Working galvanic cells

In working galvanic cells (those not balanced against an external potential), the over potential leads to a smaller potential than under zero-current conditions. Furthermore, we expect the cell potential to decrease as current is generated because it is then no longer working reversibly and can therefore do less than maximum work. We shall consider the cell M|M+(aq)||M′+(aq)|M′ and ignore all the complications arising from liquid junctions. The potential of the cell is E′=∆φR −∆φL. Because the cell potential differences differ from their zero-current values by overpotentials, we can write ∆φX = EX + ηX, where X is L or R for the left or right electrode, respectively. The cell potential is therefore E′=E+ηR−ηL To avoid confusion about signs (ηRis negative, ηLis positive) and to emphasize that a working cell has a lower potential than a zero-current cell, we shall write this expression as E′=E−|ηR|−|ηL| With E the cell emf. We should also subtract the ohmic potential difference IRs, where Rs is the cell’s internal resistance: E′=E−|ηR|−|ηL|−IRs The ohmic term is a contribution to the cell’s irreversibility—it is a thermal dissipation term—so the sign of IR sis always such as to reduce the potential in the direction of zero. The overpotentials in eqn 25.61 can be calculated from the Butler–Volmer equation for a given current, I, being drawn. We shall simplify the equations by supposing that the areas, A, of the electrodes are the same, that only one electron is transferred in the rate-determining steps at the electrodes, that the transfer coefficients are both1^–2, and that the high-overpotential limit of the Butler–Volmer equation may be used. Then from eqns 25.46 and 25.61c we find

Where j_0L and j_0R are the exchange current densities for the two electrodes. The concentration overpotential also reduces the cell potential. If we use the Nernst diffusion layer model for each electrode, the total change of potential arising from concentration polarization is given by eqn 25.59 as

This contribution can be added to the one in eqn 25.62 to obtain a full (but still very approximate) expression for the cell potential when a current I is being drawn:

E′=E−IRs− ln g (I)

With

This equation depends on a lot of parameters, but an example of its general form is given in Fig. 25.48. Notice the very steep decline of working potential when the current is high and close to the limiting value for one of the electrodes. Because the power, P, supplied by a galvanic cell is IE′, from eqn 25.64 we can write P=IE−I²Rs− The first term on the right is the power that would be produced if the cell retained its zero-current potential when delivering current. The second term is the power gener ated uselessly as heat as a result of the resistance of the electrolyte. The third term is the reduction of the potential at the electrodes as a result of drawing current. The general dependence of power output on the current drawn is shown in Fig. 25.48 as the purple line. Notice how maximum power is achieved just before the con centration polarization quenches the cell’s performance. Information of this kind is essential if the optimum conditions for operating electrochemical devices are to be found and their performance improved.

Electric storage cells operate as galvanic cells while they are producing electricity but as electrolytic cells while they are being charged by an external supply. The lead acid battery is an old device, but one well suited to the job of starting cars (and the only one available). During charging the cathode reaction is the reduction of Pb2+ and its deposition as lead on the lead electrode. Deposition occurs instead of the reduction of the acid to hydrogen because the latter has a low exchange current density on lead. The anode reaction during charging is the oxidation of Pb(II) to Pb(IV), which is deposited as the oxide PbO₂. On discharge, the two reactions run in reverse. Because they have such high exchange current densities the discharge can occur rapidly, which is why the lead battery can produce large currents on demand.

Fig. 25.48The dependence of the potential of a working galvanic cell on the current density being drawn (blue line) and the corresponding power output (purple line) calculated by using eqns 25.64 and 25.65, respectively. Notice the sharp decline in power just after the maximum.

A fuel cell operates like a conventional galvanic cell with the exception that the reactants are supplied from outside rather than forming an integral part of its construction. A fundamental and important example of a fuel cell is the hydrogen/oxygen cell, such as the ones used in space missions (Fig. 25.49). One of the electrolytes used is concentrated aqueous potassium hydroxide maintained at 200°C and 20–40 atm; the electrodes may be porous nickel in the form of sheets of compressed powder. The cathode reaction is the reduction O₂(g) + 2 H₂O(l) + 4 e⁻ →4 OH⁻(aq) and the anode reaction is the oxidation H2(g) + 2 OH−(aq) →2 H₂O(l)+2 e⁻ For the corresponding reduction, E7 =−0.83 V. Because the overall reaction 2 H₂(g) + O₂(g) →2 H₂O(l) E7=+1.23 V is exothermic as well as spontaneous, it is less favourable thermodynamically at 200°C than at 25°C, so the cell potential is lower at the higher temperature. However, the increased pressure compensates for the increased temperature, and E ≈+1.2 V at 200°C and 40 atm. One advantage of the hydrogen/oxygen system is the large exchange current density of the hydrogen reaction. Unfortunately, the oxygen reaction has an exchange current density of only about 0.1 nA cm−2, which limits the current available from the cell. One way round the difficulty is to use a catalytic surface (to increase j0) with a large surface area. One type of highly developed fuel cell has phosphoric acid as the electrolyte and operates with hydrogen and air at about 200°C; the hydrogen is obtained from a reforming reaction on natural gas: 

Anode: 2 H₂(g) →4 H⁺(aq) + 4 e⁻

Cathode: O₂(g) + 4 H+(aq) + 4 e− →2 H₂O(l)

This fuel cell has shown promise for combined heat and power systems (CHP systems). In such systems, the waste heat is used to heat buildings or to do work. Efficiency in a CHP plant can reach 80 per cent. The power output of batteries of such cells has reached the order of 10 MW. Although hydrogen gas is an attractive fuel, it has dis advantages for mobile applications: it is difficult to store and dangerous to handle. One possibility for portable fuel cells is to store the hydrogen in carbon nanotubes (Impact 20.2). It has been shown that carbon nanofibres in herringbone patterns can store huge amounts of hydrogen and result in an energy density (the magnitude of the released energy divided by the volume of the material) twice that of gasoline. Cells with molten carbonate electrolytes at about 600°C can make use of natural gas directly. Solid-state electrolytes are also used. They include one version in which the electrolyte is a solid polymeric ionic conductor at about 100°C, but in current versions it requires very pure hydrogen to operate successfully. Solid ionic conducting oxide cells operate at about 1000°C and can use hydrocarbons directly as fuel. Until these materials have been developed, one attractive fuel is methanol, which is easy to handle and is rich in hydrogen atoms:

Anode: CH₃OH(l)+6OH−(aq) → 5 H₂O(l)+CO₂(g)+6 e⁻

Cathode: O₂(g) + 4 e− + 2H₂O(l) →4OH−(aq)

One disadvantage of methanol, however, is the phenomenon of ‘electro-osmotic drag’ in which protons moving through the polymer electrolyte membrane separating the anode and cathode carry water and methanol with them into the cathode compartment where the potential is sufficient to oxidize CH3OH to CO2, so reducing the efficiency of the cell. Solid ionic conducting oxide cells operate at about 1000°C and can use hydrocarbons directly as fuel. A biofuel cell is like a conventional fuel cell but in place of a platinum catalyst it uses enzymes or even whole organisms. The electricity will be extracted through organic molecules that can support the transfer of electrons. One application will be as the power source for medical implants, such as pacemakers, perhaps using the glucose present in the bloodstream as the fuel.

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مواضيع ذات صلة

Units

Names of quantities

Electrolysis

Experimental techniques

The rate laws

The electric potential at the interface

The structure of the interface

Catalytic activity at surfaces

Mechanisms of heterogeneous catalysis

Mobility on surfaces

The rate of desorption

The rate of adsorption