74.922

33

Arsenic

Sb-3,+3,5

6311750

121.75

51

Antimony

Bi+3,5271

1560

208.98

83

Bismuth

S-2,+2,4,6

113445

32.066

16

Sulphur

Se-2,+4,6

217685

78.96

34

Selenium

Te-2,+4,6

450990

127.60

52

Tellurium

Po+2,4,6

254962

208.98*

84

Polonium

Cl-1,+1,3,5,7

-101-35

35.453

17

Chlorine

Br-1,+1,3,5,7

-7.259

79.904

35

Bromine

I-1,+1,3,5,7

114184

126.90

53

Iodine

At-1,+1,3,5,7

302337

209.99*

85

Astatine

Kr+2,4-157-152

83.80

36

Krypton

Ar0

-189-186

39.948

18

Argon

Xe+2,4,6

-112-107

131.29

54

Xenon

Rn+2-71-62

222.02*

86

Radon

Ce+3,4799

3426

140.12

58

CeriumPr

+3,4931

3512

140.91

59

PraseodymiumNd

+310213068

144.24

60

NeodymiumPm

+311682460

146.92*

61

PromethiumSm

+2,310771791

150.36

62

SamariumEu

+2,3822

1597

151.97

63

EuropiumGd

+313133266

157.25

64

GadoliniumTb

+3,413563123

158.93

65

TerbiumDy

+314122562

162.50

66

DysprosiumHo

+314742695

164.93

67

HolmiumEr

+314972900

167.26

68

ErbiumTm

+2,315451947

168.93

69

ThuliumYb

+2,3819

1194

173.04

70

YtterbiumLu

+316633395

174.97

71

Lutetium

Th+4

17504790

232.04*

90

ThoriumPa

+4,51600

231.04*

91

ProtactiniumU

+3,4,5,611323818

238.03*

92

UraniumNp

+3,4,5,6640

3902

237.05*

93

NeptiniumPu

+3,4,5,6641

3232

244.06*

94

PlutoniumAm

+3,4,5,6994

2607

243.06*

95

AmericiumCm

+3,41340

247.07*

96

CuriumBk

+3,4

247.07*

97

BerkeliumCf

+3,4

251.08*

98

CaliforniumEs

+3

252.08*

99

EinsteinumFm

+3

257.10*

100

FermiumMd

+3

258.10*

101

MendeleviumNo

+2,3

259.10*

102

NobeliumLr

+3

260.11*

103

Lawrencium

IA 1

IIA2

IIIB3

IVB4

VB5

VIB6

VIIB7

VIII8 9 10

IB11

IIB12

IIIA13

IVA14

VA15

VIA16

VIIA17

0 18

Co

+2,315352750

58.933

27

Cobalt

AtomicNumber

Symbol

Relative AtomicMass

Oxidation StatesMelting Point °CBoiling Point °C

Non-MetalsAlkaline Earth Metals

Noble gasesAlkali Metals

Platinum Group Metals Other Metals

Magnetic Metals

Transition Metals Lanthanides

Actinides

Lanthanides

Actinides

*Hahnium (USA)Kurchatovium (USSR)

#Rutherfordium (USA)Nielsbohrium (USSR)

Values of Useful Constants

Absolute zero temperature -273.2 oC Acceleration due gravity 9.8067 m s-2 Avogadro constant 6.022 x 1023 mol-1 Boltzmann constant 1.381 x 10-23 J K-1 Faraday constant, F 96490 C mol-1 Molar gas constant , R 8.315 J K-1 mol-1 Molar Volume of ideal gas (1 bar) 0.022712 m3 mol-1 Standard atmosphere 1.013 x 105 Pa

2.303RT/F = 0.0591 V at 298K

Useful Thermodynamic Formulae

G = H – T.S

G = -RT.lnK

G = -nF.E

E = Eo – RT/(nF). ln {[Red]/[Ox]}

= Eo -0.0591/n . log {[Red]/[Ox]} at 25oC

HTo = H298

o + 298T Cp

o dt

GoT = Ho

298 -TSo298 +(T-298) Cp

o]T298 - T Cp

o]T298 ln(T/298).

4

Class and Workshop Problems

Class Problems

Class Problem 1 An ore contains chalcopyrite, covellite and chalcocite as the only minerals of copper, iron and sulfur. Chemical analysis gives 0.60% Cu, 0.137% Fe and 0.312% S. Calculate the % of each of the minerals in the ore. Check your answer using the Mineralogy option in HSC. How much copper (tonnes/a) could be produced in a plant treating 10000t/d of the ore if the recovery of copper is 45% from chalcopyrite, 75% from covellite and 95% from chalcocite ?

5

Class Problem 2 An ore consists of 80% quartz, 10% Cu2O and 10% chalcopyrite. If 1 kg of ore is reacted with 1 L of 1 M HCl in the absence of dissolved oxygen only the Cu2O dissolves. The pH is maintained by addition of 10 M HCl (density 1.18 g/cm3). You can assume an initial and final solution density of 1.02 and 1.08 g/cm3 respectively.

