475
but this value is measured at pH 11 where hydroxide ion may interfere. (4) The stability constant for ring closure is 2.5 X lo3, so that only 0 . 0 4 x of Ni(en)sZ+ can exist in solution with five nitrogens coordinated.
(5) The results support the suggestion of the internal conjugate base mechanism. Acknowledgment. This investigation was supported by National Science Foundation Grant No. GP-6725X.
Reductions of cis- and trans-Diformatobis( ethy1enediamine)cobalt (111) by Chromium( 11). Doubly Bridging and Acid Catalysis'" J. Richard WardIb and Albert Haim
Contribution from the Department of Chemistry, State University of New York, Stony Brook, New York 11790. Received July 2, 1969 Abstract: The reductionsofcis-and trans-Co(en)2(HC02),+by Cr2+obeythe rate laws - d(ln [~is-Co(en)~(HCO~)~+])/ = (ko klQIH+I)[Crz+l,respectively. At 25 O dt = ko[Cr2+]/(l Q[H+]) and -d(ln [trans-Co(en)z(HCOz)~+l)/dt and [C104-] = 1.0 M , ko(cis) = 434 -f 11 M-1 sec-1, ko(trans) = 10.2 f 0.3 M-l ~ec-l,Q(cis) = 0.44 f 0.07 M-1, klQ(trans) = 15.0 f 0.7 M-2 sec-1. Protonation of cis- and trans-Co(en),(HCO,),+ is invoked to account for the observed kinetic patterns. Protonation of the cis complex decreases its reactivity toward chromium(I1) reduction, whereas protonation of the trans complex increases its reactivity. Both the ko and kl paths for the trans complex proceed uia inner sphere mechanisms with transfer of one formate ion from cobalt to chromium. The reaction of the cis complex proceeds via parallel singly and doubly bridged transition states with transfer of one and two formate ions, respectively, from cobalt to chromium. Various mechanistic details of these and related reactions are discussed.
+
+
T
he possibility that a doubly bridged transition state would provide a favorable pathway for electron transfer reactions was suggested long ago.2 Early attempts to find evidence for this type of mechanism in the reactions of c i s - C ~ ( e n ) ~ ( O H ~and ) ~ ~ cis-CrF2+ + with chromium(I1) were unsuccessful.3~4 In 1952, Snellgrove and King5 provided the first conclusive evidence for a pathway involving a doubly bridged transition state: the dominant reaction that takes place when cis-Cr(N3),+ and Cr2+ are mixed is the exchange of chromium atoms between the two chromium species (eq 1). It was shown subsequently that, concomitant
cis-*Cr(N3)a+
+ Cr2+
(1)
with the exchange reaction, but proceeding at a slower rate, a net reaction involving a singly bridged transition state (eq 2 ) was also important in this system.6 cis-Cr(N&+
+ Cr2+ --t [cis-NaCrN3Cr3+]* -+CrN3*++ Na- + Cr2+ (2)
(1) (a) This work was supported by Grant GP-6528 from the National Science Foundation. (b) Abstracted in part from the Ph.D. dissertation of J. R. Ward, State University of New York at Stony Brook, Feb 1969. (2) H. Taube and H. Myers, J . Amer. Chem. SOC.,76, 2103 (1954)~ (3) W. Kruse and H. Taube, ibid.. 82, 526 (1960). (4) Y. T. Chia and E. L. King, Discussions Faraday Soc., 29, 109 (1960). (5) R. Snellgrove and E. L. King, J . Amer. Chem. Soc., 84, 4609 ( 1962). (6) A. Haim, ibid., 88, 2324 (1966).
