KCl + HgCl2 : Hg the electrodes are symmetrically placed, and consequently neutralise each other in electromotive force. Of the four liquid junctions those marked (b) and (d) are equal, in virtue of the superposition principle, and being oppositely directed, neutralize; (a) and (c) alone, therefore, contribute to the electromotive force. But each of these can be calculated by the formulæ given above; the sum may therefore be compared with experiment. The results of measurement of several such groups were The observed values are regularly about 10 per cent. too low. This is, perhaps, due to incomplete dissociation. The theoretical treatment has not yet been extended to incompletely dissociated electrolytes. While measurement of the potential difference due to a liquid contact is very difficult, there is fortunately a simple means of rendering it negligible that can very often be applied. This is to mix both solutions with a strong neutral electrolyte ; then, as most of the current flows through the neutral electrolyte, the liquid is, with respect to it, homogeneous, and no potential difference arises. This was done, e.g., by Palmaer, in the measurements quoted on p. 197. There the solution of the normal electrode was saturated with HgCl2, while the liquid into which the dropping electrode dipped contained only Hg2(CN)2; this would cause a potential difference to occur between the two, were it not that the conductivity of both the mercurous salts is drowned by that of the KCl, which is T. P. C. Р present equally in both. By this device (known as an electrolytic short circuit) the measurements of electrode potentials are freed from error due to liquid contacts. For further information as to the influence of neutral electrolytes on liquid contacts, see Bugarsky,1 Abegg and Bose,2 and Sackur.3 (v)-CONCENTRATION CELLS. A voltaic cell is essentially a means of employing any store of free energy by the transport of electric charges. Accordingly, cells may be grouped according to the nature of the energy they employ. The most ordinary kinds use energy of chemical combination, but cells can also be devised in which the active process is of the kind usually known as "physical" rather than "chemical," though there is no distinct line between the two. Among physical processes that have been so used are falling under gravity, equalisation of gas-pressure, equalisation of the strength of solutions, of amalgams, etc. Cells based on these processes are rarely of any practical value, but have been much studied on theoretical grounds: it is often possible to calculate the change of free energy in them in a non-electrical way, and so obtain valuable confirmation of the principles involved. We shall discuss at length one or two cases, especially of the so-called "concentration cells," but first may be taken the gravity cell, on account of its simplicity. Such a cell was realised by Des Coudres. He used two mercury electrodes and a solution of a mercurous salt. But for pressure differences this arrangement would be perfectly symmetrical, and so yield no electromotive force. In order to admit of difference of pressure, the masses of mercury were separated from the solution by stout membranes of parchment paper, which affords mechanical support without breaking the electrical circuit. Then if one of the electrodes consists of a 1 Zeitschr. phys. Chem., 14. 150 (1894). 2 Ibid., 30. 545 (1899). 3 Ibid., 38. 129-162 (1901). 4 Wied. Ann., 46. 292 (1892). long column of mercury, the other a short column, there will be a tendency for the mercury to drop from the long to the short side; this will be accomplished by mercury going into solution on one side and coming out on the other, carrying with it, of course, an electrical charge. Now, gravitational energy is all "free," as is well known, for it is easy to devise a mechanism by which all the energy of a falling body shall be converted into work. Hence the calculation of electromotive force is very simple: in one of Des Coudres' experiments the pressure difference was 113 cms.; then one equivalent (200 grams) would in falling do 113 × 200 gram-cms. = 113 X 200 × 981 ergs = 113 X 200 X 981 joules of work, and would convey 96,600 coulombs. Hence E.M.F. = 113 X 200 X 981 10 X 96,600 = 23 X 10-6 volts The observed amount was 21 X 10-6—a satisfactory agreement, considering the smallness of the quantity to be measured. Now, this process is independent of temperature, and accordingly in the fundamental equation We have here a case in which (i.) The free energy is identical with the total energy; (iii.) The E.M.F. is independent of temperature. Again, as a very simple instance of a cell which works by equalisation of concentration differences, we will take the combination Hpt: HCl : HgCl2: Hg i.e. a platinum sheet saturated with hydrogen, and a calomel electrode both dipping in hydrochloric acid. Set up a pair of such, one with centinormal acid, the other with millinormal, and join them in opposition. These low concentrations are chosen in order that we may assume the acid to be completely dissociated. Now, the only want of symmetry in the arrangement is in the strength of acid; and the two acids will tend to become equal in strength. There will, therefore, be a tendency for H and Cl' ions to be discharged from the stronger electrolyte, and to be formed from the electrodes of the weaker until the two solutions are of the same strength. The work this process is capable of doing may be calculated by means of the analogy between a solution and a gas. Since one equivalent of dissociated hydrochloric acid contains as many particles (in the sense of Avogadro's law) as two mols of gas, the work is At atmospheric temperature (= 291° abs.) this is 2 X 8316 X 291 X 2*3026 = 11,200 joules But as one equivalent carries with it 96,600 coulombs, the 96600 = The argument just given is essentially identical with that on p. 162, where the dependence of the separate electrode potentials on concentration was dealt with. It follows at once from what is there said that the potential of the hydrogen electrode of the cell with the stronger acid is o'058 volt higher than that with the weak acid. The same difference, but with the opposite sign, exists between the calomel electrodes; for in these "electrodes of the second kind" the liquid is saturated with calomel; according to the law of mass action, therefore, the product of the concentrations of the ions Hg ̈ and Cl' must be constant; hence when, in passing from the first to the second cell the concentration of acid (and hence of Cl') is decreased tenfold, that of the mercuro-ions is increased tenfold, and the potential of the mercury raised by o'058 volt. 1 See Donnan, Thermodynamics (in this series). Thus, on the whole, the E.M.F. of the cell with stronger acid is o'116 volt less than that of the other. Thermodynamically this cell is very different to the gravity cell, and may be taken as an opposing type. Its action depends on the tendency to equalisation of strength between the two electrolytes. But, it is well known, no heat is evolved on mixing very dilute solutions. Hence the "heat of reaction" Q is zero, and in the fundamental equation (i.) The total energy of reaction is zero; (ii.) Consequently the latent heat is equal to the free energy of the reaction; and (iii.) The electromotive force is proportional to the absolute temperature. In the gravity cell the electrical work is done entirely at the expense of gravitational energy, and no thermal changes occur; in this concentration cell the electrical work is done entirely at the expense of the cell's own heat, and it accordingly cools in action. The pair of accumulators discussed on p. 182 form a concentration cell of the same type as this hydrogen-mercury combination, except that the acid in them is far from dilute; and as the mixture of sulphuric acid and water in moderate concentrations evolves a notable amount of heat, the deduction as to influence of temperature does not hold. Another form of concentration cell is more familiar than the above; viz. a cell in which the liquids of different concentration are put into immediate contact. This can be made from the preceding form by mere omission of the second (mercury) electrode. Thus Hpt: HCl (dilute): HCl (concentrated): Hpt may serve as example. The action here, too, depends on equalisation between the strengths of the two solutions, and |