smaller than in the absence of methanol. Curve C in Figure 3 is that calculated in the presence of 0.5M of the strong hydrogen bond donor p-bromophenol. The heteroconjugation constants of AHR- and A(HR)*-, A- denoting 3,5-dinitrobenzoate and HR, p-bromophenol are 3.6 X lo2 and 3.9 X 103, respectively, as determined previously (2). The dissociation constant in A N of p-bromophenol is of the order of 10-27, that of 3,5-dinitrobenzoic acid is lo-” (6), so that negligible proton transfer occurs in the reaction between 3,5-dinitrobenzoate and the phenol. The potentiometric titration curve in the presence of 0.5M p-bromophenol is virtually identical with that of a weak acid in water and the apparent pKdHAis 3 units smaller than in the absence of the
phenol. Use of this effect can be made in the titration of mixtures of acids in AN. In conclusion, acid-base equilibria in A N are generally much more complex than in aprotic protophylic solvents like dimethylsulfoxide. The latter solvents are much to be preferred over A N for the titration of weak acids. On the other hand, A N is one of the best solvents for the titration of weak bases, as will be shown in a subsequent paper.
RECEIVED for review April 17, 1967. Accepted May 5, 1967. Acknowledgment is made to Air Force AFOSR Grant No. 1223-67.
A Mechanistic Investigation of Molybdenum Blue Method for Determination of Phosphate S. R. Crouch and H. V. Malmstadt Department of Chemistry and Chemical Engineering, Uniaersity o j Illinois, Urbana, 111. The major chemical steps in the molybdenum blue method for the determination of phosphate are described in detail with the aid of precision spectrophotometric measurements. A stoichiometric study of the reaction between phosphate and molybdate to form 12-molybdophosphoric acid is described which indicates that Mo(V1) exists largely as a dimer in strong sulfuric or nitric acid solutions and that an interaction occurs between sulfate and the heteropoly acid. The kinetics of the reaction between phosphate, Mo(VI), and a reducing agent to form the heteropoly blue species are discussed. The rate law is in agreement with a mechanism involving an equilibrium to form 12-molybdophosphoric acid and a subsequent reduction step. 12-Molybdophosphoric acid is a reactive intermediate in the overall reaction. The kinetic results are in general agreement with the experimentally determined stoichiometry of the equilibrium step and indicate that the initial reduction of 12-molybdophosphoric acid proceeds by a 2-electron step, while reduction by 1-amino-2-napthol-4 sulfonic acid is complex.
ANALYTICAL METHODS for the determination of phosphate are usually based on the formation of 12-molybdophosphoric acid from phosphate and molybdate in acid solution and subsequent reduction to a blue heteropoly compound ( I ) . Although a voluminous literature exists on the analytical method and its numerous modifications, many basic questions concerning the major chemical steps leading to the blue species (referred to in this paper as phosphomolybdenum blue) remain to be answered. For example, a quantitative description of the steps leading t o phosphomolybdenum blue requires knowledge of the predominate equilibria among isopolymolybdates in strong acid solution. Such equilibria have been well studied over the pH range 6-1.5 (2-4); however, the predominate Mo(V1) (1) W. Rieman and J. Beukenkamp, “Treatise on Analytical Chemistry,” I. M. Kolthoff and P. J. Elving, Eds., Part 11, Vol. 5, Wiley, New York, 1961, pp. 317-402. (2) L. C. W. Baker, G. Foster, W. Tan, F. Scholnick, and T. P. McCutcheon, J . Am. Chem. Soc., 17, 2136 (1955). ( 3 ) I. Lindqvist, Acta Chim. Scand., 5 , 568 (1951). (4) Y. Sasaki, I. Lindqvist and L. G. Sillen, J . Znorg. Nucl. Chem., 9, 93 (1959).
