function of the concentration of the ion in solution and of the pre-electrolysis time. Sensitivity appeared to be improved by about a n order of magnitude over that reported for the corresponding direct current stripping method (6). Thus, it is possible to perform analyses a t concentration levels about 10-fold more dilute than in the d.c. technique, or alternatively, to achieve a saving in time by employing shorter pre-electrolysis times a t the same concentration levels. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ANAL.CHEW 35, 1859 (1963).
(2) Breyer, B., Bauer, H. H., “Alternating Current Polarography and Tensammetry,” pp. 101-3, Interscience, New York, 1963. (3) Ibid., p. 128. (4) Delahay, P., “New Instrumental
Methods in Electrochemistry,” Chap. 6, Interscience, New York, 1954. ( 5 ) Ibid., p. 54. (13) DeMars. R. D.. Shain., I.., ANAL. -~~ CHEM.29; 1825 (1957). (7) Erbelding, R. F., Ph.D. Thesis, Cornel1 University, 1961. (8) Erhelding, W. F., Cooke, W. D., Division oflAnalytica1 Chemistry, 140th Meeting, A.C.S., Chicago, Ill., September 1961. (9) Gerischer, H., 2. Physik. Chem. 198, \ - I
~
286 (19.51). \----,
(lO)Hung, H. L., Smith, D. E., ANAL. CHEM.36, 922 (1964). (11) Jessop, G., Brit. Patent 640,768 (1950). (12) Juliard, A. L., J . Electroanal. Chem. 1, 101 (1959). (13) Kolthoff, I. SI., Lingane, J. J., “Polarography,” pp. 219-20, Interscience, Kew York, 1952. (14) Lingane, J. J., J . Am. Chem. SOC. 68, 2448 (1946). (15) hlatsuda, H., 2. Elektrochem. 61, 489 (1957). (16) Ibid., 62, 977 (1958). (17) Meites, L., ANAL. CHEM.27, 416 (1955).
(18) Nicholson, R. S., Shain, I., Ibid., 36, 706 (1964). (19) Reinmuth, W.H., J . Am. Chem. SOC. 79, 6358 (1957). (20) Sevcik, A , , Collection Czech. Chem. Communs. 13, 349 (1948). (21) Senda, XI., Tachi, I., Bull. Chem. Soc. Japan 28, 632 (1955). (22) Shain, “Treatise on Analytical Chemistry,’;’I. XI. Kolthoff and P. J. Elving, eds., Part I , See. D-2, Chap. 50, Interscience, Kew York, 1963. (23) Smith, D. E., ANAL. CHEM.35, 602 (1963). (24) Ibid.) p. 1811. (25) Smith, 11. E., Ph.D. Thesis, Columbia University, 1961. (26) Smith, D. E., Iieinmuth, W. H., A N ~ LCHEM. . 32, 1892 (1960). (27) Ibid., 33, 482 (1961). (28) Underkofler, W. L., Shain, I., Ibid., 35, 1778 (1963). (29) Walker, I). N., Adams, R. N., Juliard. A. L., Ibid., 32, 1526 (1960). RECEIVED for review October 21, 1964. Accepted December 11, 3964. This work was suppoited in part by funds received from the U. S. Atomic Energy Commission, under Contract No. AT(11-1)-1083.
Ultratrace Determination of Metals Using Coordination Chain Reactions D. W. MARGERUM and R. K. STEINHAUS Department o f Chemistry, Purdue University, lafayette, Ind.
b A chemical kinetic method is proposed for the detection and determination of ultratrace quantities of metal ions. A coordination chain reaction system involving the exchange of triethylenetetrarnine-nickel(l1) and (ethylenedinitri1o)tetraacetatocup r a t e (11) is used. This exchange proceeds b y a chain mechanism where the chain centers are the free ligands: EDTA and trien. The rate of the exchange reaction is followed by its color change and is responsive to 10-gM concentration changes of EDTA. The theoretical limits for metal determinations suggest that analysis down to the 10-gM level with *5% accuracy should be possible. Experimental results are given down to lO-*M. AS little as mole of sample can b e analyzed with the theoretical limit around mole. Any metal ion which complexes EDTA can b e determined.
