I n using the weighted ordinate method to determine the complementary color points of the copperdye mixtures, the absorbance at two wave lengths was zero, and three of the other wave lengths fell a t points where only minor changes in the spectra occurred as the copper ion concentration was increased. As the treatment of the spectral data was purely mathematical, an attempt was made to mako better use of the differences in the series of spectra. Ten new wave lengths n-ere chosen, with 15-mp intervals instead of the usual 30-mp interval. Because the analog computer had been designed and standardized using the normal C I E tristimulus parameters for illuminant C, these same parameters nere employed a t the new wave lengths. The wave lengths normally used were reassigned as follows: 415 nip = 415 mp, 445 = 430, 475 = 445, 505 = 460, 535 = 475, 565 = 490, 595 = 505, 625 = 520, 655 = 535, 685 = 550. A plot of the x,y points obtained from these calculations is shown in Figure 5 , C. The similarity t o Figure 5 , B, is
immediately apparent and the same relationships discussed previously are valid for this plot. A slight improvement mas made over the normal tristimulus method, in that the distance between the x,y points of the 1 to 2 and 1 to 1 metal-dye complexes was increased. This allows more accurate determination of the intersection of the two lines and hence of the mole ratio of the first complex (this case being a 1 to 1 complex). Alteration of the X,Y , Z parameters is a possible means of further improving the tristimulus approach to this type of analysis. To simplify further the determination of the formula of a complex ion, the “abbreviated three wave-length method,” discussed previously for threecomponent analysis, n-as used. The three wave lengths chosen were: 505 mp (the absorbance maximum of the free dye a t p H 6.6),460 mp (the absorbance maximum of the 0.5 mole ratio Cu++/dye mixture), and 445 mp (the absorbance maximum of the 2.5 mole ratio Cu+’/dye mixture). From the follovl-ing relationships values of x and y were calculated: 5 = &c5
+
8505
A460
+
A4445
A460
A505
+ Am +
- 4 ~ 6
A plot of the x,y values obtained for each solution is shown in Figure 5, D. As expected, the plot is very similar to those in Figures 5, B and C, and the two lines intersect a t approximately the same point. LITERATURE CITED
( 1 ) hIellon, M. G., “Analytical Absorption Spectroscopy,’’ pp. 530, 538, TVileJ-, New York, 1950. ( 2 ) Reilley, C. K.,Flaschka, H., Lanrent, S.,Laurent, B., ANAL.CHEU.32, 1218 (1960). ( 3 ) Willard, H. H., Merritt, L. I,.) Jr.,
Dean, J. A., “Instrumental Xethods of Analysis,” p. 182, 2nd ed., Van Kostrand, New York, 1951. (4) Wright, W. D., “Measurement of Color,” p. 114, Rfacmillan, New York, 1958.
RECEIVEDfor review May 9, 1960. Accepted June 6, 1960. Division of Analytical Chemistry, 137th Meeting, ..ZCS, Cleveland, Ohio, April 1960. Research supported by the United Statrs -4ir Force through the Office of Scientific Research, Air Force and Development Command, under Contract No. AF 49( 638)-333.
Coulometric Passage of Reagents through Ion Exchange Membranes RAYMOND B. HANSELMAN1 and L. B. ROGERS Departmenf o f Chemistry and laboratory for Nuclear Science, Massachusetts Institute o f Technology, Cambridge
,Reagents, some o f which are not readily obtained b y conventional coulometric techniques, have been “generated” b y passage through ion exchange membranes. Chloride, bromide, iodide, hydroxide, dihydrogen (ethylenedinitrilo) tetraacetate, silver(l), hydronium, and calcium ions have been generated a t constant current with efficiencies between 90 and 105% and standard deviations of about 1.5%. Variables that will b e important in extending the technique to other reagents have been evaluated.
titrations a t constant current require that a specific osidation or reduction be devised for each species that is to be generated. Many reagents, such as chloride, cannot be conveniently generated. The method devised by Reilley and Porterfield (10) for the electrochemical release on,omTRIc
1240
0
ANALYTICAL CHEMISTRY
of (ethylenedinitri1o)tetraacetic acid (EDTA) from a very strong mercury complex is a n interesting solution to this problem; but other electroactive species, if present, could interfere seriously. I n principle, the controlled passage of leagents through selectively permeable membranes offers a more general solution to the problem. For example, to titrate silver ion with chloride, a solution of sodium chloride is placed in a generator cell, one wall of \vhich is a membrane permeable to anions. A platinum generator cathode is dipped into a cell containing a n electrolyte which, in turn, is placed in the solution of silver ion plus the same electrolyte. (The platinum generator anode is connected to the silver solution through the usual salt bridge.) Passage of current liberates hydrogen a t the cathode and forces chloride through the membrane at a n efficiency which is a function of the anion transference number of the membrane.
39, Mass.
