Differential Kinetic Analysis of the Metallic Elements Dale W. Margerum, J. B. Pausch, G. A. Nyssen, and Gregory F. Smith Purdue Unioersity, Lafayette, Ind. 47907 Qualitative and quantitative analysis of mixtures of metal ions is achieved by observation of the rate of reaction of the metal-CyDTA (tranr-1,2-diaminocyclohexane-N,N,N',N'-tetraacetate) complexes with acid or with an exchanging metal ion. Kinetic data are reported for more than 30 metal ions. The reactions of the CyDTA complexes are first order in metalCyDTA, first order in hydrogen ion, and independent of other metal ions. The rate constants vary by a factor of 10l2 and qualitative analysis is achieved by the detection of absorbance-time signals at various time scans (msec to min) and acidities (10-*M to 1M [H+]). Each metal or group of metals is observable at a specified combination of acidity and time scan. The resulting absorbance-time signals give quantitative determinations of metal ions down to 10-eM with an accuracy of 10% or better. Analysis of mixtures of lanthanides, transition metals, group II and group 111 metals is possible.
PREVIOUS STUDIES of the metal substitution reactions of CyDTA have shown the importance of the cyclohexane ring in preventing this ligand from undergoing direct exchange reactions between two metal ions (1-3). Kinetic studies of more than 30 metal complexes including the alkaline earths (4), lanthanides (3, transition metals (3), and group I11 metals (6) have shown in every case that the exchange reactions are first order in the metal-CyDTA complex and first order in hydrogen ion. There is no direct attack of one metal on another metal-CyDTA complex, although in special cases metals can suppress the rate of exchange (7). The result is that each metal-CyDTA complex has a characteristic dissociation velocity at a specified acidity, independent of other metals which may be present. This unique kinetic behavior results from the rigid cage structure of CyDTA which cannot accommodate more than one metal at a time. Consequently, the reaction velocity of a metal-CyDTA complex may be used for qualitative identification of the metal. In fact, the reaction rates are so widely separated that it is necessary to use different acidities to give convenient observation times. In some instances two to four different metal complexes will react within the same time scan but can be identified by calibration runs. The concentration-time scans are analyzed to give quantitative determinations using differential kinetic methods where necessary. Thus, with a series of kinetic runs at different acidities and time scans, most metals capable of being complexed can be detected and determined. The general kinetic system is metal-CyDTA
+ Hf rate-detr. HCyDTAa- + metal ion
(1)
(1) D. W. Margerum and T. J. Bydalek, Inorg. Chem., 2, 683 (1963). (2) D. L. Janes and D. W. Margerum, ibid., 5, 1135 (1966). (3) D. W. Margerum, P. J. Menardi, and D. L. Janes, ibid., 6, 283 (1967). (4) J. B. Pausch and D. W. Margerum, ANAL.CHEM., 41, 226 (1969). (5) G. A. Nyssen and D. W. Margerum, Purdue University, 1968, unpublished work. (6) D. W. Margerum and G. F. Smith, Purdue University, 1968, unpublished work. (7) G. F. Smith and D. W. Margerum, Znorg. Chem., 8,135 (1969).