CURATE
determination of metal ions in solution becomes increasingly difficult as the concentration of the metal is reduced below 10-6M. Some conventional trace analysis techniques are applicable down to 10-661, but beloa this level it has generally been necessary to use different methods. I n this paper a new kinetic method of analysis is proposed for ultratrace metal 222
ANALYTICAL CHEMISTRY
where trien = triethylenetetramine determinations-for metal concentrations of less than 10-6Jf and samples (H2NCH2CH2XHCHzCH2XHCHzCH2NH2) and EDTA = (ethylenedinitri1o)containing less than 1 pg. of metaltetraacetate [(OOCCH2)zKCH2CHzPbased on the chemical behavior of (CH2COO)2]-4. The reaction is coordination chain reactions. initiated by the dissociation of very The exchange reaction of two metal small quantities of the complexes or by complexes in aqueous solution can the addition of traces of free EDTA or proceed by a chain reaction mechanism free trien. The two free multidentate (20). This leads to a rate of exchange ligands are the chain reaction centers much faster than the rate of dissociation and the chain-propagating steps are of either complex. The chain centers in these coordination chain reactions are EDTA Nitrien+2 --t trace concentrations of the niultidentate KiEDTh-2 trien (2) ligands involved in the complexes. The ligands can originate from the pure trien C u E D T h + -+ complexes or can be added separately. Cutrienf2 EDTA (3) Just as a source of free radicals greatly accelerates a free radical chain reaction, The number of protons and the charge so the addition of a free ligand greatly on the ligands have been omitted in accelerates a coordination chain reEquations 2 and 3 because they vary action. I t is the kinetic response of the with pH. exchange reaction to free ligand at conThe addition of trace quantities of centrations of 1 O - g X and less that perfree ligand to the pure reactants greatly mits the ultratrace determinations. A accelerates the exchange rate and kinetic study of one coordination chain simplifies the rate expression. The exreaction system has been reported change rate is easily adjusted to a first(20). Recent additional kinetic inorder dependence in one of the reactants formation about the reactions in this where the first-order rate constant system (f4,16, 83) makes it possible to depends on the free ligand contreat it in theoretical detail. Thus, the centration. Thus, although the free method is based on the exchange reE D T h concentration may be only action of Fitrien+2 and C U E D T ~ ~ - ~ 10-’.11, it can control the rate of conversion of l O - 3 N ?iitrien+2to Cutrien+2. NitrienC2 C U E D T A - ~+ The bright blue color of Cutrien+2 is used to follow the progress of the Cutrien+2 4- XiEDTA+ (1)
+
+
+
+
+
reaction. Anything which alters the EDTA concentration will change the rate of the exchange reaction. I n the above case a metal at 5 X 10-sM can react with EDTA, reducing the exchange rate by 50%. The metal ion detected in this manner need have no connection with the reactant metals, but only be capable of reacting with EDTA. Other complexes are known to undergo exchange reactions by similar chain mechanisms (15). Each system will undoubtedly have its special features which will affect its usefulness in analytical application. Some of the specific limitations discussed in this work may be peculiar to the h'itrienC u E D T h chain system, but many of the same factors must be taken into consideration with each system and therefore deserve detailed discussion.
Table 1. Experimental conditions for Trace Metal Determination ( 1 O-'M) with EDTA Added to Coordination Chain System
Reactants. lO-*M Nitrien and 2 X 10-8 M Cu-EDTA Catal st (0.5 to 3.0) X 10-eM EDTA Metarconcentration determined. ( 2 to 5) x 10-7~ Ionic strength. NaCl or KCl 0.01 to 0.05M
Buffers. Na2Ba07-H3B03 (0.005M) or 2,6dimethylpiperidine and its ClOl salt pH range. 7 to 12 Tem erature. 25.0" f 0.1' Totay reaction volume. 100 ml. Other conditions. 10-cm. cell, 550 mp, and customary reaction times between 10 and 15 minutes Order of addition of reagents. 1. Metal sample and EDTA mixed 2. Cu-EDTA, buffer, and NaCl mixed 3. Solutions 1 and 2 mixed and,diluted and Nitrien added immediately
EXPERIMENTAL
and some variation in oxy a M y
a N i t ~ - i e n + ~ 2OH- + Niztrien3+4
+ ?ji(OH):!
appears to take place very slowly a t high pH. However, the nickel-trien solution can be safely stored for months a t p H 8.5 without the appearance of any solid Ni(OH)*. Trien was prepared from triply re-
[MY]
= -
=
[HzY-*] crystallized trien disulfate and EDTA was prepared from the triply recrystallized acid. Copper sulfate (J. T. Baker Chemical Co.) and nickel nitrate (Fisher Scientific Co.) salts were used which had low values for metal contamination. A Na2B407-H3B03buffer was used for o H 9. Athieher uH (10.5 to 11.5) a bkffer of 2,6-&methylpiperidine and its perchlorate salt was used. This compound was redistilled and the salt was prepared and recrystallized. Reaction rate studies were followed with a Beckman DU spectrophotometer in a 10-cm. cell thermostated a t 25' i 0.1'. The copper-trien absorption peak a t 550 mp was used and the reactions were followed for a t least one half life, so ' t h a t changes of 0.1 to 0.15 absorbance unit were customary. Table I summarizes the experimental conditions used to test the determination of more than ten metals in the 10-7M range. The order of addition of reagents can be important. Unless otherwise stated, the sample containing the metal and the EDTA catalyst were mixed and then the copper-EDTA, buffer, ionic strength control, and water were added. The reaction was initiated by the addition of the nickel-trien solution. I n general, the length of time for a single determination is 10 to 15 minutes. About 2 hours would be required for a five-point calibration curve and a sample analysis in triplicate. Excellent first-order rate plots were obtained for all reactions. I n general, only a few points are needed to obtain the rate constant. A calibration curve was prepared of the rate constant against EDTA added and then the metal sample was analyzed in triplicate. The effective stability constants (22, $4) of the complexes are very useful in predicting metal ion response. Graphs of Ksff plotted against pH were prepared for each metal. Thus for the E D T A complexes
+ [MYOH] + .
