Photometric Titrations with Dichromatic Light Anders Ringbom, Bengt Skrifvars, and Ebbe Still O
0
Department of Chemistry, Abo Akademi, Abo, Finland A two-cell titrator in which two light beams of different wavelengths are used and the photocells are connected i n opposition-i.e., a dichrotitrator-offers particular advantages i n photometric titrations. I n titrations with indicators, the zero point of the net photocurrent coincides with the equivalence point. The coincidence can be made very precise and independent of the concentration of the indicator by choosing “corresponding wavelengths” according to theoretical principles. The zero point can also be made independent of the concentration of the sample solution. Knowledge of the absorbance value at the equivalence point is not needed. Accurate complexometric and acidbase titrations are possible even when the color change at the end point is far too gradual for visual detection (stability constant below lo4). A dichrotitrator is particularly well suited for automatic relay titrations. No derivative signal or preset end point value is necessary and slow titrations are possible.
ALTHOUGH PHOTOMETRIC TITRATIONS have grown in importance in the last few years, their use is still rather limited. The high sensitivities of photocells are not fully utilized as a rule, and titrators are mainly used for analyses that can also be performed visually ( I , 2). However, the future of these methods depends in a high degree on their extension to analyses that cannot be made visually. Moreover, the suitability of phototitrators for automatic titrations is an important asset. The aim of this paper is to point out ways of extending the range of application of photometric titrations. We limit our presentation to titrations with indicators, whereas methods based on self-indicating systems in which the end point is detected by linear extrapolation [slope methods (31are not discussed. The limitations of visual titrations are connected with the fact that only reactions characterized by a sufficiently high value of the equilibrium constant can be utilized. Almost the same difficulties arise when commercial phototitrators are used. When the phototitrator requires a derivative signal, the variation of the photocurrent with the added volume of titrant will be too small unless the equilibrium constant has a rather large value. Incidentally, the inflection point of neither the absorbance curve nor the transmittance curve coincides exactly with the equivalence point ( 4 ) . It is also difficult to titrate to a fixed absorbance value corresponding to the equivalence point, since this value is very sensitive to even small changes in experimental conditions. One could ask: In what way should an ideal phototitrator function to satisfy the analyst’s demands on accuracy, simplicity, and versatility? We feel that the operation of an ideal titrator should require only adjustment of the wavelength scale, adjustment of the zero point of a photocurrent meter, addition of indicator, and titration (possibly automatically) until the current meter again indicates zero. (1) J. B. Headridge, “Photometric Titrations,” Pergamon Press, London, 1961, p. 28. (2) A. L. Underwood, AdGan. Anal. Chem. Itistr., 3,98 (1964). (3) H. Flaschka, Pure Appl. Chem., 10,(2), 165 (1965). (4) E. Still and A. Ringbom, Anal. Chim. Acta, 33, 50 (1965).
Figure 1. Diagram of dichrotitrator L = lamp; M,, M2 = mirrors; C = titration cell; F,, F2 = monochromators; s,, S2 = shutters; Pl, Pz = photocells; R = resistor for sensitivity adjustment; UOut = connection to galvanometer, relay, or recorder
Such a simplified procedure implies that a titration should not need any preset end point value, which often requires expressly calibrated devices and varies with the experimental conditions*.g., with the concentration of indicator and the species in the sample solution. The sensitivity of the photocell or photocells should be so effectively utilized that satisfactory results are obtained when the color transition is very gradual. Derivative currents that require complicated apparatus should be avoided. In the following, it is shown that very accurate titrations can be performed in a simple way by using a two-cell phototitrator with two light beams of different wavelengths. To illustrate the principles a diagram of such an instrument, which, for simplicity, we call a ”dichrotitrator,” is shown in Figure 1. Light from lamp L is split into two beams which are reflected from mirrors M I and M 2 . The light beams pass through monochromators Fl and F2, shutters S1 and SZ,and a titration cell, C, and then fall upon a pair of photocells, PI and P2,which are connected in opposition over a load resistor, R, for adjustment of the sensitivity. At the beginning of a titration one light beam is strongly absorbed but the other only slightly, provided that the two wavelengths are properly chosen; beyond the transition point the roles of the beams are reversed. Consequently, when the indicator changes color, the net photocurrent passing through the galvanometer will be zero at the end point, as shown in Figure 2. If the photometer is used for automatic titrations, a relay connected to the shutoff valve of a buret is inserted in the circuit. The titrator can also be connected to a recorder. Instead of shutters, appropriate resistors can be included in the circuit, As far as we know, no photometer using such a photocell arrangement is commercially available, but we have noted the same idea in the textbook by Ewing (5) and in papers by Osborn, Elliott, and Martin (6), Nichols and Kindt (7), and Fog and Jellum (8). Recently we found a note by Ito and Musha (9) on a “distimulus titrator,” an instrument of somewhat similar construction. ( 5 ) G. Ewing, “Instrumental Methods of Chemical Analysis,” McGraw-Hill, New York, 1960, p. 64. (6) R. H. Osborn, J. H. Elliott. and A. F. Martin, IND.ENG.