HCyDTA8-
+ C U ~(or+ xH+)
+
CuCyDTA2- (or H,CyDTA4-')
(2)
where Reaction 1 is the rate-determining step with a characteristic rate for each metal. Reaction 2 is rapid and copper is added as a scavenger to force the acid dissociation step in Equation 1 and to permit spectrophotometric observation of the extent of the reaction. Lead(I1) or excess acid also may be used in Equation 2. For any given metal-CyDTA the exchange rate equals kd[metal-CyDTA] and is equal to d[CuCyDTA 2-]/dt. The metal-CyDTA species may include MCyDTA, MHCyDTA, and M(X)CyDTA and kd may include kHMCY, kHMHCY, and kHMXCY times the hydrogen ion concentration, where X refers to halide or other monodentate ions. These various forms of metal-CyDTA complexes all have the metal inside the coordination cage and are in rapid equilibria relative to the dissociation rate. A generalized expression for kd is given in Equation 3 kd
=
where K M H C =~[MHCyl/([MCyl[H+I) and KXXC,= [MXCYIIII ([MCy][X-I). Equation 3 tends to make kd look more complicated than is generally the case because only a few metals give appreciable concentrations of MXCy and because the kHMHCY values parallel those for kHMCY. Hence, knowledge of the kHxcy rate constants is sufficient to establish the approximate acidity and time scale appropriate for each metal. Figure 1 shows the enormous range of kHMCY values found for 30 metals at 25.0 "C. The magnitude of the range of rate constants is illustrated by the fact that when the acidity is adjusted to give a half life of 10 mseconds for barium, the half life calculated for nickel is one century. It is obvious that a wide range of [H+] must be used to give more suitable half lives. The metals may be grouped, depending on the acidity and time scan used, as either too fast to observe, as observable, or as too slow to observe. Reactions run at pH 7.5 on a stopped-flow apparatus for the determination of barium, strontium, and calcium would place all other metals with the possible exception of magnesium in the too-slow-to-interfere category (4). Similarly, reactions run below pH 4 for the transition metals need not be concerned with the alkaline earths which are now in the too-fast category. Even the lanthanide metals have a lo4 spread between La and Lu, so that it is possible to analyze one end of the period without interference from the other end. It can be noted in Figure 1 that some metals fall very close together in their kinetic behavior and would appear to be difficult to distinguish. This is not a serious problem with the transition metals because secondary effects can be used to remove the degeneracy of these rates. A kd ratio greater than two is sufficient for analysis. The secondary effects include the factors given in Equation 3. The kd ratios can change with different acidities or with moderate concentrations of added salts. The values given in Figure 1 are at 25.0 "C and naturally will shift with temperature. The activation energies for kd are not the same for different metalVOL. 41, NO. 2, FEBRUARY 1969
* 233
-4 I
-2
0
t2
t4
+8
t6
1
I
I
MU I
co II C.
I
80
I
AI
I
I
I I
sc I
I
Zn I ua
I
I
1
I
r 111 Ver Slow
curve shape has the advantage of eliminating interference from any possible constant sources of absorbance. The present work describes analyses using stopped-flow mixing as a convenient and rapid method. With the exception of Sr and Ba, all of the determinations could be done with conventional spectrophotometers by using less acid reaction mixtures. The chemical procedure for the method is to add CyDTA in slight excess over the total metals present in the sample-e.g., a crude titration-and to adjust the pH to a level to ensure complete formation of the complexes. The resulting solution is mixed with excess copper(I1) buffered at the desired pH for the kinetic analysis. Qualitative identification and quantitative determinations are based on the absorbance-time signal in comparison to that found for the pure components. EXPERIMENTAL
I
Gd
I
tDY
I
un I
I
Er I Tm I
t h
I
I
I
I
I
I
I
I I
Figure 1. Rate constants for the reaction of hydrogen ion with metal-CyDTA complexes at 25 "C The reaction half-life can be calculated from the pH, 10'pH + pk - ,IE), where pk refers to -log kaMcy
tllz
(sec) =
RESULTS
