by the other. As a very great range of concentration has to be considered in practice, it would not be convenient - 0.560 Volts to take the abscissæ as proportional to the concentration; the formula itself suggests a logarithmic scale. This accordingly is adopted, and o representing normal concentration, +I will represent ten times normal (log C = 1), - I decinormal (log C = — 1), etc. Then taking zinc in zinc chloride solution as an example, the point E, representing the electro-affinity will lie at - 0'493 If the concentration be made decinormal, the electrode potential becomes 0'4930'029 FIG. 30. on the axis of potential. 0'521, in accordance with the rule given above, zinc being divalent; in centinormal solution 0'550. Thus the line of electrode potentials given by Nernst's rule is straight. Actually the rule may be taken as true with regard to centinormal and more dilute solutions, but above that point the potential deviates considerably from the straight line, partly on account of the incomplete dissociation of the solutions, partly on account of deviations from the gaseous laws. The potential in a normal (not "normal ionic ") solution has been found to 0502 volts. The influence of concentration on electromotive force may be illustrated by considering in detail the voltaic cells already mentioned, and the most important cases of electrolysis. be 1. The Daniell consists of two electrodes of the first kind. Therefore at each, the electrode potential is raised by increase of concentration. This may be represented graphically as in Fig. 31, where the full lines are intended to show the potentials of the zinc and copper when the solutions are of normal (ionic) strength; the dotted lines a greater strength. The change is not in either case precisely that given by Nernst's law, but since both metals are divalent it is about the same for each, and is in the same sense. Hence the rule, long known, that the electromotive force of a Daniell cell is practically independent of the density of the zinc and copper sulphates, provided they are equal. If one be changed without the other, the E.M.F. is of course changed, e.g. if the copper sulphate be diluted, the potential of the copper electrode is lowered towards that of the zinc. A curious experiment has been explained on these grounds. If potassium cyanide be added to the copper sulphate solution in a Daniell cell, it first precipitates the copper and then on adding more redissolves it; the solution, however, has no longer the blue colour indicative of copper ions. It is probable that the double cyanide K„Cu(CN), is formed, and that so far as this is dissociated, it is mainly into K cations, only to a minute extent into Cu". The concentration of the Cu ions is thus enormously lowered, and the potential of the copper electrode is actually reduced below that of the zinc, so that the zinc becomes the positive terminal of the cell. 2. The Clark Cell consists of an anode of the first kind (reversible with respect to the cation) and a cathode of the second kind (reversible with respect to the anion). Fig. 32 shows the effect of change of concentration of the solution. The dotted lines show the effect of increase in concentration, and it is seen that the effect is to raise the potential of the zinc and lower that of the mercury; hence on both accounts to diminish the E.M.F. of the cell. The Clark cell used as a standard is made up with saturated solution, containing about six gram-equivalents per litre. Its E.M.F. is 1°428 volts at 20°; a similar cell made with normal solution gives 1464 volt. These concentrations refer, as usual, to the total weight of dissolved salt: a normal-ionic solution, as remarked on p. 159, is not obtainable. CL 3. Electrolysis of Hydrochloric Acid between Platinum Plates. The platinum being unalterable, the electrolysis is carried on by discharge of Cl' at the anode and of H at the cathode. The potentials are shown in Fig. 33. A solution containing rather less than 5 per cent. of HCl by weight (14 normal in total concentration) is probably normal-ionic. For this the potentials are +0277 and +1694 (p. 159), the electromotive force required for the electrolysis consequently 1417 volt. Increase of concentration raises the potential of the hydrogen and lowers that of the chlorine, hence on both accounts lowers the E.M.F. That is to say, as common sense would indicate, it takes less work to electrolyse strong acid than weak: when there are many ions in the electrolyte it is easier to discharge a given number of them than when there are few. H FIG. 33. The numerical values just given are from Wilsmore's papers. There seems to be considerable uncertainty, however; Le Blanc gives 4. The Lead Accumulator. The partial reactions in this are (p. 152), at the negative atthe positive Pb+SO," PbSO, +20 = = Ө PbO + H2SO + 2H + 2 = PbSO, + 2H2O Both these are reversible, the phenomena of charge being the exact converse of those of discharge. Hence the negative electrode may be regarded as one reversible with respect to an anion (SO), i.e. of the second kind; the positive one of the first kind. Accordingly increase in density of the acid causes the potential of the negative to be lowered, that of the positive to be raised, and so on both accounts increases the E.M.F. of the cell. This is the well-known fact discussed from the thermal point of view in § 2, and more fully below, page 183. It is indicated in Fig. 34, where, as usual, the dotted. lines indicate an increase of concentration. Since, however, the strength of acid used in accu- Pb mulator practice is far beyond what can be considered a dilute FIG. 34. solution, the logarithmic rule must not be applied here. The numerical data will be given later. It may be noted, however, that neither of the electrode potentials can be taken from the table on p. 159, even if the acid were normal; for the electrodes are not of the simple kind implied in that table. The positive is effectively reversible with respect to hydrogen, it is true; but it is not a hydrogen electrode with an electroaffinity of o 277, for elementary hydrogen does not exist in the electrode material, and there are other factors in the reaction which must be taken account of, and which largely modify the potential. In fact, the electrode potential must always be looked on as a measure of the work done in a particular reaction; thus o 277 volt is the measure of the reaction H1 = 2 H (in normal solution) + 20 H2 Ө This is obviously quite a different process from that occurring at the positive of an accumulator. § 5. CONCENTRATION POLARISATION There is another aspect to the effect of change of concentration on electromotive force, which must now be dealt with. The electrolytic action itself tends to produce changes in the liquids of the cell, and so reacts on the electromotive force producing it; it is therefore not enough to determine the concentration of the solutions used in the cell at starting. Take as example the electrolysis of copper sulphate between copper plates, as in the industry of copper refining. The chemical action consists merely in solution of copper at the anode and deposition of an equal amount at the cathode; in terms of the ionic theory, Cu Cu" + 2 at the anode, and the same reaction reversed at the cathode. There is, therefore, no chemical work to be done, and whatever potential difference occurs at one terminal should occur with reversed sign at the other, so that no electromotive force should be needed to electrolyse, beyond that required to overcome the resistance of the solution, in accordance with Ohm's law. It is true that when no current flows the two electrodes are at the same potential; but now consider more precisely what happens when a current is passed through. At the anode, fresh copper sulphate is formed in solution. We have already, in fact, calculated the amount (p. 35); it is, for one faraday, a gramequivalent, (where x = migration ratio of the SO"). Similarly the combined effect at the cathode of deposition and migration is to remove x equivalents from the solution. Hence, according to the principles of the last section, the potential |