Fluorometric Study of the Beryllium-Morin System MARY H. FLETCHER U . S. Geological Survey, Washington, D. C.
b Three principal beryllium-morin 1 ) monomer, a complexes, a ( 1 (1 1 ) dimer, and a ( 1 2) complex are found and conditional equilibrium constants for their formation are evaluated. Approximate ionization constants, absorption spectra, and the relative fluorescence intensities for five ionic species of morin are also determined in a spectrophotometric and fluorometric study of rnorin. The following interrelationships are discussed: pH, ionization of morin, absorption spectra of the various ionic species of morin and of the berylliummorin complexes, equilibria for the reactions between beryllium and morin, the period of time between preparation of the solution and measurement of the fluorescence, and fluorescence intensity.
+
+
M
+
is probably the most sensitive reagent for beryllium; several very sensitive and excellent fluorometric methods for the determination of beryllium with morin have been published ( I S , 18-60). The effect of the independent variables on overall sensitivity, selectivity, or stability of the final measurement has usually been studied. But little has been reported concerning the specific changes which occur in the chemical and fluorescence systems to produce the net effects that have been observed. At the time this study was commenced, little had been published regarding the nature of the complexes. While this work was underway several papers were published on the determination of beryllium with morin. Bril and Pruvot (3) as well as Minczewski and Rutkowski ( 1 6 ) attribute the fluorescence to a Bea(morin)z complex, whereas Sill, Willis, and Flygare (20) attribute it to a (1 1) complex. 2) compound is not found in The (3 the present study. -4(1 1) complex is found; however, the system is considerably more complicated than indicated by Sill and coworkers. ORIN
+
+ +
EXPERIMENTAL
Apparatus and Reagents. A Beckman DV spectrophotometer equipped with a IVarren Spectrocord recording attachment was used for all absorbance measurements. The transmission fluorometer described by Milkey and Fletcher ( 1 4 ) ani! 1y Fletcher ( 5 )
550
ANALYTICAL CHEMISTRY
was used. Instrumental sensitivity was adjusted so that the uranium glass standard gave a reading of either 1.0 pa. with 443 mp excitation or 5.0 pa. with 365 m p excitation. Primary filters, arranged in order from lamp to sample, were as follows: to isolate 443 mp, Corning filters 1-56 and 3-73, Photovolt GAB interference fiIter 443, and Corning 5-58; to isolate 365 mp, Corning filters 0-52, 7-39, and 7-37. Secondary filters, arranged in order from sample to phototube, were Corning 1-57, 4-64, Photovolt GAB interference filter 550. A Beckman Model G pH meter was used for pH measurements. hlorin was obtained from T. Schuchardt, Munich. General Procedure. The course of the reactions was followed by measuring both the absorbance, A , and the fluorescence intensity, F . Full absorption spectra for wavelengths between 350 and 750 mp were plotted. Fluorescence intensities of 1, 2, 5, 10, 15, 20, and 25 ml. volumes of solutions were measured. The optical cells used gave solution depths, b, of 0.1296 cm. per ml. All fluorescence intensities correspond to maximum sensitivity (S. L. 2.28) defined previously (6), unless otherwise stated. Measured vaIues were adjusted to S. L. 2.28 where necessary. The absorbance of fluorescence a t S.L. 2.28 for the total morin blank was always included in the blank corrections even when beryllium was in excess and morin varied. Excitation with both 365 and 443 mp was used. The wavelength 443 mp is in the region where a mixture of morin with a large excess of beryllium in 0.04.V KaOH gives the greatest positive difference from the morin blank, and where the blank is reproducible and well above instrument noise. All fluorescence measurements were made a t 550 mp; the soIutions do not absorb a t this wavelength. Reaction between Beryllium and Morin. Several series of solutions in
which either the beryllium or morin was constant and the other varied over a wide range were used t o determine the character of the complexes. The conrentrations of other reagents were approximately those used by May and Grimaldi ( I S ) . NaOH was added to neutralize the acid added with beryllium, then all soIutions were made 0.04M in NaOH and 5.372 x lO-3M EDT-4; all contained 1.2 ml. of ethyl alcohol per 25 ml. The reagents were added in the following order: Be, EDTA4,NaOH, morin. The beryllium and morin concentrations for these
mixtures are given in Table I. Here and throughout this paper the symbols Beo and M Oare used without brackets to denote the concentrations of total beryllium and total morin. Data from these solutions are presented in Figures 1-5. Series 1-3 were prepared during the same period of study from the same reagents, and were treated in the same manner. Fluorometric measurements for each series were made between 3.5 to 4.5 hours after preparation. Series 4a, b, and c and series 5a and b were prepared about 21/* years later using all new reagents. Fluorometric measurements on 15- to 20-ml. aliquots of these solutions mere made periodically as described later. Ionization Constants for Morin. The solutions used to determine the ionization constants for morin had acidities covering almost the entire p H range (approximately - 2 to +15). All solutions were 2.366 X lO-5Jf in morin, 5.372 X 10-3M in EDTA, and all contained 1.2 i d . of ethyl alcohol per 25 ml. of solution. Low pH levels were obtained with hydrochloric acid and high pH levels with potassium hydroxide. Solutions in the intermediate pH range were buffered with standard mixtures of di-hydrogen potassium phosphate and potassium hydroxide. Potassium chloride was used to adjust the ionic strength p , to a value of 0.6, but none was added where p was greater than 0.6. When the pH was either too low or too high for accurate measurements, pH values were calculated as -log u R + or [14 log (OH-)] from the concentrations of (H+) or (OH-) added taking into consideration the activity of H + in HC1 solutions and the buffering effect of EDTA. Approximate values for the constants were determined from curves of absorbance plotted against pH. Absorbances at 362, 388, 396, and 425 mp were especially useful. The approximate values were: pK1 = - 1, pK, = 4.8, pK3 = 7, pK, = 9, and pK5 = 13.
