Electrowinning course notes hydrometallurgy

MTRL 358 Electrowinning and Electrorefining

2014

Metal recovery is the final step in most hydrometallurgical processes. This is commonly practiced for aluminum, copper, zinc, nickel, cobalt and gold. (Aluminum cannot be obtained by electrolysis from water; it is too strongly reducing. Molten salt electrolysis is used instead.) In all hydrometallurgical processes metals are present in solution as complexes of the metals in positive oxidation states, e.g. [Zn(H2O)6]+2. All metal recovery processes then necessarily involve reduction. Hence all these processes require a reducing agent. The process may be thermodynamically favourable (like hydrogen gas reduction of [Ni(NH 3)n]+2 complexes (n = 2, for instance) or unfavourable (like electrowinning of copper in which water is forced to be the reducing agent). When the process is thermodynamically unfavourable (E < 0, by definition) it is categorized as an electrolysis. Electrolysis for metal production is called electrowinning. Briefly, a copper EW plant may have many cells (hundreds). Each cell is a little over 1 m wide, ~1.5-2 m deep and several meters long. They contain several dozen cathodes and the same number + 1 anodes. Metal is plated onto both sides of the cathode sheets, while water is oxidized to form O 2 and H+ at the anodes. A schematic illustration of a cell is shown in the diagram below. Enriched electrolyte supplied from solvent extraction stripping is fed into the cells. It passes through a cell once and then is returned to SX stripping as the lean electrolyte. Once the copper has been plated to a thickness of about 0.5 cm, the cathodes are removed from the cell and the copper is prepared for sale.

Figure 1. Schematic illustration of a copper electrowinning cell.

1

Pyrometallurgically produced metals are often not sufficiently pure to be sold as high purity products. They are usually further refined and often using electrolysis. Molten, as-produced metal is cast into electrodes (~1 m x ~1 m) and these are interleaved with metal sheets in cells. The cast, impure metal electrodes are anodically polarized to electrochemically corrode them (a form of leaching), while the interleaved sheets are cathodically polarized to plate out the dissolved metal ions. A very pure metal product is formed. This is called electrorefining. Background Electrochemistry The relevant electrochemistry was developed in the Eh-pH diagram course notes and should be consulted. Reminder on calculating  E° or  E: The potential difference or voltage generated by an electrochemical cell at a certain temperature is strictly a function of the composition of the cell, i.e. activities of the reactants and products. It does not depend on the charge that passes through that potential (i.e. nF). The energy associated with passage of the charge through the potential difference does depend on the amount that is passed: Energy = voltage x charge. But, the potential itself generated by the cell has nothing to do with the charge that is passed. Therefore DO NOT multiply E°’s by n numbers to calculate E° or E for a cell!

Electrowinning Equations (Faraday's Law Relationships) (1) Farady’s Law Faraday’s law states that the number of moles of metal produced in an electrolysis is directly proportional to the charge passed. The constant of proportionality is nF, where n = moles of electrons per mole of metal produced (an integer) and F is the Faraday which is 96485 C/mole e -; a mole of electrons has a charge of 96485 C. (i.e. 6.02205 x 10 23 e-/mol e- x 1.60218 x 10-19 C/e-.) Taking into account the fact that charge, q = current x time for fixed current (or the integral of I vs. t for a varying current) and that the moles of metal produced = mass/atomic weight leads to the formula provided. Moles of metal plated  q (charge passed in the electrolysis)

{1}

moles metal = nM = q/nF

{2}

The units of q/nF are C/(mole e-/mol metal x C/mole e-) = mol metal. Charge passed at constant current is q = It. Moles of metal = M/AW where M is the mass of metal plated and AW is the atomic weight in g/mol. Then moles metal plated is, nM = It/nF = M/AW

{3}

2

Rearranging gives, M = It AW nF

{4}

From Faraday’s law it is obvious that the lower n is, the less electricity that will be required per unit mass of metal plated. Some metal ions have more than one oxidation state. For typical copper electrowinning the cathodic half reaction is, Cu+2 + 2e- = Cu

(1)

Alternative leaching processes have been developed that form cuprous complexes: Copper sulfides

air, Cl-

CuCl2-aq

(2)

In this case the cathodic half reaction is, CuCl2- + e- = Cu + 2Cl-

(3)

which would use half the electricity. (No such process is currently commercially applied.) (2) Current Efficiency The simple formula above determines mass of metal plated for a given current and time, or vice versa. If the only cathodic (reduction) process operative is metal ion reduction to metal, then the formula gives an accurate indication of the mass of metal for a given current and time. However, other reduction half reactions may also occur simultaneously. These unwanted side reactions also consume electricity (current) and result in a lowered efficiency of use of current for metal plating. This leads to the idea of current efficiency. Current efficiency (CE) for metal plating then (or any electrolytic process), is the ratio of actual mass of metal plated to the theoretical mass based on Faraday’s law. It is usually given in %. CE =

actual mass metal plated x 100 theoretical mass expected

{5}

The theoretical mass is given by Faraday’s law. CE =

100M It AW/nF

= 100nFM It AW

{6}

Now M is actual mass of metal plated. For instance, calculate the current efficiency for the following conditions: 100 g of copper was plated in a copper electrolysis experiment using a constant current of 4 A for 23 hours. What was the current efficiency?

3

CE = 100 g Cu x 100 x 2 mol e-/mol Cu x 96485 C/mole e- = 91.7% (23 hr x 3600 sec/hr x 4 C/sec x 63.546 g Cu/mol Cu)

{7}

(3) Energy Efficiency There is a theoretical minimum energy required to electroplate a metal. This is the thermodynamic minimum voltage times the charge passed at 100% current efficiency. Electrical work (energy) is voltage times charge (more generally, ∫Vdq if the voltage varies with charge passed, which equals Vq at constant voltage). By definition 1 VC = 1 J (1 volt·coulomb = 1 joule). In practice the actual voltage will be greater than the thermodynamic minimum for a number of reasons, and due to less than 100% current efficiency the charge passed may be greater than the theoretical minimum. On both counts the energy required will be greater than the theoretical limit. Energy efficiency is the ratio of the theoretical energy required to the actual energy required, in percent. The theoretical voltage is E, i.e. the thermodynamic cell voltage. The theoretical charge required is given by Faraday’s law, q = nMnF

{8}

Hence the minimum energy requirement is, We’rev = E nMnF units in J

{9}

(Work and cell thermodynamic voltage are related by, -G = nFE = we'rev

{10}

units in J/mol; this is the difference between we'rev and We'rev.

where We’rev and we'rev are the electrical work under reversible conditions.* In electrowinning E is negative (G > 0; E < 0); the reaction as written is not favourable so we'rev < 0. The units of w e'rev are J/mol. As per the engineering convention, work done on a system is negative. The symbol W e'rev represents the work in joules. The actual applied voltage is designated Eappl. The applied voltage opposes the thermodynamic voltage and hence it is taken to be positive. For practical rates we require Eappl >  E . The current is forced to go in the opposite direction to the natural tendency of the cell.) CE = 100 nFM = 100 nFnM It AW q

{11}

* Reversible and irreversible processes are reviewed in the next section. For now suffice it to say that if an opposing voltage equal to  E , where E < 0, (an electrolysis) is applied, then the thermodynamic tendency is just matched or just overcome and the reaction is exceedingly slow, i.e. reversible.

