Sept., 1959 paper contains the results of the electrical conductivity determinations. Experimental Details The solid solutions were prepared by fusing together high purity salts in a platinum crucible. The melt was strongly chilled so as to solidify the material rapidly. The solid was then ground to a fine powder and remelted in platinum. U x on slow cooling of this melt large single crystals formed. suitable crystal was removed, ground to a regular shape and then its dimensions were measured with a micrometer. For the conductivit measurements the sample was clamped between a pair of aLminum rods through which connection was made with the rest of the measuring circuit. Contact resistance was minimized by evaporating a gold film onto the faces of the crystals which touched the aluminum bars. T o protect the sample from possible contamination by the aluminum, platinum foil was inserted between the rods and the sample. The measuring circuit employed was similar in principle to that used by Mapother, Crooks and Maurer.lo A mechanical switching arrangement supplied a d.c. ulse to the sample of approximately 0.1 sec. duration. $he conductivity was measured by observing the deflection of a ballistic galvanometer in the circuit. The procedure followed was to observe first the deflection when the sample was pulsed. Then the sample was replaced in the circuit by a precision high resistance variable resistor. The resistor was adjusted until the deflection matched that produced when the sample was in the circuit. This was taken to be the resistance of the sample. The resistivity, computed from the measured resistance and known geometry of the sample, was found to be independent of the direction of the current and of the amount of charge transported through the sample. With each composition studied the procedure followed was first to increase the temperature slowly to 500 to 550' and then maintain a constant temperature until equilibrium was established. Resistance of the sample was measured a t intervals of about hr. until a time-independent conductivity was indicated. Then the temperature was reduced 15 to 20" and the procedure repeated.
NOTES
1537
tivities must await a direct determination of their mobility, by a suitable tracer diffusion experiment or the like. TABLE I THE ELECTRICAL CONDUCTIVITIES OF KC1-KBr SOLUTIONS Temp., OC.
400 420 440 460 480 500
520 540
Conductivity, ohm-' orn.-l X 108 20 mole 50 mole % KBr % KBr Pure 80 mole 50 mole KBr yo KC1 % KC1
Pure
KCI
0.0322 0.0122 ,0449 0204 ,0617 ,0327 .OS91 .0519 ,0922 ,149 ,241 ,178 ,339 ,382 ,603 .621
VALUESOF B
I
0,00634 ,0113 ,0193 ,0337 ,0653 ,122 ,222 ,391
TABLE I1 EQUATION u =
80 mole % KBr 20 % mole KCI
0.00513 ,0145 ,0248 ,0417 ,0804
,160 ,276 ,485
-
uo EXP( B / T ) B X 10-8 Temp. below kink Temp. above kink This work Jost This work Jost
IN THE
KCI KBr 20 mole yo KBr 50 mole % ' KBr 80 mole % ' KBr
0,0145 ,0237 ,0363 .0552 ,0955 ,172 ,304 ,525
SOLID
14 19 17 19 19
23.5 23 , .
.. ..
8 13 11 14
11.5 11.5
14
..
.. ,
I
Plots of the data indicate an exponential dependence of conductivity on temperature of the form u = u,,exp(-B/T). I n Table I1 are listed values of B for the five compositions studied together with values taken from the compilation by Jost" for the pure salts, data being given for the Results and Discussion of Results regions above and below the kink. The values of Measurements were made on the two pure salts B for KBr are in reasonable agreement with those and three solutions. The data for even tempera- tabulated by Jost, the differences being about what tures are given in Table I. The temperature range one might reasonably expect from independent, covered was extended downward to the limit of determinations. The discrepancies in the case of the experimental procedure in use since the main KC1 are somewhat puzzling. They are considerinterest in the work was to obtain information con- ably larger than had been anticipated. The concerning the vacancy population a t or near room sistency of the conductivity data obtained in the temperature. No attempts were made to extend present study for KC1 is such that one would have the measurements up toward the vicinity of the expected a reliable value for B. At present the melting point. When the raw data are plotted, cause of the deviations is not known. It is to be they are found to exhibit the usual dependencell noted, however, that despite the discrepancy in of conductivity on temperature, a kink occurring slope the actual measured conductivities are in in the plot with the steeper slope on the high satisfactory agreement with literature values. temperature side of the kink. The kinks are found The values listed for KC1 in Table I fall between a t temperatures ranging froin 450 to 475". The data in Table I show that the conductivity the values found in the careful studies of Phipps of the solutions in all cases is comparable in mag- and Partridge12and Lehfeldt. l3 (12) T. E. Phipps and E. D.Partridge. J . Am. Chem. S O C . 51, , 1331 nitude with that for the pure components. Such (1929). differences as exist easily could be attributed to n (13) W. Lehfeldt, Z . Physik, 85, 717 (1933). varying mobility rather than a changing number of carriers. Thus, the conductivity measurements ACIDS AND BASES. SI. REACTIONS OP support the conclusioiis derived from the density redetermination. They give no indication of ail BORATES AND BORON ACETATE AS LEWIS ACIDS' abnormal population of vacancies. It must be realized, however, that establishment of the BY SAVERIO ZUFFANTI,RICHARD T. OLIVERA N D carrier concentration from the measured conducW. F. LUDER (9) Thanks are due Mr. C. H. T. Wilkens of the Mellon Institute for applying the gold coating. (10) D.Mapother, H.N. Crooks and R. Marirer. J . Chem. P h y s . , 18, 1231 (1950). (11) W.Joat, "Diffusion in Solids, Liquids and Gases." Academic Press. Ino., New York, N. Y.,1952, p. 179.
