Differential Kinetic Analysis of Alkaline-Earth Ions Using Stopped-Flow Spectrophotometry J. B. Pausch and Dale W. Margerum' Department of Chemistry, Purdue University, Lafayette, , h d . 47907 Exchange reactions between Pb(ll) and the alkalineearth complexes of tronr-1,2-diaminocyclohexaneN,N,N',N'-tetraacetate (CyDTA) proceed a t sufficiently different velocities to permit the kinetic determination of mixtures of Mg, Ca, Sr, and Ba. The rate-determining step with each complex is its reaction with hydrogen ion. Ultraviolet absorbance of PbCyDTA2- is used to monitor the reaction but there is no kinetic dependence on Pb(ll). Reaction rate constants are in the ratio of 1:6.5:96: 1660 for Mg :Ca :Sr :Ba. The determinations are rapid and free of interference from other metal ions.
within the cage. Hydrogen ion does react, however, and more than 30 metal-CyDTA complexes are now known to follow the same type of exchange mechanism with a firstorder hydrogen ion dependence, and a first-order metalCyDTA dependence (4). The general mechanism is MCyDTA2-
+ H+
kHXCS
+
(C~DTA)T Pb2f RAPIDQUALITATIVE and quantitative analysis of the alkaline earths is achieved by utilizing the differing reaction rates of their CyDTA complexes. The procedure is simple. A slight excess of CyDTA is added to the sample and the pH is adjusted to give the metal-CyDTA complexes. The mixture is reacted with Pb(I1) and the rate of appearance of PbCyDTAZ- is followed spectrophotometrically. Each of the complexes-MgCyDTA 2-, CaCyDTA 2--, SrCyDTA 2-, and BaCyDTAl--reacts at a different velocity and variation of the time scan indicates which ions are present. Stoppedflow mixing is necessary for strontium and barium and it is a convenient method for all the ions. The transmittance-time signal is analyzed using computer or graphical techniques to give quantitative determinations. Other metal ions react to give CyDTA complexes but their exchange reaction with Pb(I1) is so much slower than the alkaline earths that very few interfere. The success of this differential kinetic analysis method rests in part in the distinctive kinetic behavior of the CyDTA complexes ( I , 2). The cyclohexane ring in CyDTA restricts the
+
( C ~ D T A ) T M2f
(1)
kUCY
lipbc: PbCyDTAZ-
(2)
where the rate-determining step is Reaction 1 and the exchange rate leading to lead-CyDTA is given by Equation 3 provided that kpbC~[Pb2+1 >> ~ M ~ Y [ M ~ + I . exchange rate
=
k ~ ~ ~ ~ y[MCyDTA2-] [H+]
(3)
The kinetic behavior of CyDTA has significant advantages in analytical applications. First, when excess scavenger is present-Le., Pb(I1) in this case-each metal-CyDTA complex reacts independently of the other complexes or of other metal ions present in the solution. Second, because of the restrictive reaction mechanism (compared to EDTA for example), the CyDTA exchange reactions tend to be slower. The velocities of substitution reactions of the alkaline earths often are extremely rapid but with CyDTA the acid dissociation rate in Equation 3 can be observed by stopped-flow methods. Third, the hydrogen ion concentration can be adjusted to give the desired pseudo first-order rate constant, k d x C Y = kE"CY[H+],and hence give the desired reaction halflife. THe rate expressjon for a mixture of alkaline earths at a fixed hydrogen ion concentration is given in Equation 4 and analytical determinations are accomplished by the solution of
+
d[PbCyDTA 2-] = kd"'pCY[MgCyDTA2-] dt kdCaCY[CaCyDTA '-1 kdSrCY[SrCyDTA2-] kdBaCy[BaCyDTA2-] (4)
+
I