Because membranes currently available are not perfectly charge selective, our primary goal was to attain a rcproducible current efficiency close to
100%. This generation technique differs from the usual one in that the net reaction a t the generator electrodes is unimportant; it is almost allvays the electrolysis of solvent. The actual generation reaction is ion transfer across a membrane. This use of the membrane differs from that recently published b y Feldberg and Bricker ( 3 ) in which the membrane n-as used as a selective salt bridge to prevent contamination of the titrated solution with products of the electrode reaction. Titrations of silver ion with chloride. hromide, and iodide were examined first because those anions have not
1 Present address, Union Carbide Plastics Co., Bound Brook, N. J.
been generated previously and their reactions are easy to follow. The reverse titrations with silver(1) ions can, of course, be performed directly with a silver anode, b u t silver(1) was used in this study to evaluate the behavior of a cation-permeable membrane. Calcium and dihydrogen (ethylenedinitri1o)tetraacetate were selected to demonstrate the behavior of multivalent ions. Although the halide titrations indicated the difficulties arising from ionpair formation in the membrane arid from interdiffusion (nonfaradaic addition of reagent ions in the membrane by their exchange with ions of the same charge type from the supporting electiolyte in the titrated solution), these effects Jyere investigated more tho! oughly in acid-base studies. Mein111 ane polarization effects (8),which could be significant in other titiatioiii, n ('I P shonm to be less important in acid1m.e work. EXPERIMENTAL
Reagents and Solutions. Standard solutions of silver, halides, acid, and base were prepared a n d standardized b y accepted procedures. A standard solution of E D T A n a s made u p by 11eight from t h e disodium dihydrate. T h e value checked within 0.05% when riin against a standard solution of zinc made u p b y direct weighing from zinc metal. A solution of calcium nitrate I\ as standardized using this solution of E D T A . Sodium naphthalene-2-sulfonate was prepared by sulfonation of naphthalene ( 4 ) followed b y three crystallizations from water at temperatures belon60" C. Tetraalkylammonium nitrates were pi epared from the respective halides (Rastman Kodak Co., White Label) by adding silver nitrate and filtering off the silver halide. Tetra-n-butylamnionium nitrate was purified by several recrystallizations from benzenechloroform; tetraethylammonium nitrate was recrystallized from etherchloroform. A11 crystallizations were carried out below 60' C. t o avoid decomposition. Apparatus. Membranes obtained from National illuminate Co. were used t o obtain all of t h e d a t a presented here. T h e cation-permeable nienibrane was Salfilm 1; t h e anionpermeable membrane was Nalfilm 2. The moisture contents of Nalfilm 1and 2 in the hydrogen and chloride forms were 20.2 and 16.57, nhen dried over magnesium perchlorate at rooni temperature using a vacuum of less than 0.01 mm. of mercury. Their respective capacities were 0.96 to 0.87 meq. per gram of dried membrane. Figure 1 shows how membranes were mounted in a cell constructed from a screw-capped glass vial from ivhich the bottom had been removed. The height of the cell was increased b y scaling it to
Figure 1.
shortest for membrane cells n hich, after equilibration n ith internal membranecell solution, had heen stored vith distilled water outside the membrane. Storage in an electrolyte r a s less satisfactory, whether the electrolyte chosen was that of the membrane-cell solution or of the supporting electrolyte of a sample that was to be titrated. Samples were added to pretitrated supporting electrolyte from a calibrated Krogh-Keyes syringe-type buret fitted n ith a glass capillary tip t o avoid corrosion. One milliliter \vas delivered with a precision better than 0.1% A minimum of four successive titrationn a s usually run, but 6 to 10 titration< were frequently made. Usually 150 to 500 seconds were required for a titration. Alkaline solutions ryere deaerated n ith prepurified nitrogen t o minimize uptake of carbon dioxide. Interdiffusion runs nere made in the iame way as a titration except that the cwrrciit generator was disconnected. The amount of interdiffusion was usually measured after a relatively long time had passed in the hope that the calwlated average rate 1%ould be cloqe to a steady-state or limiting onr. T h r rate< ('re reproducible to about 5%.
