THE EFFECT OF STIRRING ON CELLS WITH CATION EXCHANGER MEMBRANES Ag(s) AgCl(s) BY G. SCATCHARD AND F. HELFFERICH Massachusetts Institute of Technology Cambridge 39 Massachusetts U.S.A. Max-Planck-Institut fur physikalische Chemie Gottingen Germany Received 20th January 1956 I solution 1 AgCl(s) Ag(s) (1 .l) cation-exchanger 1 membrane solution a We have measured the effect of stirring one or both solutions on the electrical potentials across cation exchanger membranes in concentration cells bi-ionic cells and cells with ions in the membrane which are not in either solution with dilute solutions containing HCl NaCl CaC12 or mixtures. Very large effects are obtained with systems containing two cations with different valences. With HCl + CaC12 bi-ionic cells changes up to 80 mV with reversal of sign have been observed.With CaC12 concentration cells and membranes containing Na+ the membrane potential is doubled when stirring is stopped. The quasi-thermodynamic equation for membrane potentials is integrated with some simplifying assumptions and the concentrations at the membrane surfaces are calculated from the electromotive force. The very large changes in electromotive force are related to the great preference for bivalent ions of the exchanger in contact with dilute solutions. When a cation-exchanger membrane is inserted between the two solutions in a concentration cell with transference the electromotive force of the cell is changed by a difference between the membrane potential EM and the liquid junction potential EL. If the ionic concentrations in the solutions are very much smaller than the concentration of fixed ions in the membrane the membrane shows prac-tically ideal permselectivity for cations and the membrane potential approaches the thermodynamic value for transfer of cations only.Membrane potentials smaller than the ideal value may be due to several causes, and have been discussed quantitatively.1-20 Potentials larger than the ideal can not be explained by a simple thermodynamic theory. Nevertheless such abnormal potentials ranging up to four times the ideal value have been reported by Wyllie,21 and by Coleman,22 and Scatchard23 for calcium chloride solutions and cation exchange membranes. They attributed the effect to sodium ion left in the membrane and found that the abnormal effect disappeared when the last trace of sodium was removed.The purpose of our investigation was to determine how the Na+ produced the effect. We find that the effect can be suppressed completely by violent stirring, and can be produced or suppressed at will by stopping or starting the stirring. We have measured the effect of stirring on both sides either side and neither side on the potentials of a number of cells of the type with solutions of NaCl HCl CaC12 or mixtures of two of them and with membranes equilibrated with these solutions or with packs of membranes equilibrated with different solutions. Symmetrical cells have a single cation throughout and the concentration of 0 is the same as that of p so the only difference is in the stirring. Concentration cells have a single cation throughout and the concentration of a is different from that of ,B (the ratio was 4 to 1 in most of our measurements).7 G . SCATCHARD AND F. HELFFERICH 71 Abnormal cells differ from symmetrical or concentration cells in that the mem-branes contain a different cation from the solutions. Bi-ionic cells have different cations in a and p but the same equivalent concentration. SYMBOLS a activity, E electric potential difference, F Faraday, rn molality, R gas constant, T absolute temperature, t transference number (negative for anions), u mobility (negative for anions), z ionic valence (negative for anions), y activity coefficient. Subscripts A B X refer to the ions A B and X ; subscript R to the fixed resin anion ; subscripts i j Ic refer to any ionic species i j k.Superscripts cc and j3 refer to the left and right solution a and b to the interfaces on the left and right side of the membrane ' and " to left and right sides of any phase. Bars denote quantities within the membrane. 