1084
e
ANALYTICAL CHEMISTRY
equilibria in the pH range of 0.7-0.0, a pH range in which direct reduction of Mo(V1) does not occur in the absence of phosphate, are uncertain. High polymers ( 5 ) and a dimeric cation of the form HMo?O6+ (6) have been found in strong acid solutions. A second related question concerns the effect of acid concentration on the overall phosphomolybdenum blue reaction. It seems clear that the pH and the Mo(V1) concentration determine the predominate equilibria among the isopolymolybdates. Beyond this, however, the hydrogen ion concentration may affect the formation of 12-molybdophosphoric acid and the reduction step. At acid concentrations high enough to avoid direct reduction of Mo(V1) some workers have found that variations in the acidity have little effect on the amount of blue product formed (7), while others have found the amount of product to be acid dependent (8). A third question concerns the role of unreduced molybdophosphoric acid in the overall process. Early views considered phosphate to be a catalyst in the direct reduction of Mo(V1) (8); however, most modern observers agree that the formation of the heteropoly blue takes place through the reduction of 12-molybdophosphoric acid. Finally, the nature of the blue species formed in the method is still a controversy. Some workers, assuming that the heteropoly blue contains the same number of molybdenum atoms as the unreduced molybdophosphoric acid, have found heteropoly blues with Mo(V1)-Mo(V) ratios of 2:1 and 5 : l depending on the reducing agent and the time allowed for reduction (9-II). (5) Climax Molybdenum Co., New York, Bull. Cbd-12 (1960). (6) Y. Sasaki and L. G. Sillen, Acta Clzim. Scand., 18, 1014 (1964). (7) . , J. T. Woods and M. G. Mellon, IND.ENG. CHEM.,ANAL. ED. 13, 760 (1941). (8) J. Berenblum and E. Chain, Biochem. J . , 32, 286 (1938). (9) R. Arnold and S. M. Wacker, J . S. African Chem. Inst., 9, 80 (1956). (10) E. Bamann, K. Schriever, A. Freytag, and R. Toussant, Ann. Chem. Liebigs, 605,65. (11) H. Hahn and G. Schmidt, Naturwissetlsc~laften 49, 513 (1962).
TIME, seconds
-
too-
I
90
-
Figure 1. Effect of "01 on rate of formation of phosphomolybdenum blue = 8.45 mM, KH2P04 = 2.26 p M , aminonaphtholsulfonicacid = 0.171 mM
Mo(V1)
In the present study the stoichiometry of the formation of 12-molybdophosphoric acid from phosphate and molybdate has been evaluated in strong H?S04 and HNO, solutions using precision spectrophotometric measurements capable of detecting absorbance changes of 10-5 unit. In addition, the kinetics of the overall reaction of phosphate, molybdate, and a reducing agent to give phosphomolybdenum blue have been evaluated under conditions used in analytical procedures. EXPERIMENTAL
Spectrophotometric Measurements. Spectrophotometric measurements of the formation of 12-molybdophosphoric acid were made on a sensitive, stable photometric system, which consists of a reliable interference filter photometer, a reaction vessel thermostated to =t0.1" C, a phototube transducer, and a recording photometer described in detail in a recent article (12). The filter photometer was the Spectro section of the Spectro-Electro titrator (E. H. Sargent and Co., Chicago, Ill.). A General Electric No. 68 light bulb, powered by a 12-volt power supply, was substituted for the source on the commercial instrument. T o minimize the effect of line voltage fluctuations, the power supply was operated from a Sola constant voltage transformer. Maximum drift over a 6hour period was less than absorbance unit with this single beam system. The thermostated reaction cell has been described (13). A General Electric 929 phototube was substituted for the detector supplied with the instrument. For absorbance measurements of molybdophosphoric acid at 350 mp, the nominal 500-mp interference filter on the titrator was used with a visible cutoff filter (Corning No. 5860) to isolate a narrow band of radiation near 350 mp. For studies at 400 mp a Bausch and Lomb 400-mp interference filter with a half-band width of 15 mp was employed. With this photometric system, full-scale sensitivity could be increased to less than 0.01 absorbance unit, which allowed detection of absorbance changes as small as unit. All equilibrium absorbance measurements were made against (12) H. V. Malmstadt, R. M. Barnes, and P. A. Rodriguez, J . Chem. Educ., 41, 263 (1964). (13) H. V. Malmstadt and S. I. Hadjiioannou, ANAL.CHEM.,34, 452 (1962).