flexibility of the ligand and tends to hold metal ions in a coordination cage. Structure I indicates this cage of nitrogen and carboxyl groups-the actual number of dentate groups coordinated may be less and no attempt is made here to show the known chair configuration of the cyclohexane ring (3). Other metal ions do not react directly with metal-CyDTA complexes because they cannot be accommodated sterically Correspondence to be addressed to this author. (1) D. W. Margerum, P. J. Menardi, and D. L. Janes, Znorg. Chem., 6, 283 (1967). (2) D. W. Margerum and T. J. Bydalek, ibid., 2,683 (1963). (3) J. L. Sudmeier and C. N. Reilley, ANAL. CHEM.,36, 1707
(1964). 226
ANALYTICAL CHEMISTRY
+
this equation in terms of the transmittance-time signal observed on an oscilloscope. In practice, only three of the four terms contribute significantly to the rate at any given condition because the ratio of rate constants k d B n C y / k d l r g C y is very large. EXPERIMENTAL
Apparatus. Two stopped-flow systems were used in this work. One was constructed using a design similar to that of Sturtevant (5). It has a 4-jet tangential mixer and an observation cell with a 0.20-cm light path. Two 2-ml syringes are used with a manual pushing block. Sample volume was (4) D. W. Margerum, J. B. Pausch, G. A. Nyssen, and G. F. Smith, Anal Chem., 41, 233 (1969). ( 5 ) J. M. Sturtevant in "Rapid Mixing and Sampling Techniques in Biochemistry," B. Chance er al., Eds., Academic Press, New York, 1964, p 89.
Pb(I1) in 0.5MNaC2H302.-pH 5.62,25.0 "C 0.25 ml per push. It was attached to a Beckman D. U. monochromator. A 1P28 photomultiplier was used with a Tektronix 564 storage oscilloscope equipped with a Type 2A63 differential amplifier and a Type 2B67 time base. The stored image was photographed on Polaroid film. The other stopped-flow unit was a Durrum-Gibson unit, Durrum Instrument Corp., Palo Alto, Cal., with a 2.0-cm observation cell. A Kel-F cell was used to avoid metal contact with the solutions. A calibrated zero suppression control was added to permit the selection of the desired range of per cent transmittance. About 0.2 ml of sample was used per measurement and the mixing time is about 2 mseconds. The exchange of lead with magnesium-CyDTA and calcium-CyDTA at pH 7.0-7.6 was followed with a Cary 14 recording spectrophotometer using a small plastic plunger to obtain 10-sec mixing in a 1-cm rectangular cell. Ternary mixtures and some binary mixtures required more than one oscilloscopic sweep and it was desirable to have different time scans to accommodate data from reactions with quite different half lives. A delay-timing device was used to provide a second triggering pulse for the scope and the time base was changed manually during the delay. All reaction rate studies were carried out at 25.0 f 0.1 "C. Reagents. The CyDTA was obtained from LaMont Laboratories in the acid form. It was recrystallized by dissolution in dilute base followed by addition of dilute acid. A standard copper solution was used to titrate CyDTA solutions using murexide indicator. Metal solutions of strontium, barium, and lead were prepared from their nitrate salts (J. T. Baker Co.) and used without further purification. Magnesium and calcium solutions were prepared from their carbonate salts. The metal ion solutions were standardized by complexometric titration with EDTA or CyDTA. Reagent grade sodium acetate was used for ionic strength control at 0.5M and also served as the buffering agent below pH 7, and 5 X 10-3M borate-mannitol (2.6%) buffered the reactions above pH 7. Procedure. The metal-CyDTA complexes are formed by adding about 10% excess CyDTA, buffer, and sodium acetate to the solution of metal ions. A 25-1111 sample is recommended but as little as 10 ml could be used. The solution is transferred to a stopped-flow syringe. The other syringe contains Pb(I1) and sodium acetate, the former being in 8- to 10-fold greater concentration than the total CyDTA. The flow reaction is initiated and when the flow stops suddenly the oscilloscope is triggered. The scope is first calibrated for 0 % and for 100 % transmittance and a suppression voltage is used to expand the transmittance scale so that small changes (a few T) can be recorded with precision. The oscilloscope