Cuiitribution f r o m the Department o/ Chemistry, Northeastem University, Boston, Mass. Received February 67,1969
In the preceding paper of this series2 evidence was presented that both stannous chloride and
1538
NOTES
antimony tribromide behave as secondary acids3 toward piperidine in dimethglformamide. Continuing this investigation of the manlier in which various substances behave as acids according to the electronic theory of acids and bases, the work reported in this paper provides examples of the first three of Lewis’ phenomenological criteria. Also, in the behavior of boron acetate an interesting contrast with that of antimony tribromide, as reported in the preceding paper,2 has been noted. Experimental All the boron compounds (as listed in Table I ) were supplied at no cost by the American Potash & Chemical Corporation, Los Angeles 54, California. Further purification of these compounds was unnecessary for the purposes of this investigation. However, because they are all reactive toward moisture they were opened and handled in a large dry-box filled with nitrogen. (a) Effect of Borates and Boron Acetate on Indicators.The first of the Lewis criteria tested was the effect of the compounds upon more than twenty indicators in benzonitrile, using piperidine as the base to establish the basic color of the indicator as described in a previous paper.4 The boron compounds that were soluble in benzonitrile gave typically acid colors with these indicators. MoRt of the colors were the same as those observed in water solutions of hydrogen acids. These experiments were repeated with six of the indicators using methanol as the solvent. All of the boron compounds were soluble in methanol, and exhibited the acid colors of the indicators. In these experiments the piperidine and the solvents were dried over suitable drying agents, refluxed and distilled. The solutions were made up in the dry-box. (b) Neutralization and Displacement.-The other two criteria considered, neutralizat,ion and displacement reactions, were investigated by letting the boron compounds react in methanol with the base, sodium methoxide, according to the procedure described by Fritz.6 Although several indicators, including thymol blue and azo violet, were tried, phenolphthalein gave the best reproducibility. Usually, at least four runs were made which checked within three parts per thousand. The results are summarized in Table I.
Results The second column of Table I gives the molarity of each acid solution calculated from the weight of each sample dissolved in methanol. The third column gives the normality of each acid solution as obtained in the titrations with sodium methoxide. Considering that the acids were used as obtained without further purification, the agreement is sufficiently close to indicate that each molecule of borate is reacting with one methoxide ion. Thus these reactions illustrate the first of the Lewis criteria, the neutralization of a primnry acid. (1) Abstracted from a thesis submitted by Richard T. Oliver to the faculty of Northeastern University in partial fulfillment of the requirements for the M.S. degree, June, 1955. (2) W. F. Luder and L. S. Hamilton, THISJOURNAL, 60, 1470 (1958). (3) W. F. Luder and S. Zuffsnti, “The Electronic Theory of Acids and Bases,” John Wiley and Sons, Inc., New York. N. Y . , 1946. (4) R. B. Rice, S. Zuffanti and W. F. Luder, Anal. Chem., 84, 1022 (1952). (5) J. S. Fritz, “Acid-Base Titrations in Nonaqueous Solvents,” G.Frederick Smith Chemical Co., Columbus. Ohio, 1952.
Vol. 63
TABLE I NEUTRALIZATION AND DISPLACEMENT REACTIONS OF BORON COMPOUNDS AS ACIDS REACTING WITH SODIUM METHOXIDE IN METHANOL USING PHENOLPHTHALEIN AS THE INDICATOR Acid
Tri-( n-dodecyl) borate Tri-(methylamyl) borate Tri-( tetrahydrofurfuryl) borate Tri-( 2-ethylhexyl) borate Tri-(n-butyl) borate Boron acetate
Equiv.
llolarity by wt.
Normality by titration
0.0912 ,00970
0.0909 ,01020
1 1
.lo44 .lo70 ,1214 .lo41
.lo22 .lo31 .1184
1 1 1 4
.4008
per
mole
According to the theory the base donates a share in a lone pair of electrons to the vacant orbital in the acid, forming a coordinate covalent bond between the two D R
R
R-A I
+ (:O-l-H)-’
R (primary acid)
H
-1
--+(R-i:O-i-H)
(base)
However, the last pair of concentration values in Table I shows that one molecule of boron acetate reacts with four methoxide ions. This behavior apparently involves the third of the Lewis criteria, displacement. The acetate ion is a much weaker base than the methoxide ion and the other radicals in the borates. Therefore, the methoxide ion besides adding to the vacant orbital in the boron atom can also displace the three acetate ions6 0
II
B(O-C-CHJ3
+ 4(OCH3)-’ + B(OCH,),-1
0
+ 3(0-
II
-CH3)-‘
The contrast between this reaction and one reported in the preceding paper2 SbBrs
+ 3CsHI1N4 Sb(CsH11N)a+3+ 3Br-1
is readily explained by the Lewis theory. Unlike the boron compounds, antimony bromide docs not have a vacant orbital but does have a lone p:Lir of electrons. Therefore, it can act only as n secondary acid in reactions with bases that displace a maximum of three bromide ions. The second of the Lewis criteria illustrated by this investigation, as mentioned above, was the observation of typically acid colors produced by the effect of the boron compounds on a large number of indicators. (6) Two points may be of interest. First, no t h e - l a g was noted in this titration (nor in the others). Second, the acetate ion (for examole, in sodium acetate) is not a strong enough bsse to give phsnolphthalein its basic. color in methanol.
1
C