CyDTA complexes and therefore a 10 to 20 "C change in temperature can be used to spread the kd values. Finally, a change in oxidation state can greatly alter the kinetic behavior-for example, Co(II)CyDTAz- is readily oxidized to the inert Co(1II)CyDTA- complex. Equation 4 gives the expression for an absorbance-time signal which results from a mixture of metals MI, Mz, M3. . .Mi, reacting with kd values of kl, kz, k3. . .kt, respectively, where copper is the scavenger. A/b
=
+
ecucy[C~DTA]exceas e~u([C~tota~l -
[CyDTAlex)
(1
+ (€cucy -
- e-"lf)[M&,itisl
+
+ +
[(I - e-k'?[M~linitia~ (1 - e-kat)[M3]initial .... . ECJ
Calibration runs with pure metal-CyDTA solutions under the same reaction conditions give the rate constants. The shape of the absorbance-time curve depends only on the metals reacting at the acidity and time scans used. Therefore, Equation 4 can be solved for the initial concentrations of MI, Mz, and MI from the curve shape as opposed to its displacement. If M( has completely reacted when the first point is taken, it contributes to the other constant terms affecting the displacement of the signal but otherwise does not affect the solution for the best fit of concentrations for MI, Mz,and M3. A similar situation exists if the Mi-CyDTA complex is essentially unreacted. Concentrating on computer solutions (or graphical solutions if only two variables) of the 234
ANALYTICAL CHEMISTRY
A Durrum-Gibson (Durrum Instrument Corp.) stoppedflow instrument was used for most of the analyses reported in this work. It has a 2.0-cm observation cell made from Kel-F and uses about 0.2 ml of sample per measurement with transmittance-time a mixing time of about 2 msec. The signal from the stopped-flow spectrophotometer was observed with a Tektronix 564 storage oscilloscope and the stored image was photographed with Polaroid film. Transmittancetime data (30-60 points per curve) were used as the variables to solve Equation 4 with a linear regression analysis program on an IBM 7094 computer. Wavelengths of 300 and 260 mp were used to observe CuCyDTA2- and PbCyDTAz-, with Cu(I1) and Pb(I1) as scavengers, respectively. Most of the rate constants were determined first at much lower acidity than in the analysis scans using Cary 14 or Beckman D U spectrophotometers. The detailed kinetic studies for these constants are reported elsewhere as referenced. In general the conditions were 25.0 "C and a ionic strength of 0.10M maintained with NaC104.
Table I summarizes the rate constants known for the acid dissociation reactions of 30 metal-CyDTA complexes. The metals are arranged in order of their reaction speed based on the second-order hydrogen ion rate constant of the parent complex, kBMCY.The dissociation rate of the transition metals as well as magnesium and calcium show negligible contribution from the nonacid path--i.e., kbfcy[metal-CyDTA]. However, this path is appreciable with barium and has been detected for strontium and many of the lanthanides. In general the kMcyvalues can be neglected at low pH and with the exception of barium would make no contribution to reactions fast enough for stopped-flow experiments. Many of the metals form protonated-metal-CyDTA complexes and the corresponding rate constants, kHMHCY, are given in Table I for the few cases where this terms is known-namely for copper, cobalt, and nickel. If metal-H-CyDTA species are present in appreciable concentrations, the kd value will be altered in accord with Equation 3. This can be used to advantage to separate close kd values but in general does not cause large shifts in the characteristic kinetic behavior. Nevertheless the pH range of the kinetic studies is given to indicate the extrapolation necessary for estimated kd values. Typical stability constants (8) for the divalent transition metal-H-CyDTA complexes are lo3. Halide ion effects with Hg-CyDTA are enormous, as seen in Table I. For example, HgICyDTA*- reacts 2 X lo4 (8) L. G. Sillen and A. E. Martell, "Stability Constants of MetalIon Complexes," The Chemical Society, London, 1964, p 690.
Table I. Dissociation Rate Constants for Metal-CyDTA Complexes at 25.0 "C
Other kinetic information
Metal Ba Sr
Ca Mg Ivln(I1) Zn
La Ce(II1) Cd Pr Pb
Nd Sm Cu(I1) Co(I1) Hg(II)
1.1 x 6.1X 4.1 x 7.1X 6.3x 5.6 x 3.2X 1.7X 1.3 X 53 42 35 23 16 5.1 3.9 3.2 3.1
10s 106
102
102 lo2
0.58 0.36
DY
0.26
Th Ho
0.23 0.13 0,053 0.037
sc Lu At
Ni
0.023 0.019 0.017 0.011 3.4x 10-4 2.5x 10-4
0.5MNaAc 0.5MNaAc 0.5M NaAc 0.1M NaC104 0.5MNaAc 0.1M NaC104 0.1M NaC104 0.05M NaC104 0.1M NaC104 0 . 1 M NaC104
...