4

Since M/AW = nM and It = q, q = 100nMnF CE

{12}

Then the actual energy input is, -We’ = Eappl q = 100EapplnMnF CE

{13}

(-We' is a positive number.) The energy efficiency is: 100 E nMnF 100Eappl nMnF/CE

EE = 100We’rev = We’

=  E CE Eappl

{14}

Take an example again of 100 g of copper plated as above at a voltage of 2.0 V with 91.7% current efficiency. (If the cell is large and relatively little copper is plated, the applied voltage will be about constant, as will be the current.) E = -0.89 V (= E° assuming standard conditions; 0.89 V = the necessary applied voltage to just overcome the thermodynamic negative cell voltage. (In reality the Nernst equation E would be required for a real cell with non-standard activities.) EE = 0.89 x 91.7/ 2.0 = 40.8%

{15}

This is not very high. Reasons for this will be explained later. (4) Specific Energy Consumption This is the actual energy requirement in units of energy per unit amount of metal plated (e.g. J/mol). The derivation above employed the energy consumption, i.e. Eappl q. -We’ = 100Eappl nM nF CE

{16}

Divide both sides by the moles of metal (n M here) to get the specific energy consumption in J/mol (designated -we’): -w’e = 100 nFEappl CE

{17}

A more conventional unit is kilowatt-hours per tonne of metal. A kWh is 1000 watts for 1 hour = 1000 J/sec x 3600 sec = 3.6 x 10 6 J. To convert the energy consumption number to kWh/t metal involves only unit conversions: -w’e J

x

1 kWh

x 1 mol metal x 10-6 g

{18}

5

mol

3.6 x 106 J

AW g

t

For copper this works out to -we’ J/mol x 0.0043713 kWh/t. J/mol For copper electrowon as above at 2 V and 91.7% current efficiency, -w’e = 2 mol e- x 96485 C x 2.0 V mol Cu mol e91.7 x 0.01

= 4.209 x 105 J/mol Cu

= 4.209 x 105 J/mol x 0.0043713 kWh mol / J t = 1840 kWh/t Cu

{19}

{20}

In practice a typical energy requirement for copper EW is about 1900-2000 kWh/t. (5) Metal Production Rate Starting with Faraday’s law and current efficiency again, q = 100nMnF CE

{21}

nM =

{22}

q CE 100nF

where nM is the moles of metal produced. Only CE% (e.g. 91.7%) of the total charge passed goes to plate metal. The charge at constant current is q = It. nM = It CE 100nF

{23}

Metal is plated onto both sides of a cathode starter sheet (e.g. a steel sheet in copper electrowinning). The total plating surface area for a number N cathodes is AcN, where Ac is the surface area per cathode sheet. Taking j as the current density in A/m2, the current being passed is j times the total plating area, i.e. I = jA cN. nM = jAcNt CE 100nF

{24}

i.e. j (C/sec m2) x surface area (m2) x time (sec) = charge (C). Next, rearrange to obtain: nM = dnM = jAcN CE t dt 100nF

mol/sec

{25}

AcN is the total plating surface area. This may be obtained in two ways, either using N to be the number of cathode starter sheets with A c being the area of both sides combined, or with N being the number of plating surfaces and A c being the surface

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area of just one side. Either way is equivalent. Regardless, the fact that metal is plated on two sides is factored in. The area of the narrow sides is negligible and little copper plates there since the electric field is rather diffuse at the sides anyway. In practice, edge strips may be used to prevent plating there. This makes removal of the plated metal sheets much easier. To get plating rate in mass per unit time, multiply dn M/dt by appropriate conversion factors. This depends on the metal being plated since it involves the atomic weight. For tonnes per day: dM = dnM mol x AW g x 10-6 t x 3600 sec x 24 h dt dt sec mol g h d

{26}

For copper, dMCu = dnCu mol x 63.546 g x 10-6 t x 3600 dt dt s mol g

s x 24 h = 5.49037 dnCu t Cu/day h d dt {27}

A typical EW cell would contain 60 cathodes 1 m wide x 1-1.2 m deep and 61 anodes. Copper is plated on both sides of the cathodes. Typical current densities range from 200-350 A/m2. For copper the cathode production rate for a cell with 60 cathodes per cell, each with length x width = 1 m x 1m, at 200 A/m 2 current density and 91.7% CE is: 200 C x 2 m2 x 60 sheets x 0.917 2 dnM = sec m sheet dt 2 mol e- x 96485 C mol mol e-

{28}

= 0.11405 mol/sec dMCu/dt = 0.11405 x 5.49037 = 0.6262 t Cu/day Note: the cathode sheet has dimensions of 1 m x 1 m. The plating area on one side is 1 m2. The plating area of the whole sheet is 2 m 2; we plate on both sides. The calculation above allows estimation of copper production based on current and current efficiency. This aids in design of an actual EW tankhouse. The number of cells needed to achieve a desired production per year can be readily determined. How many cells of 60 cathodes each would be needed to achieve 50,000 t/yr of copper production under the conditions we have been using in the calculations above? 0.6262 t Cu/day/cell x 365 days/y x S cells = 50,000 t/y

{29}

S = 218.8

7

We would need 219 cells. The total number of cathode sheets that must be employed then is 219 x 60 = 13,140. If a fully plated copper cathode is 0.5 cm thick on average and 1 m long on each side, and given that the density of copper is 8.92 g/cm3, the average weight of a cathode would be: 100 cm x 100 cm x 0.5 cm x 8.92 g/cm3 = 44.6 kg (0.0446 t)

{30}

This means that 1.1211 x 106 sheets of copper have to be handled per year, or 3071 per day. If the current density was increased the number of cells required could be lower. Often cathode quality issues limit the current density. How long would it take to plate a copper cathode to a thickness of 0.5 cm? The metal production rate equation can be rearranged to obtain time. Since the current is constant, dM/dt is constant as well, so the mass M plated over a specified time t equals dM/dt: MCu = jAcN CE x 63.546 g/sec t 100 nF

{31}

t=

{32}

100 nF MCu sec jAcN CE x 63.546

where MCu in g. Now Ac is the area for a single sheet (on one side), i.e. 1 m 2 in this case. N now is 1. (We are considering the time to grow a single cathode copper sheet.) For MCu = 44.6 kg = 44,600 g as above, plated at 200 A/m 2 with 91.7% CE: t=

100 x 2mol e- x 96485 C x 44,600 g mol mol e = 7.385 x 105 sec 2 200 C x 1 m x 91.7 x 63.546 g sec m2 mol

{33}

= 8.55 days Obviously the higher the current density, the shorter the plating time. The five relationships above are summarized in the table below. Table 1. Summary of the Faraday's Law relationships. M = I t AW in g Faraday’s law nF CE = 100nFM Current efficiency It AW EE =  E CE Energy efficiency Eappl -w’e = 100 nFEappl in J/mol Specific energy consumption CE Metal production rate dnM = jAcN CE in mol/s

8

dt

100nF

Thermodynamics of Electrochemical Cells Reversible and Irreversible Processes In thermodynamics a reversible process is one for which the direction of a process (such as a reaction) can be reversed by an infinitesimal change. For example, if a process is operating reversibly, an infinitesimal change in pressure or temperature or concentration can reverse the direction of the process. Reversible processes are in thermal equilibrium with their surroundings. They are also at equilibrium in other respects, e.g. chemically or mechanically. How then can there be any actual change of state? Suppose there is a chemical reaction occurring, A = B. And suppose the system is at equilibrium. Increase the concentration of A by d[A], an infinitesimal change. The reaction proceeds to the right to an infinitesimal degree. Continue to increase the concentration of A in infinitesimal steps. The reaction proceeds to produce additional concentration of B by d[B] increments. In the limit of infinite time a finite extent of reaction will have occurred. Note that at any stage during the process the reaction can be reversed by adding an infinitesimal concentration of B. This is a reversible process. Truly reversible processes are of no practical use; they occur infinitely slowly. But, they are a condition or case that thermodynamics can use to tell us something about theoretical limiting possibilities. It helps us to answer questions like, "What is the minimum possible heat we can put into a process to make it go?" Or, "What is the maximum possible work we can get out of a process?" Naturally then, real processes are always irreversible. (Irreversible does not mean that it cannot be reversed, but, rather the opposite of thermodynamically reversible.) They have a finite (not infinitesimal) driving force to proceed in one direction. Stopping or reversing the process requires a finite change in a variable. Real processes sometimes can approach, but never truly attain reversibility. A reversible process always has associated with it the minimum possible heat flow. (This can be qualitatively understood from an example. If you very slowly and gently set down a large rock on a surface there will be little or no perceptible change in temperature of the rock and the surface. If you drop the rock it will hit the floor with substantial force and generate a substantial rise in temperature. Both cases involved the same change in gravitational potential energy. The latter was the most irreversible case.) Real processes involve conditions that are far from equilibrium. They move spontaneously towards equilibrium. If a process is exothermic, for instance, the heat loss is larger than would be the case under reversible conditions. Heat loss from the system is negative and q irrev < qrev, i.e. qirrev is a bigger negative number than qrev (qirrev > qrev). With respect to galvanic electrochemical cells (favourable reaction) under hypothetical reversible conditions, the heat flow is the minimum, while the work that can be done is the maximum. Recall that the change in internal energy for a

