1. When a metal is immersed in a solution of its most stable ions, there are two possible reactions which may occur. These are: (a) the metal ions may leave the surface of the metal lattice and go into solution, resulting in the development of a negative charge on the metal surface (see Figure 8.1(a)), or (b) the metal ions from the solution may be deposited on the metal surface, resulting in the development of a positive charge on the metal surface (see Figure 8.1(b)). Both (a) and (b) result in a potential difference existing between the metal and the solution.

2. The reactions can be expressed by the general equation

$Massofsilverwillbe108\times \frac{600}{96500}=0.67g.$

where M is any metal and n is the oxidation state of the metal ion When equilibrium is displaced on the right, the reaction corresponds to reaction (a) described in para 1. Displacement of the reaction to the left corresponds to reaction (b) described in para 1.

3. Any metal in contact with a solution of its ions is called a half-cell, and the potential difference of the half-cell is called the electrode potential of the half-cell. The symbol denoting the electrode potential is E, and the quantity is measured in volts.

4. The electrode potential of a half-cell cannot be determined independently, but is measured by placing it in series with a different half-cell. These are joined together by a salt bridge, and a voltmeter is connected across the complete circuit to measure the voltage produced.

5. The electrode potential of a half-cell is dependent on three factors. These are:

Because of this dependence, a set of standard conditions have been selected for use in the measurement of electrode potentials. These are:

When measured under these conditions the values become standard electrode potentials and are given the symbol E, the units of which are also in volts.

6. Since the electrode potentials of half-cells can only be determined when placed in series with a known potential half-cell, a standard electrode has been selected for this purpose. The standard reference electrode is the standard hydrogen electrode which is shown in Figure 8.2.

The electrode consists of a piece of platinum foil coated with platinum black embedded in the walls of a glass tube. This foil is connected by means of a platinum wire to the external lead. The platinum black material is very finely divided platinum and it catalyses the reaction which occurs between hydrogen gas and hydrogen ions as shown in the equation

$Massofsilverwillbe108\times \frac{600}{96500}=0.67g.$

The hydrogen gas is bubbled through the electrode at a pressure of 101.325 kPa, and the concentration of the acid solution must be exactly 1.00 molar strength with respect to hydrogen ions.

During experimental work to determine standard electrode potentials, the acid solution must be thermostatically controlled at 298 K. By mixing together the hydrogen gas and the hydrogen ions in the presence of the platinum electrode, the electrode potential is developed between the element (hydrogen), and a solution of its ions (hydrogen ions). When the electrode is set up in this way, the standard electrode potential which is developed is defined as zero.

7. The standard hydrogen electrode requires considerable time and care to set up, and it is difficult to move from one experiment to another. Consequently, alternative reference electrodes have been devised, an example being the calomel reference electrode which is shown in Figure 8.3.

In this standard electrode, the platinum electrode provides the contact between the mercury and the calomel paste, which contains mercury (I) chloride, Hg₂Cl₂ as the source of Hg⁺ ions. The concentration of the mercury (I) chloride is maintained by placing it in contact with 0.1 molar potassium chloride solution. The electrode potential of this electrode, with respect to the standard hydrogen electrode, is + 0.336 V. Thus when the standard calomel electrode is used, + 0.336 V must be added to any standard electrode potential which is measured.

8. When the standard hydrogen electrode is connected in series to another standard half-cell as shown in Figure 8.4 the direction of the current flow is dependent on the particular metal/metal ion electrode system which is used. The convention which has been adopted is that, metals which release hydrogen gas from a solution of hydrogen ions are designated as negative (– ve) with respect to the standard electrode. Metals which do not release hydrogen gas are designated as positive (+ ve) with respect to the standard electrode. Examples of some E values are shown in Table 7.1, page 44.

9. When two different standard half-cells are connected in series in a circuit, they form a galvanic cell as shown in Figure 8.5. The resultant potential difference of the two standard half-cells is called the standard electromotive force of the galvanic cell, and is symbolised by E_cell.

