April 20, 1054
THESYSTEM POTASSIUM CIILOBIDE-SODIUM CjHLowm IN WATER
ment of high stability in the resulting chelate. Acknowledgment.-The authors are indebted to the U. S. Navy Office of Naval Research for sup-
2157
port of this research project under Coiitract Nonr596(00). WORCESTER, MASS.
[CONTRIBUTION FROM THE CHEMISTRY DEPARTMENT, UNIVERSITY
O F TORONTO]
The Determination of the Adjusted Indicator Concentration behind a Moving Boundary in Dilute Solution; the System Potassium Chloride-Sodium Chloride in Water at 25" BY D. R.MUIR,J. R. GRAHAM AND A. R. GORDON RECEIVEDDECEMBER 7 , 1953
A method is described for determiuing the adjusted indicator concentration behind a moving boundary in dilute sulutiotis. T o test the procedure, the system KCl-XaCl was investigated. It is shown t h a t the Kohlrausch ratio can be determilied with a precision comparable with t h a t obtainable in moving boundary determinatiotis of transference numbers, and t h a t the ratio, measured over a range of concentration, can be extrapolated unambiguously t o zero concentration. Prom the limiting ratio and the limiting equivalent conductances of leading and indicator salts, limiting ionic conductances may be obtained a t once. Thus limitirig ionic conductances can be determined in any solvent in which precise conductance measurements are possible, without carrying out any transference measurements in the ordinary sense of the term. Possible applications of the method are discussed.
I n 1934, Hartley, Drew and Collie' reported a method for measuring the transference number of a slow ion by determining the adjusted indicator concentration of that ion behind a boundary for which the transference number of the leading fast ion was known. The basis for the procedure was the familiar Kohlrausch2 condition for a stable two salt boundary of the type MA/hliA CJC = t i / t = r
(1)
dipole interaction unobtainable from the equivalent conductance data, and since the procedure outlined above would eliminate the need for transference measurements in the ordinary sense of the term, it seemed desirable to investigate this possibility. The system chosen for investigation was KC1/ NaCl in aqueous solution a t 25". The reasons for this choice were first, that for both salts the transference numbers were well e ~ t a b l i s h e d , ~and - ~ second, that owing to the relatively rapid change of the transference number for NaCl with concentration as compared with that for KC1, this system provided a good test of any extrapolation procedure. Experimental
where C and C i are the concentrations of the leading and indicator ions M and M i , respectively, t and ti are the corresponding transference numbers, and r is the Kohlrausch ratio. As originally developed, the method was not capable of high precision, but i t did permit approximate determinaA series of tests with the cells previously employed (see tions of the transference numbers of certain paraf- Fig. 2 of ref. 6 ) and with various modifications of them, fin-chain salts.3 Years later, and using modern showed that the desired precision in the measurement of the techniques, analogous measurements were carried adjusted indicator concentration (0.02'%) could not be attained, but partly by accident it was found that a much out by Longsworth4 to test the Dole theory5 of simpler technique could, with care, provide data of the acpolysalt boundaries, but on the whole the possi- curacy desired. Essentially the cell is a conventional fallbility of obtaining reasonably precise transference ing boundary cell of the type used for many years in this data in this way has received little attention. I n a Laboratory with a type VI11 shearing mechanism (see Fig. 1 of ref. 6). It differs only in that the channel is somewhat recent papera dealing with adjustment of indicator longer (approximately 30 cm.) than in earlier cells, and that concentration during moving boundary measure- there is an additional shearing stopcock a t the base of thc ments, it was shown that with the type of cell there channel. As in earlier cells, the channel is 2.5 mm. internal employed, i t was possible to determine the indica- diameter and cadmium and silver-silver chloride electrodes serve as anode and cathode. T o fill, KC1 solution is forced tor concentration behind the boundary within a upward into the channel until it rises just above the top of part in 500 or so; this suggested that if the preci- the upper shearing stopcock, which is then closed. The sion of such measurements could be raised to a level reservoir above the stopcock is then repeatedly flushed with comparable with that obtainable in the usual mov- the NaCl solution; after filling, the cell is brought to temperature equilibrium in a bath regulated to f 0 . 