R ~ I S U R E M I C N TOF TRANSPORT NUMBERS IN PURE FUSICD SALTS
,Jiitie, 1055
TABLE I1 EQUILIBRIUM PRESSURE I N PRESENT WORE REQUIRED TO PRODUCE SAME ADSORPTION FIGUREAS IN PREVIOUS W O R K Gas
Hydrogen Carbon monoxide Carbon dioxide
Present work
2 X
Previous work
mm.
1 X 10-83
X
4 . 5 X 10-4 mm.
3 X 10-6-6 X
G.5 X IO-Brnni.
3 X 10-"3
X
This was checked on each of the four filaments used, with different samples of gas but the same values wore obtained in each case.
540
7.0. Summary 7.1 .-The adsorption of carbon monoxide, carbon dioxide, nitrogen and hydrogen on a germanium filament has been measured at several temperatures and at pressures between and lo-' mm. 7.2.-Calculated heats of adsorption show that all except hydrogen are physically adsorbed. 7.3.-A roughness factor of 1.3 for a CP-4 etched surface was measured. 7.4.-Various methods for cleaning the siirfncc! have been investigated.
THE MEASUREMENT OF TRANSPORT NUMBERS I N PURE FUSED SALTS1 BY FREDERICK R. DUKEAND RICHARD W. LAITY Contribution No. 3r4, Institute for Atomic Research and Department of Chemistry, Iowa State College, Ames, Iowa Received January Y, 1986
Transport numbers are here defined as the fractions of current carried by the ions when their motion: relative to the bulk of the liquid, rather than to the electrodes, are considered. They are measured by means of a cell whlch has two electrode compartments separated hy a porous membrane. The displacement of an air bubble in a capillary tube connecting the two compartments serves to indicate the volume changes occurring on electrolysis. These data combined with known density data are used to calculate the transport numbers, assuming the simplest formulas for the current-carrying ions. The use of the membrane is justified for fused PhClz by showing that three very different membranes, of porous glass, porcelain and mbestos, give substantially identical results, the indicated value of 1- being 0.75.
I n one sense the concept of transport numbers in pure fused salts is meaningless.2 Thus, if molten lead chloride is electrolyzed between lead electrodes, the requirement of over-all electrical neutrality within all parts of the liquid permits no concentration changes to occur, so that relative to the two electrodes the chloride ions do not move. Using chlorine electrodes, on the other hand, it would appear from similar reasoning that the chloride ions carry all the current, while the lead ions stand still. It is clear, then, that taking the electrode surfaces as reference points from which to compare the relative velocities of the ions the transport numbers depend on the particular electrode processes taking place. Consider, however, an ionic liquid subject to neither gravitational nor atmospheric restoring forces, so that its surface is not constrained to lie flat and horizontal. Let the liquid be lead chloride and once again use lead electrodes. As electrolysis is begun, an excess of lead ions is formed momentarily around the anode, while an equal number are removed from the liquid surrounding the cathode. This gives rise to a very slight increase in the volume of the anolyte and, of course, a corresponding decrease in the catholyte. Now the ions that comprise the liquid begin to move in order to re-establish electrical neutrality. If the lead ions carry all the current, the original volume changes in the liquid will be exactly nullified, but any conductivity by chloride ions will lead t o a net gain in the quantity of lead chloride around the anode and a corresponding loss from the catholyte. Here the motion of the current-carrying
ions relative to the bulk of the liquid might be used to define transport numbers which are properties of the salt alone and do not depend on the electrode processes. In the situation described this would mean letting t- (the transport number of the chIoride ion) be the fraction of an equivalent of lead chloride transferred from catholyte to anolyte during the passage of one faraday of electricity. Since the conditions suggested above cannot, of course, be realized experimentally, Karpachev and Pal'guev3 tried inserting a membrane between the anode and cathode compartments which would restrain the flow of the bulk of the liquid under a small gravitational gradient, but permit the passage of ions under an appreciable potential gradient. For this purpose they used a plug of tightly packed asbestos. Their tedious procedure of breaking open the cell following each electrolysis to determine the changes in weight of anolyte and catholyte gave results of poor reproducibility, but indicated that transport numbers independent of the electrode reactions might be obtained by such a method. They failed to show with any conclusiveness, however, that the use of such a membrane was not introducing surface effects which would cause the ions to behave differently than in the bulk or' the liquid. The present work was an attempt to establish the validity of using such a membrane, and to develop a method of greater sensitivity than that employed by the Russian workers. A preliminary report of the results appeared in an earlier communi~ation.~
(1) Work was performed in the Ames Laboratory of the Atomic Energy Cornmiasion. (2) H.Sehwarz, 2. Wcktrochem,, 46, 740 (1939),
(3) 8. Karpachev and S. Pal'guev. Zhur. Fia. Khim., 23, 042 (1949). (4) F. R. Duke and R. Laity, J . Am. Chem. Soo., 76,4046 (1954).