,
[MY 1
(6)
The value of ay changes by a factor of lo4in the p H range 6 t o 11. ffy
Some difficulty was encountered with variable trace metal contamination from several sources. The use of Teflon bottles to store reagents and to mix the reactants proved very helpful. All the distilled water used was passed through a column of mixed-bed ion exchange resin. This appeared to reduce metal contamination below 10-8M. The recrystallization of NaCl and KC1 (used to maintain constant ionic strength) was helpful. Glassware was rinsed consecutively with 0.5M HC1, 0.01,1.1 EDTA (alkaline), and deionized water. Care was taken to use the same pipet and same buret for the same reagent. An effort was made to reduce the general dust level in the laboratory in order to avoid airborne contamination, but the precautions were not elaborate. On the other hand, fluctuation of metal impurities a t 10-8M levels undoubtedly reduced the accuracy of many determinations. An exact stoichiometric preparation of copper-EDTA and of nickel-trien is important. The copper-EDTA solution caused no difficulty, because it can be prepared by the addition of excess copper to EDTA, followed by the precipitation and removal of the excess as Cu(OH)*. The copper hydroxide was precipitated a t about pH 10.5 and filtered after 30 minutes. I t was adjusted to p H 9.8 for storage as 0.05-Tf copperEDTA. The nickel-trien solution was prepared in a similar manner, but care has to be taken to filter the h'i(0H)z soon after the initial precipitation is complete. After filtering, the 0.03M nickel-trien solution was stored a t pH 8.5. A ?;iztriena+4 complex has been reported (11) and the reaction
+
where K M y is the stability constant of the metal-EDTA complex. Change of pH causes large variation in ax,
+ [HYW3]+ [Y-'1 E-41
(7)
RESULTS AND DISCUSSION
Chain-Propagation Steps. The ad: dition of a trace of free ligand to the copper-EDTA and nickel-trien reaction mixture greatly accelerates their exchange and essentially eliminates the kinetic contribution of the initiation and termination reactions (20). As a result, the rate of product formation is governed by the reaction cycle in Equations 2 and 3. A steady-state condition is reached shortly after mixing, so that Reactions 2 and 3 proceed at the same rate
Rate of exchange = ~ T ~ ~ ~ [ T ] [ =kyXiT[Y] C U Y ] [NiT] (8) where Y = EDTA, T = trien, and the rate constant for the reaction of T and CuY, etc. (Charges are omitted from the ions throughout the paper because the charge varies with pH.) If free EDTA is added to the reaction mixture, it will increase Reaction 2 compared to Reaction 3 until the buildup in trien concentration and the decrease in EDTA concentration which result readjust Reactions 2 and 3 to the same rate. The ratio of [ Y ] / [ T ] is important in the selection of optimum operating conditions and is important in giving a simple rate expression. From Equation 8 k ~ C uis~
but this ratio is pH-dependent because both of the rate constants are pHdependent, as shown in Figure 1. This graph summarizes kinetic data from several studies of the individual multidentate ligand exchange reactions. The VOL. 37, NO. 2, FEBRUARY 1965
223
d[CuT] ~at
-d[SiT]
at
- k,[NiTl
(10)
where
k, = kyNLT[Y] (11) but when metal ions are present that react with EDTA
[ Y ] = [k',] - [metal]
(12)
so that
k,
PH Figure 1 . pH profile of chain propagation rate constants 25'C., p = 0.1 kp"'. Second-order rate constant for reaction of all forms of trien HzTfz, HT+, and T ) with copper-EDTA (HzTf3, k;lT. Second-order rate constant for reaction of all forms of EDTA (H2Y -z, HY -3, and Y - 4 ) with nickel-trien and its hydroxide complexes Curves plotted from resolved rate constants from several studies 0 Specific experimental points ( 1 4 ) using temperature-jump relaxation techniques. These paints permitted upper part of kp"' curve to be drawn
k$"' plot below p H 8 is from one study (20), while above pH 8.5 the data were obtained from another study (14) using the temperature-jump relaxation method ( 5 ) . The data below pH 8 are more accurate, but the 1000-fold increase in the value of the constant from pH 7 to pH 11 is unmistakable. The krXiT plot is from spectrophotometric exchange studies ( 2 3 ) . The values for both rate constants are estimated a t pH 12. R a t e Expression. For analytical applications it is desirable to have a simple rate expression and t,o know accurately the distribution of the added free ligand. Regardless of whether EDTA or trien is added, the chainpropagation steps will give the same ratio of [ Y ] / [ T ] in accordance with Equation 9 and Figure 1. It is assumed that both reactants have much higher concentrations than the added free ligand. One way to keep a constant ratio of [Y] '[TIduring the reaction and therefore to have a simple rate expression is if [CuY] = [KiT]. This will give a first-order rate expression in accordance with Equation 8, because both [ Y ] and [TI will be constant. 1-nder the ronditions summarized in Table I , [CuU] = 20 [SiT] and above pH 8 kT('uu > k r ~ ~ so T ~that [Y]>>[T]. Thus, [ Y ]is constant throughout the reaction. If there are no EDTA complexing metal ions present, then [ Y ]is equal to the EDTA added ( ITa). 224
ANALYTICAL CHEMISTRY
=
k y X ~ ~ ( [ k-' ~[metal]) ]
(13)
The experimentally observed first-order rate constant is k,. A calibration curve as shown in is prepared of k , against Figure 2. I t ib possible to reverse the ratio of free ligands below pH 8, so that IT]>> [Y]. This is the case because k T C u Y drops rapidly with decreasing pH. The rate expression then becomes
Figure 2. Calibration curve of firstorder rate constant against EDTA added
CUT] - -d[CuY] ~dt dt
25.0°, p = 0.01 KCl; CuY = 2.3 x 10-3, NIT = 1.3 X lo-' A. Theoretical line, if no metal ion impurities
k,'[CuY]
= kTcuy
[TI [GUY] (14)
However, this does not preclude the detection of metals which react with EDTA and not trien. The reaction sequence
?vl
T
+Y
+
+ CuY
MY removing Y
+
+ CUT Y replenishing Y with the loss of T
can take place, so that after only a few cycles the rate will reach a steady state comparable to the initial removal of T in Equation 14. Similarly when Y >> T it is still possible to remove Y from the system by having metals which first react with T. I t is apparent from Figure 1 that pH control is essential for reproducible rate constants. Kinetic Titration Curves. Figure 2 illustrates a type of behavior which is conveniently discussed in terms of a kinetic titration, although the analysis results reported here were not performed in this way. Our determinations used procedures similar to that outlined in Table I. However, if EDT.4 were titrated into the reaction system, essentially no exchange would take place until the EDT.4 added were greater than the metal impurity present. The exchange rate would then increase rapidly with increasing E D T A addition. The sharpness of the break representing the instantaneous change of exchange rate depends on the Keirof the metal-EDTA complex. k, and
present Experimental calibration line as Y, (EDTA added) is varied. Total of 5.2 X lo-' metal impurities present in reaction mixture C. Change in experimental value of k , when sample is present at Y, = 11.0 X 1 O-' D. Difference on Y, scale corresponds to concentration of metal ion determined [2.0 X 1 O-'M Zn]
6.