appropriate blank solutions. Absorbances of the blanks were seldom more than a few per cent of the total measured absorbance. For expanded-scale measurements, a differential method was used. For studies on 12-molybdophosphoric acid, molybdate and acid were added to the reaction cell and the 100% T was adjusted in the normal manner. Darkness was used to set the 0 % T . Then precision, calibrated feedback resistors (12) were used to expand the scale by accurately known amounts. For example, by expanding the scale exactly 10-fold, % T values between 100 and 90 could be accurately measured. At the highest sensitivity employed, a correction for the dilution caused by the addition of 0.1 ml of phosphate to the 5-ml volume was T measurements were then necessary. Expanded-scale converted to absorbance values in the normal manner. All measurements were made on the same reaction cell. The cell was not moved during a series of measurements to minimize scattered light changes. Solutions were emptied with an aspirator, and the cell was thoroughly cleaned between measurements. All spectrophotometric measurements were made at 30.0 i 0.1 ' C. Kinetic measurements were made with the same photometric system. Initial reaction rates were measured graphically by evaluating the initial slopes of absorbance cs. time curves after the short induction period had passed. No more than 5 Z of the total reaction curve was used in evaluating initial rates. The usual procedure in making kinetic measurements was to pipet aliquots of standard molybdate, acid, and phosphate solutions into the thermostated cell. After waiting a few minutes for temperature equilibration, the reducing agent was injected into the cell with a hypodermic syringe to initiate the reaction. Because of the efficient stirring on the titrator unit, mixing times were of the order of a few seconds. The rate of formation of phosphomolybdenum blue was followed at 650 mp by dialing the 650 mp interference filter on the titrator and using an ultraviolet cutoff filter to isolate the visible band. Phosphomolybdenum blue has been shown to follow Beer's law at this wavelength (14). Reagents. Stock solutions of Mo(V1) were prepared or (NH4)6M07024. from either reagent grade N a 2 M o 0 42H20 . 4H20. Early in this investigation, it was noted that freshly (14) D. F. Boltz, and C . H. Leuck, in "Colorimetric Determination of Nonmetals," D. F. Boltz, Ed., Wiley, New York, 1958, pp. 29-46. VOL. 39, NO. 10, AUGUST 1967
1085
~~
Varied NazMo04 KHzP04 "0s
Varied NazMo04 KHzPOa
Table I. Reaction Coefficients in Nitric Acid Solutions CMO(V1)t CXH,PO, CHNO~ io-L5 x 10-3~4 1.2 x 1 0 - 3 ~ 0.82M 7 x 10-3~4 6 x 10-3-6 x lO-4M 0.82A4 5 x 10-3~ 1 . 2 x 10-3A4 0. 5 0 .82M Table 11. Reaction Coefficients in Sulfuric Acid Solutions CKH~PO~ cH@Od 10-2-5 x 1 0 - 3 ~ 1.2 x 1 0 - 3 ~ 0.41M 1.1 x 10-2M 5 x 10-3-5 x 10-4714 0.41M 1.1 x 10-2M 3.0 x i o - 4 ~ 4 0.30-0.41 M
Rxn. coefficient
C1fotvI)t
prepared solutions of Mo(V1) gave different kinetic and equilibrium results than solutions which had been allowed to stand a few hours. Although this aspect has not been studied in detail, it presumably indicates a slow step in the equilibration of isopolymolybdates. All results reported here were obtained on Mo(V1) solutions which had been prepared several hours before use. After this period, results were independent of the age of the Mo(V1) solution and the original form of the Mo(V1). 1-Amino-2-napthol-4 sulfonic acid solutions were made 1.46M in sodium bisulfite and 0.04M in sodium sulfite. A prepared solid mixture of the acid, sulfite, and bisulfite (available from Sigma Chemical Co., St. Louis, Mo.) was also used. All other materials employed were reagent grade and used without further purification. RESULTS AND DISCUSSION
Preliminary observations on the reaction of phosphate, Mo(VI), and either 1-amino-2-napthol-4 sulfonic acid or ascorbic acid to form phosphomolybdenum blue indicated that the rate of formation of the blue product is highly acid dependent. The effect of nitric acid on the reaction rate is the shown in Figure 1. Over the range of 0.3 to 1.ON " 0 3 amount of blue product formed is independent of the acidity, but its rate of formation decreases sharply with increasing solution acidity. Identical results were obtained with sulfuric acid. These observations indicated that acid was not involved in the final reduction step, but was involved in the formation of an intermediate, presumably 12-molybdophosphoric acid. A study of the formation of 12-molybdophosphoric acid was made to elucidate the stoichiometry of its formation under conditions used in analytical procedures. Stoichiometry of the Formation of 12-Molybdophosphoric Acid. Upon mixing aqueous solutions of phosphate, Mo(VI), and nitric acid or sulfuric acid, 12-molybdophosphoric acid rapidly forms. This species is yellow in color and has an ultraviolet absorption spectrum remarkably similar to that of acidic Mo(V1) solutions (3, 15, 16). The spectrum of the heteropoly acid, however, extends more toward the visible region. Between 350 and 400 mp, the absorbance of 12molybdophosphoric acid (12-MPA) can be measured with only a small blank due to unreacted Mo(V1). Measurements in this study were made at both 350 and 400 mp. Solutions of reagent grade 12-MPA were observed to follow Beer's law at both wavelengths.