0 1 " , thc ing boundary determination, and that if the Kohl- junction is formed a t the top of the channel, and the current rausch ratio, measured over a range of concentra- is started. It should be noted that only an approximate tions, could be extrapolated to infinite dilution, the knowledge of the current and the time of electrolysis is necesresulting limiting ratio could be combined with the sary. Fifteen or twenty minutes after the time calculated for the boundary t o pass the lower stopcock, the current corresponding limiting equivalent conductances t o is stopped and both cocks closed, thus isolating a column of yield limiting ionic conductances. Since limiting indicator solution. For a system for which the transferionic conductances provide information as to ion- ence number of the leading ion was not known, a preliminary series of measurements would obviously be required t o de(1) G. s. Hartley. E.Drew and B. Collie. T Y Q ~Faraday S. Soc., 30, termine the length of electrolysis necessary for the concen-
648 (1934). (2) F. Kohlrausch, Ann. Physdk. Chsn., 61, 209 (1897). (3) G. S. Hartley, B.Collie and C. S. Samis. T m n s . Faraday Soc., 31, 795 (1936). (4) L. G . Longsworth, THIS J O U R N A L67, , 1109 (1945). ( 8 ) V. P. Dole, i b i d . , 67, 1119 (1945). (0) A. R. Gordon a n d R . L. K a y , J. Chem. P h y s . , % l131 , (1953).
tration of the solution in the channel to become independent of further passage of current. (7) L. G. Longsworth, THIS J O U R N A L , 64, 2741 (1932). (8) R. W.Allgood. D. J. LeRoy a n d A. R. Gordon, J . Chem. Phys., 8 , 418 (1940). (9) R. W. Allgood and A. R. Gordon, ibicl.. 10, 124 (1042).
The solution above the upper stopcock is then removed under suction with a fine pipet, the stopcock is opened, and the solution in the channel down t o a level 2 cm. below the stopcock is removed under suction with a capillary pipet. A second capillary pipet, with a tip 30 cm. long and with a reservoir of 1-cc. capacity, is nest inserted well into the channel; the contents of the channel are then removed under suction. It should be rioted t h a t the sample of indicator solution removed is only that part between levels 2 cm. below the initial position of the meniscus in the channel and 2 cm. above the lower stopcock. The pipet is then withdrawn, the outside of the tip dried with Kleenes and, after extruding a few drops, the solution is introduced into a small conductance cell of approximately 0.8-cc. capacity. This cell has bright platinum electrodes 8 m m . in diameter, compktely filling the ends of the cell and sealed in the glass; the electrode spacing is 9 mm. Obviously in work with a volatile solvent, before employing the procedure described above, both sampling pipet and conductance cell would be flushed with a saturated atmosphere of the solvent to minimize evaporation losses. The conductance cell is then placed in a bath a t 25.000 f 0.002", and the apparent resistance determined on an a.c. bridge with n'agner ground a t 1000 C.P.S. Since the indicator solution might have its resistance altered by the handling procedure, blank esperiments were carried out a t each concentration. The transference cell was completely filled with a IiaC1 solution of the appropriate concentration, current was passed for a time corresponding to the number of faradays required t o move the boundary from end to end of the channel, a sample was withdrawn as described, and its resistance determined; this was compared with the resistance of the same solution when the sample was transferred directly from the solution flask into the conductance cell. At the lowest NaCl concentration studied, 0.0016 N , the resulting blank correction amounted