+
Effects of p H . A series of unbuffered 2.366 X 10-5.Tf morin solutions were prepared a t pH's which would give a single ionization species or a mixture having one species as the major component. The optimum pH values were determined from normalized curves for the fraction of morin in each ionization state as a function of pH. These curves were based on the step ionization constants determined in this study. Either HCI or KaOH was added to give the desired pH. The required
Table I.
Composition of Mixtures Used to Study Beryllium-Morin Reaction KO.
Series
of
1
solns. 10
2
12
2 251
3
21
4a 4b
7 7 2
from 2 251 X 10-8 t o 2 218 x 10-3 4 435 x 10-4 4 435 x 10-1 4 435 x 10-4
5,
11 11
SO.
4c
5b
Be0 4 435 x 10-4
hl,
from 2 366 X 10-8 to 2 366 X lW5 from 5 915 X 10-7 to 5 915 x 10-5 2 366 X lW5
x 10-6
from 0 to 4 435 X 10-4 from 0 t o 4 435 X 10-4
amounts were calculated using a logarithmic diagram (11) which gave the distribution of the EDTA species as a function of pH. Data from these solutions are presented in Figures 6 and 7 . Data and pertinent details for systems with excess beryllium appear in Figure 8. Four groups of Inorin blanks and 4.435 x 10-8M beryllium standards were prepared. The first two groups contained 2.958 X 10-6M and 3.549 X 10-6JI of morin, respectively: together they covered the pH range from 11 to 13.9 and were prepared by adding the reagent's in the normal order. The data from these solutions are given in Table 11. The third group was similar to the first two but was prepared by adding XaOH after morin. The fourth group was a t p H 14 and covered the morin concentration range from 2.958 X 10-6M to 5,915 x lO-6M. These solutions were prepared by adding the reagents in the normal order. Effects of Time. The morin blank solutions were t h e same ones used to study the effect of p H . Measurements were made periodically. Pertinent d a t a are given in Figure 9 and 10. Periodic fluorometric measurements (443 mp excitation) were made on a series of solutions containing excess morin, such as are used t'o obtain standard curves. These solutions conor 4.435 X lop8tained 0, 2.218 X .11 of 13e with 2.958 X 10-6M of morin. The pH was 12.6. The effect of time on systems with excess beryllium was studied using several sets of solutions similar to series 1, hut prepared by slightly different mixing procedures. All solutions were 0.08-11 in NaOH when morin was added. However, in Set A, beryllium wa5 in admisture with 0.5.11 S a O H for ahout, 0.5 hour before further dilution and addition of morin: in Set E,beryllium was in admixture with 0.08111 SaOH for about 1 to 1.5 hours before addition of morin; in Series 4c, beryl-
from 0 to 1 183 X 10-8 from 0 t o 7 098 X 10-9 2 366 X 1 183 X 7 098 x 10-9 1 183 X lo-*
lium was in admixture with 0.08JI NaOH for only a minute or two before morin was added. I n Set 13 and Series 4c, beryllium was never in a NaOH solution stronger than 0.0831 NaOH. Fluorometric measurements (443 mp excit'ation) were made periodically on fresh aliquots of the solutions. The data are suniinarized in Figure 11. A large excess of beryllium (4.435 X 10-4JI) was added to solutions of H114- or A I 5 - (2.968 X 10-6-11) at' 22 and 72 hours after the original solutions were prepared, and considerable fading had occurred. Periodic fluorometric nieasurenients (443 mp excitation) were made on both the original and "spiked" solutions. RESULTS
Evidence of Several Complexes. Curves for the fluorescence difference from the blank for series 2 and 3 show less divergence at low concentrations than do the analogous curves for the absorbance difference in Figure 1. Otherwise the two sets of curves were similar. The upper part. of the fluorescence curves approach a plateau a t approximately the same concentrations as do the absorbance curves in Figure 1 thus
Table II.
a
b
110*1 -111
am-,,-ai
Figure 1 . Absorbance difference from blank at 4 4 3 mp 1 -cm. light path Curve A: series 2 (Beo = 2.251 X lO-'M) Curve 6: series 3 (Mo = 2.366 X 10-5Ml
showing the absence of any serious quenching in the fluorescence system. Furthermore, the upper portion of all the fluorescence and absorbance curves is essentially horizontal when the major component is roughly twice as large as the minor component (either Beo or 1120) and for series 3, the curves are still horizontal when the Beo/hIoratio was 100/1. These data indicate that the ratio of beryllium to morin in any complexes formed should fall within .the limit's of 2/1 to 112. A beryllium/ inorin ratio of 112 for the complex with the highest mole fraction of inorin would be expected as beryllium has a valence of 2 and a coordination number of 4. h limiting value of 211 for the beryllium/niorin ratio in the complex with the highest mole fract,ion of beryllium rules out the possibility that morin reacts with one of the highly polymerized hydrat'ed beryllium ions which form in alkaline solutions (4,7 , 10, la).