The factors governing the relative efficiencies of doubly and singly bridged paths are not apparent from the limited amount of data available, and a systematic study of a variety of systems featuring parallel singly and doubly bridged pathways seems to be called for. The report' that 69 of the chromium(II1) produced in the chromium(I1) reduction of C ~ ~ - C O ( N H ~ > , ( C H ~ C O , ) ~ + has a unipositive charge (presumably cu-Cr(OHz)4(CH3CO&)+ encouraged the initiation of a study of the chromium(I1) reductions of cis-dicarboxylatocobalt(II1) complexes, and the results obtained with the cis-diformatobis(ethylenediamine)cobalt(III) complex are reported here. In addition, because of the interest of the authors in the relative reactivities of cis and trans isomers in redox reactions,s the results obtained for the chromium(I1) reduction of trawdiformatobis(ethy1enediamine)cobalt(II1) are also reported. The comparison of the kinetic behavior for the cis and trans isomers is of particular importance in the present system because formate ion is the conjugate base of a weak acid. For the analogous reactions of complexes containing basic ligCr2+ ands, namely cis- and trans-CoA4(CH3COz),+ and cis- and t r a n ~ - C o ( N H ~ ) ~ (A = NH3 or 1/z(en)71gs10 Fez+, contrasting kinetic behaviors have (N3)2+ been reported; regardless of geometry, the diacetato complexes exhibit acid-catalyzed paths, whereas for the diazido system only the trans isomer exhibits an acidcatalyzed path. Consequently, the hydrogen ion de-
+
+
(7) R. T. M. Fraser, ibid., 85, 1747 (1963). (8) D. E. Pennington and A. Haim, Inorg. Chem., 5, 1887 (1966), and references therein. (9) K. D.Kopple and R. R. Miller, Proc. Chem. Soc., 306 (1962). (IO) R. T. M. Fraser, Inorg. Chem., 2,954 (1963). (11) A. Haim, J . Amer. Chem. Soc., 85, 1016 (1963).
Ward, Haim / Reductions of cis- and trans-Co(en)2(HC02),+by Cr2+
476 Table I. Electronic Spectral Data for Formatoamine-Cobalt(II1) Complexes A, nma
Complex
A, M-1 cm-1
Ref
cis-Co(en)z(HCO&+
501, 362, 224= 128. 85.0. 1.8 X lo4 d d 501, 362, 224" 128; 84.3; 1.8 x 1046 d 540, 453, 357, 233 51.4, 30.6, 66.5, 1.6 X lo4 d 66.5, 54.4, 1 . 3 x 104 501, 349, 232 (sh) 503, 352 58.9, 44.7 f 503, 351 69.2, 55.0 g a Wavelengths for absorption maxima. Molar absorptivities at absorption maxima. From [ C O ( ~ ~ ) ~ C O ~ ]and ( C ~formic O ~ ) acid. perchloric acid, and sodium formate. See text. M. Linhard and M. Weigel, 2. See text. This work. e From [C0(en)~C03](ClO~), Anorg. ANg. Chem., 264,321 (1951). 0 K. Kuroda, Nippon KagakuZashi, 82,1481 (1961).
pendences of the cis- and trans-Co(en)z(HC02)z+-Cr *+ reactions have been investigated in detail.
Cr(OHz)5(HC02)a+ and cis-Cr(OH2)4(HCO,),+. In order to obtain high recoveries of these complexes, it was necessary to use Dowex 50W X-2 in the sodium form, to elute the chromium(II1) cations with sodium perchlorate solutions, and to carry out the ion exchange Experimental Section operation near 0". In spite of these precautions, blank experiments indicated approximately 95% recovery of the complexes. Although Materials. Chromium(I1) perchlorate stock solutions were prethe recoveries were somewhat less than quantitative, good separapared by reduction of chromium(II1)perchlorate with amalgamated tions of the complexes could be achieved. After various attempts, zinc. Lithium perchlorate and sodium perchlorate were prepared it was found that slow elution with 0.1 M sodium perchlorate-0.01 by neutralization of standard perchloric acid solutions with anhyM perchloric acid cleanly separated c ~ ~ - C ~ ( O H ~ ) ~ ( H Cfrom O&+ drous lithium carbonate and anhydrous sodium carbonate, respecC~(OHZ)~(CHO~ and ) ~ +that , Cr(OH2)5(HC02)2+was cleanly s e p tively. Sodium oxalate (Baker Analyzed Reagent), used in the arated from Cr(OH2)e3+by elution with 0.5 M sodium