550
FREDERICK R.DUKEAND RICHARDW. LAITY Experimental
Materials .-Fisher certified reagent lead chloride was used. Further purification did not seem necessary, since small amounts of impurities had no apparent effect on the results. The lead metal was “Baker Analyzed” reagent grade. The metal itself acts as an impurity by dissolving to some extent in the molten salt. The reasons for not considering this to be a significant factor in the experimental results will be discussed. Apparatus.-The important features in the design of the cell which roved to be most practical have already been described.’ %he dimensions of the cell were chosen to permit convenient use in the particular muffle furnace to be used and are not critical. It is about 5 inches high and 4 inches wide. The piece of tungsten wire sealed through the bottom of each vertical compartment emerges into a hollow g l y s foot, where it is fused to a more flexible piece of nickel wire. The nickel wire projects from the cell where it can be connected to a power source. I n this work the following different membranes were used to !:parate the two compartments: fritted glass disks of coarse,” “medium,” “fine” and “ultrafine” porosity; a plug of finely shredded asbestos, tightly packed between “coarse” porosity fritted glass disks; a porcelain disk cut from an unglazed plate. The power supply used was a pair of standard six-volt storage batteries connected in parallel. The current was measured by noting the scale deflection on a Leeds and Northrup galvanometer connected in the circuit with appro priate resistors after careful calibration. A Hoskins electric furnace was used to maintain the cell and salt at the desired temperature, this being determined with a chromel-alumel thermocouple the tip of which was located near the center of the cell. A hole in the rear of the oven serves to allow light from a bulb hung behind the furnace to fall upon the capillary of the cell inside. A hole in the door a t the front allows the capillary of the cell to be observed with a cathetometer located about one foot away. Procedure.-Sufficient molten lead was added to each compartment of the cell to form pools which covered the tungsten wires and thereby served as lead electrodes. Care was taken to prevent atmospheric oxidation of the lead, either by melting it under nitrogen, or by dropping solid pieces of lead into molten lead chloride. The remainder of the cell was filled to a point just above the level of the capillary with fused lead chloride. This was done in such a way that an air bubble about 0 . 5 cm. long was trapped in the horizontal capillary. Observation of the bounding surfaces of this bubble through the telescope showed that there would be no tendency for any liquid to flow around the bubble, and hence that the bubble would move along with the column of liquid in the capillary. On passing a current of about 0.5 amp. through the cell, the bubble was observed to move slowly in the direction of the cathode compartment. As the trailing edge of the bubble passed the vertical crosshair of the cathetometer, a timer was started and the exact current noted. About 0.5 g. of powdered lead chloride was then weighed onto a deflagrating spoon. This was inserted into the oven and emptied into the flared top of the cathode compartment, causing the bubble to move rapidly back to the other side of the crosshair. As the trailing edge of the bubble once more arrived at the crosshair the timer was stopped. The current was again observed, and the exact time of the run noted. During each run the temperature also was noted. Such an experiment took about 700 seconds. After each two or three runs the direction of current flow was reversed. This procedure could be continued as long as the level of liquid in each vertical compartment remained within the uniform section of the column.