9

change of state (e.g. 1 mol A aq  1 mol B aq, as above) is the sum of heat flow minus work flow, (U = q - w; work done by the system is positive by definition and heat exiting the system is negative.) Internal energy is a state function, i.e. it depends only on the final and initial states, not how you get from one to the other. Then, the less heat evolved for a given change, the more work that was extracted from that change. For a real cell, operated under real conditions, the process is necessarily irreversible and the heat flow is greater than in the reversible case, so the work obtainable is less. The farther from reversibility (or the more irreversible the process), the more the heat and the less the obtainable work. Extending the idea that reversible processes run infinitely slowly, the faster the process is run, i.e. the more rapidly the battery is discharged, the more irreversible the process, and the more of the energy that is lost as heat.) The reversible case defines the limiting possibility. Some examples of irreversible processes include: 1. Flow of heat from a hot body to a cold one 2. Water flowing downhill 3. Hydrometallurgical leaching reactions 4. The conversion of chemical energy into electrical energy in galvanic cells. 5. An electrolysis. Once the final equilibrium state is reached the capacity of the system to do further work is exhausted. In example 1, the two bodies reach the same temperature, and in example 4 the battery goes dead. Real processes involve finite changes of state with finite energy changes. There is a driving force, or potential for the process to occur. If the change is thermodynamically favourable then the process is spontaneous and irreversible. (Recall that for a spontaneous process, G < 0. The Gibbs free energy function expresses the requirement that spontaneous processes must increase the net entropy of the system plus its surroundings.) If the process is not favourable it is not spontaneous and does not naturally tend to occur. The reverse (opposite) process is actually favoured and naturally does tend to occur. The non-spontaneous process can be forced to occur by input of sufficient energy, and when this is done the real process is also irreversible. A Review of Some Relevant Thermodynamics Next, a refresher on some aspects of the thermodynamics related to electrochemical cells is needed. Enthalpy is the sum of internal energy + PV, where P = pressure and V = volume. H = U + PV

{34}

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U = q – w, staying with the engineering convention that work done by the system is positive and heat flow out of the system is negative. dH = dq – dw + d(PV) {35} (H is very similar to U, but more convenient at constant pressure.) For a reversible process the heat flow is denoted dqrev. Then, dqrev = TdS

{36}

where T is the absolute temperature and dS is the entropy* change of the system (this from the definition of entropy). Under reversible conditions, the system can do its maximum possible work, and the heat flow is the minimum possible, i.e. -dw = -dwrev = maximum work possible

{37}

G = H –TS by definition

{38}

where G is the Gibbs free energy. At constant temperature, reversible conditions: dG = dH - TdS

{39}

dG = dU + d(PV) – TdS

{40}

dG = dqrev – dwrev + d(PV) - TdS dG = TdS – dwrev + d(PV) – TdS

{41} {42}

Generally, the work is comprised of pressure-volume work and non-PV work, such as electrical, gravitational etc. (the former is of interest here). The work term is, -dwrev = -PdV – dw’rev

{43}

where dw’rev is the non-PV work (electrical work here) under reversible conditions. At constant pressure, and,

dG = -PdV – dw’rev + PdV + VdP = -dw’rev

{44}

G = -w'rev

{45}

since dP = 0 (constant pressure). (The cancelling of the PdV terms is what makes the enthalpy function convenient.) Hence the maximum non-PV work (w’ rev) is equal to -G (at fixed P, T), and this is obtainable only under reversible conditions. This is a limiting case. Electrochemical cells commonly do operate under conditions of constant temperature and pressure. However, real cells cannot operate under truly reversible conditions. Sometimes real cells may come moderately close.

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* Entropy can be thought of as the inverse of the "concentration" or "quality" of energy. Energy naturally tends to disperse: heat flows to cooler bodies, unequal concentrations tend to equalize, light moves away from its source, and so on. All this occurs naturally without having to be forced. It just happens. Thus the "concentration" of energy always tends to drop; energy wants to become more diffuse. This is the entropy effect. Thermodynamically speaking, entropy naturally tends to increase; the dispersal of energy increases. THIS IS WHAT DRIVES ALL SPONTANEOUS PROCESSES. If a process is spontaneous (or favourable) it means that overall there is a net increase in entropy; a degradation of the "concentration" of energy. It may occur within the system of interest (a reaction in a cell, for instance) or it may occur in the environment surrounding the system (the "surroundings") or both. Regardless, it is the inviolable requirement for any process to be spontaneous. What is so marvelous about the Gibbs free energy function is that it accounts for both the change in entropy in the system and in its surroundings. To provide a brief and less than rigorous rationale for this, consider that G = H - (TS) = H - TS at constant temperature. Then G/T = H/T - S, where S is the entropy change for the system. And, H/T is q/T when the pressure is constant (U = q - w and at constant pressure w = P V, i.e. pressure-volume work, such as the expansion of a gas. Then H = q - PV + PV = q = heat flow at constant pressure, often denoted q P.) Under reversible conditions H/T = qrev/T = the heat flow into the surroundings over T. Then H/T is the entropy change in the surroundings. The minus sign in G = H - TS accounts for the fact that heat flow out of the system into the surroundings is the opposite of heat flow in the surroundings to the system; it takes care of the sign convention issues. Thus if G < 0 there is a net increase in entropy within the system + surroundings, and the process is spontaneous. If G > 0 the reaction is unfavourable (not spontaneous); if it were to occur there would be a net decrease in entropy. This cannot naturally occur, though it can be forced with energy input.

Energy relations for electrochemical cells Recall the first law of thermodynamics, which states “the energy of the universe is constant,” or “energy is neither created nor destroyed.” In any system energy can be transferred to or from the surroundings as heat or work. These are forms of energy in transit, i.e. both are flows of energy. This is expressed mathematically as, U = q - w

{46}

The equation follows the engineering sign convention where, q < 0 means heat flows out of the system into the surroundings (exothermic) q > 0 means heat flows into system from surroundings (endothermic) w < 0 means work flows into the system from surroundings w > 0 means work flows out of system into the surroundings Heat flow is considered from the perspective of the system, while work flow is considered from the perspective of the surroundings. (In the SI convention both work and heat flows are considered from the perspective of the system. Either means of energy flow into the system is positive; either means of energy flow out

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of the system is negative. Most chemistry texts follow the latter convention.) By definition, G = U + PV – TS = H – TS

{47}

If a system undergoes a change from state 1 to state 2, G2 – G1 = U2 – U1 + (P2V2 – P1V1) – (T2S2 – T1S1)

{48}

Since U2 – U1 = q - w

{49}

G2 – G1 = q - w + (P2V2 – P1V1) – (T2S2 – T1S1)

{50}

and at fixed P and T, G2 – G1 = q - w + P(V2 – V1) – T(S2 – S1)

{51}

w is the total work, including work other than pressure-volume work (PV work; e.g. expansion of a gas against some external pressure P). For an electrochemical cell where electrical work is also possible (by means of electrons flowing through an external circuit), w = w’ + P(V2 – V1)

{52}

where w’ represents the electrochemical work. Substituting this into the preceding equation yields, or

G2 – G1 = q – w’ – T(S2 – S1)

{53}

G = q – w’ - TS

{54}

Again, this applies to a process at fixed P and T. Since, G = H - TS

{55}

It is then apparent that, H = q – w’

{56}

which is equal to the heat flow at constant pressure. For a change of state achieved reversibly, at constant temperature and pressure, we would have the equation, G = qrev – w’rev - TS

{57}

An electrochemical cell for which G < 0 (favourable or spontaneous) operated reversibly will generate the maximum possible amount of electrical work, -w’rev = -w’max = G

{58}

13

as per equation {45}. Substituting this into the equation above, G = qrev + G - TS

{59}

or, as we would expect, qrev = TS

(at constant temperature)

{60}

This is the flow of energy as heat in a cell operated reversibly and represents the minimum possible heat loss (again for a cell where G < 0 which does electrical work). Real cells, operated irreversibly will generate less work and more heat. For an electrolytic cell (G > 0; not favourable), the minimum possible work that we can input to force a reaction to go in the unfavourable direction is again -w'rev (< 0). To make the reaction go at a practical rate, making the process irreversible, the actual work input will be > -w'rev. Definitions The cell potential is also called the EMF (electromotive force). It is the voltage of a cell under reversible conditions (no current is flowing, or, the current is infinitely small). It represents the driving force for electron transfer. When E > 0 the cell reaction is spontaneous. When E < 0 the reaction as written is not spontaneous, i.e. is not favoured. (Recall that G = -nFE.) In this discussion, in order to distinguish charge from heat flow, the charge will be symbolized as q c. Work (in joules) = voltage (V) x charge (C). The cell potential E and the reversible electrical work w’rev have the same sign (for the engineering convention, not the SI convention) and are related as follows, -G = nFE = w’rev = qcE

