and similar experiments. The symbol Q represents the charge/cm2 for the peak designated by the subscript. A superscript D indicates the quantity was calculated from the relevant disk electrode experiment, while the superscript R signifies that the quantity was calculated from ring electrode data by dividing by the collection efficiency. I n the case of ring electrode experiments, the ring potential is given in the footnote to Table V. The areas corresponding to these symbols are indicated by the shaded areas in Figures 1, 2, and 3. I n calculating these various charges, appropriate consideration has been taken for the difference between the ring curves observed as a result of change of disk potential scan direction; i.e., in Figure 2, at +0.25 V 5 ED 5 f0.55 V, there is a separation that results from a n instrumental artifact. Certain capacitors are required in the 4-electrode potentiostatic circuit t o reduce the ring current noise (8), and produce this shift. I n the absence of adsorption phenomena, the true current would lie exactly midway between the separated scan currents. This shift was taken into account in the adsorption calculation by superimposing the anodic scan curve o n the cathodic scan curve, and then calculating the various Q's. From Table V it is seen that Q I D is greater than QIR by 31 pC/cm2 indicating that more underpotential Sn(0) is deposited at the disk than is detected at the ring. Similarly fromthis QzD is greaterthan elRby 34pC/cm2. We observation that the underpotential deposition to sn(o) at the disk at -0.15 v during the cathodic scan involves both ~~
(8) L. P. Morgenthaler, "Basic Operational Amplifier Circuits for Analvtical Chemical Instrumentation," McKee-Pedersen Instruments, Danville, Calif., 1967, pp 25-27.
the reduction of Sn (11) species diffusing from the bulk of the solution as well as the reduction of some of the Sn(II),,,, already present at the disk. During the anodic scan, the underpotential Sn(0) deposit is oxidized t o Sn(I1) at the disk, most of which diffuses t o the solution, while some (-34 pC/ cmz) remains adsorbed at the electrode. The agreement between - elR)and ( Q z D - Q z R ) is within the experimental error. Q8" represents the total amount of Sn(II),d, which is removed o n oxidation a t $0.2 v. QbsPR represents a fraction of Q3", since at --0.1 V (where the gap ends) there is still incomplete adsorption at the disk. The sum el") = 229 pC/cm2 therefore represents the total adsorption at the disk during the cathodic scan, where the adsorbed species at the disk would be Sn(I1) and Sn(0). The quantity (Qz" Q3") would represent the oxidative desorption of Sn(0) t o Sn(I1) and of Sn(II),d. t o soluble Sn(1V) (see Figure 3). This sum is 230 pC/cm2, which agrees satisfactorily with the previous quantity. Hence, a quantitative consideration of the observed processes show that the total amount of Sn(I1) adsorbed and/or reduced t o underpotentially deposited tin can be accounted for by oxidation t o soluble Sn(I1) or Sn(1V) o n the anodic scan.
(elD
(egap" +
+
RECEIVED for review August 2, 1971. Accepted September 22, 1971, V.A.V. gratefully acknowledges the study grant awarded to her by the Rockefeller Foundation. The support of the Air Force Office of Scientific Research under Grant No. AFSOR-70-1832 is gratefully acknowledged by S. B.
Fast Reaction Flow System Using Crystal-Membrane Ion-Selective Electrodes H. I. Thompson and G . A. Rechnitz' Department of Chemistry, State University of New York, Buffalo, N.Y. 142I4 A rapid-mixing, continuous flow system using ionselective membrane electrodes as sensors is designed and evaluated for the study of fast solution reactions. The system considerably extends the applicability of ion electrodes in kinetic measurements and i s constructed to be compatible with commercially available electrodes. The study of a model reaction and theoretical evaluation shows that the system is capable of measuring reactions with rate constants as large as 108M-' sec-I under favorable conditions.
USEOF ION SELECTIVE electrodes in studies of reaction kinetics provides a convenient, sensitive, and accurate method of monitoring the progress of chemical reactions not readily accessible by other techniques (I-3). Most studies have been of relatively slow reactions-e.g., half lives of several seconds to minutes-with the electrode as a continuous sensor in a static To whom all correspondence should be addressed.