Results and Discussion ’ The equation relating transport numbers to measured experimental quantities is derived as follows. We first assume that the only current-carrying species in the melt are Pb++ and C1-. Although it has been suggested that there may be an appreciable amount of complexing in fused lead chloride,5 (6) (a) G . Wirths, Z. Eleklroehem., 45, 486 (1937); (b) H. Bloom and E. Heymmn, Proc. Row. Xoc. (London), 188A, 392 (1947).
Vol. 59
this has never been adequately shown by experiment. Radiotracer experiments are presently under way to determine whether any appreciable fraction of the current is carried by complex ions. If positive results are obtained, the data can readily be reinterpreted in terms of the entities involved. On passing n faradays of electricity, then, we assume that nt+ equivalents of Pb++ ion migrate from the anode into the cathode compartment, and nt- equivalents of GI- ion pass through the membrane in the opposite direction. At the same time n equivalents of P b + + ion are being formed from the lead of the anode, and a like quantity discharged at the cathode. The net result is thus the transfer of nt- equivalents of PbClz from cathode to anode compartment, and a transfer of n equivalents of P b from anode to cathode compartment. Letting dpbcl2 and dpb be the respective densities of the two liquids, this amounts to a transfer of (nt- X eq. wt. PbC12/dpbc12) - (n X eq. wt. Pb/dpb) cc. of liquid from cathode to anode compartment, so that the bubble must be displaced by an equal volume in the direction of the cathode. Since the bubble is in the same place at the beginning and end of one experiment, the addition of the powdered lead chloride to the cathode compartment must have exactly nullified this displacement. And since both compartments are of the same diameter and uniform at the surface of the liquid, onehalf of the volume of the added liquid must flow through the capillary from the cathode toward the anode compartment in causing this counterdisplacement of the bubble. (Reversing the direction of current frequently and averaging the results takes care of any lack of symmetry in the cell.) The former volume may therefore be equated with onehalf the latter nt- X eq. wt. PbCI2 - n X eq. wt. P b dpb
~
-
wt. PbClz added
l / ~
dPbCli
Solving for the transport number gives (wt. P b F l added t- =
) + (eq. wt. P b X
eq. wt. PbCh
The current remained very nearly constant during the course of a run, usually show5ng a slight drift in one direction. I n view of this, an accurate measure of the number of coulombs passed was obtained by merely taking the product of the time and the average current. The ratio RpbclZ.Of (wt. PbC1, added/coulombs passed) determined in each experiment should be a constant. Multiplication of RPbClZ by 96,500/2 gives the first term of the numerator in equation 1. I n principle it should be possible to measure the ratio of densities required in the second term using the same cell. Thus, if lead were added to the cathode compartment during an experiment instead of lead chloride, a new ratio Rpb would be obtained. The desired density ratio would then, of course, be given by dPbClz
RPbOlz
dpb
Rpb
It was found, however, that the addition of lead gave results of poor reproducibility, due to the
SUMMARY O F
TABLE I RESULTS O F TRANSPORT NUMBEREXPERIMENTS ON FUSED PbClz d T 565’ Membrane
a
551
MEASUREMENT OF TRANSPORT NUMBERSIN PUREFUSED SALTS
June, 1955
“Coarse” porosity fritted glass disk “Medium” porosity fritted glass disk “Fine” porosity fritted glass disk “Ultrafine” porosity fritted glass disk Asbestos packed between two “coarse” porosit,!: dislts Porcelain disk cut from unglnzetl plate Bubble did not move.
No. of expts.
1
RPbCl2
(av.)
x
On
108
USING VARIOUS hfEMBRANER Av. dev. of RPbClz t- (av.)
...