[H+]X 108,M_ Figure 2. Hydrogen ion dependence of the observed first-order rate constants, kd, for BaCyDTA2-, SrCyDTA2-, CaCyDTA2-, and MgCyDTA2Pb(I1) in 0.5M NaC2H802is used for the reaction at 25.0 "C
trace is photographed and the transmittance-time data are taken off the photograph. Three to six stopped-flow reactions are run in immediate succession. The metals being determined are run as pure components with two runs before and two runs after any series of samples. The Exchange Reaction. In previous studies ( I , 2, 6) copper(II), cobalt(II), and lead(I1) have been used as the scavenging metal in Reaction 2 but some of the alkaline earth reactions are so fast that a high pH was necessary to reduce the rate given by Equation 3 to a level which could be accommodated by stopped-flow detection. The requirements of the scavenging metal ion are that it not precipitate up to pH 8, that it react with free CyDTA rapidly, and that it have a reasonable absorbance shift when it forms the CyDTA complex. A fourth requirement for the scavenging metal is that its conditional stability constant be sufficient to drive the reaction to completion. The system selected was Pb(I1) in 0.50M sodium acetate. The high acetate concentration prevents lead hydroxide precipitation without diminishing appreciably the rate of Pb(I1) reaction with CyDTA. The lead acetate complexes also may prevent any possible lead suppression of the normal hydrogen ion reaction of the (6) D. L. Janes and D. W. Margerum, Znorg. Chem., 5, 1135 (1966). VOL. 41, NO. 2, FEBRUARY 1969
227
_
_
_
_
~
~
____~ ~~
Table I. Molar Absorptivities of Reactants and Products Molar absorptivity Species 244 mp 260 mp Acetate ion 0.04 0.01 3 740 340 Pb(IIy PbCyDTA2- (pH 6.7) 8250 2135 CyDTA (pH 9.0) 155 35 MgCyDTA*31 5 CaCyDTA269 6 SrCyDTA285 9 BaCyDTA2117 15 a In 0.5M acetate ion with correction for acetate absorbance. Table 11. Rate Constants for the Dissociation of MCyDTA2- Complexes MCyDTA2- ~ H M C YM-1 sec-1 k"Cy sec-l Mg 6.33 f 0.19 X lo4 0 Ca Sr
4.14
=k 0.18
X lo6
0
6.06 f 0.16 X IO' 0.030 f 0.006 Ba 1.05 f 0.10 X 108 4 . 4 r t 0 . 4 a. 25.0 rt 0.1 "C. b. p = 0.5. c. 25-54 individual kd values.
pH range 5.5-7.6 5.5-7.6 5.5-7.6
7.0-7.6
type observed with cadmium (7). Lead-CyDTA has a large absorption maximum at 244 mp and in fact there is such a large A A change that it was more convenient to use 260 mp. Table I gives the molar absorptivities. Single component systems gave excellent first-order plots as shown by the linearity of the log ( A , - A ) plot in Figure 1. The general absorbance expression for a binary mixture of calcium and magnesium is given by Equation 5.
(Library No. 0.2.01, Statistical Section, Computer Sciences Cents, Purdue University). The solution for [Mgli and [Cali is independent of the first two terms in Equation 5 because these are constant. Similarly, any absorbance due to nonreacting species will not affect the results. RESULTS
Dissociation Rate Constants. The exchange reaction of each alkaline earth-CyDTA complex with lead acetate gave kinetics first-order in M-CyDTA and zero-order in lead. The lead concentration was varied over a 20-fold range from to 6 x 10-8M. In general at least an eight- to 103 X fold excess of lead to M-CyDTA was maintained in each reaction. Figure 2 shows the dependence of the observed first-order rate constant on the hydrogen ion concentration. In order to give a comparison of all four metals on one graph only a fraction of the observed kd values are shown. The nonzero intercept indicates that Equation 3 needs to be altered for barium as given in Equation 6. rate [MCyDTAz-]