The differences in the shapes of the lower sections of the curves in Figure 1 indicat'e that the reaction in t,he presence of excess beryllium is different from that in the presence of excess morin. Alt'hough the difference is more apparent in the absorption curves than in the fluorescence curves, absorption measurements were very insensitive compared to fluorescence measurements. Thus, fluorescence measurements were used to resolve the system.
Fluorescence of Blanks and Samples and Sensitivity Index as Functions
of pH Fluorescence, pa. pH (calcd.) Blank Sample AF 11 0a 0 042 0 047 0 005 11 5a 0 045 0 052 0 007 12 0a 0 043 0 051 0 008 12 6 a 0 044 0 052 0 008 13 0 0 036 0 044 0 008 13 0 0 036 0 045 0 007 13 3* 0 028 0 034 0 006 0 023 13 5 h 0 026 0 003 13 6 h 0 019 0 022 0 003 13 7 * 0 017 0 017 0 13 8* 0 015 0 016 0 001 13 9 * 0 013 0 013 0 llorin concn., moles/liter, 2.958 X principal species H M 4 Morin concn., moles/hter, 3.549 x 10-6; principal species >I&-.
AF ~
Fbiank
0.12
0.16 0.19 0.18 0.22 0.19 0.21 0.13 0.14 ...
0.07
VOL. 37, NO. 4, APRIL 1965
...
551
(I!,'
1 +% - +
'
20
'
1
1
'
25
bXI0.I
Figure 2. Fluorescence difference from blank per mole of morin per cm. depth of S.L. 2.28 as function of morin concentration Curve I : series 1 Curve 2: series 2
Curves for total fluorescence values for the solutions of series 1 plotted against their morin concentrations had a constantly increasing slope. However, when log total fluorescence (from unadjusted experimental values) was plotted against log morin concentration for each volume of solution measured and against log depth for each morin concentration, two families of parallel curves were obtained. All curves were straight lines except for short regions of a few where total absorbance was great enough to lower the sensitivity level appreciably. All the straight line portions of the curves plotted as a function of log depth had a slope of 1.0; these curves have been published ( 5 ) . Those plotted as a function of log morin concentration had a slope of 1.1. Similar curves with a slope of 1.1 were obtained also Khen either log total absorbance or log total fluorescence was plotted against log niorin for those solutions of series 2 that are represented by the lower region of curve A in Figure 1. All the log-log curves showed that the instrument was performing as it should and that both fluorescence emission and light absorption occurred in an orderly and predictable fashion that could be expressed approximately by the analogous relationships: Total F EZ f(cl ' b ) Total .4 f(cl l) for a 1-cm. light path where c is the morin concentration and b is the length of the light path through the solution. According to accepted theory, the exponents for both c and b should be equal to one if there were only one complex, or a mixture of several mononuclear species in constant ratio in series 1. As the exponent for b is 1.0, fluorescence intensity varies directly with solution depth as it should. Moreover, as both absorbance and fluorescence emission obey the same law, and as estremely small slits were used for the absorbance measurements, the changing slope of the fluorescence-concentrations curves cannot be attributed to a lack of monochromaticity in the exciting light. The complication is obviously associated 552
a
ANALYTICAL CHEMISTRY
solely with the concentration of morin and indicates that a t least one polynuclear species is present and that more than one complex is formed in the presence of exceSs beryllium. Dimerization Reaction. Evidence of a polynuclear species is shown. in Figures 2 and 3. The fluorescence difference from the blank per mole of for a solution depth total morin (M,,) of 1-cm., (AF'/M0b), for series 1 is plotted against morin concentration in curve 1, Figure 2 and against the reciprocal of the morin concentration in Figure 3. Both curves show the dependence of ( A F / M o b ) on the concentration of morin, the minor and variable component in the solutions. The shape of curve 1, Figure 2 indicates that the weakly fluorescent species formed with low concentrations of morin reacts to yield increasing amounts of strongly fluorescent polynuclear species as morin is increased. Assuming as a first approximation that all morin is combined in only two end products, a weakly fluorescent or a strongly fluorescent complex, extrapolation of curve 1, Figure 2, to a zero abscissa value gives a fluorescent difference of 3.00 X 105 per cm. depth for each mole of morin combined in the weakly fluorescent complex while extrapolation of the curve in Figure 3 gives a fluorescence difference of 10.0 X lo5 per cm. depth for each mole of morin combined in the strongly fluorescent compound. The reaction to form a polynuclear complex is expressed in a generalized way in Equation 1 which contains allinclusive terms for other possible reactants and products.
nW
+ aC F? S + bZ
(1)
I n this equation, W is the weakly fluorescent complex, c' is a possible reactant and might be Be+*, OH-, or EDTA; S is the strongly fluorescent complex which has the composition ( W , - bZ)Ua; and Z is anything (such as OH-, EDTA4,or H20) that might be liberated in the reaction. The equilibrium for the reaction in Equation 1 is givdn in Equation 2.
The terms (Z)*and (C). are constants for series 1 because the concentrations of Be, OH, and EDTA were all constant and large in relation to morin; Equation 2 was therefore simplified to give Equation 3 for application to the data from series 1;
(S)/(U')"
=
kn,
(3)
where k,, equals k , ( L 7 ) n / ( Z ) * . When Equation 3 is rearranged and put in logarithmic form, Equation 4 results.