=
kyNlT[Y]
where J ~ Tis the total metal concentration present in all forms M T =
11
+ MY, Y,
=
Y
+ MY
(16)
From Equation 15
+
[YI2
( M T
- I',
+ K i f YaKeif-' - 9 [Yl -
=
0
(17)
This equation can be solved to find the free EDTA concentration and therefore the exchange rate constant for each addition of EDT.4. BEFORETHE END POINTwith a strong complex (large Kerfvalue)
so the plot of k , against I', will have a n upward curvature (see Figure 3). At the half-way point in the titration, k, = kyXIT/K,ii, for strong complexes, but k , will be greater for weak complexes. AT THE ENDPOINTif the complex is sufficiently strong for Y, >> Y, then
otherwise
AFTER THE EXDPOINTfor a strong complex k,
=
ky""
(Ya-
inherent limitations on how low a level of metal ion may be determined. 1. The metal ion to be determined must be capable both kinetically and t'hermodynaniically of forming a corn-plex with the very low concentration of free ligand present. 2. At least 95% of the exchange reaction should proceed by the two chainpropagating steps (Equations 2 and 3) as opposed to alternative paths. 3. The minimum possible levels of free ligand concentration are determined by the relative formation and dissociation rate constants of the complexes. This can appear as an equilibrium concentration or as a steady-state concentration, depending on the conditions. 4. The chain center (free ligand) concentrations should be constant to at, least i 5 Y , during the reaction time to give linear kinetic plots.
(211
but with a weaker complex the slope will not be as steep. Figure 3 gives five theoretical kinetic titration curves. Four of the curves are for different values of Kerfwhen titrating 2.0 x 10-fiM metal. The fifth curve shows X-, when no metal is present t,o react with t,he EIITh added. Experimental points are given for the values of k,, with 13at2, which has an effective stability constant of 2.8 X lofi at p H 8.9. The theoretical curve for this value of K e f fis seen to give excellent agreement with experimental behavior. Curves with sharp breaks have been shown previously (20) and have been observed routinely in this work-see Figure 2, for example. This leaves little doubt about the accuracy of the rate expressions derived in Equations 18 to 21. The data in Figure 3 suggest that a kinetic titration procedure could be used to determine strongly complexing metals in the presence of weakly complexing metals. -1 constant rate of addition of EDTA1to a reaction mixture will have no effect until the end point of the strongly com])lexing metal is reached; then the exchange rate will be suddenly initiated and indicated by a color change. In general, for a very sharp break the product of Keff should be greater than 1000. Theoretical Limits in Ultratrace Detection. The stability constants of the c~omplexes and the nature of the coordination chain reaction place some
1. FORMATIOX OF A COMPLEX with E D T A concentrations as low as 10-lo.Tf is thermodynamically possible for inany metal ions, so this is not a serious limitation. The Kef*values of EDTA complexes are pH-dependent and this serves as a means of selective determination of metals, as discussed later in this paper. I n Figure 3 at I', = 2.0 x the difference between the k , value without metal present and k , values with metals of differing Kefi indicates t,he sensitivity of kinetic response to the stability constant. A second consideration is that the complex must be kinetically capable of forming. Many reactions between metal ions and EDTA are so fast (6) that even when both concentrations are 10-9X the complex xi11 form in a matter of seconds or minutes. However, at high pH, with soluble
PH Figure 4. pH profile of first-order dissociation rate constants of nickeltrien and copper-EDTA 25.0°, 0.1 w. All values extrapolated from data a t pH 7 or lower Further estimates
-___
forms of metal hydroxide complexes, there are no kinetic data to indicate the rate of reaction with EDTA. The present study indicates that a number of metals have rapid reactions with lO-'JI EDT.4 at p H 9. 2. Two ALTERXATE REACTION PxrHs can be expected to compete with the chain propagation steps, depending on the pH and ratio of reactant concentrations. At high pH with a large value for kTCuY the reaction sequence k+NiT
+T CUT + Y
NiT s h'i krNl
T
+ CuY
-+
(22) (23)
kyX>
/
// I
/
Y + Xi
+
KiY
(24)
could give the exchange products by the dissociation of NiT. In order for this sequence to be less than 5% of the overall exchange rate, it can be shown that kv"lTIY]
[XiT] > 20 kdNITINiT] (25)
or the minimum value of [ Y ]is
y+g.l,zl~o j K.,,
- 2 n '01
,
2.00
3.00
,.,
I
~
,
4.00