( I ) G. A. Rechnitz and 2. F. Lin, ANAL.CHEM., 39, 1406 (1967). (2) K. Srinivasan and G. A . Rechnitz, ihid., 40,1818 (1968). (3) B. Fleet and G. A. Rechniti, ihid., 42, 690 (1970). 300
system. For fast reactions, however, it is necessary t o resort to rapid-mixing flow techniques of the continuous or stoppedflow type. The continuous flow technique, also used in the present study, involves the construction of concentrationtime relationships from concentrations (or activity) measurements taken after various elapsed reaction times. Such times are a function of flow rates and reaction chamber volume, the lower limit being set by the mixing efficiency and mixing chamber volume. Measured times of 10-2-10 sec are generally accessible by this technique. For stopped-flow systems, rapid monitoring and recording of concentration-time profiles are made after the flow has been arrested and reaction times of sec can be achieved. Clearly, the response rate of the monitoring sensor is critical for stopped-flow applications but is somewhat less important for continuous flow measurements where a steady state situation is maintained a t the observation point. Ion selective electrodes display the sensitivity, selectivity, and response time characteristics required by this technique. In a previous study (3) we employed liquid membrane type ion electrodes t o study several complex formation reactions.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
Lack of rigidity of the membrane material, however, restricted the reactions studied t o those requiring fairly low flow rates. Higher pressures at faster flow rates distorted the membrane. The purpose of the present study was to design a system capable of withstanding higher pressures and, hence, measuring faster reaction rates by using crystal membrane electrodes. At the same time we wish t o demonstrate the usefulness of newly developed differential circuitry (4)t o eliminate the problems of liquid junction potentials and streaming artifacts in the flow system. Crystal membrane electrodes are available for both cations and anions. The fluoride electrode developed by Frant and Ross (5) uses a europium doped lanthanum fluoride crystal and has been shown t o be capable of measuring free fluoride concentrations as low as 10F9Min fluoride buffered solutions (6) provided the total fluoride concentration is >lO-SM. Pressed crystals of silver sulfide can be used to monitor silver or sulfide ion concentrations of lO+M (7) while heterogeneous crystals of silver and copper, cadmium or lead sulfides are capable of estimating free heavy metal ion concentrations below 10-loM (8). Halide electrodes using heterogeneous crystals of silver sulfide and the appropriate silver halide can monitor free halide or cyanide ion concentrations as low as 10-5M. All of these electrodes suffer from some interferences but these are not serious in most kinetic studies where pure solutions are used. The response times of these electrodes depend largely on experimental conditions and concentration levels. The fluoride electrode is the most satisfactory in that its response time is much less than one second at total fluoride concentrations in excess of lO-4M. In addition, the electrode displays a n almost perfect Nernstian response t o 10-9M free fluoride. Other crystal membrane electrodes show slightly longer response times but are still generally suitable for continuous flow experiments. The present paper details the construction and testing of a flow system using the fluoride electrode as sensor and the study of the iron 111-fluoride complex formation reaction as a model system. The investigation shows both the advantages and limitations of the flow technique using solid state ion-selective membrane electrodes. EXPERIMENTAL
Chemicals. All chemicals used were of reagent grade. Sodium fluoride stock solution (0.1M) was made by weighing accurately the required amount of the salt, which had been dried overnight at 100 "C,and dissolving in water. Stock iron solutions were made from ferric perchlorate (G. F. Smith Chemical Co.) and standardized complexometrically. Reaction solutions were made from appropriate amounts of these stock solutions, perchloric acid to give the desired acidity and sodium perchlorate to adjust ionic strength ( p = 1.0). A Corning pH glass electrode (No. 476022) was used t o measure hydrogen ion concentrations. Deionized water was used throughout. Apparatus. A schematic diagram of the flow apparatus is shown in Figure 1. The drive motor was a Bodine Electric Co. HP, 1725-rpm single phase unit with a Minarik Model SH-63 speed control. The motor was coupled to the drive shaft of the syringe ram uia a P.I.C. model ES-2 speed reduction gear having a 3 :1 reduction ratio. The relatively (4) M. J. D. Brand and G. A. Rechnitz, ANAL.CHEM.,42, 1659
(1970). M. S. Frant and J. W. Ross, Jr., Scieme, 154, 1553 (1966). E. W. Bauman, J. Inorg. Nucl. Chem., 32, 3823 (1970). Instruction manual Orion No. 94-16, Sulphide Ion Electrode. Instruction manuals Orion No. 94-48, 94-29, Heavy Metal Ion Electrodes.