Membrane cell
a piece of glass tubing. A hole was drilled in the cap to expose a membrane area of about 0.20 sq. em. The cap was sealed n i t h Apiezon W wax to prevent leakage. Resistances of mounted membranes, in equilibrium with 0 . 5 H sodium chloride, were measured a t 1000 c.p.5. with a Model RC 1B conductivity bridge from Industrial Instruments, Inc. Values close to 800 ohms mere obtained, whereas in the absence of a membrane the value was 10 ohms. The titration setup in Figure 2 shonq the two platinum foil generator electrodes which were connected to a source of constant current, modified to give eter from Applied Physics Corp. n a ~ used to measure potentials of the silver glass, and p M ( 1 1 , 12) indicator elecstrodes against a Laturated calomel electrode (S.C.E.). Appropriate salt bridges n ere used. Procedures. About 50 nil. of supporting electrolyte were placed in the cell and titrated b y intermittent generation of reagent t o t h e predetermined equivalence-point potential. This pretitration, if evtended over a b o u t 100 seconds, not only took care of the blank but also brought the current efficiency t o a stable value. The time required to reach R qtable efficirnc? 15 a'
E = (2
- 2 t ~ ) ( 1 2 T / FIn)
(A,/A2) ( 1 )
where E , R, T , and I.' have the usual meanings. This crude equation can be derived from Scatchard's treatment (14) by neglecting R-ater transport and assuming that transference numbers are constant across the membrane. RESULTS
Chloride. Table I gives typical results. Presumably larger amounts could have been determined routinely becalm) there was no evidence in this seriw. or in later ones with other halides, of surface blockage b y precipitatr. Smaller amounts were not examined because t h e solubility of silver cshloride led to poor end point
Reference
Table I. Chloride Titrations of Silver in 0.5M Sodium Perchlorate
EleCtrOdk
(20.00 ma./O.5M
sodium chloride in membrane cell)
Sample Current Std. Dev; Eq. x 10' Efficiency: % %
1.005 1.005 0.500'2 0.5002 0 . 5002a Figure 2. Titration "generating" anions
setup
for
a
97.6 97.1 06.0 96.3 96.4
0.38 0.20 0.65 1.08 0.45
10.00 ma.
VOL. 32, NO. 10, SEPTEMBER 1960
1241
Table II.
Effect on Titrations of Silver of Supporting Electrolyte and Concentration of Iodide in the Membrane Cell
Sodium Iodide, M
Sample,
Current, Ma.
Eq. X lo7
Current Efficiency, %
Std. Dev.,
70
A. 0.5111 Sodium Perchlorate Supporting Electrolyte
0.5
1000 500.0 50.25
0.5
0.5
20.00 10.00 2.000
50.5 52.7 62.4
0.75 3.77 10.71
B. 0.005M Sodium Naphthalene-2-sulfonate Supporting Electrolyte 0.05 0.01 0.005 0.005 0,005
0,005 0,005 0,005
5.015 5.015 10.03 5.015 5.015 2.507 2.507 1 254
0.1500 0.1500 0.3000 0.30OO 0.1500 0.1500 0.0750 0 0750
Table 111. Anion Transference Numbers in Nalfilm 2 from Potentiometric Measurements 8,
ta
A2
A. Sodium Iodide 0.009076 0.04145 0.04145 0.07905 0,07905 0.3640 0.3640 0.7411
0.997 0.738 0.601 0.532
B. Sodium Bromide 0.009078 0.04131 0,04131 0.07831 0.07831 0.3488 0.3188 0.6899
0.991 0.954 0.909 0.872
Table IV. Titrations of Silver Ion in 0.5M Sodium Perchlorate with 0.5M Sodium Bromide in Membrane Cell
Current, Sample Current, Efficiency, Std. Eq. X lo5 Ma. % Dev., 5% 10.00 20.00 80.3 1.56 5.005 10.00 80.5 3.21 1.001 98.1 3.01 2.000 0.5005 1,000 100.8 4.74 5.005" 10.00 87.0 4.48 a 0.lM sodium perchlorate supporting electrolyte; 0.1M sodium bromide in membrane cell. breaks. Attempts t o decrease the solubility b y addition of ethyl alcohol led t o other effects which will be discussed later. A slow drift of potential was observed near the equivalence point when current was not flowing. The drift was presumably due to interdiffusion-exchange of chloride in the outer surface of the membrane by perchlorate in the titrated solution-because drift stopped when the membrane cell was removed from the solution. I n general, the net effect of interdiffusion will be at a minimum when current is flowing because most of the interdiffused perchlorate will be transported back into the sample. Such transport will be less effecthe at lower current densities. 1242
ANALYTICAL CHEMISTRY
97.3 99.2 95.3 94.9 100.7 97.3 100 7 101 3
0.86 0.61 1.67 1.88 1.49 0.99 2 01 3 01