...
... ...
104
Tb Y
Yb
4.4sec-I 0.03sec-'
106 104
2.2 1.3
Er
=
106
Eu Gd
Tm
kBaCy =
kSrCy
Conditions Ionic strength pH range 7.0-7.6 5.5-7.6 5.5-7.6 5.5-6.3 5.5-7.6 5.3-6.7 4.7-6.1 4.5-6.8 4.0-5.4 4.0-5.4 3.8-4.7 4.0-5.4 4.3-5.8 4.0-5.4 4.0-5.4 2.9-4.8 3.1-5.5 5.9-7.0 5.8-7.1 6.8-8.8 4.66.0 4.0-5.4 4.0-5.4
E, = 17.0kcal E , = 8.7kcal E, = 13.6kcal kCeCr = 2 x 10-4 sec-1 Pb and Cu suppression O.lMKN08 0.1M NaC104 k- = 1 .o x 10-4S W - ~ E, = 17.3kcal 0.1M NaC104 kydry = 9 X 10-6 set-1 0.1M NaCIO4 kSmCY 4 x 10-5 set-1 0.1MNaC104 kHCUHCY = 4.9M-1sec-1 0.1M NaC104 kHCOHCY = 12M-1 set-1 0 . 1M NaC104 k"gCyC1 = 2.6 X 1OSM-Isec-l 0.1M NaC104 k + C ~ ~ r = 1.3 x 104M-1sec-1 0.1M NaC104 k"gCsI = 5.9 X 104M-' sec-1 0 . 1 M NaClO4 kHHgCsSC" = 2.3X 103M-l sec-1 0.1M NaC104 kEuCy 10-4 set-1 0.1M NaC104 E, = 13.4kcal 0.1MNaC104 J@Cxr = 1.0x 10-6 sec-1 kTbCy E 3 x 10-8sec-1 0.1M NaC104 4.0-5.4 E, = 15.3 kcal 0.1MNaCIOa 4.0-5.4 k Y C y = 1.7x sec-' E, = 13.3 kcal 0.1M NaC104 4.0-5.4 kDyCy = 1 ,2x 10-8 sec-1 (This value is in 1-2M HCIO4 and acid forms of Th-CyDTA may be present) kHoCs 9 x 10-7 set-1 0.1.44NaC104 4.0-5.4 kErCy E 6 X 10-7 sec-1 0.1M NaC104 4.0-5.4 E, = 18.0kcal 0.1MNaC104 4.c-5.4 kTmCy = 2.3x 10-7 sec-1 kYbCy = 5 X 10-8set-1 0.1M NaC104 4.0-5.4 ,.. 0.1M NaCIOa 3.0-3.7 E, = 19.8kcal 0.1MNaCI04 4.0-5.4 kLuCy = 1 x 10-7sec-1 kHA"CY 2.1M-1set-1 0.1 M NaC104 2.0-2.8 ... 0.1MNaC104 4.0-5.2 kHXiHCY = 5.9x 10-4M-1set-1 1 .25M NaC104 1.5-3.5 kHBiHzCy = 2.2x 10-3M-1 set-1 1.25MNaC104 1.5-3.5
Table 11. Calibration of Rate Constants Using Pure Components and Stopped-Flow
Results are the average of four runs Standard concn M Metal
PH
Conditions
Zn Mn
2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
0.1M NaC104 1M HAC 0 . 1 M NaC104 1M HAC
Cd Pb
La Ce Pr Nd
Hg CO Sm Eu Gd Tb
1.1
1.1 1.1 1.1 1.1 1.1
0.1MNaCI04 1MHAc 0.1MNaC104 1M HAC 0.1MNaC104 1M HAC 0.1MNaC104 1M HAC 0.1MNaC1041MHAc 0.1MNaC104 1M HAC O.1M HClO4 0.1MHClO4 0.1M HClO4 0.1MHCD4 0.1MHC104 0.1MHClOa
x
106
4.17 4.07 4.00 4.03 7.08 6.15 4.65 6.60 4.14 5.05
7.02 8.50 4.66 6.60
Concentration, Found 107 101 98 97 104 107 90 96 101 104 106 102 95
92
kd,
u
2.8 1.3 0.6 0.8 4.1 2.3 1.1 1.6 7.9 1.0 2.2 0.3 0.8 0.7
SeC-'
Found
%.