(5) (6) (7) (8)
A B
- drive
motor
- reduction
gear
C- polyethylene syringes D - 3-way E F
valves
- reactant reservoirs - mixing chamber
G- sensing e l e c t r o d e
H I
E? 9D
- reference - differential
J -pen
amplifier
recorder
J
I
V
Figure 1. Schematic of flow system high pressures associated with fast flow rates necessitated the replacement of standard g l a s s syringes with less fragile ones. Though stainless steel syringes could have been used, it was much more convenient to encase polyethylene disposable syringes in thick Plexiglas sheaths. This prevented distortion of the syringe chambers while at the same time permitting easy reading of volume graduations. The materials used in these syringes are essentially inert to most chemicals and require no greasing t o achieve good plunger to barrel sealing. Luer-Lok syringe outlets were connected to miniature, 3-way, inert Hamilton valves capable of withstanding pressures of 100 psi. The second port of each valve led cia Tygon tubing to a reagent solution reservoir while the third outlet was used t o take the flow to the mixing chamber cia 2-mm i.d. Teflon (Du Pont) tubing and a two-way Plexiglas stream splitter. The mixing chamber was also constructed of Plexiglas with four inlet ports at right angles to each other around its circumference. The two halves of each stream were admitted through diametrically opposing ports. The mixing space of the chamber had a diameter of 4.8 mm and a depth of 1.3 mm with a single stainless steel 18-gauge outlet needle vertical to the plane of the inlet ports. All tubing and needle joints were secured with epoxy resin. Intramedic polyethylene or Teflon tubing, approx. 1.1-1.3 mm i.d., was used to take the reacting stream t o the sensing electrode cap and from there to the reference electrode. While a flow-through reference electrode could have been used, the technique of dipping a regular double junction reference electrode into a small Teflon beaker, through which the flow was passed before being led to waste, was perfectly satisfactory. This technique, in conjunction with a differential amplifier ( 4 ) having two high impedance inputs, allows any dipping electrode t o be used as a reference so long as the concentration of the ion it senses remains constant throughout any set of experiments. For example, the use of sodium perchlorate to adjust the ionic strength of reacting solutions permitted a sodium glass electrode to be employed as a reference, thus eliminating all liquid junctions from the system. Both reference systems were used in the present study. The output from the differential amplifier was fed directly to a Beckman 10-inch
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
0
301
K-electrode.
L
-sensing
1 2 m m O.D.
crystal,
8mm
io.
M-Teflon
sleeve,
N-
washer, 18mm 0 . 0 . .
1 2 m m 1.0.
8 m m I D., 0.4 m m Th.
0- Plexiglas c a p ,
18 m m I.D.,
2 b m m 0. D.
P - outlet needles,
2090.