Determine

1) the minimum volume of 10M HCl required.

2) the final concentrations of dissolved species

3) a mass balance

6

Class Problem 3 Consider the hydrolysis equilibrium:

Fe3+ + H2O = Fe(OH)2+ + H+ : K1 = 10-2.2

Show that

pH = pK1 + log {[Fe(OH)2+]/[Fe3+]}

Plot the variation of [Fe(OH)2+] and [Fe3+] as a function of pH in the range pH 0-3 and total [Fe(III)] = 0.1M

7

Class Problem 4 What is the fraction of copper(I) present as CuCl2

- in a 1M chloride solution containing 0.01M of total copper(I). Use HSC to obtain the relevant stability constants.

8

Class Problem 5 Estimate the enthalpy (per mole Cu produced) associated with the electrowinning of copper at 298K and 1 atmosphere pressure by the reaction CuSO4(a) + H2O(l) = Cu + H2SO4(a) + 1/2O2

9

Class Problem 6 Sketch the curve for the ratio of NH4

+/NH3 as a function of pH.

10

Class Problem 7

Copper(I) and (II) ions both form strong complexes with ammonia. Calculate the formal potential of the Cu(II)/Cu(I) couple in 1M ammonia solution using the data in Table 3.3 and Table 3.5 of Module 3.

11

Class Problem 8 The measured pH of 2 mol/L HCl at 298 K is –0.63. Calculate aH

+, γH+ and

aOH- of the solution.

12

Class Problem 9 An ore contains CuO and Al2O3. On leaching the ore, an equilibrium [Cu2+] of 0.1 mol/dm3 is obtained at 25oC. What is the pH in the leach and the equilibrium [Al3+]?

Class Problem 10 Assuming that the pH and the dissolved oxygen concentration are maintained at 2.0 and 1 mM respectively, calculate the half-life of a solution containing 0.1 M Fe2+ at 25oC using the rate equation below with k = 0.015 min-1.75 .

13

-d[Fe2+]/dt = k [Fe2+]2.[O2]/[H+]0.25

If the activation energy for the reaction is 80kJ/mol, calculate the half life of the reaction at 90oC. Assume the same parameters as the above problem but allow for the lower solubility (0.40 of solubility at 25oC) of oxygen at the higher temperature.

Convert the above equation to one for the rate of disappearance of oxygen and calculate the pseudo-1st order rate constant for [Fe(II)] = 0.1M and pH 2.

Class Problem 11 Using the data provided in relevant table in the notes, calculate the overpotential you would expect for the reduction of Cu ions (1M) at current densities of 200 and 300 A m-2. Use the “high field” approximation.

14

Do the same for the evolution of oxygen on the lead anode at the same current densities assuming the high field approximation.

What would be the actual potentials(versus SHE) at the anode and cathode for a solution with unit activity copper and hydrogen ions for each current density?

Class Problem 12 Calculate the initial rate(g s-1) of dissolution of copper from a suspended spherical 100m particle of CuS in a 0.01M ferric solution assuming that the rate is controlled by the mass transport of ferric ions to the surface and that the product is Cu2S.

15

Class Problem 13

Calculate the cell voltage for the EW of copper using the results (anode and cathode potentials) of Class Problem 4 i.e. a cell operating with an electrolyte

16

containing 40 g/L CuSO4 and 175 g/L H2SO4 at 300A/m2 . Assume an anode/cathode spacing of 50mm.

Class Problem 14 Copper can be dissolved in aerated acidic aqueous solutions by the reaction

Cu + O2 + H+ Cu2+ + H2O

17

The rate of reaction is controlled by mass transport of dissolved oxygen from the gas phase into the solution. Estimate the maximum rate of dissolution (in g copper h-1) of copper powder suspended in a stirred reactor with an air/solution interfacial area of 1m2. The aqueous phase mass transfer coefficient for oxygen is 1 x 10-3 cm s-1 and the solubility of oxygen in equilibrium with air is 2.5 x 10-4 M.

18

Workshop Problems

Workshop Problem 1 Species Distribution

You are required to derive the species distribution using HSC for a solution containing 0.1M FeSO4 + 0.05M Fe2(SO4)3 at pH values between 3.0 and 1.0 at 80oC by adding increasing amounts of H2SO4 to the above solution. Repeat the calculation for an initial solution containing 1M H2SO4 to which is added increasing amounts of Na2SO4 up to 2M.