[Yo] x IOS Figure 3. Simulated kinetic titration curve showing effect of EDTA added on first-order rate constant of exchange
The value of the dissociation rate constant, k 2 I T S relative to the chainpropagation rate is seen to be important. This can also be expressed in terms of the chain length of the reaction, which is defined as the ratio of t h r rate of chain propagation to t'he rate of creation of chain centers
reaction Theoretical curves for K,ii values indicated when MT = 2.0 X 10-W Rate expression corresponding to Equations 10 and 1 1 Experimental points for 2.0 X 10%4 Bai2 (corrected for other trace impurities present) at p H 8.9, w = 0.05, 25.0' where K,ft = 2.8 X l o 6 ( 2 ) . Experimental procedure similar to that outlined in Table I
Chain length
=
k,~1T[Y]
~
20,000 a t [Y] =
pH 9
Figure 4 gives a pH profile of the VOL. 37, NO. 2, FEBRUARY 1965
225
much free ligand is present. To accomplish these objectives it would be possible to start with 0.1Jf NiT and CuY solutions stored a t p H 8 to 9. When these solutions are diluted directly PH to lO-4M a t the desired pH, the im6 mediate free ligand concentration pres7 8 ent from the reactants is 10-lo or less. 9 If EDTA is added separately at 10-8 10 to 10-9M concentrations, the induction 11 period is avoided. There will be no de12 crease in ligand because the initial free 2. Steady-State Concentration of EDTA when Y > T C U + and ~ concentrations are too PH [Yl low and there can be no increase in free ligand concentration greater than the 7 5 . 7 x 10-9~ 8 3 . 8 x 10-9* steady-state level. Equation 34 con9 2 . 0 x 10-9c siders this situation. 10 5 . 3 x 10-9' The steady-state calculation of [Cu+2] 11 5 . 3 x l0-8c in the reaction sequence in Equations 12 1 . 5 x I0-6c 27 to 29 gives the same value as the 10-4M NiT and 2.5 X 10-2M CuY. equilibrium concentration from CuY, * 10-4M NiT and 4 X 10-$M CuY. c 10-4M KiT and 2 X 10-4M CuY. but NiT can dissociate independently, building up the [TI to its equilibrium level. This is the case because under these conditions the rate-determining proceeds through the chain-propagation dissociation rate constants of both step is the reaction of T with CuY. steps in Equations 2 and 3. complexes. The values of kd"T are 3. EQUILIBRIUM AND STEADY-STATE As a result, a t p H 6 and 7, the equilibcalculated from rium value of [TI determines the REQUIREMENTS for minimum free ligand k d N i T = k N > T + kHxlTIH+] minimum ligand concentration possible. concentrations are given in Table 11. 4. A CONSTANTCHAIN CENTER k2"lT [H+I2 The equilibrium concentrations are calCONCENTRAION of * 5 % during one culated from the values of Keff. Howwhere kH"T and k z ~ " l Thave been deterhalf life of the exchange reaction is recever, during the exchange reaction it is mined and k x ~ Tis predicted (16). The ommended to give reasonably linear possible for the values of T to drop well value of k d C u Y is calculated from formakinetic plots. The &5% criterion is below their equilibrium level. This can tion rate data ( 1 , l?'), which gives the easily met if the minimum free ligand be seen from a steady-state calculation acid term. concentration is dependent on the for nickel ion in Equations 22 to 24. equilibrium concentration of a reactant kdCuY kCuY + k H C u Y [ H + ] and the reactant is in large excess. This is also true if the added ligand is The value of kc"' was estimated to be more than 5 times the concentration of 1.6 X sec.-l from the rate of other But > and the predominant the equilibrium or steady-state concopper formation reactions ( 4 ) and the chain-propagation reaction which is centrations of Xi+2 and Cu+2 (see stability constant ( 2 ) . I t is possible going on simultaneously forces [Y] > Table 11). From the fact that Y , that at high pH hydroxide ion might in[TI above p H 8. As a result the nickel [CUI [Nil = [TI [Y] using crease the dissociation rate of these ion concentration is not determined by Equation 32 for nickel and using the complexes. I n any event, all our the equilibrium of NiT but by the ratio copper equilibrium when Y > T, then evidence points to exceedingly slow disof rate constants in Equation 32. sociation rates up to p H 12. [Yl2 - Y,[Yl Equation 26 can be used with Figures 1 and 4 to show that [Y],,, by this kdNiT[NiT] kdCYY[cUY]) = 0 (34) criterion is less than 10-gJf at p H 8 or kNIY kcuY higher. The minimum concentration of ligand At pH 6 to 8 where kyxiT > k~~~~ Equation 34 can be used to calculate the can be calculated from the fact that another reaction sequence concentration of [Y]during the reaction. [ C U + ~ ] [Ni+'] = [TI [Y], so tha If the lowest possible concentration of CUY 8 Cu Y when Y >> T (27) ligand to meet all