Iodide. This halide was studied next because t.he lower solubility of its silver salt permit's small quantities to be titrated. Table 11, A shows results obtained using t h e same supporting electrolyte and two of t h e same amounts of silver as in t h e earlier titrations with chloride. One striking feature is the decidedly lower current efficiencies, which must have been the result of membrane deactivation by formation of ion pairs in the membrane (2, 6 , 16). Confirmation of the lower anion mobility is shown by the results in Table 111. A second feature is the higher efficiency and standard deviation encountered a t the 5 beq. level, probably as a result of interdiffusion. U y using a lower concentration of iodide (to shift the ion-pair equilibrium) and a larger anion than pcrchlorate (to decrease interdiffusion), these effccts were almost entirely counteracted, as shown in Table 11, 13. Ho~vevcr,the efficiencies over 100% indicatc that some interdiffusion still occurred with the larger naphthalene-sulfonate ion c w n though its concentration was only 1'53 of that of the pcrchloratc. Neasurement,s of intc,rtliffusion by "current-off" titrat,ions gave values of 4.35 X 10-l' and 3.98 X 10-l' equivalent per second for 2880 an ! 12,600 scconds, respectively. 13ecausc a current of 0.15 ma. corrcqonds to 1.55 X 10-9 equivalent' per second, interdiffusion n-as adding iodide a t 2 . i % of the faradaic rate. The last figure should not be taken too literally because the interdiffusion rate decreases continuously with time, because of changes in concentration gradients, particularly in the first 400 seconds. I n the intermit,tent method of titrat'ion used in our study, the error \\-as worse for smaller samples because shorter times and smaller currents had to be used. Bromide. Few results are shown in Table I V for bromide because the
behavior, as anticipated, was intermediate between t h a t of chloride and iodide. Increases in current efficiency with decreases of bromide concentration and current were due t o ion-pair formation (Table 111, B) and interdiffusion effects. Silver. Tetra-n-butylammoniuni nitrate was selected as t h e supporting electrolyte in t h e hope t h a t t h e large cation ~ o u l dhave a lower mobility in the membrane. Results in Table V follow the same pattern as those for the halides. I n these titrations, the platinuni anode in t h e membrane cell became coated with black crystals. These crystals gave the positive qualitative tests of silver(I1) oxide (15).
Table V. Silver Ion Titrations of iodide in 0.01 M Tetra-n-butylammonium Nitrate
Current Sample Current, Efficiency, Std. Eq. X 106 Ma. 70 Dev., 70
A. 0 5%' Silver Kitrate in Membrane Cell 5 015 2 000 97.5 2 79 5 01.5 1 000 99 x _2 11 _ 2 507 1 000 100 5 0 97 2 507 0 6250 102 0 1 22 1 003 0 6250 101 3 1 45 B. 0 05;lI Silver Yitrate in Membrane Cell c5 060 0 6250 98 1 26 ~- 5 . 2.507 0.6250 99.5 1.06 1.003 0,6250 101.5 2.36 1.013 0.3000 100.5 1.58 0.5060 0.3000 100.1 1.86 1.012 0.1500 99.9 0.53 0 5000 0 1500 101 5 0 74 0 2024 0 1500 100 8 3 51 0 5015 0 0750 102 4 1 39 0 0750 0 2006 104 8 1 67 0 0750 0 1003 105 2 1 82 0 1003 0 0400 107 1 2 6'3
With silver there were no serious effects of ion association (1, 6, 7') but interdiffusion effects were larger. This afforded an excellent opportunity to compare relat'ive rates of interdiffusion for different cations at different levels of silver. Ta.ble VI shows that a deci'ease in concentration of sodium ion lowered the rate of interdiffusion. Furthermore, the rate decreased on going from sodium ion to tetraethylammonium to tetra-n-butylammonium. The difference between the first and last species is greater than can be accounted for by the 2.5-fold greater mobility of sodium ion in water ( I S ) . Mobility of the larger ions must be relatively smaller in the membrane because of steri-ceffects. A dependence upon the concentration of silver ion can be seen by comparing the two runs of 0.01.11tetra-n-butylamnioniuin nitrate. Hydroxide. T h e standard devia-
Table VI. Limiting Rates of Interdiffusion for Titrations with Silver
AgSOs,
,%I in hlembrane Cell 0.1 0.1 0 1 0 0 0 0 a
1 05
05 05
Bu
=
Supporting Rate Eq./ Electrolyte, AI5 Sec. X l o g 0 . 5 xaC104 1.71 0 . 1 xaClO4 1.55 0 01 XaC10L 1.29 0 01 Bu4ru’S’03 0 38 O 24 0 1 BU4NxO3 0 23 0 01 Bu4NSO1 0 01 Et4NSOt 0 38
n-butyl; E t
=
Table VII. Hydroxide Titrations of Perchloric Acid in 0.1M Sodium Perchlorate
Sample,
1
Std.