=
kdMCs = kMCy + kHIICy[H+]
Table I1 lists the rate constants and their standard deviations determined for 25-54 individual runs in the presence of 0.50M sodium acetate and the pH range indicated. Strontium also has a small contribution from khfcy. The constants are the best fit from the WRAP calculation using a weighting factor of (l/kd)l which is equivalent to designating the same relative error to all rate constants regardless of the acidity. It is of interest to compare the experimental values of kMCy with the values which would be predicted from the characteristic water substitution rate constant (IO) of each metal ion. The predicted values for kJfcycan be obtained by considering the rate of the reverse reaction in Equation 7 k\rcr
MCy2-
M2
+ Cy4-
(7)
kXCY
where k, = kdMgCy and kz = kdCaCY, When there are additional components the equation can be expanded accordingly. For a binary mixture the well known graphical solution (8, 9) may be used where the data (log [ A , - A ] against time) first are plotted for the region where the faster component has essentially all reacted-Le., where (1 - e-kzt) approaches unity. Rather than determine the faster reacting metal by difference we prefer to extrapolate the faster reaction component to zero time using A , values which are corrected for the slower metal. Equation 5 also can be solved directly without recourse to graphical methods by simultaneous equations, which if all the data are to be used call for digital computers. The values for the rate constants were determined for each analysis set by running the pure components before and after the mixtures using the same buffer and other conditions. The variables put into the computer (IBM 7094) consist of 30-60 sets of absorbance us. time data and the unknowns solved are [Mgli and [Cali. (The data were actually transferred in terms of millimeters measured on the film which is proportional to the per cent transmittance.) The input information also requires assigned constants for kl, kS, and A€. A linear regression analysis program (WRAP) was used for the calculations (7) G. F. Smith and D. W. Margerum, Znorg. Chem., in press. (8) B. E. Saltzman, ANAL.CHEM., 31, 1914 (1959). (9) S. Siggia and J. G. Hanna, ibid., 33, 896 (1961). 228
0
ANALYTICAL CHEMISTRY
to equal kM-HaOK0,[M2+][Cy4-] where kM-H20 is the characteristic water substitution rate constant and KO.is the outersphere association constant between M2+ and Cy4-. Thus,
where KsICYis the equilibrium stability constant. The predicted values are 5.4 x 10-5, 1.8 X 0.72, and 230 sec-l for Mg, Ca, Sr, and Ba, respectively. These predictions are based on KO,= 50 for the outer-sphere association constant between the 2f metal ion and the 4 - ligand and kIf -H,o equal to 1 x 105, 5 X los, 5 X lo8, and 2 X l o 9 sec-' for Mg, Ca, Sr, and Ba (10) and KarcYvalues (11) of 9.3 X lolo, 1.4 X 1013, 3.5 x 10'0 and 4.4 X lo*. The predicted values do not disagree with our observations that k ' g C y and kCacyare negligible. However, the experimental values for kYrCy and kBaCy are much less than the prediction. Similarly all the kH3fCy values are much less than would be predicted by this approach and it is clear that the characteristic water substitution rate constants, which are valid for monodentate substitution reactions, do not hold for the alkaline earth-CyDTA complexes. This is discussed elsewhere ( I ) in terms of a simultaneous bond (10) M. Eigen, Pure Appl. Chem., 6, 105 (1963). (11) G. Anderegg, Helu. Chim. Acta, 46, 1833 (1963).