the other criteria is desired, the *5% condition can become Y NiT -+ NiY T (28) Ymin. = important. This is indicated in Table T Cu + CUT (29) 111. It can be shown using Equation 34 that this stipulation forces the could compete with the rate-determining minimum ligand concentration up by a chain step in Reaction 14. Thus, Thus, at p H 8 and [NIT] = and factor of about 2 when one reactant is [CuY] = 4 X lo+, Equation 33 gives twice the concentration of the other a minimum ligand concentration value and equilibrium (or steady-state) conthat of the equilibrium free ligand ditions prevail. For example, in Table concentration (see Table 11). and [TI,,, is 5 X 10-6Jf a t p H 6 and I11 a t p H 10, the steady-state conThe reaction path in Equations 22 to 3 x 10-85f a t p H 7 . centration of EDTA from the pure 24 can serve to keep a low value of free Although these values of [Y],,, and reactants will decrease slightly as the ligand concentration while still carrying [TI,,, could be important limits, there reaction proceeds (see Equation 33). less than 5% of the total reaction. are other factors which force higher To keep this within the k501, level, It is desirable to avoid a long time values of Y and T concentrations. The about 1 X lO-*M free EDTA must be interval in reaching a steady-state result is that conditions are usually such added to give a total EDTA concentracondition and to know exactly how that more than 99% of the reaction tion of 1.4 X 10-8.1f. Tab1 e II. Free Ligand Concentrations from Chain System 1. Equilibrium Concentrations from 10-4M Reactants Total Free Ligand [CUI = [YI [Nil = [TI [TI [YI 8.5 x 8.9 x 8 . 9 x 10-8 2 . 4 X 10-lo 4 . 1 x 10-7 4 . 1 x 10-7 3 . 9 x 10-10 3 . 5 x 10-8 3 . 5 x 10-8 1 . 2 x 10-9 5 . 0 x 10-9 6 . 2 x 10-9 5 . 1 x 10-9 3 . 7 x 10-9 8.8 X 5 3 x 10-8 2.3 X 7 . 6 X 10-8 1.5 x 4 . 4 x 10-7 1 . 9 x 10-6
+
+
+
(
+
226
+
+
+
+
ANALYTICAL CHEMISTRY
+
+
+
+
Table 111.
pH 6 7
Minimum Theoretical Free Ligand Concentrations Possible for Accurate Kinetic Analysis
Conditions [NiT] [CUYI 2 X 10-4
PH Figure 5. p H profile stability constants
of
effective
pH vs. log K,fi for EDTA complexes of Fe(lll), Mg(ll), Ni(ll), ond Cu(ll) and for trien complex of Ni(ll) To calculate Keff, soluble hydroxide constants were needed as well os constants for mixed complexes with hydrogen or hydroxide ion and EDTA. These constants were obtained from the following references for each metal. Ma Species Ref. (25) MgOHC MgY, MgHY (2)
-
. .. Ni
Species NiOH", Ni(OH)z, Ni(OH13NiY - 2 , NiHY cu CuOH -,CU(OH),, Cu(OH)s-, Cu(OHh-' CuY -z, CuHY Fe FeOHi2, Fe(OH)z+, Fe(OHI3 Fey-, FeHY, FeYOH-z
Ref. (7, 8 )
(2)
(3, 13, 18, 19, 2 1 ) (21
(9,IO, 12) (2)
Above p H 11 the K,,I values for S i Y and CuY fall off rapidly (see Figure 5) and the dissociation of CuY can lead to increasing EDTA concentrations. Equation 35 is derived by neglecting the recombination reactions and assuming no more than a 570 increase in [ Y ]during one reaction half life in the conversion of XiT to CuT. t1/2
=
0.693
-
[YImin. =
Using the initial concentration of
CuY and NiT in Table I11 for an approximation gives a [Y],,, value of
3 x lo-*. I t is, in fact, only the slow dissociation of both compleses that permits so low a value of free ligand
8 9
10-4
lo 11 12
10-4 10-4
10-4 10-4 2 . 5 x 10-2 4 x 1 x 10-8 2 x 2 x 10-4 2 x 10-4
3Iinimuni [Ligand]
[YJ/[Tl 1/120
2.5 X 1 3 X 6.7 x 4.6 X 4.1 X 1.4 x 3 x 3 x
1/50 50/1 50jl 500/1 160/1 no/i ioo/i
Limitation
[TI [TI 10-9 = I Y ~ = [Y] = IY] 10-8 = [Y] 10-8 = [ Y ] 10-8 = [ Y ] = =
4O 3-.4 3 - ~ 4b , 3-B, 4 b
3;B 4 4c 4c
Limitations. K e f {value of metal complex. 1. 2. 95yc of exchange reaction should proceed by chain-propagating steps. 3-A, Equilibrium level of free ligand from reactants. 3-B. Steady-state level of free ligand during reaction. Chain center concentrations constant to .t5% during reaction. 4. This a Free trien must be added to hold the [TI constant while [NiT+2] changes. increases the minimum [TI above the value of the trien in equilibrium wit,h the pure reactant, NiT+2. b Eq. 34 applies. A small amount of free EDTA4must be added to keep [Y] constant as [ N T ] changes. Compare to steady-state concentration in Table 11. c Eq. 36 applies. Steady-state and equilibriiim conditions are not reached because of slow dissociation
