No. 6,
“or,. 42.
THE JOURNAL OF THE
erican Chemical Societ with which has been incorporated the
American Chemical Journal (Founded by Ira Remsen)
THE EXTRAPOLATION OF CONDUCTIVITY DATA TO ZERO CONCENTRATION. 11. EY EDWARD W. WASHBURN. Received January 19, 1920.
The recent series of papers by the writer and 13. J. Weiland,l dealing with the. equivalent conductance of electrolytes in dilute aqueous solution, has recently been made the subject of adverse criticism by Kendal12 and by K r a ~ s . ~ Kendall’s criticism is to the effect that the method described by the writer for evaluating A, is “identical with, and founded on precisely the same assumption” as a method which Kendall employed in 1912, and is, therefore, not a new contribution, while Kraus’s criticism is in substance to the general effect that the method in question is illogical, incorrect and quite unjustifiable either mathematically, physically, or chemically. As the points at issue deal with questions of fundamental importance t o our interpretation of the behavior of strong electrolytes in dilute solution, it seems to the writer justifiable t o discuss here in some further detail the method which he employed in evaluating A,, especially with respect t o those features of i t which have been adversely criticised. THISJOURNAL, 40, 106-158 (1918). 3
Ibid., 40, Ibid., 42,
622
(1918).
I (1920).
endallgsCriticism. Kendall’s criticism, aside from its implication of carelessness on the part of the writer in failing to give him due credit for originating the method, would also imply that the agreement of potassium chloride with the massaction law a t high dilutions, as shown by Weiland’s investigation, was due to the fact that the method 0-C selecting A, was based upon the a priori assumption that within the range covered by the lowest concentrations measured, the mass-action law must be obeyed. Kendall applied his method only to acids, using it as a method for determining the conductivity of the hydrogen ion. He describes his method in the following words:* “The value of K, is found from the conductivity results of a series of dilutions by use of that particular value for the velocity of the hydrogen ion that gives values for
a2c I - a
(= ICE), slowly falling as dih-
tion increases and ultimately approaching (so far as can be perceived within the experimental error) a limiting value.” His method tlius involves the assumption that within the range covered by the data there shall be a series of (io e,, more than 2) values of ICE which are constant within the experimental error. Such constant values do in fact appear in all of the tables (14 to IG, inclusive) which he uses to illustrate the application of his method. There is no suggestion in his paper that he considered his method to be a special case of a more general one which would be applicable also to cases where the observed values of K E could not be made to become even approximately constant with any value of A, which might be selected. This is further borne out by the Pact that when he has to deal with strong electrolytes, Kendall entirely abandons his mcthod and employs a method which implicitly assumes that such electrolytes will not obey the mass-action law over any finite concentration range whatever. Further, in speaking of the behavior of hydrochloric acid, he states that “the values QE
s____
1--c?
certainly do
fall away as dilution increases to a Limiting value KO,but that limiting value is zero,” thus apparently implying that he did not regard the value zero as necessarily inconsistent with the assumptions upon which his method was based. Now a limiting value of zeroa €or K E or an asymtotic (i. e., asymtotic to the ICE axis) approach to some finite limiting value are both directly contradictory to the assumptions upon which the writer’s method is based. Furthermore, his mexhod is entirely applicable to the corrducJ. Chem. Soc., 101, 1291 (1912). To state that the ionization constant of an electrolyte is zero is equivalent to stating that its free energy of ionization is infinite, in other words, that it is a “non etectrolyte ’’ I
2
EXTRAPOLATION OP CONDUCTIVITY
DATA,
xr,
1079