2. EXPERIMENTAL CELL The membrane (or membrane pack) was clamped between two Plexiglass half cells 2 x 2 x 2 in. (fig. la) with circular holes of 8 mm diameter (or slits 8 x 1 mm for most of the experiments with membrane packs to ensure that the membranes were pressed tightly together with no aqueous pockets between). Thin rubber gaskets were used between the membrane and Plexiglass. The removable Plexiglass cover had four holes over each half cell for the solution inlet and outlet the electrode and a thermometer.The solutions were stirred violently by circulation through thermostatted glass turbines (fig. 16) in such a way that a jet of about 3 ft./sec was directed sideways across the membrane surface. This was found to be a most efficient way of agitation at the membrane surface The cell tem-perature was 25 & 0.2" C. Potential readings were made with a Leeds and Northrup type K-1 potentiometer and no. 2430 galvanometer or with a Ruhstrat " technischer Kompensator " Knick amplifier and Metrawatt microamperemeter. ELECTRODES Ag/AgCl electrodes were prepared by coating a previously annealed and etched Ag wire spiral cathodically with Ag-in KAg(CN)2 solution and then anodically with AgCI in NaCl solution. The spiral was then cut in half to give the two electrodes.The asymmetry potential of a pair of electrodes was nearly always less than 0-3 mV and usually less than 0-1 mV. In some of the measurements the electrodes were shielded from the turbulent stirring with glass tubes (see fig. la) though no difference was noted between shielded and unshielded electrodes. MEMBRANES The membranes were either Amberplex C-1 made by Rohm and Hass Co. Philadelphia, Pa. or phenolsulphonic acid-formaldehyde membranes prepared by us by the method of Schlogl and Schodel.24 The most important properties of the resins in the leached hydro-gen form except for one conductance are (with the Amberplex Iisted first each time): equivalents of fixed charge per kg of water = 5.1,0*85 ; % water = 43-0 74.3 ; thickness 0.65 0.45 mm ; specific conductance = 3.8 X 10-3 15.5 x 10-3 mhos ; specific conduc-tance of Na+ form25 = 0.48 X 10-3 mhos .. . ; water permeability = 6-27 x 10-9, 1.29 x 10-11 cm3 dyne-1 sec-1. Before each experiment except with abnormal cells the membranes were thoroughly equilibrated with the solution used or with a mixture of the two solutions 72 EFFECT OF STIRRING SOLUTIONS All solutions were prepared by dissolving analytical grade reagents (Malinckrodt or Merck) in conductivity water. The concentrations ranged from 9.5 x 10-5 to 2 x 10-2 N. a A n L P J b FIG. 1.-Apparatus. (a) The cell. In the front-view only solution inlet and outlet are shown in the left half cell, and only the electrode in the right half cell. In the top-view all equipment is omitted.A B C D E F G H J K L M N 0 P Q R S 3. RESULTS The membrane potential is the total cell potential minus potentials calculated as (RT/F) In (a&/&) assuming that ycl and ycl = y$ for CaC12. (b) The whole assembly. Plexiglass half cell rubber gaskets membrane Plexiglass cover . solution inlet (glass) solution outlet Ag/AgCl electrode electrode shielding clamps hole for solution inlet hole for solution outlet hole for electrode hole for thermometer thermostat vessel glass turbine motor thermometer stirrer the difference in electrode = YLt for HCI and NaCl CONCENTRATION CELLS The potentials obtained with CaC12 HCl and NaCl with stirring of both solutions of the more concentrated solution only of the more dilute solution only and with no stirring are listed in table 1.Stopping the stirring results in most cases in a decrease of the membrane potential which is usually more pronounced with the thin and more permeable membranes and on the side of the more dilute solution. There are however exceptions. Restarting the stirring of the more dilute solution causes an initial overshooting with a subsequent drop to the steady value. A representative potential against time curve is shown in fig. 2a. Membrane potentials between CaCl2 solutions containing up to 20 equiv. % of NaCl differ by no more than a few mV from those between pure CaClz solutions and show the same behaviour with respect to stirring. SYMMETRIC CELLS In a cell with two identical solutions separated by a membrane in ion-exchange equili-brium with the solution a potential usually arises when one solution is stirred.The result G. SCATCHARD AND F. HELFFERICH 73 are shown in fig. 2b and fig. 3. Except for the higher concentrations of NaCl and CaC12 the stirred solution is the more negative. The changes are somewhat slower than the changes with concentration potentials (fig.2b). FIG. 2.