, , Ternory
I
I
I
I
2.4t
TOP Sweep
o
MtddIeSweep
Mkxture of Mg ,Co ond Sr
BattomSweep31
E
12 41
51
Binarv Mixwe
2
3
4
5
40
3.0
20
IO
8
22
20 61
71
50 sec see 81 sec
of Ma and CO
I
6
7
8
Time, sec. Figure 3. First-order rate plot for the reaction of a mixture of 1.11 X lO-4M Mg2+ and 2.00 X 10-4M Ca2+ with 3.0 X 10-8M Pb2+in 0.5M total acetate at pH 5.50 The larger intercept gives Mg2+found as 1.14 X 10-4M and the smaller intercept gives Mg2+and Ca2+which by difference gives eaz+ found as 1.82 X lO-'M. Points are taken from a continuous oscilloscope trace dissociation mechanism, where the reactions are slower because several coordinated groups must be displaced almost simultaneously. The present work shows this to be true whether or not hydrogen ion is involved in the reaction. Differential Kinetic Analysis. CALIBRATION OF RATE CONSTANTS.The rate constants, kl and kz, in Equation 5 are needed to obtain a nongraphical solution of the data. These rate constants are very sensitive to hydrogen ion concentration and are best determined by calibration runs with the pure components using exactly the same buffer and ionic strength medium that are to be used in the determinations. Thus, errors in pH adjustment where 10.02 pH unit corresponds to + 5 % in the rate constants are eliminated, as are other possible variations in the rate constants due to temperature or ionic strength adjustments. Although sufficient data points would be available from each kinetic run of a reaction mixture to solve Equation 5 for kl and k2 as well as [Mgli and [Cali, this is not advisable because the accuracy falls off markedly with the addition of these variables and the simultaneous solution of the resulting nonlinear equations is difficult and increases the computer costs. Table I11 gives the precision for the rate constants and concentrations of individual alkaline earth solutions where two to three runs were immediately before and two to three runs were immediately after the kinetic determinations of the mixtures. The relative standard deviations for the rate constants and concentrations average 3 to 4%. BINARY MIXTURES.Table IV presents the results for binary mixture of alkaline earths including Mg-Ca, Ca-Sr, and Sr-Ba. Other binary alkaline-earth mixtures are easier to analyze kinetically because the ratios of rate constants are greater. In a number of runs, both graphical and computer analysis were obtained and were generally comparable. Figure 3 is an example of a conventional graphical resolutioni.e., without correcting the A m value for extrapolation of the
30
70
Sec
Figure 4. Oscilloscope traces of transmittancetime signals for stopped-flow reactions of metalCyDTA complexes using Pb(I1) (4.6 X 10-4M) in 0.5M NaCzH as the reactant at pH 6.60 Binary mixture is 3.07 X 10-jM Ca and 1.29 X 10-jM Mg. Ternary mixture is 0.49 X 10-jM Sr, 1.53 X 10-5M Ca, and 1.93 X 10-5M Mg
Table 111. Calibration of Rate Constants and Check of Concentrations for Pure Components Using Stopped-Flow Mixing Concn. addeda
Precision, % u Rate constant Concn. ___.-__
Concn. accuracy % found
Metal
M X lo5
pH
Mg
1.29 2.14 8.50 8.56
6.6 5.9 6.2 6.6
3.8 1.8 6.6 5.8
1.9 0.9 5.3 4.6
110h 105b 98c 1034
Ca
3.07 3.07 5.15 8.24 8.24 8.24
6.6 6.8 5.9 6.2 7.5 6.6
3.4 5.8 0.6 2.1 0.7 2.3
1.4 2.2 1.8 2.7 1.1 4.8
85b 91b 102b 10 6 c l0lc 109~
Sr
1.97 7.90 7.90
6.8 6.2 7.5
1.8 0.2
7.9
0.4 9.2 3.3
102* 101c 106~
5.91 7.90
7.5 7.5
3.2 6.9
4.1 3.8
96~ 99c
Ba
b e
Concentration after mixing. values transferred from Cary 14. values determined with Durrurn-Gibson.