t o 20 ohms on a measured resistance of approximately 6000 ohms; it was however independent of current, was remarkably reproducible for a given concentration, and accordingly was applied before interpreting apparent resistance in terms of concentration. This increase in conductance could be due to contamination either from the sampling pipet or from the transference cell itself. T o distinguish the two effects for reasons discussed below, samples were transferred from the solution flask t o the conductance cell by pipet, and ( t o take the measurements a t 0.0016 N NaCl as an example) it was found that one-half the decrease in resistance was due to the pipet; the remainder must then be due to contamination in the transference cell, ; . e . , the effective solvent conductance in greater than the the actual measurements was 3.3 X measured conductance of the solvent used in making up the solution. Moreover, it was found t h a t this increase was approximately independent of NaCl concentration, so that in computing the solvent correction, the specific conductance of the solvent was taken as 1 . 1 0 X (see below). The cell was calibrated for each run by measuring the resistance of sodium chloride solutions whose known concentrations were 1 or 2 % greater and less than t h a t of the indicator solution. For the narrow concentration ranges involved, calculation showed that linear interpolation of the reciprocal of the resistance against concentration fixcd the concentration of the unknown solution within experimental precision-0.01% in the apparent resistance or better. In this way, since all measurements were effected a t the same frequency and a t the same input, systematic errors in the interpretat ion of the conductance measurements in terms of concentration were eliminated as completely as possible. One word of caution is perhaps desirable in connection with such miniature conductance cells. (1) In our experience, a cell should stand for a t least three months after manufacture if consistent, reproducible results are to be attained; this is probably associated with the release of slight strains in the glass, which are particularly serious in such a small cell in view of the method of mounting the electrodes. ( 2 ) The cell should be protected as conipletely as possible against changes in temperature; a cell left inadvertently in bright sunlight for an hour, was useless for several days as a result. ( 3 ) One cell, after giving escellent service for several months, suddenly gave highly erratic results; after standing for several months, it again performed satisfactorily. For this reason, it is advisable to have a number of cells of different vint;igv i n rrier\-c., i l l order to nvoid lois of t iiiie and tciiiper.
The solutions were prepared as previously described The conductivity water, which was equilibrated with atmospheric ( 2 0 2 , had a specific conductance of 7.5 t o 8.0 X 10-7. .*m0
Results
A s an example of the results obtained, the data from a series of runs with 0.002 N KC1 are suminarized in Table I. I n all, the concentration of the leading solution differed only by a fraction of a per cent. from this value, and for this reason, the quantity tabulated is Ci/C, the ratio of the measured indicator concentration to that of the leading solution, since for the concentration range involved this is independent of C. Table Ia shows the results of preliminary measurements such as would be required with a system for which 110 transference data were available. In the first series a deliberately bad choice of Cf,the initial indicator concentration, was made-roughly onehalf the Kohlrausch value; even so, and in spite of the fact that the measured Ci/C are definitely current dependent, an adjusted concentration in the neighborhood of 0.001G N is indicated. In the second series, with Cp = 0.0014 N , the current dependence is less marked, and the ratios are larger, while in the measurements of Table Ib, with Cp/C between 0.79 and O.SO, the observed Ci/C are independent of current-a criterion which must be satisfied if the true adjusted indicator concentration is being determined. TABLE Ia PRELIMIXARY VALUESOF Ci/C
cp/c= I , camp.
60
C,!C
90
0.002 S KCl
Cp/C I , wmp.