perchloratestandardization of potassium permanganate solutions, was dried 0.05 Mperchloric acid. at 105" for 3 hr. The cation exchange resins Dowex 50W X-8 Formatopentaaquochromium(II1)was prepared and isolated in and X-2 (5&100 mesh) were purified by pretreatment with warm solution in two ways. In the first method, 10 mg of [c0("3)5alkaline hydrogen peroxide. Triply distilled water was used to (HC02)](C104)2 was dissolved in 15 ml of water and 1 ml of 2.36 M prepare all of the solutions. perchloric acid at 0". The solution was deaerated by bubbling Manipulations involving oxygen-sensitive solutions were carried argon for 20 min. A stoichiometric amount of chromium(I1) out in an atmosphere of argon. The argon was purified by passing was added, and the solution was allowed to stand for 30 min. The it over a BTS catalyst (B.A.S.F. Colors and Chemicals, Inc.). solution was added to a 15 X 1 cm column of Dowzx 50W X-2 All other chemicals were reagent grade, and were used without fur(50-100 mesh, sodium form) surrounded by ice. The resin was ther purification. washed with 50 ml of 0.1 M sodium perchlorate-0.01 M perchloric Preparation of FormatoamineCobalt(II1) Complexes. The prepacid, and then the Cr(OH2)5(HC02)2+ ion was eluted with 0.5 M aration of cis-diformatobis(ethylenediamine)cobalt(III) perchlorate sodium perchlorate-0.05 M perchloric acid. Under these condiwas initially attempted by the method of Linhard and Stirnla starttions, Cr(OH2)5(HC02)*+ moves slightly faster than Co2+,and thereing with [Co(en)2C03](C104). The molar absorbances of the matefore, the chromium(II1) complex collected for identification conrial obtained were lower than expected, perhaps because of incomtained no cobalt(I1). The spectrum of the eluate was recorded, plete conversion of C o ( e n ) ~ ( 0 H ~to ) ~cis-Co(en)z(HC02)z+, ~+ Linhard and Stirn give an alternate preparation of cis-[Co(en)~(HCO~)~]- and aliquots were removed to determine the chromium content. In the second method, 21 ml of 97% formic acid was added to a Consequently, the (Clod) starting from [Co(en)~(OH~)~](C104)3. solution containing 0.6 g of potassium dichromate, 3 ml of 11.8 M material from the first preparation was assumed to be contaminated by the diaquo complex, and was converted to cis-[Co(en)~(HCO~)~]- perchloric acid, and 21 ml of water. The resulting solution was allowed to stand at room temperature for 3 hr, and the color (C104) by the alternate method. Anal. Calcd for cis-[Co(en)zchanged from orange to gray-purple, indicating reduction of chro(HCOz)2](C104): C, 19.55; H, 4.92; N, 15.20; Co, 15.99. Found: mium(V1) to chromium(II1). The solution was diluted threefold, C, 18.46; H, 5.28; N, 15.53; Co, 15.89. A second batch of cisand the Cr(OHz)j(HC02)2+ion was isolated as before. [Co(en)~(HC0~)~l(Cl04) was prepared by treating 5 g of [Co(en)2cis-Tetraaquodiformatochromium(II1)was prepared in solution C03](C10a)with 30% perchloric acid until the evolution of carbon by the chromium(I1)reduction of cis-Co(en)2(HC02)2+.A solution dioxide ceased. Sodium formate (2.3 g) was added, and the mixture containing 10-15 mg of cis-[Co(en)~(HCO~)~](C104) in 20 ml of was evaporated to near dryness at 50". The crude product was water was deaerated by bubbling argon for 20 min. One ml of 2.36 recrystallized from water, and the resulting crystals were washed Mperchloric acid was added, followed by the stoichiometricamount with ethanol and ether, yield 3 g. Anal. Calcd for cis-[Co(en)zof chromium(I1). After 1 min, the resulting solution was diluted (HC02)2](C10d): C, 19.55; H, 4.92; N, 15.20; Co, 15.99. Found: threefold, and then added to a 15 X 1 cm column of Dowex 50 W C, 18.75; H, 4.93; N, 14.49; Co, 15.73. AsshowninTableI, the X-2 (50-100 mesh, sodium form) surrounded by ice. The resin materials obtained by the two methods exhibit essentially