C‘ Eq. X lo6 /o Ma. Dev., % A. 1.0M Sodium Hydroxide in Membrane Cell
19 38 19 38 9 691 9 691 4 845 4 845 2 422
ethyl
tions obtained in this series (Ta!,le VII) ivvere consistently lower than in all b u t t h e titrations of large amounts of chloride. This was due in part t o faster equilibration of the system and faster electrode response, both of which would result in shorter periods for “current-off” interdiffusion. In addition, the fact that the current efficiency was constant over a range of current densities from 25 to 400 ma. per sq. em. in 1.0.11 sodium hydroxide and as low as 5 ma. in 0.LU indicates that membrane depolarizat’ion must have occurred through dissociation of water ( 8 ) . I n this case: the depolarization reaction at the membrane surface (lid not affect current efficiency because the p1,oduct (hydroxide ion) was the same as that in the desir,ed faradaic process. The effects on current efficiency of changes in the nature and concentration of supporting electrolyte are shown in Table VIII. The marked d t cw a s e found in 1 , O X sodium perchlorate is probably due to ion pairing and to Donnan invasion of the resin by the salt. Donnan invasion would mcan that a large number of mobile cations ryere in the resin, so the transference number of the anion woulcl he reduced. One would expect 1 . O X solutions of nitrate, sulfate, and chloride to show the same effect. However, the decrease was riot as pronounced in the:>e cases Iwause of thcir smaller tentlencies to form ion pairs. A study of the limiting rates of int>erdiffusionbrought out several interesting features. The high rate reported in Table IX for a solution containing 1.ON sodium hydroxide and 0.1JI sodiuin perchlorate was not signifirantly lower than the initial rate. It is possible that diffusion of sodium hydroxide-equivalent’ amounts of sodium and hydroxide ions-through the membrane may have occurred in addition bo replacement of hydroxide by perchlorate (interdiffusion). The fact that substitution of naphthalene-2sulfonate for perchlorate reduced the rate may indicate that the formcr was sterically blocking the pores of the
Current Efficiency,Current,
Table IX. Limiting Rate of Interdiffusion for Titrations with 0.1 OM Sodium Hydroxide in Membrane Cell
1 938 0 9691 0 4843 0 2422 0 2422
04.8 94.9 95.7 96.8 95.2 95.4 95,3 96.0 95.7 04.4 06.6 07.0
80.00 50.00 50.00 24.00 24.00 12.00 12 00
5.000 5.000 2,500 2,500 1,250
0.55 0.17 0.87 0.66
0.22 0.96 0.29 0.45 1.91 3.77
B. 0.1ON Sodium Hydroxide in ?\Ternbrane Cell 0.9691 95.8 2 .m n fin 0 4815 94 i 2 500 o 93 0 4845 95 2 1 250 0 89 0 2422 97 0 1 250 1 67
membrane (a). This conclusion was supported by the lower rate found on going from 0.01 to 0.1J1naphthalene sulfonate a t the 0.1X level of sodium hydroxide. K i t h 0.1JI sodium hgdrouidc in the membrane cell, the limiting rate passed through a maximum a t 0.1M sodium perchlorate. The lower rate a t 1 . O J I perchlorate may have resulted from invasion of the membrane and ion-pair formation. Both factors would tend to reduce m-elling of the membrane and hence the intramembrane volume ai-ailable for diffusion. Deswelling may a140 account for the lower value with 1.0V sodium chloride, though the observed decrease is within experimental error. The ralues for 0.1N sodium sulfate and nitrate, Tyhich are loner than that
Table VIII. Effects of Supporting Electrolytes on Titration of 2.422 X Equivalent of Perchloric Acid
loG
(Current of 1.250 ma. and 0.1J1 sodium hydroxide in the membrane cell) Supporting Current Electrolyte, Efficiency, Std. 5% Lkv.,yc 1. O SaCIOd 45 9 13 51 0 10 SaC104 97 0 1 67 0.01 SaC104 1 72 97 9 1. O S a C l 88 6 4 80 0.10 XaC1 1 31 108 7 0.01 S a C l 1 33 100 0 1.0 N?I 48 1 0 74 0.10 h a 1 97 6 1 05 1.0 NaNO1 0 73 63 8 0.10 XaXO, 103 8 1 12 1.0 Sa?SOA 84 0 1 20 0.10 sa,so, 98 2 1 82 0.10 NaKaph 91 5 0 58 0.01 NaKaph 91 9 0 85 Naph = 11 aphthalene-2 -5Ulflmate. 5
A
0.54
2.09
Supporting Rate, Eq./Sec. Electrolyte, M a x 109 0.10 KaCIOL 4.13 0 10NaXadh 2.66b 1 0 NaCIOl O..X 0.10 SaC104 0 82 0 01 xaClO4 0.68 0 10 Nall‘aph 0 13 0 01 SaNaDh 0.40 1. O NaCl 2.38 , O . 10 NaCl 2.41 0.01 NaCi 1.64 0 10 Sa2SO4 2.06 0 10 NaiSOs 1.99 S a p h = naphthalene-2-sulfonate 1.0.11 NaOH.