(15) D. F. Boltz and M. G. Mellon, ANAL.CHEM., 20, 749 (1948). (16) B. E. Reznik and L. P. Tsyganok, J. Inorg. Chem. ( U S S R ) , 10, 1042 (1965). 1086
Rxn. coefficient y = 6.10 f 0.18 x = 0.99 f 0.03 z = 9 . 1 zt 0.3
ANALYTICAL CHEMISTRY
y = 4.95 zk 0.16 x = 0.95 i.0.05 z =
1.07 f 0.23
Preliminary studies on the formation of 12-MPA revealed that the amount formed was highly acid dependent. Increasing acidity led to a sharp decrease in the absorbance at 350 or 400 mp. Increasing concentrations of both phosphate and Mo(V1) led to an increased amount of 12-MPA. To determine the reaction stoichiometry, spectrophotometric studies were undertaken under conditions in which the reaction was quite incomplete. Under these conditions it was assumed that the equilibrium concentrations of the reactants were equal to their initial concentrations. The reaction to produce 12-molybdophosphoric acid was assumed to be
+
x H ~ P O ~yMo(VI)t,tal
e (12-MPA) + zH+
where M O ( V I ) ~refers ~ I to the total amount of unreacted Mo(VI), and x, y and z refer to the number of moles of phosphate, molybdate or H+ which form or react with one mole of 12-molybdophosphoric acid. The formation constant for the reaction can be expressed in terms of the absorbance ( A ) of 12-MPA, the molar absorptivity, (E) of 12MPA, and the cell length b.
By choosing conditions such that the amount of 12-MPA formed is very small, the initial concentrations of the reactants, C H ~ P OC~A , I ~ ( Vand I ) ~ ,CH+can be substituted for the equilibrium concentrations and Equation 1 rearranged to give
and log A = log Kfcb
+ x log
+ y log CMo(V1)d
- z log c H + (3)
If the initial concentrations of acid and Mo(V1) are held constant while the phosphate concentration is varied, a plot of log A us. log C H ~ Pshould O ~ give a straight line of slope x. Similar plots for variations of C R ~ ~ (and V I CH+ ) ~ should yield slopes of y and -z. Treatment of the data in this manner gave the results shown in Table I for nitric acid solutions and the results shown in Table I1 for sulfuric acid solutions. It should be noted that, because of the large coefficients of Mo(VI), and acid in the reaction, concentrations could not be varied over a wide range without forming an appreciable amount of 12-MPA or obtaining immeasurably small absorbances. The maximum concentration of 12-MPA formed in all these experiments was
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PH Figure 2. Absorbance of 1Zmolybdophosphoric acid us. pH for HzSOJ and " 0 3 M O ( V I ) ~= 9.84 mM, KHzP04 = 0.30 mM
1.3 X lO-5M which was negligible with respect to initial reactant concentration. This concentration was calculated from the experimentally measured molar absorptivity of 12-MPA, obtained by forcing the reaction to completion with high Mo(V1) concentration. Approximate molar absorptivities of 3.23 X l o 3liters/mole-cm and 3.4 X lo2 liters/ mole-cm were found at 350 and 400 mp, respectively. The results shown in Tables I and I1 were independent of the age of the solutions [as long as the Mo(V1) was prepared several hours in advance], the original form of the Mo(VI), and the wavelength (350 or 400 mp). The data in Table I indicate that the stoichiometry of the reaction in nitric acid can be described by H3P04
+ 6 Mo(V1)t e (12-MPA) + 9H+
This stoichiometry is evidence that Mo(V1) is appreciably dimerized in solutions of 0.5 to 0.8M H N 0 3 . A dimeric cation such as that suggested by Sasaki and Sillen (6) and Souchay (17) may be the predominate Mo(V1) species in strong acid solutions. It should be pointed out that under the conditions in which these experiments were carried out, these data do not necessarily indicate that all the Mo(V1) is dimerized. Since the amount of reaction was purposely kept very small, any equilibria among Mo(V1) species would not be appreciably disturbed by the reaction with phosphate, The stoichiometry written above does not indicate that the actual mechanism involves the reaction of phosphate with a dimeric Mo(V1) species. One possible reaction scheme which would lead to an identical stoichiometry under the conditions used in these studies, involves a pH dependent Mo(V1) equilibrium between the Mo(V1) dimer and a higher Mo(V1) polymer which would then react with phosphate (17) P. Souchay, Pure App/. Chem., 6 , 61 (1963).
