between two accumulators (p. 182), and can accordingly be treated by the method of vapour pressure. The treatment is, in fact, easier, for the vapour pressure of HCl over a solution of the acid is measurable; whereas that of H2SO, is immeasurably small, and an indirect process, depending on the vapour pressure of water, has to be used instead. Dolezalek (loc. cit.) compares the vapour pressures and E.M.F.'s for hydrochloric acid of 5 to 12 times normal, with very satisfactory results. (iii) SINGLE POTENTIAL DIFFERENCES AT ELECTRODES. The same thermodynamic treatment may be applied to single electromotive junctions. We may consider separately the chemical reaction occurring at one pole of a cell; estimate its free energy by the potential difference it produces; and, if we have any means of measuring the heat of reaction, compare it, by the Gibbs-Helmholtz formula, with the change in free energy. Unfortunately, as the partial reaction necessarily involves the formation or destruction of free ions (unaccompanied by the corresponding ions of opposite sign), there is no means of studying it, independently of the complete electrochemical process of which it forms part; hence the heat of reaction in such cases cannot be measured. The measurements that can be made are of (a) the single potential difference, (b) the temperature coefficient, (c) the latent heat (sometimes called, in this case, the Peltier effect). (a) Numerous measurements have been made, by the calomel or other standard electrode, of single potential differences; but the value of such measurements depends entirely on the absolute determination in some one case. Thus, suppose it is desired to know how much of the E.M.F. of an accumulator is produced at each pole, we may proceed to measure the cells and Pb PbSO, H2SO: Hg2SO: Hg i.e. each half of the accumulator combined with a standard mercury electrode. The former E. M. F. may be written C - A, the latter CB, where A, B are the potentials of the lead and lead peroxide plates, C that of the standard. By this means A and B are referred to the same standard; but there is no means of knowing their actual values unless that of C is known. We need, therefore, an electrode whose potential either is zero, or is known by independent means. Two suggestions have been made, so far, for obtaining electrodes of no potential difference. The Dropping Electrode. This was suggested first by Lord Kelvin for measuring the potential of the air (water-dropper), and subsequently by Helmholtz and others for electrolyte. measurements. For the latter purpose mercury is always used, and the electrode takes the form of a fine jet of mercury delivering drops into an electrolytic solution-usually of a mercury salt. A mercury surface, in contact with an aqueous solution of a mercury salt, when at rest, assumes a definite potential with respect to the latter: say, a positive potential, as happens when any ordinary concentration of salt is used (p. 159). This means that a certain amount of (positive) electricity flows from the electrolyte to the electrode, or that the reaction HgHg" + 2 Ө In this way proceeds, to a small extent, from right to left. some free positive electricity is imparted to the electrode, and its potential raised; that of the solution lowered. This, however, sets up electrostatic attraction between the excess of positive electricity in the electrode and negative in the solution; as soon as the work to be done in overcoming the electro static attraction is too great for the chemical forces to perform the process stops. There is then a distribution of positive electricity on the metal, and negative on the solution, constituting an electrical "double layer." Now, if the mercury, instead of being at rest, is in process of forming a drop, and consequently of extending the area of contact, more ions will be needed to constitute the double layer on the new surface. These must diffuse out of the mass of electrolyte, so that the process of obtaining them is not very rapid. Hence, so long as drops are being formed, the double layer will be deficient, and even, if drops are formed very fast, almost absent, and the mercury will hardly differ in potential from the electrolyte. This state of things is capable of realisation. Attempts at it were made by Ostwald, but the experimental difficulties were first successfully met by Paschen.2 The apparatus of the latter consisted of a vertical tube about 200 cms. long, drawn out at the lower end to a bore of o'002 to o'005 cm. This is filled with mercury, which comes out in a fine jet, breaking up into drops; it delivers into a dish containing mercury, covered with the electrolyte. It is essential that the level of the electrolyte should be adjusted so that the mercury is on the point of breaking up into drops on entering it. 3 Palmaer finds the action of the electrode improved by making it with a glass stopper closing the bottom of the mercury tube, except for a number of fine rills in its edge, through which the mercury escapes (Fig. 37). The potential difference to be measured is that between the mercury in the dropping-tube and that at rest in the dish below; or else between the dropping mercury and some other electrode put in connection with the electrolyte. Paschen measured the potential difference in the dropping electrode for a number of solutions of HCl, NaCl, HBr, KBr, HI, and KI, obtaining consistent results, which were, moreover, in agreement with those of the capillary electrometer method (vide infra). He studied the influence of concentration, but without finding very intelligible variations on this account. It is on the strength of his measurements as well as those made with the capillary electrometer that the potential of the normal KCl electrode has been taken at + 0'560 volt, the decinormal FIG. 37. 1 Zeitschr. phys. Chem., 1. 583 (1887). at + 0·616 volt. 1 Palmaer has recently carried out a suggestion of Nernst that renders the method more certain and exact. The electrolyte is made a solution of mercury ions, of such diluteness that there is no potential difference between it and the standard electrode. This can be done by adding a cyanide or HS to a mercurous solution. E.g., when the composition orKCl+oorKCN+oooo8KOH +oooo25Hg(CN), (equiv. per litre) was used for the electrolyte in the dish into which the dropping electrode delivered, it was found that practically no difference of potential existed between the dropping and the fixed electrodes; and at the same time a decinormal electrode was o'5745 volts positive to the mercury in the dish. From the mean of several experiments the author concludes that the absolute potential of the decinormal electrode is 0'572 volt at atmospheric temperature, instead of o'616, as hitherto assumed. Capillary Electrometer.--Another method that has been. more frequently applied depends on the influence of electrification on the surface tension of mercury. This was discussed theoretically by Helmholtz, and worked out by Lippmann into the practical instrument for measuring electromotive forces described below (p. 235). If to such a capillary electrometer a potential difference is applied from outside, the surface tension of the mercury is changed: when the mercury in the tube is made positive, the surface tension decreases; when negative, it increases up to a maximum for about half a volt, and then decreases again. According to Helmholtz's theory, the existence of an electrical double layer at the surface between mercury and electrolyte reduces the surface tension, in whichever sense the double layer may lie, so that maximum surface tension occurs when the double layer is absent, i.e. when mercury and electrolyte have the same potential. Hence the observations are interpreted as meaning that the mercury in contact with an ordinary electrolyte is naturally positive, but that, by connecting it to the negative pole of an outside source of electromotive force of sufficient strength, the potential of the mercury may be reduced to that of the solution. The 1 Zeitschr. Elektrochemie, 9. 754 (1903). applied electromotive force necessary to effect this is, then, a measure of the absolute potential of the mercury in its natural state. The course of the phenomenon may be conveniently represented by a diagram (Fig. 38), in which the surface tension is plotted (as ordinate) against electromotive force (as abscissa). A represents the "natural" surface tension, i.e. without any outside electrification; B, the maximum; at B, therefore, the potential of the mercury is the same as that of the solution, while at A it differs by the amount HK. According to Helmholtz's theory, it makes no difference whether, in the double layer, the positive charge is on the one or the other; the curve should therefore be symmetrical about B, the surface tension being depressed equally by a given difference of potential from K on either side. Experiments by Lippmann and others have confirmed this theory in its general lines. The curve is of approximately the parabolic shape of Fig. 38; in dilute sulphuric acid an applied E.M.F. of about 1 volt causes the maximum to be reached; and as according to the theory the maximum surface tension is found when the surface is entirely free from the effect of an electrical double layer, it should be, at least approximately, the |