a
Table X. Titrations of Sodium Hydroxide in 0.1M Sodium Perchlorate Supporting Electrolyte
Current Efficiency,
Std. Sample Current, Dev., c Eq. X 104 Ma. % /O A. 1.0-If Perchloric Acid in Mcinbrane Cell 1.965 100.00 96.36 0.91 0.9823 97.51 1.44 50.00 0,9823 25.00 100.06 0.62 25.00 0.4911 100.21 1 . 3 6 0.4911 10.00 103.73 0 . 8 1 0 1965 10 00 103 61 3 16 0 1965 5 000 109 28 1 31 0 09823 5 000 112 59 1 06 B. 0.1.U Perchloric Acid in lfembrane Cell 1.965 100.00 98 99 1 39 n 9%2:1 50 00 97 07 0 .52 0 4911 25 00 98 39 0 92 0 4911 10 00 100 63 0 96 0 1965 10 00 100 48 0 88 0 1965 5 000 104 16 1 46 0 09823 5 000 104 59 0 78 2.500 114.92 1 64 0.09823 2.500 124.74 5 GO 0 04911
for 0.1X chloride, may be due to a larger energy of activation for diffusion caused by coulombic and ion-pair phenomena, respectively. Runs made in ethyl alcohol-water mixtures using 0.lM hydroxide and 0.1X perchlorate were nearly the same as those run in mater alone. Hydrogen Ion. Table X shows t h e same absence of polarization effects as reported for hydroxide and t h e usual interdiffusion effects, particularly a t lower currents where amounts added during “current-off” periods represented a relatively larger fraction of the total amount added. Effects of changes in the supporting electrolyte are given in Table XI. i i n increase of sodium perchlorate from 0.01JI to 0.1M raised the efficiencv 10% presumably by interdiffusion. Further increase to 1.0-U probably failed to produce a significant change VOL. 32,
NO. 10, SEPTEMBER 1960
1243
because of Donnan uptake of sodium perchlorate which would tend to counteract interdiffusion. The maximum efficiency shown by 0.5M tetra-n-butylammonium nitrate might indicate that Donnan invasion became greater than interdiffusion a t 1 . O M . Some association of the tetran-butylammonium ion with resin sites or stwic blocking of the memhrane may also have occurred, thereby producing the reproducible but irregular changes in interdiffusion reported in Talde XII. Lower current efficiencies were. observed for tetraethylammonium nitrate compared to tetra-n-butplammoniuni nitrate in spite of higher rates of interdiffusion (Table XII). The most reasonable explanation appears to be the probable formation of ion pairs by tetraethylammonium ions and resin sites. Likewise, the large efficiencies for tetra-n-butyl ammonium ion coupled with low limiting rates of interdiffusion may indicate rapid displacement of hydrogen ions from t h r mt:mbrane sur-
Table XI. Effects of Supporting Electrolyte on Titrations of 9.823 X Equivalent of Hydroxide
(Current of 5.000 ma. and 0.1M pcrchloric acid in membrane cell) Supporting Current Electrolyte, Efficiency, Std. Dev.,
%
%
M a
1.o NaC1O4
105.9 0.10 NaCIOa 104 5 0.01 NaCIO1 94 3 1 O B ~ ~ K N O ~101 9 0 50 BUa?i%Oa 103 4 0.10 BuaXNOa 100 6 0 05 BurNNO? 99 0 0 01 BurNNOa 95 0
3.34 0.78
0 10 EtaNXOj 0 05 EtaNxOa 0 01 EtaSNOa
0 96 0 55 0 23
0 97 1 02 1 46
0 97
0 63 1 65
99 9
98 7 $14 6
99 97 0 57 Bu = n-butyl; E t = ethyl; Me = methyl.
high cuiiciit efficiencies. The lo\\ er efficiencies for E D T A may be due t o low mobility of the ion in the membrane as a result of either steric effects or association. However, the rise in efficiency n i t h current suggests t h a t as E D T A in the membrane neared the alkaline supporting electrolyte, the ion may have been converted to the trivalent species. Such a conreision n ould hare caused an apparent dccrcase in the current efficiency calculated on the basis of a divalent apeciee. DISCUSSION 2c
-
\*
$ L '
20
0
40
60
r m g h t Percent E l h o r o l
9C
--
IO2
Figure 3. Effect of ethyl alcohol on current efficiency Electrolytes, M Supporting
H
0.5 NaCIOI
0
0.01 B u ~ N N O ~ 0.1 N a C 1 0 4 0.1 N a C l O ,
V A
Membrane cell
0.5 LiCl 0.05 AgNOa 0.1 N a O H 0.1 HClOa
face by ion-pair formation, except a t 0.01V where pairing and blocking effects were minimized. Current efficiencies in ethyl alcoholwater mixtures were a function of the nature and concent'ration of the cation of the supporting electrolyte. Efficiencies were somewhat' loi-ier than in xater because of both ion-pair formation of supporting electrolyte with resin sites and reduced interdiffusion due to the greater energies of activation for diffusion in the lower dielectric media. Calcium and E D T A . Table XI11 demonstrates t h a t divalent ions can be passed through membranes with
1 0 Me4NC1 Q
Table XII. Limiting Rates of Interdiffusion for Titrations with 0.01 M Perchloric Acid in Membrane Cell
Supporting Electrolyte, M a 0 10 NaC104 1 0 NaC104 0 10 XaClO? 0 01 NaCIOo 0 50 B ~ a X " 0 3 0 10 BuaNXOa 0 05 BU4NxOq 0 01 BuaXF03
Rate, Eq./Sec.
x
9 9 6 3
109 94h
77 21 31 0 56 1 15 0 65 2 54
1.69 1 .83 1.77 1 . 0 Rle4NCl 4.98 a Bu = n-butvl. E t = ethyl; Me = methyl. l.OM"bC104 in memhrane cell.