0.336
11 26
0.958 1.079
f0.045 f ,048
0.669f0.016 0 . 7 1 1 f ,017
22
1.213
f ,039
0,758f
20
1.165
f ,060
0.742 f ,020
25
1.190
f .OM
0.750 f ,022
tendency of the metal to cling t o the glass and oxidize there, rather than run freely into the melt. Comparison of the density ratio obtained in this way nevertheless showed good agreement with the literature value, but considerably poorer accuracy. The density figures in the literature were therefore used in calculating the transport numbers reported The results for six different membranes are summarized in Table I. It will be seen that, except for that obtained with the “comse” porosity fritted disk in which case the bubble failed to move, they are all in qualitative agreement. The last three results show excellent agreement with each other, all lying within the same range. The membranes used in these cases were the least porous, and hence least likely to permit any of the accumulating liquid to flow back through them rather than through the capillary. Such backflow was certainly the cause of the first result, and hence appears most likely to have contributed to the next two low results. The agreement among the last three results therefore appears to justify two conclusions: (1) in view of the small probability that the three very different membranes have identical resistances to flow of the liquid, the contribution of backflow in these experiments must have been small enough to be considered negligible; (2) in view of the fact that the membrane pores through which the conductivity took place were in the three cases of different size, shape and length, and that the membranes themselves were of entirely different materials, the influence of surface effects in defining the transport numbers must also be very nearly negligible. In this latter connection it might be recalled that most electrokinetic phenomena are so sensitive to the nature of the surface that it is difficult to reproduce results from one glass capillary to the next. Although the temperature was not too carefully controlled in these experiments and was probabIy not uniform throughout the cell, it is doubtful that this had any effect on the measured transport numbers. On carrying out a series of runs a t 635” the only apparent effect was on the relative densities of the liquids. The average t- for seven experiments, using the “ultrafine” fritted disk as mem(6) R. Lorens, H. Frei and A. Jabs, Z. p h y s i k . Chem., 61, 468 (1907).
(7) P. Pascal end A. Jouniaux, C o m p t . rend., 158, 414 (1914).
,014
brane, was 0.757 f 0.009, which is identical with the result of 565”. Further discussion of the significance of this temperature effect will appear in a subsequent paper. The above results are also in good agreement with those of the Russian workers cited earlier.3 In 14 experiments of the type described carried out over a temperature range of 520-G80°, they observed no temperature effect and an average t- of 0.78 f 0.03. These workers also tried methods using a radioactive isotope of lead, but the results, while showing qualitative agreement with the above, were too erratic to be conclusive. The dissolving of lead metal from the electrodes in the salt changes the color of normally yellow fused PbCL almost to black a t higher temperatures (above 600”). It is reported, nevertheless, that the solubility of the metal in the salt a t 550” is 0.0002 mole per cent., increasing to 0.0005 mole per cent. a t 610°.* To determine the influence of this metal on ionic migration in the salt the following experiment was carried out: A cell was filled with pure lead chloride so that the tungsten wires served as electrodes. Its resistance was measured as a function of temperature from 520 to GOO” using a 1000 cycle conductivity bridge. The salt was then poured over an excess of lead metal and allowed to stand at 600” until its very dark color indicated probable saturation. The solution was decanted back into the cell and its resistance again measured. At every temperature the readings mere found to be identical to those for the pure salt within the accuracy of the instrument (about one part in 300). It seems very unlikely that the mechanism of conductivity could have changed significantly while both the conductivity and its temperature dependence remained unchanged. It was therefore felt that transport numbers measured in the presence of dissolved metal are ascribable to the pure salt. I n c.onclusjon it is recommended that “ultrafine” porosity fritted glass disks be used in future work of this type, although, strictly speaking, the use of such a membrane should be justified in each specific case. An adequate justification for ignoring possible surface effects in such a membrane might be obtained by measuring the temperature dependence (8) R. Lorenz, G. Hevesy and E. Wolff, 2. p h y s i k . Chem., 76, 732 (1911).
ROLAND F. REERA,,JR,
L52
of the conductivity in cells with and without the membrane. The "activation energy of ionic migration" computed from such data is very sensitive
Vol. e59
to changes in the conductivity mechanism, and hence may be used to indicate the validity of the method.
