(21) E . S . Pilkington and W. Wilson, unpublished work, CSIRO Melbourne (1974). (22) H. Blutstein and A. M. Bond, Anal. Chem., 48, 248 (1976). (23) L. B. Sybrandt and S. P. Perone, Anal. Chem., 44, 2331 (1972). Techniaues", 2nd ed., Wilev. New York. 1965. (24) L. Meites, "POlarOQraDhiC _ . p 614. (25) M. Pinta, "Detection and Determination of Trace Elements" (English translation, Israel Program for Scientific Translations, Jerusalem, 1966), Dunod, Paris, 1962.
(26) A . Lagrou and F. Verbeek, J. Electroanal. Chem., 19, 125 (1968). (27) E. Temmerman and F. Verbeek, J. Electroanal. Chem., 19, 423 (1968). (28) D. J. Myers and J. Osteryoung, Anal. Chem., 45, 267 (1973).
RECEIVEDfor review March 9,1976. Accepted June 28,1976. The work was in part by the Zinc Company of Australasia Limited.
Double Potassium Salt of Sulfosalicyl c Acid in Acidimetry and pH Control Richard A. Butler and Roger G. Bates" Department of Chemistry, University of Florida, Gainesville, Fla. 326 1 1
Upon partial neutralization of sulfosalicylic acid, a double potassium salt of the composition KHSs*K2Ss*H20can be prepared, where Ss represents the bivalent anion -0OCC6H3(OH)S03-. The pK2for the carboxyl group has been found to be 2.85, with a variation of less than 0.01 unlt in the range 15 to 45 "C. The double salt is a promising acidimetric standard, as the equivalent weight (550) is high and the pH change near the equivalence point in the titration wlth strong base is sharper than for the titration of potassium hydrogen phthalate. Solutions of this salt are also useful for acldity control near pH 2.8.
Sulfosalicylic acid (2-HOC6H3-1-COOH-5-So3H) is a triprotic acid. The sulfonic acid group is strong ( K > O.l), the and carboxyl group is of moderate strength (K = 1.4 X the phenol group is very weak ( K 4 X in salicylic acid ( I ) ) . In 1857, Mendius (2) reported that the primary and secondary potassium salts of sulfosalicylic acid crystallize as a 1:l double salt. This double potassium salt is of some analytical interest. It can be prepared in pure anhydrous form, is not appreciably hygroscopic, and has a very large equivalent weight (550.655). Hence, weighing errors may be relatively small. Furthermore, the strength of the second acid group, coupled with the essential inertness of the phenol group, permits the double salt to be titrated with high precision to the equivalence point for the carboxyl neutralization. This substance therefore shows promise as a standard for acidimetry. In addition, the double salt is a natural p H buffer, and solutions regulated a t a p H near 2.8 can be prepared by weighing a single pure substance. In both acidimetry and pH control, this double salt appears to be superior to potassium hydrogen phthalate. We have now determined the second dissociation constant of sulfosalicylic acid, making clear these analytical applications.
SECOND DISSOCIATION CONSTANT OF SULFOSALICYLIC ACID The dissociation constant K2 of the carboxyl group was determined by emf measurements of the cell without liquid junction Pd;HZ(g,l atm)lKHSs-KzSs(m), KCl(m) (AgC1;Ag (A) where Ss represents the bivalent sulfosalicylate anion -00CC6H3(OH)S03- and m is molality. The techniques have been described in a number of earlier papers ( 3 , 4 ) .If the activity-coefficient term is represented by the Debye-Huckel
equation, each value of the emf E of cell A for solutions of known molality can be used to calculate a value for the "apparent" pK2 (designated pK2'), inasmuch as the standard emf E" of the cell is known ( 5 ) .The relationship is
(E - E")F m(m - mH) + 2AI1I2 log (1) RT In 10 m mH 1 BA11/2 In Equation 1, A and B are constants of the Debye-Huckel theory, B is the "ion-size parameter", and I is the ionic strength. The quantity pK2' becomes equal to the thermodynamic value (pK2) upon extrapolation to I = 0. The values of the ion-size parameter are chosen by trial to produce the best straight-line extrapolation. The ionic strength is given by I = 5m 2 m ~ (2) pK2' =