CHEM., ANAL. ED., 15, 642 (1945). (7) M. L. Nichols and B. H. Kindt, ANAL. CHEM., 22, 781 (1950). (8) J. Fog and E. Jellum, Aiiulyst, 87, 302 (1962). (9) M. Ito and S. Musha, Burzseki Kuguku, 13 (lo), 971 (1964); p. 64; C.A., 62; 2232 (1965). VOL. 39, NO. 11, SEPTEMBER 1967
a
1217
EX VoIume of
-----------
titrant
\
‘\ & e nt I
\
100
150
500
550
600
650
700rnt.1
;t
Figure 2. Photocurrents of individual photocells and net photocurrent as functions of titrant volume In the references cited only the general principle was given, and n o theory was proposed that applies to the appropriate use of the instrument. Therefore, its potentialities seem unknown and are discussed in the following, where the rules governing the successful use of the instrument are presented. THEORY OF A DICHROTITRATOR In the photometer shown in Figure 1 , the photocells produce photocurrents which are defined by GI
=
kill
=
kiloilO-A’
Gz
=
kz1z
=
k210?10-A’
(1)
where G is the photocurrent, lothe intensity (radiant power) of the incident light, I the intensity of the transmitted light, A the absorbance, and k , which depends on the wavelength used, the proportionality constant between photocurrent and light intensity. Index 1 refers t o one photocell, index 2 to the other. If we denote by Gol = kllol and Go> = kzlosthe photocurrents produced in the two photocells when no absorption occurs-i.e., when the titration cell is filled with pure solventit follows that GI - =
Gz
Go1
X Goz
(2)
s
or, if this equation is written in its logarithmic form, Gi log G2
=
log
Goi -
GO2
+ (A2 - Ai)
(3)
It is desirable t o adjust the titrator by shutters or resistors before a titration in such a way that the net current will attain its zero value a t the equivalence point, in other words, that G1 = Gzexactly when the right volume of titrant has been added. From Equation 3 it is seen that this condition is fulfilled when Goi
log GO2
=
Al(,,) -
A&q)
(4)
where Alceq)and Az(,,,)are the absorbance values a t the equivalence point, Equations 3 and 4 imply that when G1 = 1218
ANALYTICAL CHEMISTRY
Figure 3. Molar absorptivities a t p H 10 Free Calmagite - - _ Magnesium complex of Calmagite -Calmagite solution of phlg 5.6 (apparent absorptivity) (100 purity of indicator assumed)
G2and Ai = A2,Gol = GO*. We may illustrate the consequence of this statement by taking as a n example the complexometric titration of a metal M forming a complex MY. If the wavelengths of the two light beams are chosen so that in the presence of a metal indicator = A2(eq), the net photocurrent will be zero both when the titration cell is filled with water and when it is filled with a n indicator solution containing the metal ion at the right pMeqvalue. Moreover, in the latter case it will be zero a t any indicator concentration, a fact of considerable interest, as it simplifies the performance of a titration and improves the attainable accuracy. If A1 = A?,the average (apparent) molar absorptivity values, al and a2, are equal, and we characterize two such light beams by saying that they have corresponding wavelengths. Figure 3 illustrates the choice of wavelengths for a complexometric titration using the metal indicator Calmagite. Curves are given that plot the absorptivities of the free indicator cIn,, and its magnesium complex, c Y g l n , and the average absorptivity of a n indicator solution where pMg = 5.6 [corresponding to pMg,, when titrating a 0.001M magnesium solution with EDTA at pH 10 (IO)]. Generally, when a metal is titrated, the two points where a horizontal line intersects the absorbance curve (and thus also the average absorptivity curve) of a n indicator solution of known pM value represent a pair of corresponding wavelengths related to pM. In Figure 3 h = 486 mp and h = 580 mp are one pair of corresponding wavelengths when magnesium is titrated to pMg = 5.6. The average absorptivities, ;I and ZO.,will shift during the titration from c l ~ g ~ n to the horizontal line, as indicated by the arrows in Figure 3. A titration with a dichrotitrator thus follows the following simple general procedure.