{61}

Types of Electrochemical Cells Now different types of electrochemical cells can be compared along with their energy relations. The four common types of cells are illustrated in the Figure 2 below. A piece of zinc is suspended in a solution of ZnSO 4 and H2SO4. The other electrode is a piece of platinum. Hydrogen gas is bubbled over the platinum surface. The H+/H2 half reaction is rapid on platinum. (Rates of electron transfer depend strongly on the surface at which they occur.) The half reactions are: 2H+ + 2e- = H2

E° = 0 V

(4)

Zn+2 + 2e- = Zn

E° = -0.76 V

(5)

There are two possibilities. The favourable reaction may occur, for which E > 0. Alternatively the reaction can be forced to go in the opposite direction by applying a

14

suitably high opposing voltage. This is electrolysis. The favourable reaction involves oxidation of Zn to Zn+2 and reduction of H+ to H2. In fact there is no thermodynamic reason why the reaction should not spontaneously occur directly on the zinc surface, as illustrated in Figure 3 below. However, the reduction of H + on very pure Zn is very slow, whereas it is quite rapid on Pt. Because the reduction of H + on pure Zn is so slow, the cell can be set up with Zn metal in direct contact with H +. Otherwise two half cells with provision for ionic conduction would be used.

Figure 2. Schematic depiction of four different types of electrochemical cells [1].

(a)

(b)

15

Figure 3. Schematic illustration of hydrogen evolution on (a) a zinc surface (slow) and (b) catalyzed by Pt metal in contact with the Zn (fast). 1. First consider the short-circuited cell. There is no load (no electrical work is extracted) in the system. The reaction proceeds spontaneously since E° >0 (or E > 0 for non-standard conditions) and the process is favourable. Zn = Zn+2 + 2e- E° = -0.76 V

(6)

2H+ + 2e- = H2 E° = 0 V

(7)

The overall reaction is: Zn + 2H+ = Zn+2 + H2

E° = 0 - (-0.76) = 0.76 V

(8)

This is really equivalent to the situation in Figure 3 (b). Since the reduction of H + on pure Zn is slow, all that is required for the reaction to proceed at a substantial rate is a catalyst, which is the role of Pt. G° = -nFE° = -2 mol e-/mol x 96485 C/mol e- x 0.76 V = -1.47 x 105 VC/mol = -1.47 x 105 J/mol = -147 kJ/mol

{62}

H = q - w’ and w’ = 0

{63}

Since,

(no electrical work is being done; there is no load), H = q

{64}

All the energy is dissipated as heat. Heat flows from the system (the cell) to the surroundings, and so by convention is negative. The process is exothermic. (If you have ever short-circuited a battery by connecting a wire across both ends, you know this from experience; the wire can get red hot and the rate of discharge of the cell can get dangerously fast.) Since there is no work being extracted, the potential difference is zero (w’ = 0 = Eqc. Therefore E = 0). Note that the cell in principle is capable of manifesting a voltage E, but when short-circuited this is not realized. Cementation reactions and corrosion processes are examples of shortcircuited cells. Any redox reaction occurring directly between reagents without running the electron transfer through an external circuit is a short-circuited cell. So

16

is a cell where a wire is connected across the poles. Other examples include oxidative leaching processes of sulfides and combustion reactions. 2. Open-circuit cell. The half reactions are the same as in (1). However, if the electrical connection between the two electrodes is broken, no current flows. A voltmeter can be used to measure the potential difference. This may employ a very large resistance inside the meter. Then the current flow is so small that the rate of reaction also is extremely slow. This very nearly approaches the reversible case (a process carried out infinitely slowly). (Alternatively, an opposing voltage can be applied until the current is zero. The opposing voltage slows the reaction until a point where the reaction stops. At this point the opposing voltage is equal to the cell voltage. These devices, called potentiometers, are not much in use anymore.) Under standard conditions (298 K, PH2 = 1 atm, unit activities of the ions) the measured potential difference is 0.76 V. This indicates the thermodynamic potential difference, or driving force for the reaction. If the conditions were non-standard the potential difference would differ from E°, as per the Nernst equation, and this would indicate the driving force under those conditions. In principle, open circuit cells can be used to measure thermodynamic potentials. In practice, it is often not so easy for many reasons.  An open circuit cell is essentially a cell working reversibly; the rate of the reactions is infinitely slow by virtue of the open circuit. The cell voltage equals the thermodynamic potential. The cell can do its maximum possible work. For all practical purposes, however, we can't extract work from such a cell in a finite time. It's of no practical use as far as obtaining electrical work. It is of use for measuring cell potentials. For practical work we use the cell galvanically or electrolytically. 3. Galvanic cell (battery). In this case the electrodes are connected to a moderately high resistance device that uses electrical energy as work, such as a radio. The half reactions are the same as in (1). The reaction is favourable. The current passes at a fairly low, but, finite rate. This might be close to reversible conditions of operation, though it is irreversible. Hence the heat loss must be somewhat greater than the minimum reversible process heat loss, and the work obtained must be somewhat less than it would be under truly reversible conditions. Since the same charge is being passed as it would be under reversible conditions (2e - per Zn+2) and the available work is less, the cell voltage (denoted V) must be lower: (w’ = V qc) < (w’rev = E qc)

{65}

Therefore V < E (E is the cell voltage under reversible conditions; the maximum possible voltage). The greater the current, the faster the process and the greater the extent of departure from reversibility. Then the heat loss is greater and the work that can be extracted is lower. One way to rationalize this is that as the current gets high, the process is getting closer to operating like a short-circuited cell, where all the energy is dissipated as heat. The thermodynamic potential for the reaction is given by the Nernst equation:

17

E = E° - RTln aZn+2 PH2 nF aH+2

{66}

Say PH2 is kept constant at 1 atm. As the reaction proceeds [Zn +2] increases, while aH+ decreases. The ln term thus increases as the reaction proceeds and E drops. Eventually equilibrium is reached and no further reaction occurs. Then E goes to zero. E then is a measure of how far away from equilibrium the system is; how great the driving force is for chemical reaction to occur. The process will continue until chemical equilibrium is reached, at which point G and E for the cell both go to zero. At equilibrium there is no more driving force for the reaction to proceed; no further change occurs. At this point the battery is dead. All real galvanic cells operate at less than the thermodynamic limit of efficiency. However, if the cell is discharged slowly, the efficiency approaches that of a reversibly operated cell. This is why fuel cells are naturally quite efficient. A fuel cell is simply a galvanic cell in which the reactants are continuously replenished, and the products are continuously removed. The thermodynamics can be conveniently represented on a diagram as shown below. Recall that H is a state function, meaning that for going from a specified initial state (e.g. the left side of reaction 8 at a given temperature,

Figure 4. Summary of thermodynamic effects for galvanic and short-circuited cells. The sign of q is negative to account for heat flow from a system being taken to be < 0, while work done by a system is > 0. Note that in this case heat flows from the system. In principle qrev could be positive as well. By definition, a galvanic cell is one for which w'rev is positive; work is done by the system. pressure and concentrations) to a specified final state (e.g. the right side of reaction 8 with specified temperature, pressure and concentrations) the change in enthalpy is the same no matter how the change is effected, be it reversibly, galvanically or as a short-circuited cell. In this case H < 0; energy both as heat and work leave the system. What does depend on how we run the cell is q and w', but the sum, q - w', is always the same. The limiting case is the reversible cell;

18

 qrev is the minimum possible heat flow and w rev is the maximum possible work. Galvanic cells operate at finite rates, are irreversible in the thermodynamic sense and exhibit larger heat losses and lesser capabilities for work;  q >  qrev and w' < w'rev. In addition, the faster the cell is operated (the greater the current) the more irreversible it is and the greater the heat flow and the less the work. The quantity q is the difference bewteen w'rev and w': q = qrev + q

{67}

G = -w'rev = -nFE

{68}

Based on equation {54}, q = G + w' + TS

{69}

q = G + w' + qrev

{70}

q = -w'rev + w' + qrev

{71}

q = -w'rev + w'

{72}

-q = w'rev - w'

{73}

Then,

The heat loss is the sum of q rev + q (which is < 0). Thus the additional heat loss arises from inefficiency in operating the cell, relative to the limiting, reversible case. If the cell is short-circuited no work can be extracted and all the energy output is lost as heat. This is the other limiting case. Another possibility for a galvanic cell is when qrev > 0. This is depicted in the alternative diagram below.