5.04 0.39 0.064 0.086 0.70 0.49 0.31 0.16 2.15 0.032 0.56 0.34 0.23 0.097
5.4 2.0 3.1 1.2 3.0 4.5 4.3 3.7 15.8 1.3 1.9 2.3 0.9
VOL. 41,NO. 2, FEBRUARY 1969
2.0
235
times faster than does HgCyDTA2-. The stability constants for the mixed complexes of CI-, Br-, I-, and SCN- are 1.4 X lo2,1.6 X lo3,1.8 X lo5 and 2.0 X lo4, respectively (2). Therefore, low concentrations of these ions will drastically shift the mercury-CyDTA dissociation rate. This large an effect is exceptional, however. Most metal-CyDTA complexes do not readily add additional anions or are not affected kinetically. Small shifts in rate constants are observed when chloride ion is added to cadmium- and zinc-CyDTA and once again this can be used to advantage to separate rate constants. Table I also gives the activation energies, E,, for eight cases where temperature effects have been studied. Similar
Table 111. Kinetic Analysis of Transition Metal Mixtures, 25.0 "C Conditions for the Reaction Mixture: pH 2.4 using lMAcetic Acid, 0.1M NaC104, 1.31 X 10-3M Cu(NO&, Durrum-Gibson Stoppedflow, 300 mp, Computer Calculations. Results are from three to five repetitive determinations. Results, Std concn in Metal reacting mixture, M Found U 0.97 x 10-4 Zn 103 3.3 Mn 1.01 x 10-4 99 2.3 Zn 1.94 x 10-6 124 4.9 Mn 0.8 2.02 x 10-5 109 3.88 X 10-6 Zn 105 16.8 4.04 X 10-6 Mn 107 17.4 0.97 x 10-4 Zn 106 3.2 1.03 x 10-4 Cd 93 1.4 2.72 x 10-5 Zn 107 7.1 2.06 x 10-6 94 7.9 Cd 4.12 x 10-6 Cd 85 11.9 4.16 X Pb 109 10.0 3.88 x 10-6 Zn 106 1.9 Mn 4.04 x 10-5 102 2.7 4.12 X 94 2.6 Cd 1.94 X 123 5.8 Zn 108 1.3 Mn Cd 102 3.9 2.08 x 10-5 Pb 104 8.2 3.88 x 10-6 Zn 4.04 x 10-6 107 2.3 Mn Cd 93 1.6 4.12 x 10-5 Pb
rate constants with sizeable differences in activation energies can be separated by changing the reaction temperature. Thus kHZnCY/kHLaCY = 1.3 at 25 "C but the ratio equals 2.0 a t 10 "C. There are additional factors which may affect the rate constants such as ionic strength, general acid catalysis in the presence of high concentrations of weak acids, and a few special effects such as Pb(I1) suppression of the Cd-CyDTA2reaction (6). Therefore, it is important that kinetic calibrations of the metals in question be done in the matrix of the sample. If the sample is totally unknown, standard addition methods are suggested. The reactions are relatively free from interference and in many cases will react in accord with the kdfCyvalues but kinetic calibrations are needed for accurate quantitative measurements. An earlier paper has given determinations of mixtures of the alkaline-earth metals including the analysis of blood serum, sea water, and dolomite (4). Therefore, most of the examples in the present work deal with lanthanide and transition