Procedure. The titration cell is filled with the colorless sample solution and the monochromators are adjusted so that the scales indicate an appropriate pair of corresponding (10) A. Ringbom, “Complexation in Analytical Chemistry,” Wiley-Interscience, New York, 1963.
dp t$20 dT
0,16
0.1 2
0.08 0.01
__________------0.00
-1.2
-0.8
-0.1
-
PMtrans O.L
0.8
1.2
ApM
Figure 4. Precision of photometric determination of PM __ Precision obtained when A;: = 0.43 _ - -Maximum precision attained when absorbance = 0.43
wavelengths. The net current is adjusted to zero with shutters (or by means of resistors). Indicator is added and the sample solution is titrated until the galvanometer needle returns to zero. Near the end of the titration, the maximum galvanometer sensitivity can be used. If a relay actuating a buret valve is inserted, the delivery of titrant will be stopped a t the equivalence point. Some difficulties will arise if the corresponding wavelengths are determined with a spectrophotometer of high resolution, but the phototitrator used is equipped with interference filters with relatively large band widths and with wavelength scales of limited accuracy. Two wavelengths at which the absorbances are equal as measured with a spectrophotometer may nevertheless be noncorresponding in the phototitrator. The natural way is t o determine the pair of corresponding wavelengths with the titrator itself. The transmittance of a colored solution can easily be measured using the dichrotitrator as a single-cell instrument T o confirm that two wavelengths are precisely corresponding, indicator is gradually added to a colorless reference solution of the right pM,, value. The net photocurrent, previously adjusted to zero when no indicator is present, must remain at this value. However, the pM value of a solution containing MY may change when an indicator is added. At high pM values, a pM value will remain constant only in an appropriately prepared “metal buffer” solution. Once the corresponding wavelengths have been determined, the reference solution is no longer required. As indicator samples of different origin usually differ in their properties, the corresponding wavelengths have to be determined for every new sample. I t is possible to perform a titration even when the absorption curves have no isosbestic point or when the corresponding wavelengths are on the same side of this point. However, the sensitivity will then be low (cf. Equation 7). Of course, titrations based on the principle of corresponding wavelengths are not possible if the indicator is one-colored (since the net current would then remain zero throughout the titration). It is obvious that the indicator should be chosen so that pMtrnna is not too far from pM,,.