10. A galvanic cell can be represented systematically in the form of a cell equation. Any two half-cells can be represented by A^{x +}| A and B^y+ | B which when forming a galvanic cell can be represented by the cell equation

$A\Vert A^{x+}⋮B^{y+}\Vert B$

In this equation the solid vertical line represents the solid electrodes and the dotted line represents the salt bridge joining the half-cells together. The standard e.m.f. of the cell is defined as:

The standard e.m.f. of the cell E_cell = E (Right Hand Electrode) – E (Left Hand Electrode), which is simplified to:

$E_{cell}^{\ominus }=E_{R.H.E}^{\ominus }-E_{L.H.E}^{\ominus }$

For the general cell equation given above, A| A^x+ is the left hand electrode, and B^y+ | B is the right hand electrode. The polarity of the right hand electrode is defined as being the same sign as the e.m.f. of the galvanic cell, i.e. if the E_cell value is positive, then the right hand electrode has positive polarity. For example, when the zinc half-cell and the hydrogen half-cell are connected together to form a galvanic cell as shown in Figure 8.4 the cell equation is written as

$\begin{array}{l}Zn\Vert Z{n}^{2+}\left(aq\right)⋮H^{+}\left(aq\right)\Vert H_2,Pt\\ LHE-0.76VRHE0V\end{array}$

where LHE and RHE signify the left hand electrode and the right hand electrode respectively. The e.m.f of this cell is calculated using the equation

$E_{cell}^{\ominus }=E_{RHE}^{\ominus }-E_{LHE}^{\ominus }=E_{H_2}^{\ominus }-E_{zn}^{\ominus }$

and by substituting the electrode potential values gives

$E_{cell}^{\ominus }=0-\left(-0.76\right)=+0.76V$

This means that for this galvanic cell, the e.m.f. is +0.76 V, the hydrogen electrode is the positive electrode and the zinc electrode is the negative electrode. Similarly, for the copper electrode and hydrogen electrode the cell equation is

$E_{cell}^{\ominus }=0-\left(-0.76\right)=+0.76V$

and the e.m.f. is given by

$E_{cell}^{\ominus }=E_{RHE}^{\ominus }-E_{LHE}^{\ominus }=E_{H_2}^{\ominus }-E_{Cu}^{\ominus }=0-0.34=-0.34V$

This means that for this galvanic cell, the cell e.m.f. is −0.34 V, the hydrogen electrode is negative and the copper electrode is positive.

11. When the standard half-cells of aluminium and silver are combined into a galvanic cell using hydrogen electrodes as shown in Figure 8.5(a). The cell equation for this arrangement is

$Al\Vert A{l}^{3+}\left(aq\right)⋮H^{+}\left(aq\right)\Vert H_2,PtPt,H_2\Vert H^{+}\left(aq\right)⋮A{g}^{+}\left(aq\right)\Vert Ag$

From Table 7.1 the E values for the aluminium and silver are −1.67 V and +0.80 V respectively. The circuit in Figure 8.5(a) is a combination of the two galvanic cells in series which can be represented by the cell equations

The total e.m.f. of the two galvanic cells in series is given by

$\begin{array}{l}{E}_{Total}^{\ominus }=E_{cell(i)}^{\ominus }-E_{cell(ii)}^{\ominus }or\\ E_{Total}^{\ominus }=+1.67V+0.80V+2.47V.\end{array}$

The e.m.f. produced is + 2.47 V.

Similarly, the cell equation for the circuit shown in (b) is

$Al\Vert A{l}^{3+}\left(aq\right)⋮A{g}^{+}\left(aq\right)\Vert Ag$

Applying the equation

$E_{Cell}^{\ominus }=E_{RHE}^{\ominus }-E_{LHE}^{\ominus }$

gives

$E_{Cell}^{\ominus }=E_{Ag}^{\ominus }-E_{Al}^{\ominus }=0.80-\left(1.67\right)V=2.47V$

The e.m.f of the cell is +2.47 V.

From the results it can be seen that when a galvanic cell is formed by two half-cells, it is unnecessary to consider the standard hydrogen electrodes when calculating values of e.m.f. It should be noted that when drawing a diagram of the circuit or writing a cell equation for a galvanic cell, it is usual by convention to select the more positive electrode as the right hand electrode.