-Effect of stirring on concen-tration potentials and symmetrical potentials. The wavy line indicates that the pump is working on the respective side. Interruption of the wavy line corresponds to stopped Pump. Experimental c o n c en t r a t i o n potential, Experimental symmetrical poten-tial,-same concentration as more concentrated solution in 2a - - - same concentration as more dilute solution in 2a, concentration potential corrected for asymmetrical stirring [(2a) minus (26)].Although the potential changes are smaller than "Ol Membrane : phenosulphonic solutions CaC12, 6-020 x 10-3 - 1.505 X lO-3N. I t those with concentration cells they are no more reproducible. This is partly due to the fact that we have not reached a limiting value which would be unchanged by a further increase in stirring rate. Neither previous saturation of the solutions with AgCl or C02 nor shielding the electrodes changed the effect of stirring in the cases studied. TABLE 1 .-CONCENTRATION POTENTIALS concentrations membrane potential with stirring of theor-etical both conc. $2; neither limit-value equiv.11.mV mV mV mV mV solutions only ing membrane electrolyte zAma =AmB Amberplex CaC12 2.41 x 10-2 6.02 x 10-3 13.6 12.8 11.0 10-6 14.0 C-1 (single) 6.02 x 10-3 1-51 X 10-3 14.8 12.3 13.8 11.3 15.5 phenolsulphonic 2.41 x 10-2 6.02 X 10-3 13.2 9.6 3.5 -0.2 14.0 (single) 6.02 x 10-3 1.51 x 10-3 15.1 11.6 8.4 3.8 15.5 Amberplex HCl 2.46 x 10-2 6.14 x 10-3 33.3 32.3 32.1 32.9 34.1 C-1 (single) 6.14 x 10-3 1.54 x 10-3 33.1 31.8 33.7 32.9 34-6 1.54 x 10-3 3.84 x 10-4 32.8 31.0 34.5 33.1 35.1 A niberplex 2.46 x 10-2 6.14 x 10-3 33.4 29.9 34.4 31-2 34.1 C-1 (fourfold pack) 6.14 x 10-3 1-54 x 10-3 33.0 32-0 34.0 33.3 34.6 1.54 x 10-3 3.84 X 10-4 33.9 32.4 36.4 34.4 35.1 Amberplex NaCl 1.93 x 10-3 4-92 x 10-4 29.9 28.9 30.3 29.5 34.5 C-1 (single) ABNORMAL CELLS In solutions containing only univalent cations no abnormal effects of stirring are observed when a membrane between NaCl solutions has been equilibrated with KC1, or vice versa.Large effects are observed when a membrane equilibrated with CaCl2 i 74 EFFECT OF STIRRING inserted between solutions of NaC1 and very large effects are obtained when a membrane equilibrated with NaCl or with KCI is inserted between solutions of CaC12, (3.1) Ag AgCl I CaCl&za) I membrane (NaR) I CaCl;?(rnS) I AgC1 Ag, n V + 5 ’ 0 - 5 . - 5 -2 1 0 9 ( x i m i ) FIG. 3.-Potentials of systems symmetrical except for stirring. The potential is listed as positive when the unstirred solution is more positive than the stirred one. HCI 0 NaCl A CaClz Membrane Amberplex C-1 7 l e f t 2 0 4 0 60 8 0 100 200 5 0 0 mi n FIG.4.-Effect of stirring on the potential across a Na+ membrane between identical CaC12 solutions. The stirred solution is more negative than the unstirred solution. Membrane Amberplex C-1 ; concentration of solutions 9-24 x 10-4 N. m V + 2 0 , + 10. 0 ” -10. -20. I - ___y_______l - right - - w a m l e f t 2 0 4 0 6 0 8 0 100 100 3 0 0 1440 min FIG. 5.-Effect of stirring on the potential across a Ca2+ membrane between identical NaCl solutions. The stirred solution is more positive than the resting solution. Membrane, Amberplex C-1 ; concentration of solutions 9.84 x 10-4 N G . SCATCHARD AND F. HELFFERICH 75 When solutions x and are identical. the potential is zero if both solutions are stirred or if neither is. When only one solution is stirred the stirred solution becomes more negative.We have measured as much as 100 mV change on stirring. The effect decreases rapidly mV I FIG. 6.