For a proper choice from among all possible pairs of corresponding wavelengths, two factors have to be considered: first, the distance between the t I n and t a l l ncurves, which must be sufficiently large, and second, the sensitivity of the photocells used to light of various wavelengths. A comparison of Figure 3 and the sensitivity curves of the used photocells is advisable. Selenium barrier layer cells are sensitive to light of wavelengths between about 480 and 630 mp (maximum sensitivity at 580 mp). Corresponding wavelengths for an acid-base titration can be determined in an analogous way. A buffer solution of the right pH,, value, or a solution of the reaction product, can be used. Also for oxidation-reduction titrations with indicators the determination of corresponding wavelengths can be based on the same principles. A more complete treatment of the theory and function of a dichrotitrator, including the case where light beams of noncorresponding wavelengths are used, is given by Skrifvars (11) and Still (12). REFERENCE SOLUTIONS FOR DETERMINATION OF CORRESPONDING WAVELENGTHS
Reference solutions are not needed for individual titrations, but they are necessary for the determination of suitable pairs of corresponding wavelengths. In considering complexometric titrations, the question arises of how such a reference solution having the right pM,, value can be prepared. pM,, depends on the composition of the sample solution, which is unknown. However, in many titrations approximate values of [MY],, and pM,, [ = l/z(log Knry- log C,)] will suffice. If [MYIeq is from 50 to 2 0 0 x of [MY] in the reference solution, the uncertainty in pM is about 3~0.15unit. This precision is often, but not always, sufficient. If the color change is very gradual or a high accuracy is needed, a more refined procedure for preparing the reference solution may be required. Actually, it is possible to prepare a reference solution with exactly the right pM value according to a method suggested for acid-base titrations by Ringbom and Sundman (13) in 1939 and later applied to complexometric titrations (14). The rule is as follows: The reference solution is a solution containing the reaction product at a molarity equal to the molarity of the titrant. Moreover, the reaction product is added to the sample solution until its concentration is equal to the molarity of the titrant. At the equivalence point, the sample solution will then have exactly the same pM (pH) value as the reference solution. This rule can best be understood by considering the case where a solid sample containing an unknown amount of a metal M is titrated with a 0.01M EDTA solution. At the equivalence point, the solution will contain exactly 0.01 mole of MY per liter. If we dissolve the sample in water before titration and add MY until its concentration is 0.01 M , [MY] will be exactly 0.01M at the equivalence point. The addition of the reaction product to the sample solution will diminish the pM jump. However, if the initial volume of
(11) B. Skrifvars, Acta Acad. Aboeusis, Math. Pkys. Ser. B, 26 (9, 1 (1966). (12) E. Still, Ibid., 26, (7) (1966). (13) A. Ringbom and F. Sundman, Z . Aual. Chem.,116,104 (1939). (14) A. Ringbom and E. Wanninen, Anal. Ckim. Acta, 11, 153 (1954). VOL. 39, NO. 11, SEPTEMBER 1967
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the sample solution is small compared to the consumed volume of titrant, the accuracy will be only slightly reduced. The titration error after the addition of MY will be (Vinitial Vtitrnnt)/Vtitrnlit times larger than without any addition. When the end point of a titration is indicated photoelectrically, a decrease in the magnitude of the pM jump is of little importance, since pM changes smaller than 0.01 unit can be easily detected with many instruments. It is more important that the sample solution has exactly the right pM value a t the equivalence point-i.e., in our case the same value as the reference solution used when determining corresponding wavelengths. When this method is used, pM,, is always the same as long as the molarity of the titrant is not altered. MY can be conveniently added to the sample solution if a solution of MY is prepared whose molarity is 11 times the concentration of the titrant and a volume equal to one tenth of the volume of the sample solution is added to the latter. Thus, if the titrant is 0.01M, a O.llM solution of MY is added. This operation does not need t o be done with any high degree of precision. Buffer substances and neutral salts (if needed) can be included in the solution added.
+
ACCURACY OF TITRATIONS WITH DICHROTITRATOR
In the method described above, the photocurrent will attain its zero value exactly a t the equivalence point corresponding t o a well-defined p M or p H value. For judging the attainable accuracy one has t o know how precisely a pM or a pH value can be measured photoelectrically. We first consider a simplified case. If, in a photoelectric measurement, a monochromatic light beam is used and the wavelength is chosen so that only In but not MIn absorbs light, the following expression is valid (IO,14). 1
pM units d PM - ___ transmittance dT
z
where T i s the transmittance. As before, A is the absorbance and y is the degree of dissociation of the indicator. The maximum attainable precision will be obtained a t an absorbance of 0.434 (= log e), which corresponds t o 36.8 transmittance. Then
z
d p M -_
dT
_ _ 18 _ - 0.01 1-7
- -0.0118
(+ 1
~
(6)
This relationship is presented graphically in Figure 4. A curve is also given which illustrates the precision if the indicator concentration and light path are chosen so that AI,-= =
0.43.