+
+
+
+
In view of the appreciable acidic dissociation of the carboxyl group of KHSs, estimates of the hydrogen ion molality (mH) are needed to establish reliable values of the buffer ratio in Equation 1. In principle, mH can be derived from the emf by the Nernst equation, provided that the activity coefficient of HC1 in the buffer-chloride mixtures can be estimated with the required accuracy: -log mH =
( E - E")F + log m RT In 10
+ 2 log r+(HCl)
(3)
EXPERIMENTAL The double salt KHSwK2Ss was prepared by combining sulfosalicylic acid of commercial grade with reagent-grade potassium carbonate in the proportions of 0.75 mol of bicarbonate to 1mol of the acid. The product was recrystallized repeatedly until a sample, dried at 110 "C, assayed close to 100%by titration with strong alkali. The crystallization was effected by cooling an aqueous solution, saturated a t about 70 "C, to 20 "C. In some instances, ethanol was added to the extent of about half the volume of the saturated aqueous solution to increase the yield of the double salt. The lot of salt used had been crystallized seven times. It was titrated with equally satisfactoryresults to the calculated equivalence point (pH 7.6 in 0.05 M solution) or to the first pink color of phenolphthalein. Two weight titrations of the final product gave 100.01 and 100.00%. Recalculation of the analytical data given by Mendius ( 2 )confirms that 1 mol of the double salt contains 2s and 3K and that the compound separates from aqueous solutions as a monohydrate. The water of hydration was easily lost, however, and, in our experience, the dried salt was not appreciably hygroscopic. The salt dissolves readily in water; at room temperature, a saturated solution is about 0.2 M. Potassium chloride was purified by two crystallizations from water. The platinum bases for the hydrogen electrodes were coated with palladium black (6) after trial measurements with platinum black
ANALYTICAL CHEMISTRY, VOL. 48,
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Table I. Electromotive Force ( E , in Volts) of the Cell: Pd; H, (8, 1 atm) (KHSs.K,Ss (ml), KCl (m,) IAgCl; Ag from 10 to 50 "C m ,= m
2 0 "c 0.509 25 0.507 90 0.506 44 0.010 002 0.506 85 0.504 32 0.505 55 0.010 590 0.488 09 0.487 18 0.486 23 0.019 815 0.485 43 0.484 53 0.020 98 0.483 63 0.464 77 0.464 40 0.464 0 1 0.041 64 0.464 47 0.464 05 0.463 70 0.041 97 0.453 30 0.453 19 0.453 23 0.062 67 0.453 03 0.452 99 0.452 99 0.063 24 0.445 46 0.445 26 0.084 84a 0.445 70 0.439 87 0.439 46 0.440 23 0.106 60a a Values of E are average results obtained for two
mol kg"
10 "c
15OC
35 OC 4 0 "C 2 5 "c 30 "C 0.513 94 0.515 41 0.512 55 0.510 61 0.510 93 0.512 28 0.509 56 0.508 58 0.491 94 0.489 1 3 0.490 01 0.490 99 0.487 25 0.488 09 0.488 97 0.486 32 0.466 02 0.466 43 0.465 59 0.465 23 0.465 53 0.465 96 0.464 90 0.465 17 0.453 47 0.453 56 0.453 45 0.453 34 0.453 33 0.453 40 0.453 21 0.453 20 0.444 76 0.444 59 0.445 10 0.444 94 0.438 47 0.438 15 0.439 10 0.438 80 different solutions of the same composition.
Table 11. pK, for Sulfosalicylic Acid from 10 to 50 "C and Related Thermodynamic Constants
r,
OC
t, OC
PK,
PK,
30 2.845 35 2,846 15 40 2.849 20 45 2.855 25 50 2.862 AH" (25 "C)= 257 ri: 55 cal mol-'. ASo (25 "C)= -12.2 * 0.2 cal K-' mol-'. ACpo (25 " C ) = -42 ri: 7 cal K-I mol-'. 10
2.869 2.859 2.852 2.847
gave highly unstable values of the emf, presumably because of reduction of the aromatic ring. The cells were immersed in a water thermostat controlled within 0.01 "C of each of the nine nominal temperatures. Temperatures were measured with a Hewlett-Packard quartz thermometer which had been compared with a calibrated platinum resistance thermometer. The emf was determined with a Hewlett-Packard digital voltmeter checked from time to time against laboratory standards consisting of two saturated standard cells maintained at a controlled temperature.