5.5
4.0
-LOG
2.5
cl,2,4 ACID
Figure 3. Determination of reaction order with respect to ascorbic acid M O ( V I ) ~= 7.88 m M , KHzP04 = 0.116 "OB = 0.788M
6 MO(VI)di,,,
mM,
MO(VI)po~ymer f zH+
l t po4-3 l2-MPA Such a scheme could explain why dissolved 12-molybdophosphoric acid is stable toward concentrated mineral acids (16) in contrast to 12-MPA in equilibrium with phosphate and Mo(V1). The data in Table I1 indicate a 5;l combining ratio for Mo(V1) and phosphate in sulfuric'acid solutions. Also, only 7 moles of hydrogen ions react with one mole of 12-MPA. Several possible explanations for this difference in stoichiometry can be advanced. For example, sulfate might form complexes with cationic Mo(V1) species and disturb the dimerpolymer equilibrium. Alternatively, sulfate might interact with the heteropoly acid itself, although evidence as to the stability of dissolved 12-molybdophosphoric acid toward H z S 0 4 (16) would tend to rule out a simple interaction. Other workers have reported sulfate interactions with heteropoly- and isopolymolybdate systems (18-20). That some sulfate interaction does occur is indicated by a series of experiments comparing the absorbances of nitric and sulfuric acid solutions of 12-MPA in equilibrium with Mo(V1) and phosphate at the same measured pH. These data are shown in Figure 2. Note that at a given pH the heteropoly acid is more dissociated in H2SO4than in "03. Experiments in which sulfate and bisulfate were added to solutions of 12MPA, phosphate, and Mo(V1) while the pH was maintained constant also indicated a dissociation by sulfate. However, (18) G. C . Dehne and M. G. Mellon, ANAL.CHEM.,35, 1382 ( 1963). (19) J. C. Guyon and L. C. Cline, Ibid.,37,1778 (1965). (20) K. Schriever and R. Toussaint, Chem. Ber., 91,2639 (1958). VOL. 39, NO. 10, AUGUST 1967
1087
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Figure 4. Log-log plot for HNOI showing deviations from linearity at lower acid concentrations Mo(V1)t = 7.1 m M , KHzPOd ascorbic acid = 3.94 m M
=
1.16 m M ,
these experiments were inconclusive in elucidating the stoichiometry and nature of this interaction. Kinetic measurements on the formation of reduced 12-molybdophosphoric acid, which are discussed in the next section, indicate that this interaction is unimportant in determining the steady state concentration of 12-MPA. N o attempt was made to determine the formation constant K f , because the exact concentration of Mo(V1) in the dimeric form was unknown in these experiments. Kinetics of the Formation of Reduced 1ZMPA. The kinetics of the formation of phosphomolybdenum blue (PMB) from phosphate, Mo(VI), and ascorbic acid or 1-amino-2-napthol-4 sulfonic acid were investigated to clarify the overall reaction scheme. Both HNOBand HzS04were used. Reaction orders were obtained from the slopes of plots of log initial rate cs. log concentration of the species varied. Because the nature and concentration of the product, phosphomolybdenum blue, were not known, all plots represent relative initial rates. Because the concentration of PMB and the exact concentration of dimeric Mo(V1) were unknown in these experiments, rate constants were not determined. KINETICS I N HN03. In 0.5 to 0.8Nnitric acid with l-amino2-napthol-4 sulfonic acid (1,2,4 acid) as the reductant, the reaction was found to be first-order in phosphate, sixthorder in total Mo(VI), inverse ninth-order in nitric acid, and one-half order in 1,2,4 acid, The rate law is thus given by d[PMB] a~id]l/~ - - - K[H3P01][Mo(VI),]6[1,2,4 dt [~+19