If MIn absorbs light, Equations 5 and 6 will be slightly modified. A will be replaced by A - AMI^^^^. According to Figure 4, a precision corresponding to a shift of less than 0.05 pM per 1 % transmittance is attainable. Most photometers are sensitive to changes of less than a few tenths of 1 % transmittance-i.e., under optimum conditions t o changes below 0.01 pM or pH unit. The corresponding and can be read titration error depends on the product KMYCM from the common error diagram (IO). It seems theoretically possible to determine a metal complexometrically with a titration error below l % if KJryCniexceeds l o 2 to 10'. Thus, titration of a 0.01M solution is possible even if Knry is only l o 4 t o 103. Such analyses correspond to titrations of acid and bases whose pkDlssvalues are as high as 10 t o 11. 1220
ANALYTICAL CHEMISTRY
The equations given refer t o a photocurrent caused by a monochromatic light beam absorbed by In. For the dichrotitrator Still (12) has derived a n expression corresponding t o Equation 5 . In this case it is not practical to express the photocurrent in transmittance units. Scale units, G, of the galvanometer are more appropriate. The following expression is obtained for the quotient dpMldG:
(7) The difference between the limiting absorbance values a t the two wavelengths is denoted by A-i.e., A1 = and A? = Az.w,, - A z . I ~ . GI denotes the number of scale units when photocell 2 is covered or removed from the circuit. Equation 7 is valid a t the zero point when G1 = Gz and illustrates the fact, which is evident from Figure 2, that the sensitivity of a dichrotitrator is greater than the sensitivity of a monochromatic titrator, provided that the two wavelengths are taken from different sides of the isosbestic point. AI and AZ are then of opposite sign-ie., the absolute value of AI - AZis larger than either of the individual A values. The calculated precision also implies that metals forming complexes with stability constants K ~ I greater Y than lo7 can be determined with a very high degree of accuracy. Furthermore, titrations of very dilute solutions are possible. In the last-mentioned cases, attention must be paid to a possible indicator error, since the added indicator may alter high pM values. In most cases, the indicator error can be eliminated by using the same indicator concentration in the reference solution and the sample solution. On the other hand, if a metal buffer (or, in acid-base titrations, a p H buffer) is used as the reference solution when determining corresponding wavelengths, a n indicator correction may be required. To determine pM,, with high precision, certain trivial sources of error may need consideration. However, the balanced circuit of a dichrotitrator largely eliminates many interferences, such as variations in lamp intensity as well as fatigue and recovery phenomena of photocells. Small absorbance shifts may be caused by hydrogen ions liberated or consumed in the titration; since many conditional constants are highly dependent on pH, the sample solution must be sufficiently strongly buffered. Attention must be paid t o temperature fluctuations. If a very high degree of accuracy is desired, a correction for the temperature difference between the sample solution and the reference solution may be necessary. This correction can conveniently be expressed as a shift of wavelengths XZ in millimicrons per degree centigrade. The neutral salt effect can be eliminated by the addition of a considerable amount of a neutral salt-KNOo, for example, in EDTA titrations-to the reference and sample solutions. If monochromators of poor quality are used, the LambertBeer law is not strictly valid. A consequence of this could be that wavelength Xp corresponding t o X1 may vary slightly with the concentration of the indicator. However, a favorable fact is that the absorbance values a t the two wavelengths are the same. The slope of the pMvl,,-absorptivity curve at X1 and Xz can differ, but mostly more or less equal deviations from the Lambert-Beer law are probable a t the two wavelengths. This fact reduces the influence of limited monochromaticity of the light beams. If the indicator reacts with a metal ion in another ratio than 1 t o 1, the values of corresponding wavelengths will depend on the indicator concentration.
