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Vol. 63
valence of Ba++ ions. Carr'O has reported that appreciable amounts of Mg++ and Ca++ are bound to pepsin a t p H 7.5. (10) C. W. Carr and K. R. Woods, Arch. Biochem. Biophys., 6 0 , 1 (1955); C. W. Carr,ibid.,46, 424 (1953).
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ELECTRICAL CONDUCTIVITIES OF KClKBr SOLID SOLUTIONS1s2
.I4
BYJOHN E. AMBROSEAND W. E. WALLACE
w. Fig. 2.-The data of Fig. 1 plotted according to electrostatic theory; see equations 1 and 2 in text for significance of notations.
Contribution N o . 1039 from the Departnkent of Chemistry, University of Pittsburgh, Pittsburgh 18, Penna. Received April 16, 1969
In 1956 when the present work was initiated there appeared to be fairly convincing evidence to indiWhen Z was evaluated by the application of equation 1, a value of -15 was obtained from the cate that vacancies in KC1-KBr solid solutions slope of the straight line. That this value is reason- were abnormally abundant. The evidence for able may be demonstrated by making use of the this derived from a comparison3 of densities measanalytical data of Van Vunakis and H e r r i ~ t t . ~ured by Tanimann and Krings4 with values comIf we assume that all of the ionizable groups of puted from the unit cell determinations of Oberlies.6 pepsin are charged a t p H 6.65, then the net charge The former were found to be smaller by as much as due to hydrogen ion equilibria, is 31, since there are 2% for some compositions, indicating a vacancy approximately 37 carboxyl groups and 6 basic concentration for the solutions roughly 100 times amino acids (as well as 1 terminal carboxyl and that of the pure components. If the vacancies were indeed this abundant, it amino group). This figure should be reduced by appeared that their presence should affect physical the number of carboxyl groups not titrated a t this p H in native pepsin. I n addition Cam8 has shown properties of the system other than the density. that about 5 Na+ ions are bound to pepsin a t pH I n particular, the solutions should exhibit good 7.5.9 The combined influence of both of these electrical conductivity compared with the pure factors should reduce the net charge to below 20. salts since conductivity in the alkali halides occurs Due to a number of approximations that are made by a motion of vacancies. Moreover, such a large when equation 1 is used in this way, this kind of population of vacancies should substantially augexperiment cannot be expected to yield quantita- ment the entropy of the system. The existence of tive parameters. Nevertheless, the slope does ap- an excess entropy in the KCI-KBr system was conpear to give a reasonable value for the charge firmed6 by entropy of formation measurements considering the limitations of both theory and ex- in this Laboratory several years ago. The entropies of formation were found to be greatly in excess periment. of that expected from theory,7 even exceeding the The relatively small dependence of pH on NaC1 entropy of random mixing. However, when an concentration found with denatured pepsin reveals attempt6 was made to account quantitatively for the marked decrease in the electrostatic free en- the excess entropy in terms of the presumed ergy which results from the disorganization of the vacancy concentration, it was unsuccessful. This compact structure of native pepsin. Since Z is suggested that the extra entropy stemmed from larger in denatured pepsin than in the native en- another source and furthermore cast doubt on the zyme a t pH 6.65,4 then w must be smaller and con- validity of the data of Tammann and Krings and sequently R (effective) is considerably greater. Oberlies. According1.y it seemed desirable t o The individual charged groups, therefore, now be- redetermine the densities and unit cell dimensions have as if almost isolated from each other in de- for KCl-KBr solid solutions and a t the same time natured pepsin. This behavior is in accord with to begin measurements of their electrical conductivithe large configurational changes that occur in ties. Results of the redeterminations, which were pepsin concurrently with denaturation. quickly concluded and have already been pubEquation 1 does not strictly apply to the BaC12 lished,* were a t variance with the results of the data either, since Ba++ is also bound. A slope of 10 earlier work in that they did not indicate an ab\vas computed from the linear relationship between normal population of vacancies. The present w iuid p H . The data (Fig. 2) f:dl 011 :Lline covering ( I ) This work was assisted by the U.S.Atomic Energy Coniniissiun :t greater i-uiige of ionic strength t h m observed with (2) From a thesis submitted by John E. Ambrose t o the Graduate NaCI. The smaller slope fouiid with BaClz is pre- Faculty of the University of Pittsburgh in partial fulfillment of thc sumably due to stronger binding and the larger requirements for the M.S. degree. (3) W. E. Wallace a n d R. A. Flinn, Natura, 7% 681 (1958). d i d a t the liigli clectrical fields existing when the iirotein charge is large and but little salt is present. (7) H. Van Vunakis and R. hI. Heiriott, Biochim. Biophys. &la, 23, GOO (1957). ( 8 ) C. W. Carr, A w h . Biochem. Biophus., 6 2 , 470 (1956). (9) I t is not clear whether the pepsin C a l i eiuployed a t p H 7.5 i m s native or denatured. At vevy low ionic strengtlls pepsin can be quite stable a t this pH.
(4) G. Tammann and W. Krings, 2. anorg. Chem., 130, 229 (1923). (5) F.Oberlies, Ann. Physik, 87. 238 (1928). (6) W. H. McCoy a n d W. E. Wallace, J . Am. Chem. Soc., 78, 5995
(1956).
(7) J. A. Wasrtstjerna, SOC.Sci. Fennica, Cornmentaliones Phy8.Math. [XV], 3 , 1 (1949); V. Hovi, {bid., [XV] 12. 1 (1950). ( 8 ) J. S. Wollain a n d W. E. Wallace, THIS JOURNAL, 60, 1651 (1956).
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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. SOC.,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. Phys., 18, 1231 (1950). (11) W.Joat, "Diffusion in Solids, Liquids and Gases." Academic Press. Ino., New York, N. Y.,1952, p. 179.
Cuiitribution from 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