GO 80
0,8021 .7974 .7925
120
FOR
0.40
110 120
= 0.70
c,/c 0.8052 . so12 ,8032 .502.9
TABLE Ib Ci/C for 0.002 7\2 KCl, CP/C = 0.79-0.80 I , camp. Ci/C
50 0.8063
70 0.8057 ,8066
85 0.8060 ,8063 ,8059 ,8089
100 0.8053 .SO55
115 0.8066 .SO62 ,8061
1-10 0.8057 ,8059
It is perhaps significant in both series of Table I a that Ci/C is linear in the current, and extrapolation suggests that the correct value would be obtained a t a current of approximately 35 pamp. for C y / C = 0.4, and of 50 pamp. for Cp/C = 0.7; hence i t is possible that a t still lower currents correct current-independent values of Ci/C would result. The inordinate length of time required for such measurements makes them impracticable. Gordon and Kay6 showed that as long as there was a layer of indicator solution of the correct Kohlrausch concentration in contact with the boundary, correct values of the transference number of the leading ion were obtained froin the observed boundary movement, even if the whole column of indicator solution above the boundary were not a t this concentration; thus an erroneous measured value of Ci/C does not necessarily imply abnormal boundary movement. IYe believe the most probable explanation for the results of Table I n is that con.iecti.ie stirring, due to Joule heating, tends to dil-
April 20, 1954
T H E SYSTEM POTASSIUM
CHLORIDE-SODIUhI CHLORIDE IN WATER
2159
ute the column of solution in the channel with the After dividing by CVf = t , and rearranging, there weaker solution in the reservoir above, the effect results being more pronounced the higher the current. r = t i / t = (Ci/C - x / t ) / ( l - X ) (4) For higher KC1 concentrations, the requirement that Cp be near the Kohlrausch value if true, cur- For 0.002 N KC1, t i / t is thus 0.0022 less than the rent-independent values of C i / C are to be obtained, observed Ci/C. The resulting tilt are given in the fifth line of is not so stringent; for example, with 0.005 N KC1, current-independent values of C i / C for a current Table 11; the sixth line gives the transference num~ , ~the sevvariation of 1007, are obtained with Cp 77, below bers for K + in the leading s o l ~ t i o n ,and enth line the transference numbers for h’af, comthe Kohlrausch concentration. Table I1 summarizes the results for four KC1 con- puted from these and the values of r. The table centrations. The second line gives the number of also gives for comparison the values of t i obtained independent measurements, the third the current from moving boundary measurements with NaCl and i t is a t once evident that the agreerange, and the fourth the mean observed value of Ci/ sol~tions,~~S C; the number in brackets indicates, in units of ment is excellent. Thus, in any solvent for which the fourth decimal place, the mean absolute devia- the transference numbers for one salt are available, tion of the individual results from the average as the transference numbers for any other salt possessing a common ion can be determined readily to a printed. precision comparable with that obtaining in the TABLE I1 original transference measurements. While this THE KOHLRAUSCII RATIOAS A FCNCTIOX OP KC1 Costechnique was developed primarily for use in nonCENTRATIOS aqueous solvents, i t nevertheless could prove useC, equiv./l. 0,002 0,005 0.010 0,020 ful in aqueous solution with electrolytes not easily 14 10 6 12 No. meas. dealt with by the moving boundary technique; the 0.05-0.14 0.22-0.42 0.48-0.74 0.90-1.00 I, milliamp. iodates, cadmium salts and the soaps are obvious 0 . 8 0 2 6 (3) 0.8003 ( 2 ) 0.7976 (3) Ci/C 0.8060 (3) examples. 0.8038 0.8017 ti/t = Y 0,7999 0.7974 ,4904 ,4903 ,4902 1 ,4901 A more important and more general problem ,3931 ,3921 ,3908 tl. eq. 1 ,3942 arises, however, in cases where no transference data ,3943 3932 ,3922 li, m.b. 3907 per se are available. A s a first step, r is plotted ,8076 .8076 Y‘ ,8083 ,8092 against CL/t; the plot is definitely curved, but a Discussion “best” straight line, drawn through the three lowTo obtain the Kohlrausch ratio r = ti/t from the est points gives a provisional limiting value of the observed Ci/C, a “solvent” correction must be ap- Kohlrausch ratio, ro, of 0.8067. If An and A: are plied. If the specific conductance of the leading the limiting equivalent conductances of KC1 and and indicator salts be K and ~ i and , that of the sol- NaC1, 149.85 and 126.45, respectively,1° i t is easy vent be K ~ the , current, corrected for solvent conduct- to show that the limiting transference number for ance in the indicator solution, will differ by a fac- K + is given by tor (1 - x ) from the corresponding current in the t o = (ao - A ’ ) / ( A ~ - rd;) (5) leading