tivity data for a strong electrolyte in regions where there is not the slightest evidence of obedience to the mass-action law with any value of A, which can be chosen. 1111 these 2 fundamental respects the writer’s method differs from that of Kendall, although the 2 methods will obviously outwardly resemble each other whenever the electrolyte to which they are applied actually does obey the mass-action law over a portion of the range covered by the experimental data. T o Kendail is due full credit for developing what seeins to the writer tlie only logical method for determining A, in the case of electrolytes which obey the mass-action law within a portion of the concentration range covered by the measurements, and if the writer erred in failing t o indicate the points of resemblance of his method to that of Kendall for such cases, he is glad of this opportunity to extend his apologies. The fact that ’Xeiland’s success in extending the data on potassium chloride below O.OOQI N yielded conductivity values ,which vary with the concentration in accordance with the mass-action law makes the writer’s method7 when applied to these data, resemble, apparently quite closely, the method of Kendall, since his method applied to such data will yield the same .A, value. A very important difference, between the 2 methods, however, lies in the fact that, if the conductivity values had not been found to vary with the concentration in accordance with the mass-action law, the writer’s method of determining A, would still have been entirely applicable to the data, while Kendall’s method mould not. This can best be illustrated by applying the method to Kohlrausch’s data for potassium chloride which extend only down to o . 0001 N.I Before doing this, however, i t may be well to restate the assumptions upon which the method is based. They are as follows: (I) Potassium chloride will obey the law of mass action over some finite range of concentration, but this range might, of course, be far below any limit which could be reached experimentally. (2) In the ne.ighhorhood of a few ten-thousandths N and below, the behavior of potassium chloride with respect to the mass-action law must be such that whatever the Eagnitude of its deviation from that law may be, this magnitude will not increase (or change its sign) with further dilution, that is, the percentage change of K E with C will not increase as C decreases, after C has become as small as 0.0001or O,OOOZ AT. There is evidently no implication in either of these assumptions that the value of A, selected must be one which causes the deviations from the mass-action I n the writer’s previous paper (p. 1 3 0 ) it was stated that the method could be employed to determine ho with an accuracy of about 0.2% in the case of conductance data which did not extend below 0.0001iV,but this statement was iiot further elaborated because it seemed to .the writer that the applicability of the method to such data was suficieiitly evident from the curves in Fig. 5 of that paper.
1080
EDWARD W. WASFIBURN.
law to disappear gradually in the lower portion of the concentration range covered by the data, in fact as we shall show in a moment, values which might conceivably be assumed to produce this behavior are rejected by the
In order to illustrate this, a portion of Fig. 5 of the preceding paper (Fig. ;1 of .the present paper) lying between the concentrations 0.000I and 0 ~ 0 0 0 3 5AT xi11 be magnified and ine---+ stead of attempting Pig. I . to d r a w s m o o t h curves between points, straight lines will be used. The figure thus obtained is shown herewith (Fig. I ) . In constructing this figure the values of the ordinates of the different curves have been displaced SO as to cause the curves to intersect a t C = 0.00035 N. Applying the above 2 assumptions to this figure it is evident that the value A, = 129.34 is to be rejected and that similarly the value 129.7 (QT thereabouts) is similarly to be rejected, as are all of the values which .* he outside of the limits set by these two. It is evident from this figure tha.t no value can be selected for A, which gives a behavior w e n approximately in accordance with the mass-action law, unless indeed the vaiue 129.14should be so selected on the assumption that the datum for 0.0001 AT is inaccurate. Down to 0.0002 N the value I 29.14 evidently gives a. curve which does nor deviate very rnaskedly from the requirements of the mass-action law and if the point a t 0.0001 N were rejected (and such rejection might indeed have been justified previous t o Weilniid’s work, on the grounds that a t this low concentration small errors in the conductivity or In the method of applying the water correction would have a very large influence on the computed value of K E ) ,the applicatiori of Kendall’s method to the data for potassium chloride might point to 129.14as the most probable value for A,. This value would, however, of course berejected by the writer’s method, which method does indeed not directly determine the value of A, a t all, but merely places an upper and lower limit on it. The method is thus not a method of selection but rather a criterion €or rejecti0n.l ( N o t e by James Kendall).-“I
am entirely in agreement with the differentiation
EXTRAPOLATION OP CONDUCTIVITY
DATA.
Ir.
I081
Kraus’s Criticisms. The first part of ICraus’s paper is devoted t o a mathematical analysis of the K E - C curve and this analysis is, in the main, accurate for the aswmptions which he makes. In the interests of exactness the following points may be noted, however. The z sentences immediately following hi