RESULTS The observed values of the emf of cell A, corrected to a partial pressure of hydrogen of 1atm, are listed in Table I. I t has long been recognized that uncertainties in estimating the activity coefficient in Equation 3 and, hence, the molality of hydrogen ion, lead to appreciable errors in pK when the latter is less than 3 (7). For this reason, a close approximation to the activity coefficient of HCl in the buffer-chloride solutions was sought. It was assumed that yA(HC1) in the solutions composed of potassium salts (chloride and sulfosalicylates) will be nearly the same as the "trace" activity coefficient yktr of HC1 in KCl solutions. From the values of a 1 2 for HC1 in HCl-KC1 mixtures (8),one finds that the trace activity coefficient at 25 OC is 0.782 in 0.1 m KC1 and 0.705 in 0.5 m KCl. These values and other intermediate values derived by interpolation of a12 are closely represented by AI1I2 -log y*tr = - 0.0651 (4) 1 4.1BI1I2 which was used to obtain yk(HCl) for each of the cell solutions at 25 "C. The activity coefficient of HC1 is not very sensitive to temperature changes. Hence, y*(HCl) a t the other temperatures studied was obtained from the values a t 25 "C with the use of the temperature coefficients found by Harned and Hamer (9) for the activity coefficient of HCl(O.01 m ) in KC1 solutions. The values of mH obtained by Equation 3 were used to calculate pK2' by Equation 1. Visual examination as well as
+
1670
45°C
0.516 88 0.513 59 0.492 90 0.489 85 0.466 86 0.466 36 0.453 64 0.453 49 0.444 41 0.437 84
5 0 "c 0.518 37 0.514 89 0.493 8 2 0.490 71
0.466 79
0.453 72 0.453 51 0.444 22 0.437 49
linear regression analysis dictated a choice of B = 6 A as suitable for the evaluation of the intercept, pK2. The standard deviation about regression varied from 0.002 at 25 "C to 0.006 at 15 "C. At a few of the temperatures, these deviations from linearity are larger than those normally expected in welldesigned experiments of this type. They may indicate a slight residual tendency of the sulfosalicylate ions toward reduction a t the palladium electrode. Nevertheless, it was clear from a comparison of data at 25 "C recorded a t the beginning of the temperature series with those a t the end that any irreversibility was of little consequence. The values of pK2 a t the nine temperatures were fitted to a second-degree equation of the form proposed by Harned and Robinson (10) using the method of orthogonal polynomials described by Please (11).The result was as follows: pK2=--
1420.41
T
6.4925
+ 0.015347T
(5)
where T is the thermodynamic temperature in kelvins. The average deviation of the calculated values from the observed pK2 was 0.002 unit. Table I1 lists the values derived from Equation 5, and at the foot of the table are found the standard changes in enthalpy, entropy, and heat capacity associated with the dissociation of the carboxyl group. These quantities are given in calories, where 1cal = 4.184 J. The uncertainties assigned to the thermodynamic functions were calculated from the variance of pK2 by the method of Please ( 1 1 ) .
DISCUSSION The double salt of monopotassium sulfosalicylate and dipotassium sulfosalicylate may prove useful as a standard for acidimetry. It can be prepared in pure form and, once dehydrated, shows little tendency to pick up moisture except from very humid atmospheres. Its equivalent weight (550.665) is high enough to minimize adventitious errors in weighing due to temperature fluctuations, absorption of moisture, and the like. When the double potassium salt is titrated with strong alkali, the pH rises sharply from near pH 4 through the equivalence point. If the concentration of Ss2- a t the equivalence point is 0.05 M, the ~ U calculated H for yss = 1 is 7.77. If ysSis given a more reasonable value of 0.5, the ~ U aHt the equivalence point is found to be 7.62. Accurate titrations can be performed with phenolphthalein as an end-point indicator. The pK2 (2.85) is so low that the buffer capacity a t the equivalence point is considerably smaller than is the case for titrations of potassium hydrogen phthalate (pK2 = 5.4), and the feasibility of the titration is correspondingly greater. The double salt is also useful for pH control. As can be seen in Table 11, pK2 is a t a minimum near 30 "C. Consequently, the pH of solutions of this substance is almost unaffected by changes of temperature in the range 20 to 40 "C. Buffer solutions with pH somewhat below 3 are conveniently prepared
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
by a single weighing of a pure substance, and a buffer ratio very close to unity is assured. The usefulness of some buffer substances such as potassium hydrogen tartrate and, to a lesser potassium hydrogen phthalate is impaired by a tendency'to support mold growth. Although molding in solutions of sulfosalicylates was not specifically investigated, it seems likely that the presence of a phenol group in the sulfosalicylate molecule may provide built-in mold inhibition.
