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The dependence of the conducting-power of the chlorides on the temperature shows, according to the above, great simplicity in many respects. The universally small amount of the coefficient B proves that, with all solutions, the conducting-power increases in nearly equal proportion with the temperature; the positive sign of B, that each of the slight deviations consists of an acceleration.
With so strongly pronounced a dependence as we have here (with which 30° rise of temperature about doubles the conducting-power), this nearly equal proportional augmentation could not à priori be expected. It has, however, been observed also in sulphate-of-zinc and sulphuric-acid solutions*, and appears to be a universal property of liquid conductors. Viscous substances only, such as concentrated solutions of chloride of calcium, chloride of magnesium, and sulphuric acid, exhibit greater inequality.
A further, very remarkable fact is the near approximation to equality of the temperature-coefficients for the different chlorides in dilute solution. Those at 18°, for example, for all 5-per-cent. solutions, lie between (for LiCl) and (for NH, CI); the graphic representation permits the conjecture that with further dilution they would come still nearer together; nay, it is probable that they tend to the same limit (about). And certainly this limit cannot signify the temperature-coefficient of pure water, since the conducting-power of this is generally a vanishing quantity in comparison with the numbers in the above Table. The temperature-coefficient of sulphate-of-zinc solution, too, observed by Beetz, appears as the dilution is increased to approach towards about the same limit.
With increasing amount of salt contained, all the temperaturecoefficients at first diminish. Afterwards the substances divide themselves into two groups: KCl, NH, Cl, and BaCl, show a diminution of the coefficients up to the greatest concentration, the coefficient sinking in the case of NH4Cl to the lowest value, 4. NaCl, CaCl2, and MgCl2, on the contrary, have a minimum between 10 and 20 per cent.; and thence onward the coefficient rises, that of MgCl, even to. This group-difference appears to be connected with a maximum of conducting-power with the salt-content, exhibited by the latter substances, but not by the former. (Compare what is stated below.)
Nitric acid connects itself with the latter group. In the sign of B changing from to it agrees with sulphuric acid; yet the inequality of the augmentation between 0° and 40° is generally slight. The absolute amount of the influence of temperature is less than with the chlorides, and not very different from that observed with hydrochloric and sulphuric acids.
* Beetz, Pogg. Ann. vol. cxvii. p. 21; Grotrian, ibid. vol. cli. p. 394.
If we now consider, secondly, the dependence of the conductingpower on the amount of salt or acid contained, the only thing common to all the substances investigated appears to be the constancy of the variation. The annexed figure exhibits this
better than the numbers in the Table.
It has for abscissæ the
percentage contents, and for ordinates the conducting-powers at 18°. LiCl, so far as it was investigated, very nearly coincides with NaCl, and is therefore not delineated.
Both the absolute quantities of the conducting-powers and the laws according to which they depend on the content vary to a degree which is surprising in bodies which stand chemically so near one another. CaCl, has a maximum (at 24 per cent.), and so has MgCl, (at 20 per cent.). NaCl seems to go towards one; but it is questionable whether it reaches it before saturation (25.5 per cent.). The curve for SrCl, is moderately curved; those for BaCl, and NH, Cl are less so; with KCl the conductingpower at 18° is almost exactly proportional to the salt-content. Indeed, from the Table for 0° it is seen that at this temperature the conducting-power of the KCl solution increases somewhat faster than the percentage strength, which has not, till now, been observed in any liquid.
As the above-mentioned minimum of the temperature-coefficient (see p. 421) and the maximum of conducting-power belong to the same liquids, the two properties appear to have an intimate connexion.
In general BaCl, is the worst conductor; by far the best is NH, Cl, which in a 25-per-cent. solution conducts about half as well as the best-conducting acids known, and, at all events, is the best among all known salts. It is to be presumed, since the solubility of NH4Cl increases considerably with the temperature, that a solution saturated at 100° conducts at least as well as the best-conducting acid at the same temperature. Accordingly by
no means so high a place belongs to the acids as is generally assumed for them. In galvanic piles, for example, a nearly saturated solution of sal ammoniac can with advantage be employed in preference to the strongest acids that can be used for this purpose.
In another salt of ammonium, also, namely the nitrate, Wiedemann found a high conducting-power*.
The behaviour of MgCl, is remarkable. When the conducting-powers of its solutions are compared with those of the other chlorides of equal concentration, the former take the second place when very dilute, at 10 per cent. the fifth, and from 22 onward the last.
Nitric acid shows a maximum of conducting-power, namely for 18° when it contains 29.7 per cent. HNO,. It was already found previously that a maximum belongs also to sulphuric and hydrochloric acidst. It appears remarkable that these maximal conducting-powers of all three acids have nearly the same magnitude. Attention has already been called to this by Quincke‡.
If we try to express the conducting-power k as a function of the salt-content p, we find that for the chlorides the form k=ap+bp2+cps renders the observations with tolerable completeness; but the conducting-power of nitric acid is not even approximately represented by this expression. As, moreover, empirical laws in which the number of terms is considerable present for calculation no advantage over a Table with an equidistant argument, nor exhibit in their coefficients a recognizable physical meaning, it would be superfluous to go further into this subject.
On the contrary, it is evidently important to compare quantitatively the different substances in those solutions in which they are at once comparable—that is, in but slight concentration. For the conducting-power of pure water is, in comparison with the above numbers, to be put sensibly equal to zero; and the course of the curves (p. 422) shows that the conducting-power constantly increases; consequently dilute solutions have a limit which the ratio of the conducting-power to the salt-content approaches: it may be named the specific conducting-power of the substance in aqueous solution. If the observations for the contents 0.05 and 0-1 (i. e. 5 and 10 per cent.) be expressed in the
a will represent very nearly the specific conducting-power just
Pogg. Ann. vol. xcix. p. 228.
+ Compare Pogg. Ann. vol. cxxxviii. p. 385, and vol. cli. p. 390.
424 Electric Conducting-power of the Chlorides of the Alkalies,&c. now defined. At the same time it is immaterial for a whether the solution be reckoned in parts by weight (as is done here), or (as is more rational according to the definition of the conducting-power) by volume, since for dilute solutions the volume is equivalent to the weight. Also the quantity b, which denotes the initial deviation from proportionality, has a definite signification for each salt.
Only the results for 18° shall here be given, as their form for the other temperatures is very similar. They are:
According to this, the total character of each curve already shows itself while the content is yet very small: those substances which have a maximum of k at a definite degree of concentration, are distinguished by a relatively high value of b. (It may therefore be conjectured that LiCl also will show a maximum.)
If now we seek to connect the specific conducting-power a with other physical properties of the substances dissolved, we readily perceive that for the chlorides the quantities a stand nearly in the inverse order in a series to that of the equivalentweights A of the anhydrous salts-indeed so that, with equal amounts of chlorine in solution, the conducting-power of dilute solutions is not very different. Still the deviations of the products A. e from their mean amount to as much as 22 per cent. (Vide infrà.)
On the other hand, another accordance of an arrangement is self-evident-namely, according to the specific gravities s of the anhydrous salts. The products 8. a are, for the chlorides of the alkalies and alkaline earths, constant quantities, the greatest deviation from the mean being 12 per cent. Although this deviation is not inconsiderable, yet so simple a relation is deserving of notice. If it were rigorously exact, it would signify that equal volumes of anhydrous salts in solutions imply equal conductingpowers.
In the following Table the salts are placed in the order of their conducting-powers a, and together with their equivalentweights A and specific gravities s. For the latter I am indebted