-Effect of stirring on the potential across a membrane which is /initially not in ion-exchange equilibrium with the solutions. Membrane Amberplex C-1 equilibrated with a mixture of 4 parts 1 N CaCb solution and Solutions mixtures of the same concentration ratio ~ c ~ / w z N ~ total concentrations 1 part 1 N NaCl solution and leached with conductivity water. 1.37 x 10-3 - 3-42 x 1 0 - 4 ~ . mV f 6 0 50 40 3 0 2 0 +I0 0 FIG. 7.-Effect of stirring on the potential in the system. 1.53 x lO-3N Ca2+ Ca2+ Na+ Ca2+ Ca2+ 3-82 x lO-4N CaC12 I membrane I membrane I membrane membrane I membrane 1 CaC12 0 Membrane potential with stirring on both sides A 0 0 A = " Na potential " B = " Ca potential " (The solutions were not stirred in the intervals between the measurements).with stirring of the more concentrated solution only with stirring of the more dilute solution only with no stirring at all. (RT/F) In (rnalrnb) (RT/2F) In (rna/rnb) with time. A typical potential against time curve is shown in fig. 4. A similar curve for a membrane equilibrated with CaC12 between identical solutions of sodium chloride is shown in fig. 5. The change is much smaller and the stirred solution is positive. Similar result 76 EFFECT OF STIRRING were obtained with membranes equilibrated with NaCl + CaC12 mixtures between solutions of CaC12 or of NaCl and with membranes equilibrated with 1 N solutions of NaCl 4- CaCl2 mixtures placed between dilute solutions with the same Na/Ca ratio which are not in ion exchange equilibrium because of the shift of equilibrium with concentration.When ma -+ mB in cell 3.1 the potential with both sides stirred is the same as with a membrane equilibrated with CaC12 When neither side is stirred the potential increases. Stopping the stirring on the more dilute side only gives a still greater increase and stopping the stirring on the concentrated side only gives a smaller decrease. This effect also decreases with time. In fig. 7 are shown measurements with CaC12 solutions w = 4mB and with a sandwich of five membranes. The middle one had been equilibrated with NaCI the others all with CaC12.Initially the potentials are the same as those of a simple concentration cell (without the Na+ membrane) and the potential with both sides stirred remains almost unchanged at A typical curve is shown in fig. 6. TABLE 2.-cHANGES OF BI-IONIC MEMBRANE POTENTIALS IN 2 MIN AFTER STOPPING STIRRING OF ONE SOLUTION ONLY single membrane single membrane mV mV mV mV membrane pack membrane pack concentration equiv.11. membrane solution not stirred (1) system HCl + NaCl HCI Amberplex 2.475 X 10-2 - 2 - 3 + 2 c- 1 6-19 x 10-3 - 1 - 7 + 3 1-55 x 10-3 - 2 -15 + 3 3-87 x 10-4 - 3 - 5 + 8 phenosulphonic 2.475 X 10-2 - 3 - 3.5 - 4 6-19 x 10-3 - 2.5 - 4 f O 1-55 x 10-3 - 2 - 9.5 & 0 3-87 x 10-4 - 3 -28 + 11 Amberplex c- I (2) system HC1 + CaC12 2.490 X 10-2 2.467 X 10-2 6.23 x 10-3 6.17 x 10-3 1-56 x 10-3 1-54 x 10-3 3.89 x 10-4 phenolsulphonic 2-490 x 10-2 2.467 X 10-2 6.23 x 10-3 6-17 x 10-3 1-56 X 10-3 1.54 x 10-3 3.89 x 10-4 3-86 x 10-4 (3) system NaCl + CaCl2 Amberplex 2.460 x 10-2 c-1 6.15 X 10-3 1.54 x 10-5 3.84 x 10-4 6-15 x 10-3 1-54 x 10-3 3.84 x 10-4 phenolsulphonic 2.460 x 10-2 CNal + 3 + 4 + 2.5 + 20 - 3.5 - 2 - 10 - 12 HC1 CaCl2 + 10 + 9 f O + 25 - 5 + 42 - 6 + 25 + 10 + 18 - 1 + 10 + 15 + 25 - 1 + 28 + 14 + 28 - 7 + 14 + 20 - 1 + 5 - 2 + 30 - 4 + 45 - 20 NaCl CaCI2 + 4 - 2 + 4 + 3 1 0 - 3 + 13 + 10 - 5 4-23 + 15 - 2 - 6 + 35 + 10 - 2 4- 11 + 13 + 8 - 1 + 14 +25 4-7 - 10 + 16 +35 + 2 3.1 G. SCATCHARD AND F. HELFFERICH 77 15 mV for 70 h.After about 20 h the potential without stirring increases about 23 mV, that with only the concentrated side stopped decreases about 17 mV and that with only the dilute side stopped increases about 40mV. These values also remain nearly constant until 70 h from the start and any of the four values may be obtained at will. I -3 -2 lop m -3 -2 log m > / / / / / / mV t 4 0 (dl 3 0 2 0 3 0 4 0 30 i tbo mV 1 ( f F 1 + 10 4 0 50 60 7 0 -:I -80 + 10 4 0 so 7 0 80 / / / 1 I - 3 - i loq(z;rn;) - 3 -2 log ( r . r n l ) FIG. S.-Bi-ionic potentials. (a) Membrane phenosulphonic solutions HCI (left) NaCl (right) (6) Amberplex C-1 9 9 7 7 (c) phenolsulphonic HCl (left) CaC12 (right) (4 Amberplex C-1 Y Y 97 (4 phenolsulphonic NaCl (left) ,,.