Q - inlet
90.
n e e d l e , 18
R - L a F,
crystal
S -silver
wire
T - A g C I coating
0
U -polyethylene
tubing
V - polystyrene coil d o p e W-NaF, N a C I , AgCl filling solution
Figure 3. Construction of flow-through crystal electrode Figure 2. Detail of electrode flow chamber pen recorder with a mV source connected in parallel to provide a bucking potential for a continuously variable scale from -900 t o f900 mV. Design of the Flow-Through Sensor. Two methods of bringing the reaction mixture into contact with the sensing crystal were tried. The first, and most satisfactory method, is set out diagrammatically in Figure 2. and involved fitting a cap, in which there is a small dead space for the reaction mixture t o pass through, over a conventional electrode body. The Teflon collar was made t o be a tight press fit over the body, and the Plexiglas cap was in turn press-fitted over the collar. The use of Teflon in the collar and washer eliminated leaks from the whole cap system without requiring clamps to hold the cap in place. I n preliminary experimental designs, the pressure exerted by such clamps o n the electrode body produced a risk of cracking the sensing crystal, especially in the case of the fluoride electrode where the sensjng window is relatively thin. The internal diameter of the washer was made equal to the diameter of the crystal so that the whole crystal face was exposed to the flow when the cap was assembled. In order t o minimize the time that the solution spends in contact with the crystal and also reduce the pressure built up in the system, one inlet and four outlet needles were used in the base of the cap. These were positioned so that the flow was introduced at the center of the crystal face and was forced to exit around its perimeter. The thickness of the washer is critical in that if it is too thin, it will cause a constriction in the flow and rapid flow rates will not be possible, while if it is too thick the volume of the dead space will be much too great. In this latter case, inaccurate results will be obtained because a n appreciable percentage of the reaction will take place after the mixture has entered the cap. Since reaction time between mixing and observation is directly dependent on tubing volume and inversely on flow rate, the minimum measurable reaction time depends o n optimizing these two factors. Best results were obtained with a washer thickness of 0.4 mm which set the dead space volume a t 2.01 x ml. For this to be less 302
than 10% of the total reaction volume, the reaction tubing length was such that at pumping rates of 8 ml sec-1, the smallest measurable reaction time is approximately 25 milliseconds. A second sensing method involved passing the flowing solution directly through a channel drilled in the sensing crystal. The final form of the electrode so constructed is shown in Figure 3. The main problem encountered was of sealing the flow-through section from the internal filling solution of the electrode. This was overcome by separating the inlet tube from the internal solution by as great a surface area of crystal as possible. Thus, another hole was drilled part way through the crystal and a fine polyethylene tube was inserted and sealed into it with polystyrene coil dope. This tube was filled t o a depth of about two centimeters with a solution, 10-3M in NaF, 10-IM in NaCl, and saturated with AgCl. A silver-silver chloride connecting wire was inserted and the tube sealed at the top with coil dope. This electrode gave a Nernstian response when used either as a dipping electrode o r when an external solution was allowed only t o contact the flow through passage. Response times, however, differed greatly under these two sets of circumstances. Normal very fast response was found in the former case while equilibration times of one to two minutes were observed when operated in the flow-through manner. This may be due t o the fact that the flow-through channel was not polished o n the inside. With other crystal membrane electrocies, such as silver sulfide and heavy metal sulfide-silver sulfide heterogeneous crystals, neither the internal contact nor the hole polishing should present such problems. Direct silver wire contact t o these crystals has been achieved in this laboratory and roughness of membrane surfaces does not seem to be so important t o electrode response times. Kinetic Procedure. A solution of the required concentration of sodium fluoride and perchloric acid (adjusted to a n ionic strength of 1.OM with sodium perchlorate) is taken up into syringe 1 and pumped through the system along with a solvent blank solution in syringe 2; the blank having a n ionic strength and acid concentration the same as the fluoride solution. The base-line response corresponding to the initial