concentration. The equilibrium level of EDTA$ froni CuY is considerably higher a t pH 11 and 12. Table 111 summarizes which of the four limitations predominates a t different conditions and gives the theoretical minimum concentrations of ligand needed to give results with =t5% accuracy. The actual accuracy, of course, also depends on the variability of background contamination. The conditions are chosen so that one of the ligand concentrations will be a t least 50 times the other. At pH 7 to 10, the combination of all these limitations still allows the prediction that operation with as little as 10-8M free EDTA is possible and therefore, 10-9M metal ion concentrations could be analyzed with 5% accuracy. One drawback is that the half life of the eschange reaction is 25 hours at 25", p = 0.1, p H 9, NiT = 10-4M, Y , = 10-8M. Lowering the ionic strength will greatly speed the reaction, however. Application to Metal Ion Determination. Table IV shows t h e versa-
tility of t h e method to the determination of different metals. The conditions used are outlined in Table I. I n all these cases t h e EDT.1 was varied in the 10-6M range and no special effort was made to remove background inipurites. The results are the average of two or three determinations. By using further recrystallized KC1 and buffer, the impurity level in the reaction mixtures was lowered so that the EDTA added could be varied in the IO-7JI' range. This permitted metal determinations a t 2 X l O - * M (Table V) but the impurity background is greater than this and the accuracy is not too good. Xevertheless it is clear that the method is capable of determinations ~
Table IV. Trace Determination of Metals Using Coordination Chain Reaction
Metal detd. Zn Mn
Xi
CU
Ca
Pb co
Cd Fe
pH 8 9 8 9 8 9 8 9 8 9 8 9 8 9 7 3 8 9
Metal, .If X 10: Added Found 3 1 2 9
3 2 3 3 3 3 4
0 2 0 4 2 3 9
3 2 3 1 3 5 2 4 2 6
3 3 2 5
8 7 7 1
down to a t least 10-6M. I-nfortunately, because of the problem of background contamination, we have not yet been able to test the predicted sensitivity of 10- 9 ~ . The above determinations used 100ml. reaction volume, but Table T' s h o w t,hat it, is possible to obtain accurate analyses with 10-nil. total ~ o l u m e . Thus, 0.2 pg. of Zn and 0.08 pg. of Ca were determined. -411 reactant concentrations are the same as in Table I . A 5-ml. sample could be used in the 1O-ni1. determination volume, so that sensitivity to 5 X 10-8.11 concentrations would mean that a total ranil)le of 0.03 pg. of Zn could be determined or 6 p,p,b, of Zn in a sample. The predicted sensitivity from Table 111 ir; another factor of 10 lower. The half life of the reaction \Then EDTA is 10-6Jf a t pH 8.9. ionic st,rength0.1, is 16 minutes:. SELECTIVE DE:TE:RhIINATIOS OF METALS. Figure 5 s1ion.s how pH affects the Kef, of four complexes. The curves differ from those of Kingbom ( 2 2 ) , who did not, consider the higher hydroxide complesep of the the cometals. If Y a is lo-' t o VOL. 34, N O . 2, FEBRUARY 1965
227
Table V.
Experimental Sensitivity of Metal Ion Determination Using Coordination Chain Reaction
Metal detd.
PH
cu
8 9 10 6 11 1
Pb Zn
8 9 8 9
Zn
Ca
Table VI.
Xletal detd. Ni
Xi and Fe
(Netal) (Metal) added, found, M x 108 M x 108 A . In 100-ml. total volume 5 8 7 8 2 3 3 3 2 2 1 9 B. In 10-nil. total volume ;1.1 x 107 .If x 107 3 8 3 3 20 2 0 2 2
Trace Determination of Metals Showing pH Masking Effect
pH 10 8 8 7
Metal, JI Added Follnd 2 5 x Xi and 2 3 x 10-’Ni 1 9 X 10-6Fe 4 9 x lo-’ I i i and 5 8 X 10-7Fe 10 8 x total 8 8 x 10-7 3 0 X l I n and 3 5 X 10-7 \In 7 7 X 10-7 Cr 5 9 X 10-7 Cr 0 00 x 10-7 5 0 X lo-’ Ca and 3 9 X 10-7 Ca 5 0 x 10-7 .AI -_-_L_
lln
8 9
Blank Ca
8 9 9 0
ordination chain reaction system could selectively analyze for different conibinations of the three metals Cu(II), Fe(III), and Mg(I1). Thus, pH 7-8. Determine Fe and Cu but not LIg pH 9. Determine Fe, Cu, and M g pH 11.5. Determine hIg and Cu but not Fe pH 13. Determine only 1 I g This is a particularly favorable misture for pH selectivity, but it’ illustrates the possibilities. Table VI gives some results where at pH 10.8 Fe(II1) is not detected in the presence of Ni(II), while a t pH 8.9 both Fe(II1) and Ni(I1) are detected. Similarly, Ca(I1) can be determined in the presence of .11(III) a t pH 9 because t’he strong hydroside complexes of Al(II1) prevent it from complesing EDT;\. -Inother method of attaining selectivity is based on a secondary kinetic effect. Thus, in Table VI, Cr(II1) does not react, with EDT.1 a t pH 8.9 while r\ln(II) does react. The EDTA1 reaction with Cr(II1) is allparently too slow under these conditions to coniples this metal. There is no reason to limit the masking of metals to hydroxide ion. Other complesing agents can be introduced to give additional EUT.1 selectivity just as in the coiiimon coiniilesonietric titration methods;. The masking agent must not interfere v-ith the chain reaction or release appreciable concentrations of EDTA\ or trien., Very little is known about the kinetic effects 228
rg.