(f) Amberplex C- 1 7 9 9 9 0 single membranes stirring on both sides, 0 membrane packs 9 9 9 , 0 single membranes without stirring, x membrane packs 3 7 ?) A = liquid junction potential in aqueous solution, B = theoretical bi-ionic potential 78 EFFECT OF STIRRING BI-IONIC CELLS We have studied bi-ionic cells Ag AgCl I AClzA(ma) I membrane I BCl,B(mB) I AgC1 Ag (3.2) with the three combinations HCI + NaCl HCl + CaC12 and NaCl + CaC12 with the equivalent concentrations the same in a and in ,B in two series. In the first series there is a ~MMM - HCI -- rur CaC12 I . . 10 2 0 3 0 4 0 5 0 6 0 I80 200 2 2 0 2 4 0 3 0 0 3 2 0 min FIG. 9.-Effect of stirring on the bi-ionic potential across a single membrane.Membrane, phenosulphonic ; solutions HCl (left) and CaC12 (right) 6.225 x 10-3 N. k c nwmw mmmuwey H C I MLTM llwmw COCI - 10 2 0 3 0 6 0 7 0 8 0 9 0 1 2 0 130 900910 920 min FIG. 10.-Effect of stirring on the bi-ionic potential across a membrane pack : HCl I membrane 1 membrane I membrane I membrane I CaC12 H' H+ Ca2f Ca2+ Membranes Amberplex C-1 ; solutions HCI (left) and CaC12 (right) 6-167 x 10-3 N. single membrane equilibrated with a solution half normal in each to the two solutions. In the second there is a pack of 4 membranes. The two on the cc side are equilibrated with the cation on the cc side and the two on the ,B side are equilibrated with the cation on the t9 side. The results after establishment of a steady state are shown in fig. 8 and in table 3 G .SCATCHARD A N D F . HELFFERICH 79 The bi-ionic potential HC1 + NaCl is fairly independent of the concentration and the effect of stirring is small. The bi-ionic potentials involving ions of different valence depend upon the concentration and are extremely sensitive to stirring. Stopping and restarting the stirring may result in potential changes as large as 80mV and to reversal of the sign of the e.m.f. In the experiments with a single membrane the effect of stirring is at its maximum in a few minutes. A typical potential against time curve is shown in fig. 9. In the experiment with a four membrane pack the potential with both sides stirred is nearly independent of the time but the effect of stopping stirring is negative at first as in a concentration cell and develops to the steady state value only after hours.A typical curve is shown in fig. 10. 4. SIMPLIFYING ASSUMPTIONS (i) The concentrations in the aqueous solutions are assumed to be always so small relative to the concentration of fixed ions in the membrane that the con-centration of anions in the membrane may be neglected and (ii) so smill absolutely that the change in free energy due to the transfer of water may be neglected. (iii) The activity coefficients and the ratios of the mobilities of any two ions are assumed to be independent of the composition and the mobilities are assumed to be independent of the total concentration in the small range in which that varies in a single phase. (iv) The boundaries between the membrane and the solutions are assumed to be sharp.(v) The concentration of fixed ions in the resin is assumed to be constant and any other effects of changes in swelling pressure are neglected. (vi) If there are two cations present it is assumed that the concentration of anion in each aqueous solution is constant. The first two assumptions and the third for all the ions univalent are probably quite exact for the concentrations we have used. The last three assumptions and the third for solutions containing CaZf are inexact approximations made for the sake of mathematical simplicity. EQUATION FOR THE ELECTROMOTIVE FORCE With the assumption of sharp boundaries (iv) it is convenient to split the general equation for liquid and membrane potentials EMFJRT - Eitid In ai (4.1 ) (4.2) into five parts two Donnan potentials and diffusion potentials in each solution and in the membrane J: ti == uimi/zjZjUjnlj, (4.3) We shall limit our discussion in this paper to the use of quasi-thermodynamics to determine approximately the changes in concentrations at the membrane-solution surfaces from the changes in membrane potential.A somewhat mor 