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
free fluoride concentration is recorded. The blank solution is then replaced in syringe 2 by a n appropriate iron(II1) solution whose acid concentration and ionic strength have been adjusted as before. Steady state response to free fluoride ion is recorded at several values of reaction time, t . Variation of I is achieved either by altering the length of reaction tubing or by changing the pumping speed to. alter the flow rate. It will be seen below that the measured electrode response at any given free fluoride concentration is completely independent of rate of flow over a wide range of flow rates. Concentration/time relationships can be worked out from the recorded data. RESULTS AND DISCUSSION
Effect of Flow Rate on Electrode Response. To test the effects of flow rate o n electrode response at high rates and pressures, pumping speeds were varied to give a range of flow rates from 0-7 ml sec-1. Table I shows the results of these studies for free fluoride concentrations from 10-4-10-7M. Even at the lowest free fluoride concentrations, the electrode response is completely flat within experimental error over the range of flow rates. These results were obtained using an Orion double-junction reference electrode in the dipping manner previously described but similar results are obtained when a sodium ion glass electrode is used as reference. The excellent behavior of the fluoride electrode over this range of free fluoride ion concentrations is shown by the 59.32 mV slope and the 0.99999 correlation factor of the calibration plot constructed from these data. Free fluoride concentrations were calculated using the value of the equilibrium constant for the Hf and F- interaction at p = 1.0 of 1.26 X given by Srinivasan and Rechnitz (9). Test of Flow System. Since the reliability of results obtained from any flow system depends primarily o n the efficiency of the mixing chamber, this part of the apparatus was checked by the indicator methods detailed by Fleet and Rechnitz (3). When the visual method was used, it was only at the highest flow rates that a very slight coloration in an initial small portion of the reaction tubing could be detected. The potentiometric method involving the comparison of electrode response for mixing two solutions 10-3M in fluoride and one solution 2 X 10-3M fluoride with water showed no difference in potential readings for the shortest possible reaction tube (-2.0 cm). Thus, the slightly inefficient mixing at high flow rates shown up by the visual technique is of no significance compared with the inaccuracy introduced by the sensing space at the electrode. As has been outlined previously, this latter error was kept below 10%. As an overall test of the system, the iron(II1)-fluoride complex formation reaction was studied. Under conditions where only the 1 : 1 complex forms-Le., iron in at least twofold excess over fluoride, the mechanism of the reaction has been found t o involve the paths Fe3+
+ F-
ki
FeF2+
+ H F e FeFZ+ + H+
(11
kl
Fea+
(2)
Table I. Effect of Flow Rate on EMF at Various Free Fluoride Levels Flow rate, Concn free fluoride, M ml sec-1 EMF mV 66.6 1.38 x 10-4 7.14 66.5 5.00 66.4 3.03 66.6 2.27 66.5 1.40 0 66.7 1.26 x 10-5 6.98 127.5 5.66 127.5 3.57 127.6 2.70 127.5 1.69 127.7 0 127.8 1.25 x 10-6 6.59 187.5 4.92 187.7 3.70 187,4 2.59 187.9 1.70 188.0 0 188.0 1.24 x 10-7 6.52 246,7 6.12 247.0 4.38 246.9 3.26 246.5 2.34 246.7 1.79 246.8 0 247,7
results of a spectrophotometric study was based on the rate expression d[FeF2+] _ _ _ - kl[Fe3+][F-! +kz[Fe3+][HF] - ki [FeF2+l dr K, ki Ke
Ka
[FeF2+][H+] (3)
Integration of this expression and rewriting to include the variable measured by the electrode, Le. millivolt change x, results in the relationship
-
1 __
antilog (x/59.16)
1
cddq
- antilog 2(x/59.16)1
{kl where a
1
(9) + kz} t
const (4)
+
total iron concentration = [Fe3+] [FeOH*+] f [FeF2+] b = total fluoride concentration = [F-] [HF] [FeFz+] [FeOH2+J[H+] [H+l Kb = = Kh [H+] [Fe3+] =
-+
+
+
A kinetic examination of this reaction in a static system yielded kl and kz values of 3.73 x 103M-' sec-l and 67 M-1 sec-I, respectively (2). These values compared very favorably with those of Pouli and Smith (IO) whose treatment of From any single set of experiments an apparent rate con(9) K. Srinivasan and G. A. Rechnitz, ANAL.CHEM., 40,509 (1968). (10) D. Pouli and W. MacF. Smith, Can. J . Chem., 38, 567 (1960).
