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At the negative terminal of a Daniell cell the above reaction is reversed; there is therefore work done to the extent of 47,700 joules per equivalent of zinc dissolved, but as 67,400 joules of chemical energy are lost, 19,700 joules must appear as heat; the zinc pole is warmed during the action of the cell.

The net result in the whole cell is production of 19,700 joules of heat at one pole and absorption of 20,200 at the other, or absorption of 500 joules. Now, Jahn's direct measurement (p. 155) gives 800 joules, which is in sufficient agreement, seeing that the quantity in question is the difference between two much larger ones, and so very difficult to measure.

Ostwald has calculated the "heat of ionisation" for a number of metals, and the following table is quoted from him, with the sign reversed in accordance with the convention adopted here, and expressed in joules instead of calories; i.e. the quantity Q in the equation

M+M+Q (joules), M being one equivalent of metal.

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Many of these numbers are not obtained directly from temperature coefficients of electromotive force, but by combination of ordinary thermo-chemical data with the value of Q for some other metal. Examples of this will be of interest.

We have

Zn ̈ + − = ÷Zn = 69,500 ·

Lehrbuch d. Allg. Chem., II. (i.), 955.
2 I.e. OH′ = ‡H2O + 102+

- 88,600

and for the heat of formation of zinc chloride in solution 'from its elements

Zn + Cl2 + Aq = 1⁄2Zn ̈, Cl', Aq + 236 900

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which indicates the strong tendency of chlorine to adhere to its negative charge.

Again,

2

Zn + H, Cl',Aq = 1⁄2Zn", Cl',Aq + ¿H, + 71,800 (zinc dissolved in hydrochloric acid gives out 71,800 jcules). From this and the first equation we get

H"= H2 + 2300

The heat of ionisation of hydrogen is therefore so small as almost to lie within the margin of errors, and may be ignored. Hence the approximate rule that the heat of ionisation of a metal is practically equal to its heat of solution in dilute (i.e. completely dissociated) acid.

(iv) POTENTIAL DIFFERENCES BETWEEN LIQUIDS.

In order to complete the account of electro-chemical potential differences, it is necessary to consider the surfaces of contact between solutions. As already remarked, the potential differences arising here are usually small; they cannot, however, be neglected in an exact treatment of the subject.

The thermodynamic method so far followed cannot be applied without some loss of strictness here, because we have not to do with a state of equilibrium. Any two aqueous solutions put into contact necessarily diffuse into one another, and so suffer progressive change. Equilibrium would only be reached when the concentration of each dissolved substance was the same throughout, so that no potential difference could remain within the liquid. The state when diffusion is only beginning is nevertheless that of greatest practical importance; it is therefore necessary to find some means of discussing the..

electrical conditions at the beginning of the diffusion, i.c. immediately after the voltaic combination is put together.

This is supplied by the molecular theory, due to Nernst1 and Planck. The simplest case to consider is when two solutions of the same electrolyte but of different concentrations are put in contact. For definiteness we will suppose the electrolyte to be hydrochloric acid. Now, at the boundary there is a tendency for the ions H and Cl' which exist in the solution to diffuse from the vessel in which they are more concentrated to that in which they are less so. But His a much more mobile ion than Cl', and consequently diffuses faster; hence, after a short time, if there were no opposing force, a relative excess of hydrogen ions would have crossed the boundary, and the weaker solution would consequently have a positive charge; the strong solution would contain an excess of chlorine ions-for though it would have lost some chlorine, it would have lost more hydrogen-and be negatively charged. These positive and negative charges would, however, set up an electrostatic field tending to stop the process to which they were due; it would be so directed as to drive back the hydrogen ions, but help the negative chlorine ones forward from the strong solution to the weak. Hence, on the whole, diffusion will go on equally, positive and negative ions together; but an electrical double layer and its accompanying potential difference will be set up at the boundary between the two solutions.

It is not necessary that the boundary should be sharp. If the two solutions have partly diffused into one another, so that there is a gradient of concentration over a finite thickness, the argument is still the same.

It is easy to see from the above reasoning in which sense the electromotive force will be: the rule may be stated as follows:

"The potential of the weak solution is of the same sign as the more mobile ion."

1 Zeitschr. phys. Chem., 2. 613 (1888); 4. 129 (1889); Wied. Ann., 45. 360 (1892).

2 Wied. Ann., 39. 161; 40. 561 (1890).

Thus in acids the dilute solution is positive to the strong: in alkalis negative. If the two ions have the same mobility there is no electromotive force: this is approximately true for potassium chloride (K = 65'3 Cl′ = 65'9).

It is not difficult to show that for two univalent ions

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where u u' are the mobilities of the ions, CC, the concentration in the two solutions, and E the difference of potential produced (potential of solution that of solution 2). This is

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on the assumption of complete dissociation. In order to see the order of magnitude of this electromotive force, we will take as solutions 1 n. HCl against o'i n. HCl at a temperature of 18° (= 291° abs.)

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Actually E would be somewhat less than this on account of incomplete dissociation.

When the ions are not univalent the expression becomes

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When two solutions containing unlike ions are placed in contact, the same mode of argument shows that an electromotive force will arise, but the calculation is more difficult. For the special case of two brinary electrolytes of the same concentration (e.g. normal KCl and normal NaNO), it has been shown that

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where u1u are the mobilities of the cations, u' u of the anions. If all the ions are divalent, the electromotive force is one-half of this.

Certain deductions from the theory are important to note, both in regard to experimental verification of it, and to

measurements in cases where difficulties of calculation prevent its direct application.

When a pair of junctions is symmetrically placed, it has no resultant electromotive force. It sometimes happens that a whole series of liquid junctions can be divided into two symmetrical halves: in this case there is, of course, no electromotive force between the first and the last.

Two junctions which lie between similar pairs of solutions, with the same ratio of concentrations, have the same electromotive force, despite differences in absolute concentration. Thus, e.g., the potential difference between n. HCl and n. KCl is the same as between n. HCl and n. KCl. (Nernst's principle of superposition).

A number of junctions between the same electrolyte in various concentrations have, jointly, the same electromotive force as would exist between the first and last. For, if C1, C2, Cз, etc., to C, are the concentrations,

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Hence, if the first and last solutions are of the same strength, there will be no electromotive force.

But this proposition is not true of solutions in general. Thus, if a ring be made of a number of solutions, say

n. KCl : n. KCl : 1 n. HCl : n. HCl : n. KCl

we are not entitled to conclude that the total electromotive

force will be zero. On the contrary, if the last solution be put in direct contact with the first, there will in general be a This has been directly shown by the magnetic action

current.

of such currents.

Since it is never possible to have only one liquid junction without some asymmetry at the electrodes, measurements of such electromotive forces can only be made on groups of junctions. Nevertheless, by the use of certain devices, experiments may be made to test the theory. This was done by Nernst as follows:

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