'9 O 0O k
Figure 3. Fluorescence difference from blank per mole of morin per cm. depth at S.L. 2.28 as function of reciprocal of morin concentration Series 1
log (S) - log k,,
=
n log ( W )
(4)
To evaluate n (the degree of polymerization) the distribution of morin between the two complexes, W and S, was determined by calculation from experimental data. Introducing the following definitions and relationships, = fraction of total morin, S (1 - a - (M)/Mo) = fraction of total morin, W = moles morin per mole W P = moles morin per mole S np (M), S = a M o = np ( S ) (M), = [(l - a)Mo - ( M ) ]= p ( W ) AF, = (10.0 x 105 b) AF, w = (3.00 x 105b) [(I - a ) ~ i-o (MI 1 AF,,,,, = (3.00 x 105b) [(I - a ) ~ -. (MI] (10.0 x 105b) x
a
w s
+
(CYMO)
One obtains a =
AF/Mob
- 3.00 X 105[1- (M)/Mo] 7.00 x 105
As beryllium was in such large excess, the concentration (M) was assumed to be negligible and set equal to zero in Equation 5, then values for [ A F / M o b ] for series 1 were substituted into Equation 5 and values for a were calculated. Now as (S) = a M o / n p and ( W ) = [ ( l - a ) M o ] / p , substitution of these terms into Equation 4 leads to 4a. log aMo
- log K*
=
n log [ ( l - a)hlO] (4a)
where K* = nk,,/p"-'. According to Equation 4a, n can be found as the slope of the curve if log aMo is plotted against log [(l - a)Rlo]. When this curve was plotted, it was a straight line with a slope of 2. i i s only two moles of com-
plex W react to form 1 mole of complex S , these two end products, V and S , should be the only complexes formed in the reaction that occurs in the presence of a large excess of beryllium, unless beryllium also takes part in the reaction. I n the latter case, intermediate complexes might also be formed. T o determine whether beryllium reacts with complex W to form complex S , Equation 2 was re-expressed in Equation 6 which would hold if beryllium participates in the reaction; Equation 7 expresses the equilibrium if beryllium does not participate. a/(l
- CYI~MO = [2k,,(Be)51/p
(6)
- a)*Mo = 2kJp
(7)
or a/(l
Y)
B
9
F
s
Ed
Figure 4. Fluorescence difference per mole of minor component per cm. depth at S.L. 2.28 as function of Beo/Mo or MoBeo
where 2 has been substituted for the Curve I : series 1 exponent n of Equation 2, and where Curve 2: series 2 [(I - aY)Mol/p = ( W ) ,~ M o / = ~ P(81, Curve 3: series 3 (Be)" = ( U ) = , (2) = (OH-) and (EDTA) = constant, and k,, = k , / ( Z ) b . beryllium, and the extreme right Ratios for values of a / ( l - C Y ) ~ M small ~ represents infinitely great beryllium or calculated from data of series 1 and infinitely small morin depending upon 2 which correspond to equal concentrawhich constituent is the variable comtions of Mo in the two series are given in ponent. The curves are numbered to Table 111. As the actual morin condenote the series from which the data centrations were different in the two were obtained. All data correspond to series of solutions, the [AF/Mob] values full sensitivity and are average values used in the calculations were read from calculated from several depths of solucurves of the experimental figures. tions except for curve 3 where, because Values for series 1 were read from curve of the high blank and low sensitivity 1, Figure 2, those for series 2 were read level, only the values from 1-ml. volumes from curve 2, Figure 2. were used. The points on curve 3 The ratio of the total beryllium condenoted by cross marks were calculated centrations in the two series is 19.7. As from AF values read from a smooth appreciable amounts of the total berylcurve of AF plotted against Beo. The lium were complexed in series 2 with the scatter of the experimental points on the higher concentrations of morin, the ratios of uncombined beryllium were upper left portion of curve 3 is not alarming because at the extreme left the actually larger than 19.7. However, if blank was considerably larger than Equation 6 holds, the ratios in Table 111, AF; and normal experimental errors which range from 1.28 to 1.95 must are exaggerated by this type of plot. have a minimum value equal to (19.7)a Point P, (AF/Mob = 10.0 X lo5; which would require Q to have a maximum value that ranges from 0.083 Mo/B% = 0) , in the upper right corner, to 0.22. But a should be an integer for gives the fluorescence difference per Equation 6 to be meaningful; therefore mole of morin completely complexed as the dimer, for a solution depth of 1 cm.; Equation 7 rather than 6 expresses the equilibrium for the principal reaction this value was obtained earlier by extrapolation of the data from series 1 in when beryllium is in large excess. The principal reaction in the presence of Figure 3. As the location of this point excess beryllium is therefore a simple might be questioned, the following dimerization of complex W to form comment seems in order. The extrapcomplex S . olated point in Figure 3 corresponds to Three Principal Complexes. All a mixture containing 4.435 X lO-4Jf t h e d a t a from series 1 , 2, a n d 3 are of uncombined beryllium with l / M o given in Figure 4 . Here the fluoresapproaching 0 while the point P in cence difference per mole of total Figure 5 corresponds to a mixture conminor component, 13eo or Mo, for a 1taining 2.366 X lO-5M of morin with cm. depth of solution, is plotted as a l/Beo and (hfo/Beo) approaching 0. function of either Beo/Mo or Mo/Beo All morin in both mixtures should be where the denominator in the ratio is complexed as the dimer. the major component. Systems with The main feature to be noted in excess morin are represented by the left Figure 4 is the difference between the half of the figure, and those with excess configuration of the curves on the right beryllium by the right half. The and left sides of the figure. In passing extreme left of the figure represents from the center of the figure toward the either infinitely great morin or infinitely right, curves 2 and 3 follow divergent