stant, k '
=
(' i
kl - d ) k z , can be found by plotting the
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2 , FEBRUARY 1972
303
Figure 4. Graphical evaluation of rate constants (plot of k’ us. acidity function)
Table 11. Test of Equation 4 a t Various Acidities
to the system. Thus, for a simple second order reaction which goes t o completion
(Temp. 24 “C)
W+l ( M I 2.95 x 10-1
9.98 x
6.85 x 10-2
Time, msec 84.3 128.7 171.7 256.0 347.4 86.3 128.0 170.6 256.0 343.3 74.6 114.2 157.4 239.1 268.2 357.7
mV 8.6 12.0 15.8 21 .o 28.5 18.0 23.4 29.3 38.0 49.5 22.7 29.0 36.4 48.0 52.2 65.2
x,
2.721 2.854 3.006 3.219 3.539 3.000 3.208 3.439 3.789 4.270 3.165 3.408 3.699 4.169 4.343 4.906
logarithmic part ( r ) of Equation 4 us. time. As hydrogen ion concentration plays a large part in determining the values of constants c, d, and, hence, q, the variation of k‘ with acidity can be used t o evaluate kl and k2. With “a” values of 5 x 10-2M and “6” values of 5 x 10-3M,the results of our studies at hydrogen ion concentrations of 3 X 10-’M, lO-lM, and 7 X 10-2M are shown in Table 11. From the k’ values obtained from these data, the relationship in Figure 4 was constructed and resulted in values for kl and kz of 5.3 X lo3 M-l sec-l and 42.6 M-I sec-’, respectively, at 24 “C and 1.OM ionic strength. Again these compare very well with previous literature results (2, IO) showing the validity of the methods used and the effectiveness of the flow system. Limits and Possibilities of the Flow System. Assuming that the minimum reaction time which can be accurately measured with the present flow system is of the order of 25 msec, it is possible to predict the maximum rate constants accessible 304
0
A
r
+ B -,products
(5)
the maximum rate constant which can be estimated is given by the integrated rate expression kmaxX 2.5 X 10-2 =
For most electrodes the lowest initial reactant concentiation, a, m i n , which can be tolerated is about 10-5M, and, using equal initial concentrations of A and B, the relevant expression is 1
k,,
X 2.5
x
10-2 =
10-5
1
-x
-
10-5
(7)
The maximum range of x values compatible with a reasonably accurate study of a reaction is between 50 and 90% of aO-i.e., in this case 5 x 10-BM-9 X 10-eM. Assuming that this lower value of x is that occurring after 25 msec of reaction, the k,,, value is calculated to be 4 X 10BM-l sec-’. In cases where reaction products d o not interfere in any way, however, the sensitivity of many electrodes (to at least 10-9M free ion) allows monitoring of the last fraction of reaction. In such cases the range of ( a , - X ) studied could be lO-’MlO-9M and hence, k,,, values of 4 x 1OgM-l sec-l might be accessible. For second-order reactions in which the reverse process contributes significantly, its effect reduces the maximum values of the rate constants which can be measured. Formation constants of the products of complexing reactions dictate just how low the final concentration of free ion will be. Thus, in general, the range of applicable x values is much more restricted. Table I11 shows the limiting values of rate constants obtainable for various formation constants for cases involving the use of monovalent and divalent ion electrodes. Cal-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
Table 111. Rate Constant Limits of the Flow System Max rate const, A 4 - I sec-l Equil const, M-I Monovalent ion sensors Divalent ion sensors 103 5 . 6 x 104 1 . 4 x 104 104 5 . 5 x 106 1 . 4 X 106 5 . 5 x 106 1 . 2 x 107
106 106
1 . 3 X lo6 8 . 1 X lo6
culations are based o n 1 :1 complex formation where the initial concentration of the ion sensed is lO+M and the concentration of the other reactant is sufficient t o give a n overall change of at least 20 mV a t equilibrium. For equilibrium constant values greater than 106M-', limiting rate constant values, calculated for a reaction rate corresponding t o the mid point of the measured concentration range occurring after 25 msec, approach 108M-' sec-I. Thus, it appears that many rapid solution reactions could be studied using the present flow system, especially if the ~~~~~
~
fluoride sensing electrode is replaced by the series of other crystal membrane electrodes already commercially available. The present system is intentionally designed t o accommodate any of the standard size electrode elements. Other interesting possibilities for future development include simultaneous sensing of several ions by using a number of electrodes in the reaction stream and the conversion of the system t o stoppedflow operation. This latter step should bring even more rapid reactions into the accessible range. ACKNOWLEDGMENT
We thank Professor R. G. Wilkins for the loan of some flow system components.