0 2 0 08 0 os
may have somewhat complex kinetic aspects! but they are very simple chemical niist’ures which are easy to preliare and use. Their introduction as estreiiiely sensitive detection devices could be useful for many purposes, because there are few stable cheinical systems sensitive to 10-1‘’ mole of substance. This paper has concerned only the SiT-CuT chain reaction system because the kinetics of this system have been fully investigated. However, many iiiultidentate eschange reactions could proceed by chain reactions and even greater sensitivity seems yery likely.
ANALYTICAL CHEMISTRY
LITERATURE CITED
(1) hckernianri, H., Schwarzenbach, G. H e l r . Chini. Acta 35, 485 (1952). ( 2 ) Bjerriini, J., Schwarzeribach, G.,
Sillen, L. G., “Stability Constants,” Part I, 1957, Part 11, 1958, The Chemical Society, London. ( 3 ) Clifford, “A. F., “Inorganic Chemistry of Qualitative Analysis,” p. 232, Prentice-Hall, Englewood Cliffs, N. J., 1961.
(4) -Eigeiij .\I., Pure d p p l . Chem. 6 , 9, (1963). (5) Eigen, Dellaeyer, L., “Technique of Organic. Chemistry,” A . Weissberger, ed., \‘oL \‘III, Part 11, pp. 895-1054, Interscience, Ken York, 1063. (6) Eigen, ll.>Wilkins, R. G., “Mechaiiisnis of Inorganic Reactions,” Summer of common masking agents on the coSymposiiirii, IXvisioii of Inorganic ordination chain reactionb. Hoii ever, Cheni., ACd, J u n e 1964. ( 7 ) (:ayer, K. LI., Garrett, A . B., J . d m . preliminary work indicate> that several Chena. SOC. 71, 2973 (1949). commonly occurring metals can be ( 8 ) Gaver, K. lI., Wooiitner,. L.,. Ibid., masked without disturbing the chain 74, l”436 (1952). reaction. ( 9 ) Gayer, K. Woontner, L., J . Phys. (’hem. 6 0 , 1569 (1956). (10) Hedstroni, B. 0 . A , , L l r k i v Kemi 6 , CONCLUSIONS 1 (1954). (11) Joiiassen, .\I. B., Douglas, B. E., The CuY-NiT chain reaction syst,em J . A m . C‘hem. SOC.71, 4094 (1949). is applicable t,o ultratrace analysis for (12) Latinier, W , ll., “Oxidation Polo-’ and 10-s.ll metal concentrations. tentials,“ 2nd ed., p. 224, Preritice Hall, Englewood Cliffs, X, J . , 1932. The theoretical limitation for =k5% (13) l l c l h w e l l , L. A , , Johnston, H . L., accuracy is lo-9.11. The method reJ . A m C‘hetn. SOC.5 8 , 2009 (1936). quires very little equipment beyond a (14) JIargerum, U . K., unpublished work. temperature-controlled colorimeter or (15) lfargerum, D. W.,Carr, J . D., to be published. spectrophotometer. hctual per(16) AIargerunr, D. \T., Rorahacher, D. formance of the kinetic B., Clarke, J . F. G., Jr., I n o r g . Chem. excellent agreement with 2 , 667 (1963). mechanism. (17) llargerum, L). rV., Zabin, B. A . , to be published. S o t only is this t’ruein regard to data (18) Iiasanen, R . , Tarnninen, Y., J . in Figures 2 and 3 and in Tables IV, T’, A4ni.Chevi. SOC. 71, 1994 (1949). and VI,but also in a number of cases of (19) Oka, Y.,J . Chem. Soc. Japan 59, induction and inhibition period5 in O i l (1938). (20) Olson, L). C., llargerurn, TI. \V., J . agreement with the predicted theoretical .4ni. Chem. SOC.8 5 , 297 (1963). behavior of the chain reaction. Cal(21) Owen, B. B., Gurry, It. IV., I b i d . , culated K,,, values can be used to pre6 0 , 3074 (1938). dict which metals should or should not (222) Ringborn, A , , “Complexation in Analytical Chemistry,” Interscience, be determined. Some degree of New york, 1963. selectivity in anal (23) Rorabacher, D. B:, Nargeruni, D. pH, but other masking agents are It-,,I n o r g . Chena. 3, 382 (1964). needed. Caution should be used in (24) Schw:trzenbach,,, G., “Coinplexoapplying the method in the presence of metric Titrations, Intersrielice, S e w York, 1957. untested ligands. because it is ~~ossible ( 2 5 ) Stock, 11. I., Uavies, C. \V,,Trans. to block or to enhance the chain reFaraday SOC.44, 856 (1948). action rate. The method also ea R E C E I ~ EforD review September 16, 1964 used for ultratrace ligand ana Accepted Iiovember 9, 1964 Finaric3ial if the ligands are comlletitive \vi support of the project b) the Air Force EDT.1 or trien complexation. Office of Scientific Research 1s gratefully Coordination chain reaction systems a c k n o a ledged