80 EFFECT OF STIRKING precise and much more detailed picture is possible with the methods of the thermo-dynamics of irreversible processes.26 This will be presented in the subsequent paper by one of us.27 Our model is too simple to explain the symmetrical potentials of § 3. They may arise from the effect of stirring on a finite transition layer between membrane and solution (contrary to assumption (iv) or on a diffuse (Gouy) double layer, or from other causes.If the observed stirring effect on the concentration potential (fig. 2 4 is corrected for the potential change found with symmetrical systems (fig. 2b) a net effect is obtained (fig. 2 4 without the overshooting on starting stirring in the dilute solution. These results also show that the large effects of stirring in bi-ionic and in abnormal potentials must arise from other causes. CONCENTRATION CELLS With the assumptions of § 4 eqn. (4.3) for a concentration cell becomes With stirring on both sides our measurements correspond to the second term alone except for the decrease usually found in very dilute solutions. We assume therefore that stirring on the a side mades ma practically equal to rn and that stirring on the /3 side makes mb practically equal to- mg.It is then possible to calculate ma/rn or ~ n b ! r n ~ when stirring is stopped on one side only. For CaCl2, 6-02 - 1.53 x 10-3 N the measurements correspond to 103 rn& = 5.04 = 103 mE1 - 0.96 and 103 m& = 2.55 = 103 m& + 0-92. When stirring is stopped on both sides the change in potential is approximately the sum of the effects of stopping on a single side. The effect of stirring on con-centration cells with membranes has been discussed by Unmack 28 and by Brun.29 BI-IONIC CELLS For bi-ionic cells it is convenient to use cations A and B a s j and k respectively, and to regroup the terms to give with our simplifying assumptions The first term is the logarithm of the distribution ratio. We assume that stirring on the a side makes m; = rn and m," = Z," = 0 and that stirring on the /3 side makes irzf = m and mt = 7Zt = 0.This assumption has the further justification that in cells with multiple packs with stirring on both sides the potential is independent of time. For stirring on both sides then eqn. (4.5) reduces to -l I z A TB = In &) ( % ) I i z B - s" a 1,7j d In E 7 j - ($ - i) In 5. (4.6) mc1 Since mB is a linear function of mA and iTB of GA the integrals in eqn. (4.5) and (4.6) may be determined in any phase by the Henderson equation.30 So integrated, eqn. (4.6) may be obtained from the equation of Wyllie 31 for multi-ionic potentials, and it reduces €or Z = Z = 1 to the equation of Sollner.3 G. SCATCHARD AND F. HELFFERICH 81 From the values of MacTnnes 33 for the limiting ion conductances we obtain the following equations for the integral and the maximum values when x i = 1 and x i = 0 if xi = m>i/mkl at the left-hand side and xi = n z ~ i ' r n ~ at the right-hand side.H + Na 59.15 loglo (1 + 2.370 x&)/(l + 2.370 x;) 31.21 (4.7) H + Ca 65.21 loglo (1 + 2.137 xk)/(l + 2.137 x;) 32-40 (4.8) N a i Ca 128.25 loglo (1 + 0.069 ~ ; ~ ) / ( l + 0.069 x;,) 3.72 (4.9) In the Amberplex membrane we have used the conductance measurements in 5 2 to give ZIH/UN~ = 8 and the measurements with stirring on both sides in the H + Ca bi-ionic cell and the assumption that (YH/3/H)(?/Ca/YCa)' = 1 to give measurements of the H + Na and Na + Ca bi-ionic cells and the diffusion potentials : H + Na 59.15 loglo (1 + 7 xk)/(l f 7 Fg) 53-42 (4.10) H + Ca 61-12 loglo (1 + 15 %;)/(1 -I- 15 yz) 73.59 (4.1 1) UH/UCa 16- This gives (YNa5Na)(YH/YH) = (YNa/YNa)(YCa/YCa)' 2.From the Na + Ca 88.72 loglo (1 + xka)/(l + xGa) 26.70 (4.12) The H + Na potentials are nearly independent of the concentration and are but little changed when the stirring is stopped. Eqn. (4.6) indicates no change as the concentration changes. When the stirring is stopped the maximum change in potential corresponds to going from the change in composition being entirely in the membrane to its being entirely in the aqueous phases. The calculated change is 31.21 - (53.42 - 18.75) = - 3946mV. (4.13) However our assumption (vi) that the anion concentration is constant does not hold well here see ref. (27). When the ,8 cation is Ca2+ the membrane potential with both sides stirred becomes more negative as the concentrations decrease by about 30mV for each power of ten in agreement with eqn.