Figure 5. Alternative summary of thermodynamic effects for galvanic and shortcircuited cells. The sign of qrev is positive to account for heat into a system being taken to be > 0, while work done by a system is > 0. Note that the net heat flow depends on how much work is extracted from the cell. The net heat flow is q = qrev + q. For a galvanic cell q < 0 always; some potential work is lost as heat.

19

4. Electrolytic cell. This is what is employed in electrowinning. The electrodes are connected to an external power supply such that the voltage exceeds and opposes the thermodynamic cell voltage. In electrolysis the reaction is being forced in the opposite direction of its natural or spontaneous direction. The half reactions now are, Zn+2 + 2e- = Zn

(9)

H2 = 2H+ + 2e-

(10)

The overall reaction is how the reverse of reaction (8): Zn+2 + H2 = Zn + 2H+

E° = -0.76 V

(11)

This is NOT favourable and will not occur naturally. To overcome this, a voltage of >0.76 V (under standard conditions) is applied externally to force the reaction to go as written above, i.e. Eappl > 0.76 V. The flow of electrons is reversed and so are the electrode reactions relative to the galvanic or short-circuited cases. The H 2/H+ reaction now becomes the anode and the Zn +2/Zn process becomes the cathode. The reaction will reach equilibrium when the thermodynamic cell voltage reaches Eappl. Then it will stop. The thermodynamic potential for the reaction is given by the Nernst equation: E = E° - RTln aH+2 nF aZn+2PH2

{74}

Say PH2 is fixed at 1 atm. As the reaction proceeds aH+ increases and aZn+2 decreases. Hence the log term increases and consequently E decreases (becomes a larger negative number) as the reaction proceeds. This will continue until  E and Eappl are equal. Then the thermodynamic cell potential is just balanced by the applied potential and there is no net potential difference between the electrodes. The reaction stops. To make the reaction proceed further still, one would have to increase Eappl. Under conditions of fixed external potential, the reaction rate would decrease as the thermodynamic cell voltage decreases (because the driving force, which is the difference between Eappl and the thermodynamic  E , decreases). In practice, electrowinning is carried out under conditions of controlled current, rather than controlled potential, as was explained in the section on Faraday's Law relationships. As reactants are depleted, the applied voltage must increase to maintain the constant current. In practice, electrowinning usually takes less than 50% of the desired metal ion from the solution. The barren electrolyte after EW is recycled to increase the metal ion tenor. Considering that E changes by, 2.303RTlog(PH2 aZn+2) = 0.02958log(PH2 aZn+2) 2F aH+2 aH+2

{75}

even a 50% change in concentrations has only a small effect on the cell voltage.

20

Now work is being done on the cell by the surroundings; an external voltage is applied. Then w’ < 0, and the work done on the cell is given by, w’ = -nFEappl

{76}

where Eappl is a positive number. The work done on the cell is directly proportional to the applied voltage. The energy changes are summarized in the diagrams below. H = q - w’

{77}

Note that w' < 0, w’ < w’ rev and -w' > -w'rev. The minimum work required to drive

(a)

(b)

21

Figure 6. Summary of thermodynamic effects for an electrolytic cell. (a) q rev > 0. Once -w' becomes large enough excess heat is dissipated to the surroundings. Note that q is always < 0; excess applied energy is lost as heat. (b) q rev < 0. Additional heat over and above qrev must be dissipated to the surroundings. the reaction against its favourable direction (backwards) to effect electrolysis is -w'rev. In practice more electrical work is required to obtain reasonable rates; -w' > -w'rev. The net heat is the sum: q = qrev + q = qrev -w'rev + w'

{78}

If qrev > 0, the sign of q depends on the magnitude of w', which in turn depends on the magnitude of Eappl (Figure 6a). Once Eappl gets large enough there is a net heat flow from the cell into the surroundings. Practical electrowinning usually uses Eappl >> -E (the thermodynamic cell voltage) so that heat will be evolved. If qrev < 0 the sign of q is always negative, as indicated in Figure 6b. Referring again to the equation, q = G + w’ + TS

{79}

Substituting in, w’ = -nFEappl and w'rev = -nFE

{80}

then, q = -nFE - nFEappl + qrev

{81}

q = -nF(E + Eappl) + qrev

{82}

0

When  E = Eappl q = qrev, as we would expect; the applied voltage then just matches E and the cell operates reversibly. As Eappl exceeds  E then excess heat begins to be evolved. This discussion assumed an isothermal system. For an actual industrial cell the electrolyte temperature will rise and reach some steady state (although it may fluctuate with environmental conditions). There will be heat loss to the surroundings, but also heating of the electrolyte. Depending on the metal being electrowon, excess heat may need to be deliberately withdrawn by heat exchangers. The temperature of the solution will depend on the heat generated, loss to surroundings and the heat capacity of the solution. Electrical work is supplied to the cell in order to overcome the cell's natural thermodynamic tendency. Some of that supplied energy does work on the cell, some of it ends up as heat. Some of the supplied work energy results in an increase

22

in chemical potential energy. This is the net effect of breaking bonds (e.g. H-H bonds and Zn-O bonds in [Zn(H2O)6]+2, and forming new ones (e.g. Zn-Zn metalmetal bonds and H-O bonds in H 3O+) and, finally, changes in electrostatic interactions in the solution due to changes in composition ([H +] increases; [Zn+2] decreases). Electrostatic interactions involve charged ions (Zn +2, H3O+, SO42-) and dipoles (such as partial charge separation in H-O-H, the oxygen being more electronegative and developing a negative charge; the hydrogens having a positive charge). Rates of Electron Transfer and the Effects of an Applied Voltage The rate of metal plating is directly proportional to the current through the cell, since, I = C/sec  moles e-/sec  moles Cu+2/sec reacted, etc.

{83}

In electrowinning we set the current and allow the voltage to adjust accordingly (as governed by V = IR). Thus the higher the current, the higher the applied voltage must be. When the applied voltage precisely matches the thermodynamic cell voltage, Eappl = -E, the cell operates reversibly and the reaction is infinitely slow. When Eappl > -E the reaction proceeds at a finite rate, and the greater the difference the greater the rate. Electrode polarity For a spontaneous reaction electrons flow from (-) to (+); repelled from the negative electrode and attracted to the positive one. Hence the cathode is positively polarized and the anode is negative. This accords with the fact that the thermodynamic cell voltage is positive, E = Ecathode - Eanode > 0

{84}

In an electrolysis the applied voltage opposes the thermodynamic voltage (E < 0) and is greater than -E. Thus power supply (+) goes to the cell (+) and likewise the (-) of the power supply goes to (-) of the cell. This forces the cell to run in the opposite direction, so that now the cathode is negatively polarized and the anode is positive. In other words, the electrodes retain the same polarity in either the galvanic or the electrolytic cases, but the flow of electrons is opposite, as is the direction of the chemical reaction. Electrowinning Fundamentals After suitable solution purification a quite pure, concentrated electrolyte may be available for electrowinning. (In the case of copper, solvent extraction is the common method for solution purification.) Most commonly electrowinning is performed using sulfate solutions with oxygen evolution as the anodic half reaction:

23

M+2 + 2e- = M

(cathode)

(12)

H2O = 0.5O2 + 2H+ + 2e- (anode) MSO4 aq + H2O l = M s + 0.5O2 g + H2SO4 aq

(13) (overall reaction)

(14)

In such cases acid is generated during electrowinning. Electrowinning may also be carried out from chloride solutions in some instances. Then Cl - is oxidized to Cl2. The electrowinning reaction for copper is, CuSO4 aq + H2O  Cu s + H2SO4 aq + 0.5O2 g

(15)

The reduction reaction is: Cu+2 + 2e- = Cu

E° = 0.34 V

(16)

The oxidation half reaction is the reverse of the oxygen reduction half reaction, i.e., 0.5O2 + 2e- + 2H+ = H2O Then E° = 0.34 - 1.23 V = -0.89 V

E° = 1.23 V

(17) {85}

The reaction is not thermodynamically favourable, so energy must be supplied to make it go. The minimum energy required corresponds to the thermodynamic potential difference. In practice higher voltages are used to attain practical rates. The rate of metal plating is directly related to the current; the higher the current, the more e-/sec transferred, and the greater the metal plating rate. The nature of the relationships between the applied voltage and logI is illustrated in the figure below. This depicts the current-voltage relationship for a single half reaction. Of course another half reaction has to be at play as well; we cannot run a half reaction in isolation. However, the graph focuses on the log(current)-voltage graph for a single half reaction of interest *. As the current approaches zero (logI  -) the cell runs increasingly slowly, approaching reversible behaviour. Then the measured voltage, in principle, corresponds to E, the half reaction potential, relative to some other half reaction (e.g. the standard H +/H2