1088
ANALYTICAL CHEMISTRY
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3.8
3.6
3.4
I 3.2
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3.0 2.8 -1-06 CASCORBICACID
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2.6
2.;
Figure 5. Determination of reaction order with respect to 1-amino-2-naphthol-4 sulfonic acid MO(VI)~= 10.9 m M , KHlPOd = 56.5 p M , HzSOa = 0.375M
KINETICS IN SULFURIC ACID. In sulfuric acid solutions both reducing agents gave reaction orders which varied with the ratio of [H+]/[Red]. Figure 5 shows a typical set of data for 1-amino-2-napthol-4 sulfonic acid. At low concentrations the order is one half, while at high concentrations the slope of the log-log plot approaches zero. With ascorbic acid the limiting order at low concentrations was first. The order in sulfuric acid was also found to vary from 10th-order at high acidities to almost zero-order at low acidities with both reducing agents. The orders with respect to phosphate and total Mo(V1) were found to be 1st and 6th, respectively. These results lead to the following rate laws: With 1,2,4 acid
With ascorbic acid (4)
With ascorbic acid as the reductant, all orders were the same except that the order in ascorbic acid varied from first-order a t low concentrations to zero-order at high concentrations as shown in Figure 3, and the order in H N 0 3 varied from inverse 9th- at high concentrations to almost zero-order at low concentrations as shown in Figure 4. These results suggest that the rate law using ascorbic acid as the reductant is given by Equation 5
\[Ascorbic Acid])
I 4.0
d[PMB] --
K[H~PO~][MO(VI)~]~ (7)
dt
- ([Asc~~~~~cid]) +
DISCUSSION OF KINETICRESULTS. In general the experimental rate laws are of the form predicted by a mechanism involving a prior equilibrium to form 12-mo!ybdophosphoric acid and subsequent reduction of this species to phosphomolybdenum blue. An expression for the formation of phosphomolybdenum blue can be derived by considering the equilibria described in the previous section, and by assuming that 12-molybdophosphoric acid is a reactive intermediate. For example, in nitric acid the formation of 12-MPA can be written
HSP04
+ 6 Mo(VI), e (12-MPA) + 9 H+ ki
k-1
and the reduction of 12-MPA to phosphomolybdenum blue may be expressed as (12-MPA)
+ n Red 5 PMB + nOx
where n is the number of moles of reducing agent, Red, required to reduce one mole of 12-MPA. The reverse reaction of the second step has been neglected since initial reaction rates are considered. The rate of formation of phosphomolybdenum blue may be written as d[PMB1 = kz [12-MPA][RedIn dt Equation 9 gives the rate of formation of 12-MPA. d[l2-MPA] dt
= kl [H3P04][Mo(VI)J6
-
k- [ 1 2-MPAI[H+]g - k z [I 2-MPA] [Red]“ (9)
Applying the steady state condition to 12-MPA and substituting the resulting steady state concentration in Equation 8 gives
A similar derivation for H2S04solutions based on the experimental stoichiometry for the formation of 12-MPA yields Equation 11.