Side reactions of various compounds present may alter the theoretical pM,, value. If the same interfering substance is always present, as is often the case in routine analyses in industry, it is possible to add fairly large amounts of the interfering substance to the reference solution used for the determination of corresponding wavelengths as well as t o the sample solution. The pM jump will then diminish, but nevertheless the sharpness of a color change may often be sufficiently high for the dichrotitrator. As a n example we may mention the complexometric titration of a met.al ion MI in the presence of another metal ion, MII. The conditional constant is then [cf. (IO)] where Alog K = log KYIY- log K3rIIy. If large amounts of MII are added, the conditional constant, K I C ~ will Y ~ , be practically independent of the amount of MII in the original sample solution. To keep KIIrYtsufficiently high, the choice of complexing agent has to be based on theoretical principles. The value of Alog K is important, and in complexometric titrations other titrants than EDTA may often be advantageous. The presence of MII may affect the choice of indicator; the colors of MIIn and MIrIn must differ sufficiently. General aspects of stepwise photometric titrations were recently discussed by Skrifvars and Ringbom (15).
CONCLUSIONS
The main aim of this paper has been to clarify the basic theory of the function of a dichrotitrator, since a good knowledge of this theory is indispensable for the successful use of the instrument. The theory presented has been checked by experiments, partly using various combinations of commercial photometers, partly using a titrator of simple construction built in our laboratory (barrier layer cells, interference filters, shutters, magnetic stirrer). The results were in agreement with theory, and even titrations based on reactions with equilibrium constants below l o 4 were performed without difficulty. However, the results and experimental details will be reported in a separate paper, where the potentialities of a dichrotitrator will be discussed, taking into consideration the fact that the zero current principle of the instrument makes it particularly appropriate for automatic applications. RECEIVED for review February 13, 1967. Accepted May 24, 1967. Work supported in part by Statens Teknologiska Kommission and Oy Neste Foundation in Finland. ~
(15) B. Skrifvars and A. Ringbom, Zbid., 36, 105 (1966).
Supportilng Electrolyte Effects in Nonaqueous Electrochemistry Coordinative Relaxation Reactions of Reduced Metal Acetylacetonates in Acetonitrile Royce W. Murray and L. Kenneth Hiller, Jr.’
Department of Chemistry, Unicersity of North Carolina, Chapel Hill, N . C. 27514 The reduction potentials of a number of metal acetylacetonates in acetonitrile solvent are shifted to more positive potentials by the addition of LiClO, to the tetraethylammonium perchlorate supporting electrolyte. Studies of the F e ( a ~ a c )case ~ show that this effect is caused by a coordinative relaxation reaction of the Fe(acac)s- reduction product in which an acetylacetonate ligand becomes transferred to the lithium ion. Cyclic voltammetric data demonstrate that reoxidation of Fe(a~ac)~-can be kinetically controlled by the reverse coordinative “unrelaxation” reaction. When n < 3 in Fe(acac), complexes, coordinative relaxation of the reduced complex can also occur by ligand exchange with the diffusing electrode reactant. Preliminary electrochemical data on other metal acetylacetonates are presented.
USEOF THE WORD inert to describe the supporting electrolyte employed in a nonaqueous electrochemical investigation requires an appropriate quantity of discretion. An electrochemical o r chemical perturbation can result from interaction of the supporting electrolyte with either the electrode reactant or product, and a supporting electrolyte innocuous in Present address, Procter and Gamble Co., Miami Valley Laboratory, Cincinnati, Ohio.
these respects in an aqueous medium may not remain so when employed in lower dielectric solvents. Understanding of the role played by the supporting electrolyte in the event of such interactions is necessary for a complete appreciation of the properties of the sample system. The general effects of complexing supporting electrolytes on metal ion electrode reactants are well known. The more subtle ion-pairing effects of noncoordinating salts in nonaqueous solutions are likewise well documented, and Schaap ( I ) has developed polarographic theory for the metal ion reactant ion-pairing with electrolyte anions. The possible effects of supporting electrolyte on the product of the electrode reaction, on the other hand, have received less investigative attention. Consider, for instance, reduction of a neutral reactant toward which the supporting electrolyte is inert. This negatively charged product may now interact with the cation of the supporting electrolyte in several ways. One is an ion-pairing reaction, which may be of a simple and relatively innocuous nature, or which could be of more consequence by stabilizing a product such as an organic radical against a further reaction which might otherwise immediately (1) W. B. Schaap, J. Am. Chem. Sor., 82,1837 (1960). VOL. 39, NO. 1 1 , SEPTEMBER 1967
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