24

Figure 7. Schematic illustration of a polarization curve for a half reaction plotted as voltage vs. logI. * A "three-electrode" cell can be used for this. The half reaction of interest occurs at a "working" electrode. The potential is measured relative to a reference electrode. The current is measured between the working electrode and a "counter" electrode.

half cell.) At this point a minute change in potential can reverse the direction of the half reaction (again, consistent with reversible behaviour). For the upper branch the oxidation occurs, e.g. M s = Mn+ + ne-

(18)

For the lower branch the reduction half reaction occurs, e.g. Mn+ + ne- = M s

(19)

It all depends on how the electrode is polarized (how the external potential is applied). Consider the cathodic branch. As the potential is decreased M n+ is reduced. At first a substantial increase in reduction current results from relatively small decreases in applied voltage. Eventually a nearly linear region occurs, where logI is virtually linear with applied potential. This is called the Tafel region. Its slope is directly proportional to n, the number of electrons/mol of metal plated. (The form of the curves is well understood from electrochemical theory, but that is beyond the scope of this introduction.) The curve indicates that to obtain higher currents, higher voltages, beyond the reversible value E, are needed. The overpotential This leads to the idea of the overpotential. Overpotential (or overvoltage) is the additional potential needed beyond the thermodynamic potential E required to make the half reaction go at the desired rate. It is given the symbol . As indicated earlier, the value of n will have a direct effect on how big the overvoltage is. For a given n value (2 for EW involving Cu+2, Ni+2, Co+2 or Zn+2), the shapes of the curves are often quite similar (there are subtle differences). However, what really matters is where the curves lie horizontally. This is illustrated in the figure below. The reduction of Cu+2 on Cu is considerably faster than the reduction of Ni +2 onto Ni. This appears as a shift of the Ni +2/Ni curve further to the left (to lower currents) relative to Cu+2/Cu. As a result, at a given current Ni+2/Ni is greater than Cu+2/Cu. This has implications for the energy consumption in electrowinning of the two metals. At

25

a given current a greater overvoltage necessarily implies greater energy consumption. For electroplating simple metal aquoions three broad classes of processes must occur: 

Deformation of the aquocation complex as it approaches the metal surface and loss of coordinated water molecules.



Electron transfer to the metal cation.



Migration of the metal atom on the surface to a suitable crystallographic site.

Loss of water molecules may occur in concert with electron transfer. Each of these processes contributes to the overpotential; they all have an activation barrier, or energy hurdle that must be overcome. Sometimes one of these steps can be a major contributor to the overpotential.

Figure 8. Schematic illustration of reduction branches of polarization curves for Cu+2/Cu and Ni+2/Ni couples. For a given current the Ni +2/Ni couple requires greater overpotential than does the Cu+2/Cu couple. The anode half reaction also has an associated overpotential. Oxygen evolution is the most common anode half reaction in electrowinning. This is ubiquitous in Cu, and Zn EW, and common for Ni and Co. Chloride oxidation to Cl 2 is also employed in Ni EW. In gold EW from cyanide solution, the anode half reaction is oxidation of CN- to CNO-. Oxygen evolution has some advantages: 

No additional costly reagents are needed; H2O is the reactant.

26



Relatively less corrosive sulfate medium is suitable, and sulfate medium is the least expensive.



Lead anodes may be used, which are inexpensive.

However, the main disadvantage is that it contributes to high energy consumption. First the E° for the O2/H2O half reaction is 1.23 V. This contributes to highly negative thermodynamic cell voltages: Cu+2 + H2O = Cu + 2H+ + 1/2O2 E° = -0.89 V Ni+2 + H2O = Ni + 2H+ + 1/2O2

(20)

E° = -1.46 V

Zn+2 + H2O = Zn + 2H+ + 1/2O2 E° = -1.99 V

(21) (22)

In addition, water oxidation on most electrode surfaces is very slow. (This is an area of considerable economic and technical importance for fuel cell development too.) This results in a high anodic overpotential. Much work has gone into trying to find ways to lower the oxygen evolution overpotential as it is a significant factor in the operating costs of an EW plant. Lead has one of the highest overpotentials for oxygen evolution! However, lead is commonly used due to its low cost. Lead anodes are commonly alloyed with minor amounts of other elements to try to lower the overvoltage. The intent is to shift the polarization curve further to the right. This is illustrated in the figure below. At 300 A/m 2 current density the approximate O2 evolution overpotentials under different conditions are provided in the Table below. The most common anode material in use today in Cu EW is a PbSn-Ca alloy (~1.5% Sn, 0.1% Ca). There are numerous effects of solutes and alloy elements on anode performance and longevity. Calcium is added to increase strength. The anodes are cold rolled for the same reason. Tin lowers the oxygen evolution overpotential and improves corrosion resistance. There may be other effects as well. DSA anodes are of interest because the platinum group metal

27

Figure 9. Schematic illustration of oxygen evolution polarization curves. Various amendments may be applied to shift the polarization curve to lower . Table 2. Oxygen evolution overpotentials from sulfuric acid solutions under several conditions at 300 A/m2 current density [2]. Anode material Other conditions Overpotential (V) Pb/Sb (e.g. 6% Sb) ~0.7 +2 Pb/Sb (6% Sb) 100-150 mg/L Co ~0.6 Pb/Ca(0.1%)/Sn(1.5%) 1 ~0.6 2 DSA ~0.35 1 Preferred due to better mechanical and corrosion properties compared with Pb/Sb. 2 DSA = dimensionally stable anodes; rigid titanium sheet or mesh coated with platinum-group metal oxides. oxides used to coat the anodes (usually a titanium substrate) are very good at promoting O2 evolution. Cobalt addition is commonly practiced in Cu EW. It is believed that Co +2 oxidizes at the anode and catalyzes H2O oxidation [3]: Co+2 = Co+3 + e-

E° = 1.9 V - very high!

2Co+3 + H2O = 2Co+2 + 2H+ + 0.5O2

(anode)

(23) (24)

Co+3 is a powerful oxidant and rapidly oxidizes water. It also lessens anode corrosion and improves stability of the PbO2 layer. However, cobalt is expensive. It is added at 100-200 mg/L, beyond which it has little beneficial effect. Resistance losses Conductors that carry electricity to the electrodes have an intrinsically low resistance. However, these extend over the length of the tankhouse and overall the resistance is enough to cause a moderate voltage drop. This is lost as heat. Likewise, contact between anodes and the current distribution conductors (busbars) and between cathode sheets and the busbars also has a resistance loss (contact resistance). This is necessary since anodes and cathodes must be removed (anodes in order to be replaced, cathodes for Cu metal harvesting). The other substantial resistance in the circuit is the solution resistance. In solution the current is carried by migration of ions. This allows for a complete circuit, without which there would be no current. Cations move towards the cathode (negatively polarized) and anions move toward the anode (positively polarized). Thus electrolyte conductivity is an important technical consideration in EW. Ions in solution are capable of conducting electricity. (This was one of the key observations that lead scientists to conclude that some compounds were comprised of discrete cations and anions.) A strong electrolyte is a salt that is soluble in water

28

and which fully dissociates into ions. Ions vary in their ability to conduct electricity (per unit concentration). The hydrogen ion, H +, is by far the best conductor, followed by OH-, then other cations. H+ is at least 3 times more conducting (per unit concentration) than other cations*. Thus the presence of H 2SO4 in the electrolyte is quite beneficial. Copper EW electrolytes contain on the * The reason is believed to be due to the "proton jump" mechanism. H + is present as H3O+. An H+ in an H3O+ ion can "jump" to a neighbouring water molecule as shown below. This allows it to move through solution much more rapidly than the diffusion or migration of other ions. The same mechanism may be in effect for OH -, though it is somewhat less effective, as indicated by its lower conductance.

order of 180 g/L H 2SO4. Much beyond this and corrosion of the steel starter sheets and other parts of the plant becomes problematic. EW is operated at constant current, so based on Ohm's law the voltage drops due to resistance losses can be summed up: VIR = IRi

