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Consequently, 2 volts applied to it yield 2 × 4'8 = 9'6 amperes, and the power spent is 2 volts X 9'6 amperes

= 19'2 watts. All the work spent on the bath eventually results in heat, for no chemical work is done, the weight dissolved off the anode being equal to that deposited on the cathode. Hence in a minute the heat generated in the bath is 192 × 60 = 1152 joules.1]

When the materials of a voltaic cell react, they lose a certain amount of chemical energy. For instance, the replacement of copper by zinc in solution of the sulphates is attended by a loss of energy, for the affinity of zinc for sulphuric acid is stronger than that of copper. If no precaution be taken to make use of this energy, it will all be converted into heat and dissipated. Thus, if a stick of zinc be immersed in copper sulphate solution, this reaction will take place and some heat be evolved, though the change is too slow to cause a very noticeable rise of temperature. Wherever a reaction takes place with any facility in the ordinary chemical way, the heat produced by it-the so-called heat of reaction-may be measured by making the reaction take place in a calorimeter. Many such data have been ascertained, as may be seen from the books on thermo-chemistry; and even when a reaction is too slow, or otherwise impracticable to carry out in a calorimeter, the heat of reaction may usually be estimated indirectly, by combining the results of several easier reactions.

The heat of reaction is expressed with regard to the quantities of reagents to which the chemical equation refers; and may be simply written at the end of the equation, e.g.—

Zn+CuSO,. 100H,O=Cu+ZnSO,. 100H2O+209,910 joules i.e. when zinc replaces copper in a solution of the sulphate containing 100 mols of water to one of salt, the evolution of heat amounts to 209,910 joules for every 65 grams of zinc dissolved. Hence the heat of reaction is the loss of chemical energy of the reacting substances.

The joule is the most convenient unit of heat. The heat required to raise a gram of water through 1o centigrade is called a calorie, and is equal to 4'2 joules; but we shall not use the calorie in this book.

Such thermochemical data are of great importance in electrochemistry, for by their means an estimate can be made of the voltage of any electrolytic combination. The estimate was first made by Lord Kelvin many years ago, and it must be carefully noted that it is only an approximate one, based upon a certain assumption. If in a voltaic cell all the chemical energy lost reappears in the electrical form, then we may from its amount calculate the electromotive force of the combination. Thus in the Daniell cell, with the strengths of solution mentioned above, 209,910 joules of chemical energy are spent when two equivalents of zinc dissolve. But two equivalents of zinc carry with them two faradays of electricity; hence to get the voltage we must divide 209.910 by this quantity expressed in coulombs. The cell in question was carefully studied by Jahn,1 and as he takes 96,540 coulombs as the value of the faraday, we shall do so in this instance. Hence the voltage calculated according

to Kelvin's rule is

209,910 joules193,080 coulombs 10872 volts

=

Jahn found the voltage (at o° C.) to be 1'0962 volts; hence the assumption in Kelvin's rule is nearly correct in the case of the Daniell cell.

The rule is, however, by no means always true. Thus the thermal phenomena of the Clark cell have been very carefully considered by Cohen,2 who finds for the heat of reaction 340,700 joules at 18° C., the solution being saturated with zinc sulphate (ZnSO,.7H,O), as is the case in the ordinary construction of the cell. The electromotive force at that temperature is, however, only 1'4291, so that when two equivalents of zinc dissolve, and two faradays flow from it, the electrical work done is only

1'4291 X 2 X 96,610 = 276,100 joules

only about three-quarters of the chemical energy lost. In this case the considerable amount of energy left over appears as heat, and the cell would rise in temperature if it were possible to take current out of it at any considerable rate. In the 1 Wied., 28. 21, 491 (1886).

2 Zeitschr. f. phys. Chem., 34. 67 (1900).

Daniell, on the other hand, more electrical work—according to Jahn's measurements—is done by the cell than the chemical reaction can furnish. This is not a contradictory conclusion; it only means that some of the heat of the materials is converted into electrical energy, and the cell will cool slightly by its own action, just as a cylinder of compressed gas will cool itself when the gas is allowed to flow out.