metals. The use of stopped-flow mixing made rapid reactions possible and required higher acidity than that used for most of the determinations of kHMCY. Table 11 gives typical calibration runs with pure components to establish the kd values, to check the precision of the rate constants and concentrations and to check the accuracy of the kinetic determination of concentration. The results are the average of four runs for each component, usually two before and two after the runs with the mixtures. The standard deviations for the rate constants average 4 % and for the concentrations average 2 %. The ratio of rate constants for metals in Table I1 differs in some cases from those in Table I. Thus, in 1Macetic acid the ratio of kd(Zn)/kd(Mn>is 13 while the ratio of kHZnCy/kaMnCy is 0.53. Similarly, Cd and Pb are inverted under this condition. The spread of rate constants for the lanthanides is less at p H 2.4 and at pH 1.1 than at p H 4-5. The effect of 0.1M acid is to make the ratio kd(Hg)/kd(Co)equal to 67 compared to the ratio kHF1eCY/k$ocy of 0.97. The Hg rate is accelerated for this acidity while the Co rate is much slower than expected. Differential Kinetic Analysis of Mixtures of Transition Metals. The metal-CyDTA complexes are formed by adding 10% excess Na2H2CyDTAto the metal ion solution and adjusting to p H 8-9. The solution is transferred to a stoppedflow syringe. The other syringe contains at least a 10-fold excess of copper plus the ionic strength control and acid for the desired p H of the reaction. Three to five transmittance-time scans are recorded for each condition. Each run
Table IV. Kinetic Analysis of Cd and Zn Using a Manual Spectrophotometer Cary 16, 310 mp, 1-cm cell, 25.0 "C, pH 4.9 with 0.003M NaAc-HAC, 0.1M " 3 0 4 , 4 X 10-3M Cu(I1) Zn Cd Error, Found Added Found Added 3.17 x 10-5 3.95 x 10-4 3.95 x 10-4 ... 4.06 X IO-6 3.44 x 10-6 3.95 x 10-4 3.95 x 10-4 ... 4.06 x 10-5 1.11 x 10-4 1.22 x 10-4 2.38 x 10-4 0.4 2.37 x 10-4 1.17 X 1.22 x 10-4 2.37 x 10-4 2.37 x 10-4 ... 2 1.96 x 10-4 2.03 x 10-4 1.98 x 10-4 2.02 x 10-4 1.93 x 10-4 2.5 2.03 X 2.03 x 10-4 1.98 x 10-4 2.68 x 10-4 1.19 X 0.938 X lo-* 6.8 2.44 x 10-4 2.66 x 10-4 0.930 X 7.5 2.44 x 10-4 1.19 x 10-4 2.44 x 10-4 2.44 x 10-4 0.8 1.18 x 10-4 1 . 1 9 x 10-4 2.44 x 10-4 2.42 x 10-4 1.22 x 10-4 2.5 1.19 x 10-4 1 3.82 x 10-4 4.06 x 10-4 3.99 x 10-5 3.95 x 10-6 1.2 4.00 x 10-4 4.06 x 10-4 4.00 x 10-5 3.95 x 10-5
236
ANALYTICAL CHEMISTRY
Error, 22 15.3 9 5 3.5 5 10.0 9
...
0.8 6 1.5
Table V. Kinetic Analysis of Rare Earth Metal Mixtures Conditions for the Reaction Mixture: 1.3 X 10-3M Cu, Durrum-Gibson Stopped-flow, 300 mp, Computer calculations were used and results are the average of three kinetic runs.