12 The list of values of standard electrode potentials shown in Table 7.1 with the most negative at the top, is also called the electrochemical series. In the table, any element above another can theoretically be used to displace the lower element from a solution of its ions. For example, magnesium is above zinc in the table and the theoretical reaction is

$E_{Cell}^{\ominus }=E_{Ag}^{\ominus }-E_{Al}^{\ominus }=0.80-\left(1.67\right)V=2.47V$

Similarly, zinc is above copper and the equation of reaction is

$E_{Cell}^{\ominus }=E_{Ag}^{\ominus }-E_{Al}^{\ominus }=0.80-\left(1.67\right)V=2.47V$

Such reactions, where a metal is deposited from its solution by another metal are called displacement reactions.

13. A displacement reaction can be considered as two reactions taking place simultaneously. For the magnesium and zinc reaction shown above the reactions taking place are

Reaction (a) involves a loss of electrons by magnesium and this process is called oxidation. Reaction (b) involves a gain in electrons by zinc ions and this process is called reduction. The reactions can be called oxidation/reduction reactions or more commonly redox reactions, where red- is taken from reduction and -ox from oxidation. It is Important to remember that a reduction can only take place accompanied by an oxidation, and vice versa.

14. When a galvanic cell is formed the positive electrode undergoes reduction (gaining electrons), whilst the negative electrode undergoes oxidation (losing electrons). Since the reaction at the positive electrode involves the attraction of positively charged ions, or cations, the electrode is called the cathode. The other electrode undergoing electron loss is called the anode.

15. Applications of galvanic cells The production of an e.m.f. by chemical change offers a form of portable electricity. The production of electricity in amounts suitable for domestic and commercial purposes is achieved by arranging a series of cells into a battery. The simple cell shown in Figure 8.6 has two faults (a) polarisation effects and (b) local action effects.

16. When a galvanic cell is set up, the p.d. between its terminals when not connected to a load is the electromotive force of the cell. The e.m.f of a cell is measured by using a high resistance voltmeter connected in parallel with the cell. The voltmeter must have a high resistance otherwise it will pass current and the cell will not be on no-load. For example, if the resistance of a cell is 1 Ω and that of a voltmeter is 1 MΩ then the equivalent resistance of the circuit is 1 MΩ+ 1 Ω, i.e. approximately 1 MΩ, hence no current flows and the cell is not loaded.

17. The voltage available at the terminals of a cell falls when a load is connected. This is caused by the internal resistance of the cell which is the opposition of the material of the cell to the flow of current. The internal resistance acts in series with other resistances in the circuit. Figure 8.7 shows a cell of e.m.f. E volts and internal resistance r, XY represents the terminals of the cell.

When a load (shown as resistance R) is not connected, no current flows and the terminal p.d., V = E. When R is connected a current I flows which causes a voltage drop in the cell, given by Ir. The p.d. available at the cell terminals is less than the e.m.f. of the cell and is given by V = E – Ir. Thus if a battery of e.m.f. 12 V and internal resiatance 0.01 Ω delivers a current of 100 A, the terminal p.d.,

$V=12-\left(100\right)\left(0.01\right)=12-1=11V.$

When a current is flowing in the direction shown in Figure 30.7 the cell is said to be discharging (E> V), and when a current flows in the opposite direction to that shown in Figure 8.7 the cell is said to be charging (V < E).

18. A battery is a combination of more than one cell. The cells in a battery may be connected in series or in parallel.

19. There are two main types of cell – primary cells and secondary cells.

Advantages of an alkaline cell (for example, a nickel-cadmium cell or a nickel-iron cell) over a lead-acid cell include:

Disadvantages of an alkaline cell over a lead-acid cell include:

Alkaline cells may be used in extremes of temperature and also in conditions where vibration is experienced or where duties require long idle periods or heavy discharge currents. Practical examples include traction and marine work, lighting in railway carriages, military portable radios and for starting diesel and petrol engines. However, the lead-acid cell is the most common one in practical use.

20. The capacity of a cell is measured in ampere-hours (Ah). A fully charged 50 Ah battery rated for 10 h discharge at a steady current of 5 A for 10 h, but if the load current is increased to 10 A, then the battery is discharged in 3–4 h, since the higher the discharge current, the lower is the effective capacity of the battery. Typical discharge characteristics for a lead-acid cell are shown in Figure 8.11.