e e
VOL. 41, NO. 2, FEBRUARY 1969
229
Table IV. Kinetic Analysis of Binary Mixtures
Metal Mg Ca Mg Ca Mg Ca Mg
Ca Mg
Ca Mg Ca Mg Ca Mg Ca Ca Sr Ca Sr
Ca Sr Ca Sr
Ca Sr Ca Sr Sr
Ba Sr
Ba Sr Ba Sr Ba
2.22 x 2.00 x 2.18 x 1.21 x 1.11 x 2.00 x 1.11 x 1.50 x 1.29 x 3.07 x I .71 x 1.54 x 2.57 X 4.27 x 1.20 x 2.26 x 3.00 x 3.34 x 2.00 x 5.00 x 5.00 x 2.00 x 1.53 x 1.23 x 4.60 x 0.49 X 3.07 X 0.99 x 2.32 x 2.12 x 1.16 x 3.18 x 0.93 X 4.24 x 0.46 x 4.24 x
Results
Conditions
Std concn in reacting mixture, M 10-4 10-4 10-4 10-4 10-4 10-4
7.42
[Pb(II)I M 3.0 x 10-3
7.55
3.0
x
10-3
6
A
G
5.50
3.0
x
10-3
4
S
G
10-6
6.35
4.6
x
10-4
6
D
10-6 10-6
G, C
6.60
4.2
x 10-4
5
D
C
10-4 10-4 10-6
5.90
1.0 x 10-3
3
D
C
5.90
1.0 x 10-3
5
D
C
10-6 10+ 10-4 10-4 10-4 10-4 10-4 10-4
5.90
1.0
x
10-3
5
D
C
7.39
3.3
x
10-3
8
S
7.39
3.3
x
10-3
5
S
7.39
3.3
x
10-3
4
S
G, C
6.80
4.2
x
10-4
3
D
C
6.80
4.2
x
10-4
3
D
C
10-6 10-6
6.80
4.2
x
10-4
3
D
C
10-4 10-4 10-4 10-4
7.59
3.0
x
10-3
9
S
G, C
7.58
3.0
x
3
S
G
io-4
7.58
3.0 X
4
S
G,C
10-4 10-4 10-4
7.58
3.0 x
4
S
G
PH
No. runs 4
Instr. A
Method G
10-6 10-6
%. 4.2 3.0 6.9 7.8 4.3 14.7 11.9, 8 . 2 14.1, 8.9 6.2 2.9 3.7 5.6 2.6 0.8 5.6 2.0 4.2, 6.3 9.1, 5.0 2.3, 7 . 4 1.1,l.l 11.8, 5.4 32.5,4.8 0.6 3.5 0.7 12.5 1.3 22.2 11.7, 3.9 10.1, 15.0 6.7 1.3 6.5, 8.9 2.8, 3.7 3.7 6.2
Found 95 104 97 95 104 109 112,104 111, 101 112 89 92 75 99 105 101 107 100, 102 113, 107 98, 100 104, 99 120, 96 87. 113 114 92 95 82 124 36 101,97 98, 91 103 96 116, 81 99,102 115 91
A-Cary 14. S-Sturtevant Stopped-Flow. D-Durrum Stopped-Flow. G-Graphical. C-Computer.
faster component-for a Mg-Ca mixture where the pH and time scan were set to give all the data on one oscilloscope sweep. Although the determination is satisfactory in this instance, it is frequently difficult to obtain sufficient data this way. Figure 4 shows the type of data more frequently collected for the determinations. In the two examples given in Figure 4 there are three oscilloscope sweeps at different time scans with the time triggered by the delay-timing device. The range of concentration of alkaline earths used was 1 X 10-8 to 5 X 10-4M. The method has high sensitivity and the data needed for the analysis can be obtained in a few seconds, so the method could be very rapid if the data workup was fast. Our data acquisition and computation were not automated and the bottleneck in determination was the transfer of data from the Polaroid pictures and punching of computer cards. 230
0
ANALYTICAL CHEMISTRY
TERNARY MIXTURES OF ALKALINE EARTHScan be analyzed and results are given in Table V using the computer method. Equation 5 must be expanded for the additional term. The results are comparable to the binary mixtures. In Figure 3 Sr, Ca, and Mg can each be seen as the major contribution to the oscilloscope trace at the top, middle, and bottom time sweep, respectively. ALKALINE-EARTH DETERMINATIONS IN THE PRESENCE OF TRANSITION METALS are easily accomplished because the transition metal CyDTA complexes all react much slower with hydrogen ion. Interference was observed when the Zn/Mg ratio was 10/1 as seen in the third analysis mixture in Table VI. This would not prevent a determination if kdZnCY were included in the computation. As reported in Table VI, many metal ions can be present without causing interference including manganese, cobalt, cadmium, zinc, and mercury. These
Table V. Ternary Mixtures
Metal Mg
Ca Sr
Mg Ca Sr
Mg Ca Sr
Mg Ca Sr Ca Sr Ba
Std concn in reacting mixture, M 2.22 x 2.00 x 2.00 x 0.64 X 1.53 X 0.25 x 1.93 x 1.53 x 0.49 x 0.64 x 3.07 x 0.25 x 3.09 x 2.96 x 2.96 x
10-4 10-4 10-4
10-5 10-5
PH
[Pb(II)I M
Conditions No. runs
Results Instr.