{86}

i

The resistance of a resistor is a function of its geometry and its inherent resistivity (the resistance of a standard geometry). The longer the distance through which the electrons (or ions) must travel, the greater the total resistance; R  L where L = length. The greater the cross sectional area of the resistor, the more current it can support (more pathways for electrons/ions to move through). Hence R  1/A where A is the cross sectional area. Then, R  L/A

{87}

R = L/A

{88}

and

where  = resistivity. This is illustrated in the figure below. Thus in EW large surface area electrodes are used with a minimum practical spacing between cathodes and anodes. Limitations on these features are discussed later. Clearly the lower the resistivity the better. Thus a more concentrated solution of ions, and where feasible, high concentrations of H+ are desirable. In electrowinning of divalent metal ions from aqueous solution there is a complicating factor and that is ion pairing. This essentially the formation of a complex, e.g. M+2aq + SO42-aq = MSO4 aq

(25)

The extent to which this happens depends on the metal ion, temperature and pH; recall that SO42- is also a weak base and may form HSO4- as well. A neutral ion pair does not contribute significantly to the conductivity of the solution. Some example

29

Figure 10. Illustration of the dependence of resistance on conductor length and cross sectional area. data for simple CuSO4-H2SO4 electrolytes are shown in Table 3. Note that for a given acid concentration (50°C column) the resistivity increases with increasing [Cu+2], i.e. [CuSO4] (as well as decreased [H+] due to formation of HSO 4-), while higher acid concentrations lower the resistivity. Iron is also commonly present in copper EW electrolytes at concentrations of up to 5 g/L. It will be present in its two common valence states: Fe+3 and Fe+2. This also will affect the resistivity of the electrolyte. It is also common to consider the inverse of resistance or resistivity instead. The inverse of resistance is conductance. The specific conductance is 1/ in -1cm-1. Now higher conductance (lower resistance) is desirable. Table 3. Illustrative example data for resistivity of simple CuSO 4-H2SO4 solutions at different temperatures [4]. Resistivity  cm Cu+2 g/L H2SO4 g/L 30°C 40°C 50°C 25 71.7 3.75 3.52 3.26 35 143.4 2.29 2.09 35 191.2 1.92 1.74 40 163.4 1.50 40 182.6 1.42 50 163.4 1.71 50 182.6 1.57 55 163.4 1.76 55 182.6 1.63 60 167.3 2.37 2.15 As an example, take the cathode-anode gap to be 4.8 cm, and the immersed plating area of 1.2 m 2 (100 cm x 120 cm). A typical electrolyte might contain 40 g/L Cu+2, 180 g/L sulfuric acid and have an operating temperature of 50°C (although there may be a significant range of conditions in practice). The corresponding resistivity then is about 1.42  cm. The resistance then is:

30

1.42  cm x 4.8 cm / 12000 cm2 = 0.000568 

{89}

The voltage drop across the resistance is V = IR. For a 300 A/m 2 current density, 0.000568  x 1.2 m2 plating area x 300 A/m2 = 0.204 V

{90}

The four contributions to applied cell voltage Putting the pieces together we have the following relationship for the applied voltage: Eapplied = -E + C + A + IRi

{91}

i

The first term is the thermodynamic potential (E is negative and must be opposed). Next are the two overpotentials. The last term is the sum of the IR voltage drops. Note too that increasing the current increases this term. Likewise the overpotentials are a function of current (or current density). -E is constant for a given electrolyte composition and changes only a little through the cell as metal is plated. Ballpark estimates for the four terms in copper EW are given below:    

-E ~ 0.9 V Anodic overpotential (A) ~ 0.5 V (depends on current density) Cathodic overpotential (C) ~ 0.1 V (depends on current density) IRi ~ 0.5-0.6 V (depends on current); solution resistance ~0.3 V and i

rectifier + cell hardware resistances ~0.2 V (The rectifier converts AC power to DC power.) Total applied voltage ~2V in the example above. Depending on the source cited, there is some variability in values quoted for solution resistance and cell hardware resistances. However, a total voltage drop dues to resistance losses of up to 0.6 V or so is typical. In general industrial plants employ cell voltages of 1.8-2.2 V. Note that this significantly exceeds -E. The actual cell voltage (measured between anode and cathode) and the total applied voltage (including the power source and current distribution network) may differ somewhat, depending on whether the hardware and rectifier resistances drops are included or not. In the end, what matters is the total applied voltage and the total current. This is what determines the energy consumption and associated cost. Limiting and practical current densities From Faraday's law and related relationships, it is clear that plating at higher current densities is desirable; for a given plating surface area production increases with increasing current density. However, there are two important limitations. The first is a fundamental limit. Referring back to Figure 7, at higher currents the

31

polarization curves start to approach infinite slope (tend toward vertical lines). As metal ion is plated, the concentration drops near the surface, relative to the bulk concentration. This creates a concentration gradient, which induces mass transport of Mn+ towards the cathode. The greater the plating rate, the bigger the concentration drop, i.e. the lower the concentration at the surface. This is illustrated in the figure below. At some critical current density the concentration of metal ion at the surface goes to zero. This is the diffusion limited current and represents the maximum current that can be sustained under the given conditions. At this point the polarization curve approaches infinite slope. Further increases in current cannot be sustained by Mn+ reduction. Then the next available half reaction will begin to occur. Reduction of H+ to H2 may then occur, for which E° = -1.23 V. An increase in the applied voltage then would also necessarily occur (at constant current). This wastes electricity and would never be attempted in a normal electrowinning situation. For copper EW the diffusion limited current density is about 500 A/m 2 [5].

Figure 11. Schematic illustration of concentration profiles for a metal ion being plated at an electrode surface. Distance is measured from the cathode surface. The dashed line represents the boundary layer thickness. In practice significantly lower current densities are employed for conventional EW. This is related to a practical limitation. At very high plating rates the copper atoms deposited on the cathode surface do not have time to migrate to a suitable crystallographic site. The net result is that large numbers of new crystals form on the surface, rather than growing existing crystal faces. This makes for very crumbly deposits that adhere very weakly to the cathode surface, making cathode harvesting difficult and costly. Fine grained copper particles would spall off the cathode and have to be collected, filtered and washed. At lower, but still too high plating rates too many crystals are still forming; the deposit may be more adherent, but it will be porous as crystals grow together rapidly and trap solution between their faces. This will increase the sulfur (from electrolyte sulfate), oxygen (from water, etc.), iron, etc. impurities content in the cathodes and make them offspec. Thus in conventional copper EW maximum current densities are about 350 A/m2 [6].

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The 500 A/m2 limiting current density is for a solution without intentional agitation. The vertical line in Figure 11 demarcates the point closest to the electrode surface where the solution metal ion concentration is equal to the bulk solution concentration. This is called the boundary layer. If the boundary layer is made thinner by agitation then the concentration gradient steepens and higher limiting (and practical) current densities are possible. However this requires energy. A typical Cu EW tankhouse may have several hundred cells, each with as many as 60 cathodes and 61 anodes, closely spaced together. Agitation then becomes difficult. However, if electrolyte is directed up between cathodes and anodes using a header, this can impart some additional agitation allowing current densities to be at the higher end of the practical range. The minimum thickness of the boundary layer is about 0.01 mm, which requires intensive agitation [7] and is not achieved in EW. There are two features in an EW cell that result in a measure of natural agitation (actually convection) [5]. At the anode surface oxygen gas is evolved. This gas pushes up solution as it rises. The bubbles accumulate at the surface before rupture. Overall this displaces solution in an upward motion in the vicinity of the anode. At the electrode surface Cu +2 is depleted, lowering the [Cu +2] and decreasing the solution density. This causes solution to naturally rise near the surface of the cathode. The net result is two counter-rotating loops, as shown in the figure below, which also helps to thin the boundary layer near the cathode surface. The boundary layer thickness achieved by this natural convection is about 0.1-0.2 mm [7]. Directing electrolyte up between electrodes using a header further thins the boundary layer, though not to the limit of ~0.01 mm.