The accumulator, as ordinarily constructed, belongs to the same class as the Daniell—it cools slightly on discharge. There is a density of acid, however, for which Kelvin's rule is precisely true. This is about 1044, much below that used in practice; with such acid the chemical energy spent by the materials of the cell reappears precisely as electrical work. The heat of the reaction

Pb+ PbO2 + 2H SO, = 2PbSO, + 2H2O

can only be determined very indirectly, and so is exposed to considerable experimental errors. It has been estimated by Streintz1 and Tscheltzow.2 For acid of the above-mentioned density it is 360,000 and 368,000 joules according to these two observers respectively. Since in the reaction two faradays are involved, we may, taking the mean of the two numbers, calculate the E.M.F. as

364,000 joules (2 x 96600) coulombs = 1.88 volts Experiment gives, for the same strength of acid, 189 to 1'90 volt.

These points will be further considered below, and it will be seen that the discrepancy between Kelvin's rule and the facts has received a complete theoretical explanation. For the present it is enough if, by means of it, a definite conception of electromotive force has been arrived at.

§ 3. ELECTRODE POTENTIAL

The foregoing section shows how close is the relation between the transformations of energy accompanying a chemical reaction and the electromotive force it is capable of 1 Wied., 53. 698 (1894). 2 C. R., 100. 1458 (1885).

producing if carried out in a cell; shows, indeed, to a certain extent, that the electromotive force may be regarded as a measure of the energy change. To appreciate fully this intimate relation it is necessary to analyse the chemical changes taking place in a cell, to see where each part is located, and to trace the electromotive force corresponding to each.

If a cell such as a Daniell cell be examined and its electromotive force measured by a voltmeter or potentiometer (vide infra), it is the difference of potential between the copper wires attached to the electrodes that is really recorded on the instrument. Between these copper wires we have the chemical system

Cu Zn ZnSO : CuSO : Cu

Here are four contacts of dissimilar substances, and each one gives rise to a certain electromotive force: i.e. as an electron passes across such a contact it either does work or work is done on it, and it consequently passes to a lower or higher level of potential. Of the four, however, two only need be considered, for the most part, viz. those between metal and electrolyte. That between metal and metal is apparently always very small; that between electrolyte and electrolyte likewise small in all but exceptional cases. We shall therefore devote attention to the potential difference between the zinc and its sulphate, on the one hand, and between the copper and its sulphate on the other, and use the term electrode potential for it. In dealing with methods of measurement below, an indication of the way in which electrode potentials have been determined will be given; for the present we assume the results.

The electrode potential then represents the work done in carrying unit quantity of electricity between electrode and electrolyte; and since on the ionic theory the carriage is effected by the formation or discharge of an ion, it is the work done in this chemical process that is involved. E.g. at the negative pole of the Daniell we have the reaction

Zn = Zn + 2

Now it is found that about half a volt difference of potential

exists in this case, the metal being negative to the solution. Again, at the other pole of the cell the reaction

[blocks in formation]

involves a slightly greater potential difference (about o'6 volt), but here the metal is positive to the solution. Consequently the total difference of potential from one electrode to the other is the sum of these, viz. I'I volts, as measured.

These facts may be expressed by the simple diagram annexed, in which height represents potential: the small difference of potential between the two solutions is ignored.

It is a well-known fact that the chemical properties of a solution depend very much on its concentration; thus the affinity that causes nitric acid to Cu+attack metals is lessened by diluting

Zn

<--9.0

it with water. The same thing shows itself, of course, in electromotive force measurements, and therefore to get any standard of electrode potential Solution it is necessary to define the concen

tration of the solution. E.g. zinc will show less tendency to form ions if there are already many zinc ions in the solution, i.e. if a strong solution of zinc sulphate be used. A concentration which is normal (1 gramequivalent per litre) with respect to the ion given off by the electrode is taken as standard, and the term electro-affinity is used to express the electrode potential in this case.

FIG. 29.

The choice of this concentration as a standard is not altogether satisfactory. A normal solution of most salts is far from being completely dissociated; and not only that, but the laws of dilute solutions are so far from being true for solutions of this strength that much difficulty exists in forming an opinion as to the degree of dissociation. Thus normal KCI is dissociated to the extent of 76 per cent., to judge by its

1 Following Ostwald, "normal" is taken as I gram-equivalent per litre, "molar," as I gram-molecule per litre.

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