Method
%.
Found
13.1 16.3 10.7 16.7 3.8 42.5 4.1 1.2 9.6 4.9 1.6 4.2 4.7 2.8 12.7
82 108 112 113 112 84 102 110 106 126 102 96 86 110 93
6.30
3.3
x
10-8
8
S
C
6.60
4.2
x
10-4
8
D
C
6.60
4.2
x
10-4
4
D
C
6.60
4.2
x
10-4
4
D
C
7.5
4.2
x
10-4
4
D
C
10-6
10-6 10-5 10-5 10-5 10-5
Table VI. Binary Mixtures of Alkaline Earths in Presence of Transition Metals
Metal Mg Ca
Std concn in reacting mixture, A4
x x 10-6 x 10-5 x 10-5
Ca
1.29 3.07 1.29 3.07
Mg Ca Ca Sr Ca Sr
1.29 X 3.07 X 3.07 x 10-5 0.49 x 3.07 x 0.49 x
Mg
Results Transition metals, M
pH
Conditions [Pb(II)]M No, runs
Hg 1.0 X Cd 4.0 x 10-6 Hg 1 . 0 X 10-6
6.6
4.2
x
10-4
3
D
Method C
Instr.
6.6
4.2
x
10-4
3
D
C
Ni 1 . O X Cd 4 . 0 x 10-6 Zn 4.0 X Co 2 . 5 X loT6 Zn 1 . 9 X
6.6
4.2
x
10-4
3
D
C
Co 2 . 5 X 10-6
6.8
4.2
x
10-4
4
D
C
M n 2 . 0 X 10-6 Cd 3.9 x 10-6 Hg 1.0 X Zn 3 . 8 X 10-6
6.8
4 . 2 x 10-4
3
D
C
ions were tested because their kd values are known in perchlorate media ( I ) and are the next fastest group of metalCyDTA complexes to react. Other metals would not interfere kinetically. SEAWATER,DOLOMITE,AND BLOODSAMPLES.The application of this kinetic method to practical samples containing alkaline-earth metal ions is tested by analyzing sea water, dolomite, and blood serum for magnesium and calcium. The samples were prepared as simply as possible. Sea water, obtained from I.A.P.O. Standard Sea-Water Service, Charlottenland Slot, Denmark, was taken directly for addition to CyDTA and buffer. The dolomite sample was sintered and dissolved in dilute acid. CyDTA was added and the pH adjusted to 9. The blood serum sample was first treated with trichloroacetic acid and filtered. CyDTA was then added and the pH adjusted to 9. The results are given in Table VII. DISCUSSION
The results of the kinetic analysis indicate that individual alkaline earths can be determined in the presence of other metal ions. The general precision and accuracy to be expected for this procedure are 5-1Oz. The sensitivity is
7 2
u
Found
4.5 2.2 1.1 1.1
102 90 98 87
2.6 3.9 3.1 8.8 4.6 9.1
152 92 94 116 114 112
excellent with determination of as little as 10-BMmetal ion. Small concentrations of alkaline earths can be determined in the presence of 10-100 fold excess of most other metals. The analysis errors are higher than we had expected for the computer method. More than 30 points per run were generally used and the shape of the absorbance us. time curve determines the results rather than the initial displacement of absorbance. Hence any absorbance due to impurities or to the presence of other metals will not affect the results provided that source of absorbance is constant during the fraction of a second or few seconds required for the reaction of the alkaline earths. Drift of the 100% T balance of the singlebeam stopped-flow spectrophotometer between standardization intervals could introduce an error in the A A values and hence in the shape of the curve which fits Equation 5 . In general the drift was less than 1 T, however, and this is not a major source of error. The effect of random errors in signal noise was tested with simulated data using 1 0 . 2 2 T fluctuation for a reaction mixture with a total T change of 25. In general the noise was less than this. The resulting errors in computer analysis were 1-2Z. The accuracy reported for the oscilloscope is 1% for the displacement and 2 2 for the time base. Errors in the transfer of data are on the order
z
VOL. 41, NO. 2, FEBRUARY 1969
231
Table VII. Kinetic Analysis of Practical Samples Sample Sea water Foundc %U
Dolomite Std. c0ncn.c % Found %. Blood serum Std ConcncJ % Found %. a Atomic absorption. * EDTA titration less the Mg. c Original sample concentration. Based on nominal content.