Table 111. Ratios of Values for a / ( l - a)2Mo,Series 1 and 2 Series 1 M O , 10-6 Series 2
2.0 4.0 6.0 8.0 10.0
1.28 1.49 1.63 1.70 1.95
paths. Their positions at the extreme right are determined principally by the concentration of morin, the minor component. Curve 2 (2.251 x lo-5-14 Beo) coincides with curve 1 (4.435 x 10-4.Tf Beo) when the morin concentration is very low and the fraction of morin complexed as the weakly-fluorescent complex W is high. Curve 3 (2.366 X 10-5M Mo) intersects curve 1 a t a point that corresponds to high concentrations of morin and dimer in series 1, and thus s h o w dimer formation to be dependent upon the concentration of beryllium as well as upon the concentration of morin. An extrapolation of the steeply rising portion of curve 3 passes through the point P and thus indicates that the dimer should be the principal end product of the reaction. T h e positions of curves 1 and 3 belob! point P are in accord with the equilibrium in Equation 7 and illustrate the fact that full reaction to form the dimer requires much larger concentrations of morin than were present in either series 1 or 3. The configuration of curves 2 and 3 in the left half of Figure 4 is quite different from that on the right. In passing from the center of the figure toward the left, each curve follows its separate path because of the difference in the concentration levels of uncombined morin; however, the extrapolated portions of curves 2 and 3 intersect a t the extreme left at an ordinant value of AF/B%b = 9.34 x lo5, a figure obtained by averaging values from series 3. Hence, if a sufficient concentration of uncombined morin is present, the end product of the reaction is independent of the concentration of beryllium, and a third complex that is highly fluorescent and mononuclear is the single product. As the value of the fluorescence difference per mole of beryllium combined in this third complex is comparable to the value for the fluorescence difference per mole of morin combined in the dimer, and as both of the latter are about three times greater than values for the (1 1) complex, it is not surprising that conventional methods have failed to find a mixture of complexes. Once it is known that there are three complexes, it is evident that Job's
+
VOL. 37, NO.
4, APRIL 1965
553
method of continuous variations and the molar ratio method would not be directly applicable (8, 9, 1 6 , I?). Beryllium/Morin Ratios in Complexes W and S. The concentrations of beryllium and morin in series 4a, b, c and 5a and b favored the formation of complex TI’. The low concentrations of morin were unfavorable for formation of the dimer, and the large excess of beryllium prevented formation of the third complex. The fluorescence of these solutions decreased as time between preparation and measurement increased. The dependence of fluorescence intensity upon time and also upon the method of preparation will be discussed later. At resent it must suffice to state that, a t any time, there was a straight-line relationship between the fluorescence intensity and morin concentration for the solutions of series 4a, b, and c. Thus, in contrast to the results from series 1, AF/Moh is independent of morin concentration when the latter is very low. I n addition, after a period of about 21/2 to 4 hours depending upon the method of preparation, AF/hlob calculated from the slope of the fluorescence-concentration curves from series 4, was in the neighborhood of 3.00 X 105, which is the value for the molar fluorescence difference per cm. depth for complex 1V found earlier from series 1. Complex W’ must therefore be the sole or principal complex in these solutions. The solutions of series 5a and b which contained the largest concentrations of beryllium were similar to those of series 4 ; accordingly AF/Moh corresponding to full reaction in series 5a and b also varied with time. After 3.33 hours this value was 3.26 X lo5 for series 5a which contained 7.098 X 10-QM morin; and after 2.53 hours, was 2.52 x 106 for series 5b which contained 1.183 x 10-*M morin. T h a t the higher value corresponds to the longer time is attributed to slightly different methods of preparation. I n spite of this apparent discrepancy, both sets of data from series 5a and b can be summarized by the single curve which is given in Figure 5. Here, 8, the fraction of morin complexed, is plotted against beryllium concentration. Values for p were calculated for each set of data by dividing the fluorescence intensities for incomplete reaction by the fluorescence intensities for full reaction. If complex W7 in these solutions is assigned the general formula BedMp, then the equilibrium for its formation is expressed by Equation 8. (BedMp)/[(Be)d(M)pl= kl
(8)
As (BedM,) = [a (M0)1/p, PI) = [(I - p)h&], and (Be) E (Reo), substitution of these values in Equation 8, 554
ANALYTICAL CHEMISTRY
AF/h = 3.00 X 105(BeM)
9.34
x
+
i o y ~ e ~ , (13) )
If e is the fraction of total Be combined in the complex BeM,, the following relationships hold for this system: Be. X 0 ’ 5
(BeM,)
Figure 5. Fraction of total morin complexed as function of Be concentration 0 @:
(BeM)
=
OB%
(14)
Beo - eBeo - (Be)
(15)
=
e = AF/Beoh-3.00
X 105[(l-(Be)/Be,J]6.34 X IO5
Series 5a, Mo = 7.098 X lO-’M Series 5b, Mo = 1.183 X lO-’M
combination of all constant terms, and rearrangement lead to p/(Beo)d = k**(l
- p)p
(9)
where k** = kl(p)(llo)P-l. When Equation 9 is expressed in logarithmic form, Equation 10 is obtained. l o g [ p / ( B e ~ ) ~=l log k**
log [l
-0
*
- (Be)/Beo
log k2
+ p log (1 - 8)
(10)
According to Equation 10, a plot of log [ ~ / ( B Q ) against ~] log (1 - /3) should give a straight line with a slope equal to P. Therefore, values for were read from the curve in Figure 5 , and used to calculate values for log (1 - p) and log [p/(Beo)d]where d was set equal to 1 or 2 . The resulting values were plotted and the mean curve through points corresponding to d equal 1 was a straight line with a slope of 1.01, whereas only a curved line could be drawn through points corresponding to d equal 2. From this it is concluded that both d and p are equal to 1 and that the weakly fluorescent complex Jt’ is the monomeric (1 1) complex B e l l . It then follows from Equation 7 that the dimer S is Be2hL. Beryllium/Morin Ratio in Third Complex. The nature of the third complex was determined from the data from series 3 presented in the leftmost quarter of curve 3, Figure 4. As morin was in large excess in the solutions represented by this region of the curve and as Beo was low, only negligible amounts of the dimer would be present in the system represented here. I n moving from right to left along this portion of the curve, the values for AF/Beob increase as a result of the 1) complex reaction between the (1 and morin. Complexes form in a stepwise fashion and there is no evidence of more than two monomeric complexes, so one would expect the third complex to be Bellz. To check this point, the reaction, equilibrium, and fluorescence difference were expressed in Equations 11 - 13.
+
+
Be31
and
+ (z - 1)hI
-;t
BeM,
(11)
]=
+ (Z - 1) log (M)
(18)
But as h‘lo is much larger than Beo, and as all values for AF/Beoh are greater than 7 X lo5, the fraction of uncombined beryllium must be small in comparison to the fraction combined. The simplifying assumption that (Be) E 0 was therefore made and should introduce no gross errors in the results based on this assumption. Values for AF/h corresponding to Beo concentrations that ranged from to 1.0 X IO+ were read from 1.5 X a smooth curve of experimental values and were used in Equation 16 to calculate values for e; log [e/(i - e)] was then plotted against log (M). Values for z had to be assumed in order to calculate values for (M); when z was set equal to 2 the curve had a slope of 1.0; when x was set equal to 3, the slope was also 1.0 for the region of the curve corresponding to Beo concentrations less than 6.0 X 10-6 but it was considerably less than 1.0 for higher Beoconcentrations. According to Equation 18 the slope of the curve is equal to (Z - 1). Thus the value of z is 2 and the third complex is Be& Equations for Overall System. Specific equations for the principal reactions, their equilibria, and expressions for total morin and beryllium can now be written. They are as follows : Be
+ M e BeM
(19)
0
05
5
I
-1.92
2
20
3
5.84
4 5 6
117
2 IO
Figure 6. Absorption spectra for
90% HsM 100% H4M88% M ~ M Z H~MS98% MY484% M5-
8.0
6 %
11.0
morin species Mo = 2 . 3 6 6 X 10-W
I.4
m
370
603
450
400
7w
WAVELENGTH -mu
Mo = (M’)
+
+ + 2(BeM,)
(22)
+ (Be%)
(23)
(BeM) 2(Be2h12)
Beo = (Be’)
+ (BeM) f 2(Be2M2)
For simplicity, all charges have been omitted from these equations and (Be’) and (M’) denote all beryllium and morin species not combined in any of the three complexes. The constants k l , kD, and k z are conditional constants for the specific medium and experimental conditions used to obtain the data. The fluorescence difference from the blank, measured 3.5 to 4.5 hours after preparation of the solutions and adjusted to S.L. 2.28, for a mixture containing all three complexes is given in its simplest form in Equation 24. AF = 3.00 X 105b (BeM) f
+
20.0 X 1056 (BezhIz) 9.34 X 1056 (BeMz) (24) The relationship between this equation and the forms presented elsewhere (6) can be seen from Equation 25 where AF is re-expressed in the earlier form.
AF
=
2.28 P&[(K1€1- KMEM)(BeM) f (KDED- 2Km,t)(Be2X2)
+
(&e2
- 2KbfeM) (BehIdI
(25)
In Equation 25, Po is the radiant power of the esciting light, 6 is solution depth, K 1 , K D , K P ,and K Mare the coefficients for the conversion of absorbed energy to fluorescence intensities for BeM, Be&, BeMz, and morin, respectively; and e l , ED, €2, and e~ are their respective molar absorptivities. The values for the fluorescence difference per mole of morin or beryllium per liter per em. depth which were determined by extrapolation for each complex are related to the terms in Equation 25 as follows:
equal to zero when beryllium was in very large excess! and the concentration (Be’) was set equal to zero when morin was in large excess. S o other siniplifying assumptions were made. The value for IC,** was calculated from Equation 9 where d and p are equal to one using the data from series 5a and b where p ranges from 0.07 to 0.76. The standard deviation for kl* is larger than that for kl** but the mean
I
Y
s
~
j
Figure 7. Comparison of molar fluorescence intensities and absorptivities of various morin species
I
0
10
5
Curve I: F/Mob; 4 4 3 mp excitation, S.L. 2.28 Curve 2: F/Mob; 3 6 5 mp excitation, S.L. 2.28 Curve 3: e, 4 4 3 mp Curve 4: e, 3 6 5 mp
15.