1244
ANALYTICAL CHEMISTRY
XIII. Calcium-EDTA Titrations 0.50JI ammonia-ammonium nitrate buffer, pH 9.43 supporting electrolyte 0,.50M calcium nitrate in membrane cell Current EffiStd. Sample, Current, ciency, Eq. X lo5 % Dev., % Ma. A , Titration of EDTA v d h Calcium 1 250 12.50 96.0 1.54 6.25 97.4 1.17 1.250 97.5 1.85 6.25 0.625 98.5 1.26 0.625 3.125 Table
B. Titration of Calcium with EDTA 0.10M ammonia-ammonium nitrate buffer, pH 9.33 supporting electrolyte 0.10M EDTA (disodium salt) in membrane cell (pH 4.5) 84.9 1.16 6.25 1.258 84.6 1.62 0.6289 6.25 82.7 0.70 0.6289 3.125 3.125 81.7 0,3144 1.89
Effects of Association. I n high dielectric media, the tendency to associate increases with ionic size (unhydrated). Thus, association increases on going down t h e series: hydroxide, chloride, bromide. nitrate, iodide, and perchlorate. The most important form of association in our study was that of the "generated" ion ivith the charged sites of the rt,sin. It was shon-n that' current efficiencics of 96, 81, and 537, for chloride, hromide, and iodide, respectively, were c!osc t o the values found potentiometrically for the anion transference numbers. By reducing t'he halide concentration in the membrane cell, the degree of association tlecreased for a given ion and a higher efficiency resulted. The transport of silvei(1) was not, studied potentiomrt,ricallp but t,he results would probably have lxeii similar t>o those for bromidc or chloride. In the case of large cations, ion as5ociation with the resin sites may have caused charge neutralization (with resulting lower efficiencies for hydrogen ion transport), although blocking effwts seemed more reasonable. I n lo^ dielectric media, smaller ions are more strongly associated, the effect heing primarily one of charge density. In ethyl alcohol-water solvents, the intramembrane dielectric constant is higher than in the external solution. Thus, n-hen the external solution is io% alcohol, the internal solution is only 20% (6). This means that as t'he external solution goes from 70 to loo%, the internal solution must go from 20 to 100%. Correspondingly large changes in association would, therefore, be expected in that region. Once again, ion-pair formation might occur beta-ren two mobile ions or between one mobile ion and a resin site. Figure 3 show the effect of ethyl alcohol concentration on the current efficiencies for four ions. Because silver is believed to be somewhat associat'ed ivith resin sites even in water, i t should be most affected by alcohoI. On the other hand, the highly solvated hydroxyl and hydrogen ions behave like large ions of low charge density. Related to the subject of association
is the change in efficienry that results when an ion changes its charge within the membrane as a result of hydrolysis or dissociation. For example, some cations will hydrolyze if passed from a n acidic medium to a neutral or alkaline one; anions such as dihydrogen EDTA can pick u p or lose protons. Diffusion. In extreme cases, such as one in which 1.OM sodium hydroxide was used in t h e membrane cell, diffusion of cations and aiiionq through t h e membrane was suggested as a supplementary proccss t o interdiffusion. However, interdiffusion appears to be the factor that Kill be (Jncountered most frequently and will set the lower limit on sample size and current. Interdiffusion can be reduced hy lowering the concentration of electrolyte on the outside of the membrane and by the use of large counter ions in the supporting electrolyte. Large ions can introduce association effects, but the magnitudes of such effects should be small because of limited penetration of the membrane by the ion. Interdiffusion can also be controlled in analyses of small amounts by using smaller membrane areas. Under ideal conditions, the minimum current density was about 0.2 ma. per sq. cm., so that a membrane of 0.1 sq. cm. would permit the use of currents down to 0.1 ma. Polarization. T h e upper limit on current density is polarization of t h e membrane due t o deplrtion of reagent ions at the inner surface of the membrane (8). Polarization can be decreased by stirring the solution in the membrane cell and by increasing both the membrane area and reagent ion concentration in the cell. The use of high currents may. how-