Metal
Std concn in reacting mixture, x 105~
La Ce La Pr Ce Nd La Ce Nd Ce Pr Nd
2.4(1MHAc 0.1M NaC104)
4.60
2.4(1MHAc 0.1MNaC104)
4.60
2. q 1 M HAC0.1M NaC104)
6.60 4.45 2.30) 3.30,
2 , q l M H A c 0.1MNaC104) 2.41MHAc O.lMNaCIOa)
3.30
Srn Eu Sm Gd Sm Tb
a
Results. 7 Found
PH
l.l(O.1M HClO4)
2.34
1.1(0.1M HC104)
6.22
7.M))
l.l(O.1M HC104)
2.44
U
105 91 70 104 90 105
3.3 17.1 3.0 4.1 5.3
88 __
a
131 118 132 54 120 97 105 115 101 95 102
8.9 40.1 9.7 0.7 7.7 9.5 3.8 5.6 3.0
0.5
Single run. Table VI. Removal of Kinetic Degeneracy
Metal coa cu Cd Pb
Std concn in reacting mixture, x 105~ 5.05 6.55 5.15 5.20
Conditions
Results, Found
Temp., "C
PH
Scavenger
25.0
1.1
1.o x 1 0 - 3 ~ ~b
25.0
3.1
1.3 x 1 0 - 3 ~cu
Cd 5.15 11.0 1.1 1.3 x 1 0 - 3 ~ cu Pb 4.10 a Cobalt(I1)CyDTA oxidized to cobalt(II1)CyDTA which is kinetically inert. Poor results were obtained because the rate constants are too close at 25 "C. Better results were obtained because the ratio of rate constants is larger at 11 OC than at 25 "C.
is computed separately. Calibrations for the rate constants are run under the same conditions immediately before and after the analysis series. Table 111 gives results for mixtures of metals which are kinetically adjacent in Figure 1 and are therefore among the more difficult to analyze. Two- and three-component mixtures are determined from to 4 X 10-6M. The Cd and Pb in the four component mixtures appear as a sum because the rate constants are too close together. In addition to the stopped-flow experiments mixtures of Zn and Cd were analyzed at higher pH (where the reactions are slow) using a manual spectrophotometer. This was done to examine the effect of l O / l to 1/10 ratios of Cd/Zn on the results of the differential kinetic method. It is possible to determine metal ions in this ratio on the stopped-flow ( 4 ) but the oscilloscope range makes it difficult to obtain the sensitivity desired for both major and minor components. The
97.0 99.5 125b 53b 95c 1090
U
2.0 1.6 5.1 9.5 5.0 4.8
results in Table IV were from graphical solutions with data which were taken from 2 minutes after mixing until about 2 hours. It is clear that determinations are possible even where the reaction components are in large ratios and the rate constants are relatively close. The ratio of rate constants, kd(Zn)/kd(Cd),is 5.7 under the conditions indicated in Table IV. Differential Kinetic Analysis of Mixtures of Lanthanide Metals. The procedure is the same as that used for the transition metals. The rate constants are close together for adjacent elements and this makes the analysis less accurate. Table V shows fair results for binary mixtures including ratios of rate constants as low as 1.4 (La/Cd) and 1.7 (Sm/Eu). The ternary mixtures gave poor results. In the case La, Ce, and Nd, only one out of three runs gave reasonable results and 30-50z errors occurred with this run and with the three runs for the Ce-Pr-Nd mixture. The method works, but if VOL. 41, NO. 2, FEBRUARY 1969
237
PH 6.6 4.2 2.4
1.1
Metals Std concn M X 106 Found, % % ff,
Table VII. Multicomponent Mixture Results are the average of three runs at each pH Conditions Scavenger Reagents 0 . 5M Na Ac 1 x IO-aM Pb 0.01M HAC-Na Ac 1 . 3 X 10-3MCu 0.005M NaCl 1M HAC 1.3 x 10-~MCU 0.1M NaC104 0.1M HClOI 1.3 x 10-~MCU Results Mg Ca Zn Mn 1.27 2.96 1.40 0.97 88 92 106 94 6.2 1.2 17 2.9