identical was washed with 50 ml of distilled water, and then the cis-Crelectronic spectra. (OHz)4(HC02)2+ ion was eluted (1 mlimin) with 0.1 M sodium pertrans-[Co(en)~(HCO~)~](ClO~) was prepared and recrystallized chlorate-0.01 M perchloric acid. The absorption spectrum was following the procedure of Linhard and Stirn.l2 Anal. Calcd for recorded, and aliquots were removed to estimate the chromium and trans-[Co(en)2(HC02)2](C104):C, 19.55; H, 4.92; N, 15.20; formate contents. Co, 15.99. Found: C, 19.41; H, 5.16; N, 14.62; Co, 16.08. Stoichiometric Measurements. Stoichiometric experiments were [CO(NH~)~(HCO~)](C~O~)~ was prepared following the procedure of and Linhard and Rau. l 3 A n d . Calcd for [CO(NH&(HCOZ)](C~O&: designed to determine the amounts of ci~-Cr(OH2)~(HC02)2+ of Cr(OH2)6(HC02)2+ produced in the chromium(I1) reduction of C, 3.09; H, 4.16; N, 18.05; Co, 15.19. Found: C, 2.81; H, cis-Co(en)2(HC02)2+. The experiments were performed at [C104-] 4.26; N, 17.38; Co, 15.17. Electronic spectral data for these two = 1.0 M (the conditions used in collecting the kinetic data) and complexes are included in Table I. constant temperature. Low acid concentrations were used in order Preparation and Ion Exchange Separation of Formatoaquochroto minimize the aquation of cis-Co(en)z(HCO&+(prior to and durmium(III) Complexes. Previous investigators have reported diffiing the reaction with chromium(I1))as well as that of cis-Cr(OH2)4culties in recovering carboxylatopentaaquohromium(II1) com(HCO&+ (during elution from the resin). The desired amount of plexes absorbed on ion exchange resins by elution with acid. 14-16 ~is-[Co(en)~(HC0~)~](ClO~) (usually 2G25 mg) was dissolved in an Similar difficulties have been experienced here with the complexes amount of lithium perchlorate solution such that subsequent addition to perchloric acid and chromium(I1) would bring the total (12) M. Linhard and G. Stirn, Z . Anorg. Allg. Chem., 268, 105 volume to 10 ml and the perchlorate concentration to 1.0 M. The (1952). solution was deaerated for 20 min at O", and then placed in a con(13) M. Linhard and B. Rau, ibid., 271, 121 (1953). stant temperature bath at the desired temperature for 15 min. Pre(14) H. Taube, J . Amer. Chem. Soc., 77,4481 (1955). viously deaerated perchloric acid was added, immediately followed (15) E. S. Gould, ibid., 89, 5792(1567). by addition of the desired amount of chromium(I1). After com(16) E. Deutsch and H. Taube, Inorg. Chem., 7, 1532 (1968). Journal of the American Chemical Society
1 92:3
February 11, 1970
477 pletion of the reaction (30 sec), the solution was diluted to 100 ml with chilled triply distilled water, and then added to a 15 X 1 cm column of Dowex AG 50 W X-2 resin (50-100 mesh, sodium form) kept near 0 ” by a surrounding jacket of ice. Since the perchlorate ion concentration was 0.1 M after dilution, ions of charge $2 or higher were retained on the resin, but the unipositively charged C~~-C~(OH~)~(HC passed O Z ) Zthrough + the column. After the 100 ml of solution had percolated through the column, the column was rinsed with 100 ml of 0.1 M sodium perchlorate-0.01 M perchloric acid in order to ensure the quantitative removal of cis-Cr(OH2)4(HCO&+ in the first fraction. The ion Cr(OH2)5(HC02)2+was then removed by elution with 200-250 ml of 0.5 M sodium perchlorate-0.05 M perchloric acid. Duplicate chromium analyses were performed in each fraction. The Cr(H20)s(HC02)2+ fraction contained cobalt(I1) (which is also eluted with 0.5 M sodium perchlorate). Consequently, when this fraction was analyzed for chromium, cobalt hydroxide precipitated out. The precipitate was removed by centrifugation prior to the spectrophotometric measurements. The stoichiometry of the chromium(I1) reduction of trans-Co(en)2(HC02)2+ was determined at 25” by the same procedure, except that