Figure 12. Illustration of natural convection in an EW cell based on the rising of lower density, copper depleted electrolyte near the cathode and rising oxygen gas bubbles near the anode. Current distribution and protrusions Anodes and cathodes are large plane sheets that are kept parallel. This promotes a uniform distribution of the electric field over the surfaces (other than at the edges). This in turn promotes uniform plating rate over the surface, which is important for growing a smooth, compact deposit. This lowers porosity and helps prevent occlusion of electrolyte with the attendant increase in impurities in the

33

deposit. However, deposits are polycrystalline and surface roughness will eventually develop. Then there are high and low spots on the surface. Electric field lines tend to converge at points and diverge at depressions. This leads to the situation shown in the diagram below. This makes the tips grow faster and the depressions grow slower, further increasing surface roughness and promoting growth of protrusions. Further, the high points are closer to the anode and the depressions are further away, decreasing the IR voltage drop due to solution resistance for the high points and increasing it for the depressions. Finally, high points extend out into the boundary layer where the [M n+] is higher, making electroplating easier. All totaled these effects can result in more rapidly growing protrusions. As these extend further out from the surface their growth rate increases. Then a polycrystalline agglomeration of copper called a dendrite will extend out towards the anode, eventually making contact and causing a shortcircuit. At this point all the electrical energy in the cell is lost as heat. The current follows the path of least resistance through the short circuit, rather than through the solution to plate copper. This in part acts to limit how close cathodes and anodes can be to each other.

Figure 13. Schematic illustration of the effects of protrusions and depressions on electric field distribution. Due to differing distances IR" > IR > IR'. The figure at right is a schematic illustration of a short-circuit caused by a dendrite. Plant operators take pains to minimize this problem. This can be done by using "leveling" agents. These are often complex chemical mixtures that act by selectively adsorbing on the fastest growing sites. This increases the resistance of the protrusion and helps slow down their growth [8]. It is common practice to use infrared scanners to detect hot spots in cells where a short circuit has occurred. An operator will then go to the cell and use a bar to dislodge the dendrites to resume plating. Another approach to controlling surface roughness is periodic current reversal (PCR). The polarity of the cathodes and anodes is switch briefly at frequent intervals. The copper electrode now becomes the anode for a short time. The

34

protrusions being the most active sites, as indicated above, are most rapidly oxidized, dissolving them. This effectively prevents growth of protrusions on the cathode surface. Copper metal will plate on the lead electrode, briefly, but this will again be completely oxidized off. The duration of the polarity switch is brief. This may obviate the need for addition of leveling agents and associated costs, however, it does cost electricity. Copper Electrowinning Practice Specifications LME (London specifications:

Metals

Exchange)

grade

A

copper

has

the

following

Pb < 5 ppm S < 15 ppm Other impurities 99.993% A major source of sulfur impurity is sulfate from occluded electrolyte. Cells and hardware A diagram depicting a simplified cell is shown below in Figure 14. Cathodes and anodes are connected in a parallel arrangement. Cathodes are interleaved between pairs of anodes. A cell will have n cathodes and n +1 anodes. Then metal may be plated onto both sides of every cathode, making the most of the available plating surface area. A typical Cu EW cell will have up to 60 cathodes and 61 anodes. Cathode copper is often plated onto stainless steel blanks or starter sheets, usually ~3 mm thick and 1 m X 1-1.2 m surface dimensions [6]. Stainless steel is used to minimize corrosion. Sometimes copper starter sheets are used instead. These are plated separately and are 0.5-1 mm thick. The starter sheets are removed from a cathode substrate (such as titanium, to which copper adheres very weakly) and placed into the main EW cells. A schematic illustration of a cell is shown in Figure 15 below. Cell dimensions are on the order of 6 m long x 1.4 m deep by 1.25 m wide [9], with some variation. Long conductive bars called busbars conduct electricity to the electrodes. Previously the electrolytic cells were made of concrete and had to be lined to prevent corrosion. PVC was a common liner. Modern cells tend to be made

35

Figure 14. Schematic illustration of a copper electrowinning cell electrode arrangement.

Figure 15. Schematic illustration of a copper EW cell. of polymer concrete (aggregate in a plastic binder). Cells are electrically insulated from ground to minimize stray currents that lower current efficiency. Regular cleaning is required to remove lead sludge due to slow anode corrosion (mainly as PbO2). Excessive build-up can eventually compromise cathode quality [10]. A typical tankhouse will have hundreds of cells.

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The cathode-anode gap needs to be as small as possible to minimize the IR loss due to solution resistance. Cathodes are grown to a thickness of about 0.5 cm and due to misshapen electrodes and cathode protrusions there is a limit on how small the gap can be. The cathode-cathode centre-line spacing is commonly 9.5-11.4 cm [11]. With 0.3 cm thick steel cathode sheets and 0.6 cm thick anodes, and cathodes that grow to 0.5 cm thickness, the anode-cathode gap is about 4.35.3 cm at the start of cathode growth and 3.8-4.8 cm at the end. Steel starter sheets, being more rigid than thin copper starter sheets, have allowed for the narrowing of the cathode-anode gap, which lowers resistance losses. Anodes are typically made of a lead alloy as mentioned earlier, although the DSA's are starting to appear. Typically anodes are ~0.6 cm thick [6] and about 3 cm shorter on each side to promote uniform current distribution on the cathodes [12]. A PbO2 layer forms on the anode surface, which is also conductive. With tin alloy electrodes a SnO2 layer also forms. Due to the formation of the PbO 2 layer the corrosion of lead is very slow; PbSO4 is also quite insoluble. Gradually small particles of PbO2 spall off the anodes. This can lead to some lead contamination of the cathodes, if say, a PbO 2 particle lodges on the cathode surface. Lead anodes are chosen for their longevity and insolubility. Lead contamination of cathode copper can be kept to [Cu+2]t into EW. where Ac is the total plating area per sheet (both sides), S is the number of cells, and values for j, CE, Ac, N and S are to be chosen. Similarly, the flow rate to the cells, E, is given by the copper production rate divided by the change in copper concentration across each cell: E = 1.185499 x 10-5 (j CE)(Ac N S) [Cu+2]tL

{96}

Ideally, the flow rate E should be such that the specific flow rate is 0.12-0.14 m3/h/m2 plating area. The total plating area is Ac N S. Then, fs =

E = 0.12 (or a similar value) Ac N S

{97}

With these two equations we can solve for [Cu+2]tL: E = 0.12Ac N S = 1.185499 x 10-5 (j CE)(Ac N S) [Cu+2]tL

{98}

[Cu+2]tL = 1.185499 x 10-5 (j CE)

{99}

0.12

44

Take as an example j = 300 A/m2 and CE = 95%. Then for each cell, [Cu+2]tL = 1.185499 x 10-5 x 300 x 95 = 2.816 kg/m3

{100}

0.12 If fs is smaller, then the concentration change will be larger (lower flow, longer residence time for Cu+2 to be depleted). The mass balance for copper in Figure 18 is: dMCu = As([Cu+2]R – [Cu+2]L) = E([Cu+2]t – [Cu+2]L) {101} dt Hence, E = As [Cu+2]strip

{102}

[Cu ]tL +2

E = 350.518 m3/h x 15 kg/m3 2.816 kg/m3

= 2027.22 m3/h

{103}

Assuming a conventional cell with 60 steel cathode starter sheets, with 1 m x 1 m plating area per side, the number of cells then is given by using either equation {96} or equation {97}: S=

E Ac N fs

=

2027.22 m3/h 2 m2 x 60 x 0.12 m3/m2/h

= 140.8

{104}

There will be 141 cells in use. In a real tankhouse, there will be more cells in order to allow for downtime, maintenance and cleaning. (Typically the tankhouse is split in two, with a central cathode harvesting area. Then a tankhouse will have an even number of cells.) The nominal copper production rate will be: 1.185499 x 10-5 x 300 x 95 x 2 x 60 x 141 kg/h = 11433.2 kg/h = 50,078 t/y

{105}

The flow rates through EW will be: As = 380.5 m3/h E = 2027 m3/h E – As = 1647 m3/h The fraction of spent electrolyte going to SX stripping is: Fraction to SX = As = 18.8% E

{106}

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The strip [Cu+2] is 15 g/L (as specified) and the [Cu+2] from the tank to the cells is 32.8 g/L. Higher current efficiency, higher current density and higher cathode surface area increase the copper plating rate in the cells. This necessitates a higher circulation rate through the cells (E). The lower the copper concentration drop across the cell, the higher the specific flow rate must be, and this too requires a higher rate of flow of electrolyte to the cells. However, there is a limit to how high the specific flow rate can be; too high and spalling PbO 2 particles from the anodes may remain suspended in solution longer and contaminate the cathodes. Higher flow rates also incur greater cost for pumping. Sometimes there are two electrolyte storage tanks. Electrolyte clean-up processes may be conducted on solution flowing from the first tank (e.g. column flotation to remove entrained organic) [16]. The lean electrolyte should probably not have