solution, where x is defined by The resulting provisional values of t n and tP are 1 - x = 1 - KJKI + K*/K (2) 0.4892 and 0.3946. As a second approximation, the limiting law for For example, for C = 0.002 N , Ci = 0.001612 N , K and Ki are 291.32 X and 198.32 X 10-6. re- transference numbers is employed7 spectively,l0 and for K~ = 1.10 X x will be t = t o - aCV2 (6) 0.001s. where a = (1 2 t “ ) u / h U and u = 80.0‘3 for aqueous Consider a boundary nioving in a channel, bounded by fixed reference planes enclosing the solutions a t 25”. In the corresponding expression boundary. For the passage of 1 net faraday of for ti, to, An and C are replaced by tP, LIPand Ci = rC. charge (the charge transporting the K + and C1- ions If one neglects second-order terms, it is a t once eviin the leading solution) the boundary will move dent that the quantity through a volume Vi, and CVf will be equal to t , r { 1 - (../to - air’/2/t:)C1/2} 5 r,’ (7) the transference number of K + in the KC1 solution. In this interval (from conservation) 1 equivalent of should approach ro with decreasing C. This quanC1- will cross the boundary into the KaC1 solution, tity, in which a and a i are computed with the proand (1 - x ) (1 - ti) equivalents C1- will pass up- visional values of t n and tP given above, is entered in ward througb the upper reference plane. Hence, if the last line of Table 11, and is plotted in Fig. 1. the boundary is nioving in a steady state, 1 - (1 - Linear extrapolation gives ro = 0.8075, which may be compared with the value 0.8077, computed from .Y) (1 - ti) equivalents C1- must be contained in the volume Vf of indicator solution formed behind the the limiting transference numbers7-9 for KC1 and h’aC1, &., 0.4905 and 0.3962. The resulting t o and boundary, and, for electrical neutrality t?, computed by eq. 5 , are 0.4902 and 0.3958, and cir; = 1 - (1 - X ) ( l - ti) (3) calculation shows that a further extrapolation, (10) For self consistency, t h e equivalent and ionic conductances using these values, is unnecessary. The correused are those of Benson and Gordon (J.Chem. Phys., 11, 473 (1945)). sponding limiting conductances are 73.48, 30.05 See also Shedlovsky, Brown and hlacInnes ( T r a n s . Electrochem. Soc., 66,165 (1934)) and H. S. Harned and B. B. Owen “The Physical Chemistry of Electrolytic Solutions,” 2nd Edition, Reinhold Publ. Corp., S e w York, N. Y . , 1950, p. 590.
(11) In t h e case of a solvent where n o transference d a t a are available, a preliminary estimate of t can be made by t h e approximation prm cedure discussed below.
and 76.39 for K+, N a + and C1-, respectively; the values obtained from the extrapolated transference datal0are 73.50, 50.10 and 76.35.
relatively small difference between .ioand A:, with a resulting limiting Kohlrausch ratio not cliff ering greatly from unity. Thus to attain as high a numerical precision as possible in the ionic quantities, 0.810 I leading and indicator ions should have as large :i difference in ionic conductance as possible, and this should be borne in mind in selecting the electrolytes for study in any new solvent. I t should also be noted that while the extrapolation procedure outlined above is probably adequate 0.800 for strong electrolytes, the extrapolation, if ion pair 0 0.01 0.02 formation is appreciable, would probably require c. the use of ionic rather than stoichiometric concenFig. 1.-Thc qiiaitity 1'" AS a function of KCI coticcritra- trations in eq. 6 and in the analog of eq. 7. We tion; the radii of the circles correspond to the apparent believe, however, that these results show that liinitprecision of the measurements. ing ionic conductances can be determined with reaThe results obtained here €or the liiniting tram- sonable precision for any solvent in which precise ference numbers and ionic conductances illustrate conductance measurements are possible. In conclusion, we wish to express our thanks to one restriction on this method. Although the extrapolated Y O differs from that computed from the hlr. R. H. Chappell for constructing the conductlimiting transference data by no more than the ance cells, and to the National Research Council of numerical precision of the latter (a part in 4000) Canada for a grant in aid of this research and for the ionic conductances deviate by a part in 1800 for the award to D.R.M. of a studentship and a fellowthe faster ions, and by a part in 1000 for the slow- ship. est. Inspection of eq. 5 shows that this is due to the TORONTO, O S T A R I O , CANADA
r
t l
[CONTRIDUTIOS FROM THE DEPAR.TMEMT OF
CHEMISTRY, THEUNIVERSITY
OF
TEXAS]
The Inhibition of Urease by Various Metal Ions BY
1 ~ 1 L L 1 . 4 XH.