ever, generate in the membrane cell significant concentrations of ions of the same charge as the reagent ion. For example, if a substantial concentration of hydroxide were produced during a titration rq ith chloride, i t could be transported through the membrane and n ould thereby decrease the observed efficiency for chloride. T o minimize t h a t effect, a substantial volume of moderately concentrated reagent ion ihould be used and frequently replaced with new solution. Alternatively, solutions containing acid or a n easily reducible ion can be used in studies of anion transport, and basic solutions or oxidizable electrodes for cation traneport. If such alternatives are impractical, the electrode can hr isolated from the solution in the niemtxane cell by a fritted disk. CONCLUSIONS
Passage of ions through selective membranes enlarges the number of reagents available for coulometric titrations. I n some cases, i t also provides a convenient means for accomplishing the same goal as external generation of reagents without causing significant changes in the volume of the titrated solution. Although the current efficiency is not 100.07,. it is usually reproducible to better than 27, under any set of controlled conditions. It appears, therefore. that this technique should be useful in continuous analyses of process streams. In the future, the availability of more selectire membranes should lead to better precision and higher current efficiencies. Homogeneous membranes of higher cross linking and lower ca-
pacity should be of particular interest. Studies of other solvent systems should also be useful. LITERATURE CITED
(1) Ahrland, S., Chatt, J., Dayiee, S. It., Killiams, .4. .4.,J . Chem. SOC. 1958,
264. (2) Boyd, G. E., Soldano, B. A . , ,J. -4m. Chem. Sac. 75, 6091, 8099 (1954). ( 3 ) Feldberg, S. W.,Bricker, (T, E., ANAL.C H i M . 31,1852 (1959 ’ (4)Fieser, L. F., “Experiments I I I Organic Chemistry.” 2nd ed.. Heath. BoPton. 1941. f 5 ) Gregor, H. P., Belle, J., llarciis. R .I., J . Am. Chem. SOC. 77, 2713 I 1955); 76, 1984 (1954). ( 6 ) Gregor, H. P., Xobel, D , Guttlieh, M.H., J . Phys. Chem. 59,5lU (1955). ( 7 ) Hevmann. E.. O’Donnell. I J.. J . i’olldid Sei. 4 , 405 (1959). (8) Kressman, T. R. E., Tye. F. L., Discussions Faraday SOC. 21, I50 (1956). (9) Reilley, C. S . ,Adams, R.S . ,Furmnn, S . H., AIVAL.CHEW24, 1044 (1952). (10) Reilley, C. K.,Porterfield, IT-. TT., Ibid., 28,443 (1956). (11) Reilley, C. N., Schmid, R . \I-.!Ibid., 30,947(1958). (12) Reilley, C. N., Schmid, R. K., Lnmson, D. IT.>Ibid., 30,953 (1958 1. (13) Robinson, R. A,, Stokes, R. H., “Electrolyte Solutions,” Buttermorths, London, 1955. (14) Scatchard, G., J . A m . Chem. Soc. 75, 2883 (1953). (15) SidgLvick, S . V., “The Chemical Elements and Their Compounds,” 1-01. I, Vnivereity Press, Oxford, 1950. (16) Ketstone, 1). hI., Gregor. H. P.. J . Phys. Chem. 61,151 (19571, RECEIVEDfor review April 12, 1960. Accepted June 22, 1960. Diwion of Analytical Chemistry, 135th Meeting, ACS; Boston, Mass.,’April 1959 Taken in part from the doctoral thesis of R. B. Hanselman at the Massachusetts Institute of Technology, May 1959. \Vork SIPported in part by the U. S. Atomic Energy Commisbion under Contract -4‘Y(:30-1)UO5.
Automatic Chloride Analyzer DALE
M. COULSON
and LEONARD A. CAVANAGH
Department of Chemisfry, Stanford Research Institute, Menlo Park, Calif.
b An automatic coulometric titration method has been developed for the determination of chloride in combustible samples. The method is rapid, requires less sample, and is more accurate than methods currently used.
T
eomnionly uspd method of determining chloride, bromide, or iodide in organic materials involves the combustion of the organic material in a microcombustion furnace followed b y a separate amperometric titration with silver nitrate. T o improve the speed HE MO,T
and accuracy of this type of analysis, n completely automatic method of combustion and titration has been developed. The titration method employs a variable voltage and variable current coulometer suitable for the continuous monitoring of the chloride content of a gas stream. The titration cell is connected directly to the combustion apparatus and the titration is performed automatically during the combustion period. Previously reported coulometric circuits ( I , 2 ) utilize a constant current source and the integral of constant current multiplied by variable time is recorded. I n this
newly developed system, the current multiplied by the time is integrated and recorded. However, the current is varied as needed to maintain a constant level of silver ions in the titration cell during the titration. APPARATUS
Titration Cell. 4 coulonietric titration cell has been developed t h a t is suitable for t h e titration of 0.1 t o 1000 kg. of chloride with internally generated silver ion. Figure 1 is a perspective view of the cell. Figure 2 consiuts of cross-sectional views of the cell taken VOL. 32, NO. 10, SEPTEMBER 1960
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