Workshop Problem 2 Species Distribution and Electrochemical Potentials

You are required to derive the species distribution using HSC for a solution containing 0.1M Cu(II) and 0.1M Cu(I) as a function of the concentration of chloride from 0.5M to 5M at 25oC. Export the relevant results to Excel and calculate the formal potential of the copper(II)/copper(I) couple as a function of chloride concentration (Use HSC to obtain the standard potential for the couple Cu2+ + e = Cu+) Calculate the potential for the reduction of Cu(I) in the presence of sulfur to produce covellite(CuS) as a function of the chloride concentration assuming a concentration of 0.1M Cu(I). Thence calculate the equilibrium constant for the dissolution of covellite (CuS) by the oxidation reaction

CuS + Cu(II) = 2Cu(I) + S

as a function of chloride of concentration. What conclusions can you draw about the viability of this as a leaching process for covellite?

Workshop Problem 3 Homogeneous Kinetics

The spreadsheet (Workshop Problem 3.xls) contains information on published data for the oxidation of ferrous ions to ferric ions in sulfate solutions. This is an important reaction in the leaching of most sulfide and some oxide minerals which require oxidation of the mineral by ferric ions. The low concentration of dissolved oxygen and the very slow direct oxidation kinetics by oxygen requires a catalyst or redox mediator such as the ferric/ferrous couple in order for these reactions to proceed at an acceptable rate. The re-oxidation of ferrous to ferric by dissolved oxygen is therefore important. The rate of this reaction can be increased by increasing the temperature and the oxygen concentration (by increasing the

19

pressure) as in the so-called pressure leach process. It can also be increased in the presence of suitable bacteria as in the bacterial oxidation or bio-leaching processes.

You are required to make a study of the kinetics of this reaction using the data given as well as other appropriate data that may be required.

Write a balanced chemical equation for the reaction.

Referring to the data in section (A) of the spreadsheet, establish the order of the reaction with respect to iron(II) and use Excel to make suitable plots from which you can derive appropriate rate constants for each run.

In a similar way, establish the reaction order with respect to oxygen by using the data in section (B) and derive rate constants.

Repeat (iii) using the data in section ( C) which shows the effect of added sulfate on the rate of oxidation.

Use the species distribution diagrams obtained in Workshop Problem 1 together with the data in (V) to explain the apparent effect of acid concentration on the rate as shown in section (A).

Derive an overall rate equation which can be used to calculate the rate of oxidation as a function of the various concentrations and the oxygen pressure at 353K. This rate equation can then be used in a linear regression of all the data to obtain a “best-fit” value for the rate constant.

Workshop Problem 4 Homogeneous and Heterogeneous Kinetics

Copper(I) in ammoniacal solutions forms the stable Cu(NH3)2

+ complex ion which is rapidly oxidized by dissolved oxygen to the Cu(NH3)4

2+ complex. The rate of the reaction can be conveniently measured by an amperometric technique which measures a current that is proportional to the concentration of copper(I). The following results (Workshop Problem 4.xls) were obtained in an experiment in which the initial concentrations are shown in the second row of Table 2 below. The dissolved oxygen concentration was maintained constant by sparging air into the solution.

20

Table 1. Results of a test with initial concentrations in 2nd row of Table 2

Time, s Current0.0 1.4720.5 1.2981.0 1.1261.5 0.9932.0 0.8682.5 0.7583.0 0.6664.0 0.5195.0 0.4026.0 0.3157.0 0.2438.0 0.194

10.0 0.12212.0 0.08014.0 0.05016.0 0.029

Table 2. Pseudo-First Order Rate Constants

[Cu(I)],M [NH4+], M [NH3], M [O2],M k1, sec-1

1.00E-04 0.01 0.01 2.50E-04 0.101

1.00E-04 0.025 0.025 2.50E-04 ???????

1.00E-04 0.05 0.05 2.50E-04 0.485

1.00E-04 0.025 0.025 2.50E-04 0.253

1.20E-04 0.025 0.025 2.50E-04 0.263

1.50E-04 0.025 0.025 2.50E-04 0.258

1.00E-04 0.01 0.01 1.00E-03 0.419

1. Write a balanced equation for the reaction. 2. Graphically or otherwise, demonstrate that the data in Table 1 is consistent

with a reaction which is first order in Cu(I). 3. Using the data in Table 2, derive the reaction orders with respect to

ammonia and dissolved oxygen. 4. Write the overall rate equation and calculate values for the overall rate

constant for each of the experimental runs in Table 2.

In a pilot plant, a solution of copper(I) initially containing 1x10-4mol/l of copper(I) and 0.01M ammonia/0.01M ammonium ions is oxidised by stirring the solution in an open reactor containing 1m3 of solution. The internal diameter of the tank is 1m.

Assuming that the rate of oxidation is controlled by mass transport of oxygen into the aqueous phase, calculate the rate of oxidation of copper(I) in mol l-1

21

min-1. The aqueous phase mass transfer coefficient for oxygen from the surface of the interface is 2 x 10-4 cm s-1 and the solubility of oxygen is 2.5 x 10-4 mol/l.

Sketch a graph of the concentration of copper(I) in solution as a function of time under these conditions.

Compare the rate of oxidation of copper(I) under these conditions with that calculated for the rate of the chemical reaction.