NON-EQUILIBRIUM INHIBITION OF THE CATALASE-HYDROGEN PEROXIDE SYSTEM BY ROLAND F. BEERS,JR. Division of Biochetnisfry, Deparlinent of Biology, Massachusetts Institute of Technology, Canihridge 89, Massachusetts Received Januaqt 28, 1966
The kinetics of the catalase-hydrogen peroxide system during the period it is undergoing progressive inhibition has been examined analytically. It has been shown that because the steady state ratio, free enzyme/primary complex, is independent of the substrate concentration, it is possible for this ratio to remain constant even though both terms may be changing continuously during the inhibitory reaction. Consequently, it is a relatively simple matter to determine the concentration of active enzyme from tangents drawn along the semi-log slope of substrate us. time, ie., transient first-order constants. The kinetic data of the conversion of the primary complex to the inactive secondary complex published by Chance have been examined and found to follow the theoretical predictions of this paper. Azide inhibition is believed to involve a competitive reaction between azide and hydrogen peroxide for the primary complex, following a simple reversible first-order equation, independent of substrate concentration.
Introduction In an earlier paper1 the author examined equilibrium inhibition of the catalase-hydrogen peroxide system during the steady state, i.e., when the concentrations of the various enzyme forms are time invariant. I n this instance we were concerned with analytical methods for calculating dissociation constants of the enzyme-inhibitor complexes. I n the present paper we will consider the alternate situation in which the enzyme-substrate system is being progressively inhibited, i.e., nonequilibrium inhibittion. In particular we will explore the analytical methods for calculating the individual velocity constants. Some of the published experimental results and interpretations can profitably be examined ih the light of the concepts developed in this paper.
Theory The reaction scheme is f S k l P E+S+ES
P ES
+ S ----f E + products S
k
4
f
kp
ES
+
i I
b
ks q"
ESI
k-
6
In conformity with previous the quantities f, p? q', and q", refer t o the concentrations of the various components of the system. We continue the assumption1 that the free inhibitor concentration is equal t o the total inhibitor concentration and, therefore, is constant. Two mechanisms may produce a state of nonequilibrium between the inhibitor and the enzyme. The first., discussed briefly in the previous paper,' is found if either inhibitor-enzyme complex, L e . , (1) R. F. Beers, Jr., THISJOURNAL, 119, 25 (1955). (2) R. F. Beers, J r . , ibid., 68, 197 (1954). (3) B. Chance, D. 8. Greenstein and I?. J. W. Roughton, Arch. Baohem. Biophp?., 37, 301 (1952).
1
E1 or ESI, but not both, reacts t o an appreciable degree with the substrate. It was shown that the enzyme-substrate system cannot approach or be in a steady state. Furthermore, the degree of inhibition, reflected in the transient first-order velocity constant, becomes a function of the substrate concentration. However, these characteristics have not been observed in the catalase-hydrogen peroxide system. Never theless, Theorell and Ehrenberg4 have recently proposed that hydrogen peroxide reacts directly with the catalase-azide compound t o form the catalase-azide-peroxide compound. We shall return t o this point later (see Discussion). The second mechanism for non-equilibrium between enzyme and inhibitor is obviously an enzyme-inhibitor reaction approaching equilibrium. The concentration of the active enzyme species decreases t o a finite value during which period the time decay of the substrate is greater than first order. At equilibrium the rate of catalysis returns to first order. Since the concentrations of active enzyme species during this transient period are varying with time we must ascertain what effects this progressive inhibition has on the steady state of the catalase-hydrogen peroxide system. This has been defined by (a) dp/dt = 0 and (b) the equation6 f/p = k4/ki = Rk (1) Under what conditions when dp/dt # 0 can we assume that equation 1 is correct or a t least a satisfactory approximation? The rates of change, dp/dt and df/di, are
-
dp/dt =i (kf - k4p)s ( k @ - k-Q") df/dt = (krf - k 4 p ) ~- (khfi - k - 5 ~ ' )
-
(2) (3)
Equation 1 is an exact solution (within the limits of the steady state approximation) when the rates in equat,ions 2 and 3, specifically, (kepi Leq") and (k5fi - k-5p'), are zero. The inhibitor reactions are at equilibrium. This represents the mini-
-
(4) H. Theorell and A. Ehrenberg, ibid., 41, 462 (1952). ( 5 ) R . F. Beers, .Jr., xnd I. W. Sizer, THISJOURNAL, 67,200 (1953).
,