(4.6). Again the maximum change on stopping stirring corresponds to going from the change being entirely in the membrane to its being entirely in the aqueous phases. It is (4.14) and 3-72 - [26.70 + 18.75 - 29.58 loglo (TtiR/mgl)] for Na + Ca. (4.15) For the ratio Gjm of 103 (6 N and 6 x 10-3 N) the maximum is about 45 mV for either. With such dilute solutions the preference of the resin for the bivalent ion is enormous and the changcs we observe are over periods very short compared with the time necessary to reach steady-state flow through the whole membrane, so all changes must be near the surface.When stirring is stopped on the a (uni-valent) side the increase in Ca2f is almost entirely in the resin where the relative change in concentration must be small so there is little change in potential. When stirring is stopped on the ,B (bivalent) side the decrease in Ca2f is almost entirely in the solution and the change in potential is large. It is not difficult to obtain a point on the curve for the variations of n;ga and iZga with potential by choosing an arbitrary value of that concentration which changes most calculating the other concentration from the equilibrium relation and then the change in membrane potential by substituting eqn. (4.8) and (4.11) or (4.9) and (4.12) in eqn. (4.5). With 6 x 10-3 N solutions a ratio iu$,/rn%a = + corresponds to a change of 28 and 10 mV for the H + Ca and Na + Ca cells respectively.The measured values after 2 min are 30 and 10 mV. 32.40 - [73.59 - 29.58 loglo (ZR/rn$,)] for H + C 82 EFFECT OF STIRRING ABNORMAL CELLS The cells with membranes containing Na+ between solutions of CaC12 behave like CaC12 concentration cells when both sides are stirred. When there is much Na+ in the membrane the effect of stopping stirring is the same as that of stopping stirring on the CaC12 side of the Na + Ca bi-ionic cell. In the sandwich-pack cell of fig. 7 the effect of stopping stirring on the side with 1-53 x 10-3 N CaC12 is 17 mV which corresponds to a izg,/mf.a ratio of about 1/3. The effect of stopping stirring on the side with 3.82 x 10-4 N CaCl2 is 50 mV as measured directly or 40 mV from the difference between stopping both sides and stopping the concentrated side only.This corresponds to a concentration ratio about 1/20 or about 1 /50. The change when stirring is stopped on both sides corresponds closely to the maximum change with both Na 4- Ca junctions in the aqueous phases which is marked sodium potential in fig. 7. This may be a coincidence as the change when stirring is stopped on either side is much less than the maximum change, -64 or +81 mV. We are indebted to Dr. R. Schlogl for helpful discussions. One of us (F. H). wishes to thank the Foreign Student Summer Project of the Massachusetts Institute of Technology for a grant which provided the opportunity to start this work. 1 Teorell Proc. SOC. Expt. Biol. 1935 33 282 ; Z.Elektrochem. 1951 55 460. 2 Meyer and Sievers Helv. chim. Acta 1936 19 649. 3 Marshall J. Physic. Chem. 1939 43 1155. 4 Sollner and Anderman J . Gen. Physiol. 1944 27 433. 5 Manecke and Bonhoeffer 2. Elektrochem. 1951 55 475. 6 Schmid and Schwarz Z. Elektrochenz. 1951 55 684. 7 Lorenz J. Physic. Chem. 1952 56 775. 8 Manecke 2. physik. Chem. 1952 201 193. 9 Schlogl and Helfferich Z. 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Chem. 1953 57 687. 26 Helfferich Thesis (Gottingen 1955). 27 Helfferich Faraday SOC. Discussions 1956 21 83. 28 Unmack Kgl. Danske Vid. Selsk. 1937 15 no. 5. 29 Brun Univ. Bergen Arb;k 1954 Nr. 15. 30 Henderson 2. physik. Chem. 1907 59 118 ; 1908 63 325. 31 Wyllie J. Physic. Chem. 1954 58 67. 32 Sollner J. Physic. Chem. 1949,53 121 1 and 1226 ; Sollner Dray Grim and Neihof, Ion Transport Across Membranes (Acad. Press N.Y. 1954) p. 155; Dray and Solher Biochim. Biophys. Acta 1955 18 341. 33 MacInnes J. Franklin Inst. 1938 225 661