pH-Iwlc)
Evaluation of Conditional Constants. Although doubts must persist as to whether undiscovered complexes were present in the beryllium-morin mixtures studied, or whether the data have been properly interpreted, confidence in the proposed system is strengthened by the fact that values found for the three constants kl, kD, and kz (Equations 19a -21a) explain all the data from series 1 - 5 within the limits of experimental error. These values and their standard deviations are: kl* = 3.95 x IO5 f 1.60 X lo5; kl** = 4.28 X lo5 0.39 X lo5; k2 = 2.48 X lo5 + 1.18 X 105; kD = 1.22 x 105 + 0.50 x 105. The values for kl*, k ~ and , k D were found by Frederick B. Sower, I-.S. Geological Survey, who programed the high speed digital computer (B-220), using Equations 19a-24, the values for AFl, AFz, AFD, and all the data from series 1-3 (both concentrations and depths of solutions varied). The concentrations (11’)and (ReM,) were set
2.28 Po(Klel- KMEM) = AFl = AF per mole of (BeM) per liter per em. = 3.00 x 105 2.28 P o ( & € ~- 2k’McM) = AFD = 2AF per mole of morin complexed as Bez& = AF per mole of BeJI, per liter per em. = 20.0 X lo5 2 28 Po(Kzcz- 2KMrX) = AFz = AF per mole of Bell, per liter per cm. = 9.34 X 105 2 28 PoKXeM = FM = fluorescence per mole of morin per cm. = 0.195 x 105
value for k,* falls within the range for k,**. h n y errors in k D or kz would be compounded in the value for ICl* but would not enter into the calculation for k,**. The agreement therefore seems good for conditional constants which are a function of the specific medium, experimental conditions, and values for AF1,AF2,and AFDwhich were found by extrapolation. DISCU SSlO N
It is evident from the curves in Figures 6 and 7 that the absorption and fluorescence of morin vary with pH as a result of changes in the ionization of morin. However, this is not the whole story for an immediate and apparently nonreversible bleaching of color occurs near pH 15. The six morin species will be referred to as H&l, HJI-, HaS12-, H2L13-, HM4-, and M5-. That a t least 3 of these species react with beryllium is shown by the spectra in Figure 8. As pK1 is -1, the reactive hydroxyl group is completely ionized a t pH 1.0. Thus, when the pH is 1.0 or more, no proton is released from the morin as a result of its reaction with beryllium. In view of this, the symbol h l in the formulas BeM, Bell,, and BezhIzmay represent any of the morin species except H&. Specifically, when VOL. 3 7 ,
NO. 4, APRIL 1965
555
WAVELENGTH
- my
Figure 8. Absorption spectra for rnorin blanks (2.366 X 1 O-‘M) and mixtures of 2.366 X 1 O - W morin and 4.435 X 1 OP4MBe Curves 1, 1 a: blanks Curves 2, 20: mixtures with Be Species HM4- and M5-: curves 1 and 2, f = 2 minutes; curves l a and 20, f = 19.5 hours Shaded areas: maximum absorbance difference
pH& then dissociates slowly to give BeM. When excess beryllium is added to morin solutions that have already faded, beryllium reacts with morin or its hydrolysis products in solutions of both H N 4 - and l f 5 - . Although the original solutions of hT5- faded much more rapidly than the original solutions of HkI4-, all of the “spiked” solutions faded a t the same rate regardless of the nature of the morin species or the extent of fading before beryllium was added An attempt was made to express the overall fading rate in a simple manner. The data from curve 1, Figure 11 (1.183 X 10-aX morin 4.435 X 10-4Jf Be) and that from a 1.183 X 10-5JI morin blank prepared along with Set B were used to calculate the data given in Figure 12. In these pseudo first-order plots log. X is given as a function of time. Curves 1 and 2 give data for the beryllium-morin mixture and curve 3 gives data for the morin blank. In curve I ,
+
Figure 9. Fluorescence of blanks per mole of morin per cm. depth a t S.L. 2.28 for species HM4- and M5- as function of time
I
and in curves 2 and 3,
‘
t
.kUn
Figure 12. Evaluation of fading rates at pH 12.6. Curves 1 and 2: 1.183 X 10-W morin and 4.435 X 10-4M Be Curve 3: 1.1 83 X 1 O-5M morin See text for details
Figure 1 1.