[Mgl, M
0.039 6.1
7.05
x
10-3
104
5.3 1.66
93 0.7
x
PH
5
6.6
6.85 124 4.4
x
10-3
5
6.2
5.00
x
10-3
4
6.2
1.1
+=5z
z
ANALYTICAL CHEMISTRY
No. of runs
97
of 1-2%, but this should be a random error and hence will have no more effect than the random noise test. The data in Table I11 help to indicate the source of error because the precision in the determination of the rate constant as well as the concentration of pure components averages only 3-4% (in terms of standard deviations). The precision of the rate constant determination for a fixed pH-Le., the same buffer solution-depends largely on the efficiency of mixing and the absence of extraneous electronic or optical s i p als. The specifications for the Durrum instrument indicate 9 9 3 z mixing within 2 mseconds. This degree and speed of miring should be sufficient to prevent errors of the magnitude observed. However, the 0.5M sodium acetate solutions used in this work are a little harder to mix than more dilute solutions and this appears to be one source of error. Harder pushes to give higher flow rates and better mixing can introduce extraneous optical signals due to vibration or pressure relaxation in the cells. Errors also can arise from any fluctuations in the HPlamp or photomultiplier which occur during the run. Whatever the cause, the stopped-flow instruments themselves help to limit the precision of the method. Errors of +5z in the rate constants were tested with simulated data and with actual data and were found to cause errors in the concentrations analyzed in the range of + l to depending on the rate constant and concentration ratios. Table I11 indicates somewhat better accuracy in the concentrations found if the molar absorptivities are measured directly on the flow apparatus. Errors of 1 5 in A € cause corresponding errors in the concentrations determined. Variation of EpbCy values when Pb(I1) and CyDTA were mixed in the stopped-flow indicates that reproducibility of equal volumes from each syringe in the reaction mixture may be another source of error. This would not affect the calibration of rate constants but would affect the concentration values found in pure components or in mixtures.
232
[Gal, M
0.03b 0.037 5.3
0.04~
The results for magnesium and calcium were as good as those for the other alkaline earths although their rats constants are closer together. One difficulty with the other mixtures was that the time delay of 0.5 or 1.0 second used between different oscilloscope sweeps often cut out some useful data. A continuous data acquisition system independent of the oscilloscope and photographs should give better results and of course would save much time. A theoretical error treatment using the two point m:thod described by Mark et al. (12) indicated a 1-3 relative error should be expected in the metal ion concentration for a transmittance signal error of 0.1-0.2z T. As we have ind‘cated, there are other sources of error in the present method but it should be noted that attempts to analyze the data using the two-point method with pro2er selection of the optim m t i r e 3 f eq iently gave disasterous resu’ts with errors as hi:h as 500%. This is quite likely to occur in any real system. On error when 30 the other hand, the same runs gave only points were used. The use of pure CyDTA is important. Commxcial material sometimes contains small quantities of other substances which form complexes but react much more rapidly. In summary, stopped-flow kinetic analysis of CyDTA complexes offers a rapid and practical method for qualitative and quantitative determination of alkaline earth metals down to trace levels. The analysis can be done in the presence of most other metals.
5z
RECEIVED for review August 14, 1968. Accepted October 24, 1968. This research was sponsored by the Air Force Office of Scientific Research under AFOSR Grant 1212-67. (12) H. B. Mark, Jr., L. J. Papa, and C. N. Reilley, “Advances in Analytical Chemistry and Instrumentation,” Vol. 11, C. N Reilley, Ed., Interscience, New York, 1963, p 255.