chromium analyses were performed only on the fraction eluted with 0.5 M sodium perchlorate. Kinetic Measurements. The rates of reaction of cis- and transCo(en)2(HCOz)z+ with chromium(I1) were measured in a rapid flow apparatus constructed following the design of Dulz and Sutin.” The cobalt(II1) solution contained the necessary amount of lithium perchlorate, but no perchloric acid since the acid-catalyzedaquation of cis-Co(en)2(HCO&+is a relatively rapid process.18 The chromium(I1) solution contained the necessary amounts of perchloric acid and lithium perchlorate. Special flasks were designedlb to maintain the reactant solutions under a slight positive pressure of argon at all times. For all experiments the chromium(I1) was in sufficient excess to ensure pseudo-first-order behavior. Four to six replicate measurements were carried out for each pair of reactant solutions at 270 nm. The photographs of the oscilloscope screen were enlarged, and the transmittance readings at 12 times during 3 half-lives were recorded. The readings were fit to the following equation
R
=
(l/B)[l - (1
- RoB)e-k‘]
(3)
where R is the reading at time f, R Ois the reading at time 0, B is a constant which depends on the gain in the oscilloscope and the offset calibration, and k is the measured first-order rate coefficient. The oscilloscope readings were fit to eq 3 using a nonlinear leastsquares program. l9 Ro and k were treated as floating parameters, and R and t were the dependent and independent variables, respectively. Analytical Methods. Chromium(I1) concentrations were determined by reaction with an excess of oxygen-free iron(III), followed by titration of the iron(I1) produced with standard potassium dichromate. 20 The acid concentration of chromium(I1) perchlorate solutions was determined by the procedure of King and Neptunezl as modified by Thompson and Gordon,22 Total chromium concentrations were determined spectrophotometrically as chromate after oxidation with alkaline hydrogen peroxide.23 Cobalt was analyzed gravimetrically by conversion of the cobalt(II1) complex to cobalt(I1) sulfate. 2 4 Carbon, hydrogen, and nitrogen analyses were performed by Schwarzkopf Microanalytical Laboratories, Woodside, N. Y. Analyses of formate in solutions of Cr(OH2)j(HC02)2+and cisCr(OH2)a(HC02)2+ were carried out by treating aliquots with 1 M sodium carbonate solution to pH 8-10. Formate ion was released from the coordination sphere of chromium(III), and chromium(II1) hydroxide precipitated. Perchloric acid was then added until the precipitate dissolved,and the resulting acidic solution was added to a (17) G . Dulz and N . Sutin, Inorg. Chem., 2, 917 (1963). (18) J. R . Ward and A. Haim, in preparation. (19) The nonlinear least-squares program is described in Los Alamos Report LA 2367 (March 4, 1960) and Addenda (Jan 14, 1963). (20) I. M. Kolthoff and E. B. Sandell, “Textbook of Quantitative Inorganic Analysis,” 3rd ed, The Macmillan Co., New York, N. Y., 1952, p 579. (21) E. L. King and J. A . Neptune, J . Amer. Chem. SOC.,77, 3186 (19 55). (22) R. C. Thompson and G . Gordon, Inorg. Chem., 5, 557 (1966). (23) G. W. Haupt, J . Res. Nu?. Bur. Stand., 48, 414 (1952). (24) L. Erdey, “Gravimetric Analysis,” Pergamon Press, Oxford, 1965, p 413.
5 X 1 cm column of Dowex 50 W X-8 (50-100 mesh, hydrogen form). Chromium(II1) was retained on the resin, and the effluent, containing formic acid, was analyzed by the procedure of Vogel.25 Blank experiments with synthetic mixtures of sodium formate and Cr(OH2)2+proved the method to be reliable to about 2 %. Instruments. Spectrophotometric measurements were carried out with a Cary 14 recording spectrophotometer. pH measurements were made with a Corning Model 12 Research pH meter. The least-squares computations were made on an IBM 7044 computer at the Stony Brook Computing Center.