multicomponent mixtures of rare earths are to be determined, attempts should be made to increase the rate constant ratios by temperature change or by other effects. Removal of Kinetic Degeneracy. Variable reaction conditions force the calibration of rate constants but factors which shift rate constants are of value in removing kinetic degeneracy. Among the methods observed in this work to separate reaction rates which are too close together are a change of pH, a change of temperature, use of general acid catalysis, use of anion effects, a change of oxidation state and rate suppression by high concentrations of scavenger metal ion. Cu-co. The k ~ c u c y / k H c oratio c y is 1.2 at 25 " c but the experimental kd ratio increases to 1 1 in 0.1M HC104,apparently because of differing behavior of the protonated complexes. A determination can be done with Pb scavenger at 300 mp where the absorbance first decreases because of loss of CuCyDTA and then increases as more Pb-CyDTAZ- is formed from Co-CyDTA*-. Alternatively, oxidation of Co(I1)CyDTA2- to Co(1II)CyDTA- with HzOz makes the cobalt complex completely inert and permits Cu to be determined graphically as one component. The results in Table VI were calculated from the total metals found before oxidation and from the copper found after oxidation. Cd-Pb. The ratio of kHCdCY/kHPbCY is 1.8 at 25 " c but this ratio is reduced with copper as a scavenger because of a small slippressjon of the cadmium-CyDTA dissociation rate (7). The first set of Cd-Pb analyses in Table VI gives poor results with large errors and the computer reiterations fail to reach the usual minimum error because the rate constants are too close together. A change of temperature to 11 "C (and an increase in acidity to give a convenient time range) gives a ratio of 7.6 for the kd values and much better determination, as seen in the second set of Cd-Pb data. The data in Table I1 indicate that in 1M acetic acid Cd and Pb cannot be distinguished from one another. Co-Hg. The k ~ C o C y / k H H ratio g C y is 1.03 but as noted in
238
ANALYTICAL CHEMISTRY
Metals determined Ca, Mg Zn, (Mn Hg)
+
Mn, Cd, Hg Hg,Co
Cd 2.06 98 6.8
Hg 3.07 97 2.1
co 2.02 109 1.5
Table I1 this ratio is greatly changed in 0.1M HClOd and these metals can be determined together, as seen in the multicomponent metal mixture. Mercury also can be shifted by the addition of chloride ion. A solution 5 X 10-aM in C1- at pH 4.2 increases the kd value of Hg by a factor of 270. Analysis of a Multicomponent Mixture. A mixture of Mg, Ca, Zn, Mn(II), Cd, Hg(II), Co(II), Fe(III), and Ni was analyzed by the same general procedure except that runs were done under four sets of conditions with changes of the acidity and time-scan. The conditions used, metals analyzed, and results are given in Table VII. Seven out of nine of the metals were determined with about 10 accuracy. Iron(II1) and Ni were too slow to measure under the conditions used and were not determined. The mercury reaction appeared in three of the oscilloscope traces because the addition of chloride ion at pH 4.2 accelerated its dissociation. In this case we picked an unfortunate chloride ion concentration because it caused Mn and Hg to have similar kd values. The analysis at pH 4.2 gave the sum of these two metals in addition to a value for Zn. However, runs at other conditions gave individual determinations of Mn and Hg which agreed with the summation found at pH 4.2. The zinc reaction at pH 4.2 was 32 times greater than calculated from kHzncybecause of C1- and HAC-NaAc effects. The analysis of the multicomponent mixture demonstrates the capability of the CyDTA-kinetic method. It should be possible to work out detailed procedures for most metal mixtures and to determine the metals down to concentrations as low as IO-BM. The chemical preparation is minimal and the data can be obtained in very short times. For a large number of samples, an automatic data-handling and computer system would be advisable. RECEIVED for review August 14, 1968. Accepted October 24, 1968. Research was sponsored by the Air Force Office of Scientific Research under AFOSR Grant 1212-67.