R.
SHA\\V
RECEIVED J U N E 17, 1953 Data 011 the relative toxicity of metal ions toward the enzyme urease have been collected from the literature. I t has been found possible to arrange the common metal ions in a toxicity sequence. Correlation of toxicity with various properties of the metal ions is discussed and illustrated on the basis of a model mechanism.
Introduction The enzyme urease is highly sensitive to trace quantities of metal ions. Different metals exhibit quite different behavior in their ability to act as enzyme inhibitors. I n the case of urease, for example, the silver ion1V2is an extremely efficient inhibitor, while the manganous ion is relatively very weak.3 A search of the literature has revealed that enough data are now available to order the common metal ions in a tentative sequence of relative inhibitory efficiency. It is the purpose of this investigation: to summarize the available data in such a sequence; to define a quantitative functional measure of inhibitory efficiency; and to correlate this quantity, if possible, with soine fundamental propcrty of the metals. Mathematical Development I t was demonstrated in a previous communication4 that the inhibition index, for a first-ordrr Michaelis-Mcnten system, was given by the equation ___ ~
( I ) J . B. Surnner and K , LIyrback, %. fihysioi. C'ilcm., 189, 218 (1930). ( 2 ) J . F. Ambrose, G. B. Kistiakowaky a n d A. G . Kridl, THIS J O U R N A L , 73, 1232 (1951). (3) A . L. Dounce. National Nuclear Energy Series, Div. VI. Vol. 1, hIcCrarv-Hill Book Co.. Inc., New York, N . Y . . 1010, pp. 839-848. (4) G. €3. Kistiakuwsky a n d W. H. R . Shaw, HIS J O U R N A L , 7 6 ,
GG (1Y.53).
S is the substrate concentration, Vu is the uninhibited rate of urea hydrolysis by urease and Vi is the inhibited rate,
K , is Michaelis constant, K I the equilibrium constant for the combination of the free enzyme with the inhibitor, and Kz an analogous constant involving the enzyme-substrate. The concentration of inhibitor not bound to the enzyme6 is designated by "i." At an experimentally fixed substrate concentration, i t has been common practice t o determinc the concentration of inhibitor (I) necessary to produce some arbitrary inhibition ( @ A ) . Thus for all the types of inhihition listed in Table I, equation 1 may be rearranged to read PI = const. log Ki (SI
+
where Ki may be K1, Kz or K , and p refers to the ncgativc logarithm of the quantity involved. For an enzyme o h c y ing the inhibited Michaelis-Menten mechanism with the above restrictions, a comparison of PI'S for various inhihitors corresponds t o a comparison of functions t h a t are, a t :i given temperature, linear functions of the free energy of inhibition -AF,O = RT It1 K , ( 3I If Ki = K , the total free energy of irihihitioti will be twicc that given by equation 3, since two inhihition reactions arc involved. The larger the value of +I the more efficient the inhibitor, since there is a greater loss in the free energy of ( 5 ) I n what follows i t is assumed t h a t the amount of inhibitor bound t o the enzyme is small compared t o the total inhibitor concentration. For inhibitor concentrations t h a t greatly exceed the total enzyme ciincentration, this assumption is entirely justified. For very strong iiihibitors, such as silver ion.it should be considered a s an approxiniation.