Results Preparation and Identification of Cr(OH2)j(HC02)2 + and C ~ ~ - C ~ ( O H ~ ) ~ ( H CThe O ~ two ) ~ ~ previously +. unreported chromium(II1) complexes Cr(OH2)5(HC02)22+ and cis-Cr(OH2)4(HCOz)z+were prepared in solution, separated by ion exchange chromatography, and identified by determining the formate to chromium ratios. The monoformate complex was prepared by the inner-sphere reaction between C O ( N H ~ ) ~ ( H C O and ~)~+ Cr2+(eq 4) which, in common with other chromium(I1)
+
+
C O ( N H ~ ) ~ ( H C O ~ )C~ ~+ ( O H Z ) ~ ~5HaO+ + =
+
C O ( O H ~ ) ~ ~5NH4+ +
+ Cr(OH2)5(HC02)2+ (4)
reductions of carboxylatopentaamminecobalt(lI1) complexes, l4 features ligand transfer from cobalt to chromium. The same complex was also formed as a minor product in the reduction of chromium(V1) with an excess of formic acid.26 The complex obtained by either method was absorbed on Dowex 50W X-2 (50-100 mesh, sodium form), and eluted with 0.5 M sodium perchlorate, a behavior which strongly suggests a dipositive charge for the ion. As shown in Table 11, the samples obtained by the two different methods exhibit identical absorption spectra. The ratio of formate to chromium was 1.07 f. O.O2,*’ and it is concluded that the complex ion has the composition Cr(OHZ)@COZ)~+. Table II. Electronic Spectral Data for Formatoaquochromium(II1)Complexes” Complex Cr(OH2)5(HC02)2+ Cr(OH2)5(HC02)2+ cis-Cr(OH2)4(HC0~)~+ f
A , M-1 cm-1
A , M-1 cm-lc
20.2 f 0 . 1 20.3 A 0.1 27.4 rt 0.10
21.1 A 0 . 1 20.9 i 0 . 1 27.0 i 0 . l h
Each entry is the average value for three independent preparations. Molar absorptivity at 575 nm max. Molar absorptivity From Co(NH&(HC02)2+-Cr2+ reaction. at 412 nm max. e From (Cr(VI)-HC02H reaction. f From cis-Co(en)z(HC02)2+Cr2+ reaction. 0 Maximum absorption at 574 nm. *Maximum absorption at 413 nm. @
The diformato complex was prepared by the reaction between ci~-Co(en)~(HCO~)~+ and CrZ+ (eq 5) which
+
+
cis-Co(en)2(HC02)2+ Cr(OH&,2+ 4H30+ = Co(OH2)s2+ 2enHz2+ Cr(OH2)4(HC02)2+ (5)
+
+
(25) A. I. Vogel, “ A Textbook of Quantitative Inorganic Analysis,” 3rd ed, John Wiley and Sons, Inc., New York, N. Y., 1962, p 301. (26) The capture of ligands in the coordination sphere of chromium(111) formed by reduction of chromium(V1) appears to be a relatively common occurrence: L. S. Hegedus, B.S. Thesis, The Pennsylvania State University, 1965. (27) The excess of formate over chromium is attributed to aquation of the formate complexes during the ion exchange. During elution neutral formic acid will pass through the resin, whereas the chromium(111) species of higher charge will be retained in the resin. This will result in a high formate to chromium ratio.
Ward, Haim 1 Reductions of cis- and trans-Co(en)z(HCUdz+ by Cr2+
478 Table 111. Stoichiometry of the Chromium(I1) Reduction of cis-Co(en)z(HCOz)z+ Co(III), mmoles
Cr(II), mmoles
W+I, M b
0.132 0.135 0.146 0.136 0.063 0.066 0.064 0.14@ 0.1230
0.147 0.147 0.113 0.113 0.077 0.077 0.077 0.147 0.147
0.065-0.01 0.065-O.009 0.065-0.017 0.065-0.017 0.039-0.013 0.039-0.012 0.039-0.012 0.20-0.13 0.20-0.14
cis-Cr(OH& (HCOz)z+ 82.P 82.8d 85. Id 81.4d 79.7* 76.38 71.01
Z Cr(OH2)s-
'+
kriiksc
(HCOz)
13.7d 11.Y 9.9d 13.2d 17.96 21.18 23.4, 94.61 96.6f 19
6.4d 6.4d 8.6d 6.0d 5.2
4.18 3.0f
a@
a Total volume 10 ml, [CIOa-] = 1.0 M . Initial and final hydrogen concentrations; H+ is consumed during the reaction by the ethylto Cr(OH2)6(HC02)2+ produced in the reaction, corrected for loss of cis-Cr(OHz)(enediamine released. c Ratio of cis-Cr(OHz)c(HCOl)n+ (HCO&+ during ion exchange. d At 0". 8 At 15'. f At 25". Reactant is trans-Co(en),(HCO,),+.
proceeds in part by a doubly bridged transition state and features the transfer of two formate ligands from cobalt to chromium. For the identification of the complex, the reaction was carried out at low ionic strength, and the resulting solution was diluted (ionic strength