(3)G.D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand., 40,405 (1948). (4)G.D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand., 45,322 (1950). (5)R. G.Bates and V. E. Bower, J. Res. Nat. Bur. Stand., 53, 283 (1954). (6)H. T. S.Britton, "Hydrogen Ions", 4th ed., Vol. I., Van Nostrand, Princeton, N.J., 1956,Chap. 3. (7) R. G , Bates, J. Res. Nat, Bur, Stand,, 47, 127 (1957). (8) H. s. Harned and B. 6. Owen, "The Physical Chemistry of Electrolytic solutions", 36 ed., Reinhold Publishing Corp., New York, N.Y., 1958, p 608. (9) H. S.Harried and W. J. Flamer, J. Am. Chem. Sot., 5 5 , 2194 (1933). (10)H. S. Harned and R . A. Robinson, Trans. Faraday Soc., 36, 973 (1940). (11) N. W. Please, Biochern. J., 56, 196(1954).
LITERATURE CITED
RECEIVEDfor review April 28,1976. Accepted June 24,1976. This work was supported in part by the National Science Foundation under Grant CHE73-05019 A02.
(1) N. Konopik and 0. Leberl, Monatsh. Chem., 80, 655 (1949). (2)0.Mendius, Ann. Chem., 103, 39 (1857).
Semiintegral Electroanalysis: The Shape of Irreversible Neopolarograms Masashi Goto' and Keith B. Bidham* Trent University, Peterborough, Ontario, Canada
The equatlon of the m vs. E curve during the totally Irreversible reduction of an electroactive species is derived: it resembles an irreversible polarogram at a stationary electrode, but is less asymmetric. The effects of ramp-rate and of initial potential are evaluated, and the relationship to linear scan voltammetry is explored. Neopolarogramshave been determined experimentally, using the IO3- and Ni2+ electroreductions, and correlation between theory and experiment is sought by comparing transfer coefficlent values determined from various features of the neopolarograms.
When an electrode in contact with a solution containing a reducible species is polarized by a potential E that becomes progressively and linearly more negative, the curve which results from displaying the semiintegral m of the faradaic current vs. -E is termed a neopolarogram. If the electrode reaction is reversible, the shape of the neopolarogram is identical to that of a classical reversible polarogram (1-3). The usual equation describing this shape
may be rephrased as
Conditions wherein the electrochemical reduction
+
k(E)
Ox Ne--Rd (5) is totally irreversible or quasi-reversible have also been considered (1,2). One of the major advantages of the semiintegral method, that has been exploited by Saveant and coworkers ( 5 ) ,is its ability to analyze electrochemical kinetics without preassuming any particular dependence of the heterogeneous rate constant k ( E ) upon potential. For the present purpose, however, it will be assumed that the rate of reduction is governed by a volmerian,
h ( E ) = h , exp
(sF [E - E , ] )
dependence on potential. If the rate-determining step of the electroreduction mechanism is an initial transfer of n electrons, then a is the transfer coefficient of that step. The shape of such irreversible neopolarograms is not independent either of Eo or of u , so that it is impossible to write an equation of the form m = f ( E )in which the function f is independent of the starting potential and the ramp-rate. However, it is possible to derive an expression of the form f(m,i,E)= 0, relating potential to both the faradaic current and its semiintegral, and in which neither Eo or u appears. Such a relationship (1, 2 ) is (7)
where m is the semiintegral ( 4 ) ,d-l12 i/dt-lI2, of the faradaic current i, m, is an abbreviation for the constant
NAFC d m,
(3)
and other symbols have the significance commonly accorded them in electroanalytical chemistry. Note that the shape of a reversible neopolarogram depends on neither the initial potential Eo nor the ramp-rate u , the two constants that jointly determine how the potential
E = Eo - vt
(4)
changes with time. 1 Present address, Department of Applied Chemistry, Faculty of Engineering, Nagoya University, Chikusa-ku, Nagoya, Japan.
and has been verified experimentally. Though it certainly holds when the potential varies with time according to the linear relation 4, the validity of Equation 7 is not restricted to any particular temporal dependence of potential (6). Equation 7 cannot be said to describe the shape of an irreversible neopolarogram; what it does is to provide an interrelationship between the shape of a neopolarogram and the shape of a linear-potential-scan voltammogram. The object of the present study is to produce and test an equation that, in fact, does describe the shape of an irreversible neopolarogram by giving the value of m as an explicit function, m = f(E,Eo,u),of the variable E and the constants Eo and v. If Eo is sufficiently positive, then its precise value is irrelevant. We shall see that, in this circumstance, the equation that relates m and E is
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