1 = hours Fluorescence per mole of morin per cm. depth as function of time S.L. = 2.28 excitation = 443 mM
Curve Curve Curve Curve Curve
1: Set B, Mo = 1.1 83 2: Set B, Mo = 1.1 83 3: Set 8, Mo = 1.183 4: Set B, Mo = 2.958 5: Set 8, Mo = 5.915
X lo-* X lo-’ X X 10-6 X lo-‘
pH = 12.6 Be = 4.435 X 10-4M Curve 6: Set B, Mo = 1.1 83 X 1 0-5 Curve 7: Set 8, Mo = 2.366 X Curve la: Set A, Mo = 1.183 X Curve 1 -4c: Series 4c, Mo = 1.1 83 X 1 0-8 Curve 7a: Set A, Mo = 2.366 X
Table IV.
where t=time in hours. The latter data were calculated on the assumption that complete fading eventually occurs. For the first 10 hours there is little difference between the slopes of curves 1 and 2 in comparison to the difference between either of their slopes and that of curve 3. For periods greater than 10 hours the slopes of curves 2 and 3 are about the same. It appears that at the start, dissociation of Be2>& to yield B P M is the principal cause of fading, T \ hile later on hydrolysis or other degradation processes become dominant. F/’&fob(t = 0 ) Graphs d log. --,plotted F/Mobo = t ) against time were used to compare the overall fading rates of the various solutions. A summary of the rates which are equal to the slopes of these curves are given in Table IV. In conclusion it can be stated that the beryllium-morin system is a complicated metastable one in which three principal reactions take place. These reactions lead to the complexes of generic formulas f3eRX, T3e2M2,and Be&. The charge on the individual complexes making up any one of these groups varies with the ionization state of the morin, whereas the absorption and fluorescence characteristics vary not only with the ionization of the morin but also with its hydrolysis and perhaps even with its
pH
Rates for Fading
Contents of solution
Rate
1 2 . 6 1.183 X 10-6Nniorin 0 016 hr.-1 blank-set B 12.6 1.183 X 10-5Mmorin 0.012 hr:-l blank-set B 1 2 . 6 1.183 X 10-6Mmorin 0.019 hr,-1 blank-set A 12 6 1.183 X 10-5.!4morin 0.014 hr.-I blank-set A 11 2.958 X 10-6M morin 0.015 hr. -1 blank (Hh14-) 14 2.958 X 10-6M morin 0.058 hr. - 1 blank (>Is-) 12.6 1.183 X 10-*,11rnorin 0.22 hr.-L 4.435 x IO-‘M Be-set B 1 2 . 6 1.183 X 10-8,1f morin 0.24 hr.-1 4.435 x 10-4M Be-set A 1 2 . 6 1.183 X 10-8Mmorin 0.31 hr.-1 4.435 x i o - 4 ~ Be-series 4c 11 2.958 X, 10-6M morin 0.24 hr. - l a (species HM-4) 4.435 x 10-‘M Be added at 22 hours 11 Same mixture, species 0 24 hr. --lo HhI4- Be added at 72 hours 14 Same mixture but 0 24 hr.-la species W - Be added at 22 hours 14 Same mixture, species 0 24 hr.-ln ;LIS- Be added at 72 hours
+ + +
+
a
Average value.
degradation states. As the latter are all functions of p H and/or time, the composition and therefore absorption and fluorescence characteristics of any mixture of complexes referred to as complex B e N , Be& or I3e& are also functions of p H and time. When p H and eyeitation wave length are fixed, the molar fluorescence intensities of these complexes change with time. LITERATURE CITED
(1) Breger, I. A,, Geochim. Cosrnochirn. Acta 19, 297 (1960). (2) Breger, I. A,, “Organic Geochemistry,” Chap. 3, pp. 50-86, Pergamon Press, Oxford, 1963. (3) Bril, J., Pruvot, E., Mikrochim. Acta 1960/4, 577. (4) Carell, B., O h , A,, Acta Chem. Scand. 15, 1875 (1961). (5) Fletcher, M. H., ANAL. CHEY. 35, 288 (1963). (6) Zbid., p. 278. (7) Gilbert, R. A,, Garrett, A. B., J . Am. Chem. SOC.78, 5301 (1956). (8) Jones, SI. M., Ibid., 81, 4485 (1959). (9) Jones, M. hl., Innes, K. K., J . Phys. Chem. 62, 1005 (1958). 10) Kakihana, H., Sillen, L. G., Acta Chem. Scand. 10, 985 (1956). 11) Kolthoff, I. M., Elving, P. J., “Treatise on Analytical Chemistry,” Part I, Vol. I, Chap. 8, pp,. 284, 289, Interscience, Sew York, 19n9. 12) Mattock, G., J . A m . Chem. SOC.76, 4835-38 (1954). 13) Nay, I., Grirnaldi, F. S., ANAL. CHEM.33, 1251 (1961). 14) hlilkey, R. G., Fletcher, M. H., J . A m . Chem. SOC.79, 5425 (1957). 15) Minczewski, J., Rutkowski, W., Chem. Anal. Warsaw 7, 1107 (1962). 16) Woldbye, F., Acta Chem. Scand. 9, 299 (1955). 17) Rossotti, F. J . C., Rossotti, H., “The Determination of Stability Constants,” p. .50, McGraw-Hill, New York, 1961. 18) Sandell, E. B., “Colorimetriq) Determination of Traces of -Metals, 3rd ed., Chap. IX, Interscience, New York. 1959. (19) Sill. C. W., Willis, C. P., A N A L . CHEM.31, 598 (1959). (20) Sill, C. W., Willis, C. P., Flygare, J. K., Ibid., 33, 1671 (1961). RECEIVEDfor review June 18, 1964. Accepted January 6, 1965. Publication authorized by the Director, U. Y. Geological Survey. VOL. 37, NO. 4, APRIL 1965
557