(kz:)
d(PMB] _ _ = _ kzkl [H~PO~][MO(VI)Z]~ dt +
(11)
The kinetic data for nitric acid using I-amino-2-napthol-4 sulfonic acid (Equation 4) agree with Equation 10 if k-1[H+19 >> 1 , and n = Attempts to observe the other kz[Redj” limiting case failed with this reducing agent because of its limited solubility. Using ascorbic acid, the rate law (Equation 5) conforms well to Equation 10 with n = l. In sulfuric acid the general form of the rate laws for both reducing agents (Equations 6 and 7) agrees well with Equation 11. It is noteworthy, however, that the equilibrium data indicate that 5 moles of the Mo(V1) dimer react with one mole of phosphate, while the rate laws show a 6th-order dependence on the Mo(V1) concentration. One possible explanation is that the sulfate interaction, postulated to explain the 5 :1 combining ratio of Mo(V1) to phosphate, is slow and does not show up on the kinetic scale, inasmuch as the subsequent reduction step keeps the 12-molybdophosphoric acid concentration very low at steady state. The kinetic results seem to indicate that sulfate interacts with 12-molybdophosphoric acid after it forms rather than being directly involved in the formation. Further studies using fast reaction techniques could help clarify this discrepancy. Another discrepancy between the equilibrium and kinetic data in H2SO4may be noted in the effect of acid concentration. In the equilibrium study seven moles of acid were found to dissociate one mole of 12-MPA, while the limiting rate laws indicate an inverse 10th-order dependence. Again a possible explanation for this effect could be the interaction of sul-
fate with 12-molybdophosphoric acid or some Mo(V1) polymer. The rate law with respect to the two reducing agents yields information as to the reduction mechanism. With ascorbic acid, the rate is first order in 12-molybdophosphoric acid and first order in ascorbic acid. Although an intermediate radical has been proposed for ascorbic acid reductions (21), a single 2-electron reduction step appears more likely in strong acid solution. The stoichiometric behavior of ascorbic acid as a 2-electron reductant is well established (22, 23). With l-amino-2-napthol-4-sulfonic acid, however, a more complex mechanism must be postulated to explain the onehalf order dependence of the rate on the I-amino-2-napthol4-sulfonic acid concentration. Enough careful measurements were taken to convince us that this square root dependence on the 1, 2 , 4 acid concentration is real, and not the result of a systematic error. It is noteworthy that a plot of I/Rate us. 1/[1,2,4 acid] is decidedly nonlinear, but a plot of I/Rate 6s. 1/[1,2,4 acidll’z gives a straight line over the 1000-fold concentration range studied. Oxidation of 1-amino-2-napthol-4 sulfonic acid leads to a quinoneimine, which hydrolyzes to 1,2-napthoquinone-4 sulfonic acid (24, 25). The fractional dependence of the rate on the 1-amino-2-napthol-4 sulfonic acid concentration suggests that a radical mechanism involving the half-reduced semiquinone may be operating in this system. The detailed mechanism is further complicated by the presence of sulfite which is used to stabilize the 1,2,4 acid and is also capable of participating in the reaction. Further studies are now in progress to elucidate the detailed mechanism of the oxidation of 1,2,4 acid by 1Zmolybdophosphoric acid. CONCLUSIONS
The results obtained in this study have several important consequences to users of the molybdenum blue method for phosphate. For stoichiometric measurements of the amount of blue product formed, it is not necessary to control the solution acidity as long as the acidity is high enough to prevent direct reduction of Mo(V1) (pH < 0.7), as the acidity determines only the rate of reaction. For the most rapid results, it is desirable to use the lowest acidity feasible (0.3 to 0.51%’H z S 0 4or ”OB). It is also desirable to record the results at a fixed wavelength so that the final absorbance may be easily noted. Measurements made after a fixed time may be in error if the sample acidity is high enough to make the reaction very slow. Direct recording is also advantageous in that readings can be made within a minute or two at lower acidities. This prevents side reactions which can lead to fading of the blue color after several minutes. Conditions, based on this study, for a new reactio? rate procedure for phosphate will be presented in a subsequent paper.
RECEIVED for review April 3, 1967. Accepted June 2, 1967. Presented at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1967.
(21) R. Stewart, “Oxidation Mechanisms,” Beniamin. New York, 1964, p. 113. (22) M. Dixon and E. C. Webb. “Enzvmes.” Academic Press. New York, 1964, p. 374. (23) D. M. H. Kern,J. Am. Chem. SOC.,76, 1011 (1954). (24) L. F. Fieser, Org. Synthesis, 11, 12 (1931). (25) L. F. Fieser and M. Fieser, J . Am. Chem. SOC.,57, 494 (1935). .
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