RECEIVED for review August 30, 1971. Accepted October 21, 1971. We gratefully acknowledge the support of grants from the Environmental Protection Agency and the National Science Foundation.
~
Coulometric Microdetermination of Neodymium Using Feedback-Controlled Electrolysis Current J. E. McCracken and J. C. Guyon University of Missouri-Columbia,
Columbia, Mo. 65201
W. D. Shults Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830 Methods have been developed for the coulometric, complexometric microdetermination of neodymium using feedback-controlled electrolysis current. Determinations were made in a machined Teflon microcoulometric cell that used a mercury pool generating electrode and a Pt(Hg) indicator electrode. The intermediate electrolyte was an ammonium acetate buffer solution containing Na2HgEDTA. Three different techniques were studied and compared using this chemical system. The optimum technique exhibited a standard deviation of 0.3 pg in the sample range 1.2 to 170 pg of neodymium.
COULOMETRIC TITRIMETRY is particularly well suited for determinations of metals a t the microgram level because it is nondestructive in nature and because it allows a n absolute measurement. In such a titration it is advantageous t o use as small a n amount of solution as possible so that the blank is reduced, high concentrations of reactants are provided t o gain a well-poised indicator electrode, and the sample is easier to recover. These advantages become increasingly important when the substance being determined is available in only very small quantities. Microdeterminations by coulometric titrimetry have been accomplished with constant electrolysis current b y M o n k and Steed (1) in a scaled-down version of the general technique of Reilley and Porterfield ( 2 ) . I n the former paper, it was noted that potentiometric end-point detection at zero-current was less desirable than constant-current potentiometry because of (1) R. G. Monk and K. C. Steed, A m l . Chim.Acra, 26, 305 (1962). (2) C. N . Reilley and W. W. Porterfield, ANAL.CHEM.,28, 443
(1956).
the time required for the indicator electrode to respond t o concentration changes in the end-point region. However, electrode response poses little problem when the titration rate is decreased considerably in the region of the end point (3). This paper represents a n improvement over the method described in the above paper. The difficulties encountered with the prior method have been overcome by three distinct changes in the technique for determining neodymium. The determination of curium and other rare earths would also be improved by the following changes in technique. A machined Teflon (Du Pont) cell was designed to eliminate: diffusion between the cell bulk solution and the auxiliary and reference electrode compartments; inefficient stirring by incorporating a magnetic stirrer; sample transfer between sequential titrations through the use of fresh mercury for each titration and easy rinsing of the cell between titrations; irreproducible indicator electrode response by using a mercury-plated platinum electrode; high resistance between auxiliary and generating electrode t o allow the use of larger titrating currents; and irreproducibility of the position of the indicator electrode and the effects of I R drop o n the indicating system. A different type of electrolyte was used-HgEDTA2-buffer solution-to eliminate the necessity for prereducing the solution constituents before a titration is begun, produce lower solution resistance, and remove the dependence of analytical precision on the addition of EDTA4-. To improve the sample addition technique, weighed sample portions were added from a polyethylene squeeze bottle ( 4 ) . (3) J. E. McCracken, J. R. Stokely, R. D. Baybarz, C. E. Bemis, Jr., and R . Eby, J. Ztioug. Nucl. Cltern., in press. (4) R. S. Morse and G. A. Wilford, ANAL.CHEM., 42, 1101 (1970).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2 , FEBRUARY 1972
305
