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The boric acid-borate-mannitol system
3602
Notes
Acknowledgement-Our thanks are due to the Ministry of Education, Government of India, for the grant of Research Scholarship to one of us (U.S.C.) and to Principal R. M. Advani for providing research facilities.
Department of Chemistry Molariya Regional Engineering College Jaipur India
R. S. S A X E N A U. S. C H A T U R V E D I
J. inorg,nucl.Chem.,1971,Vol.33, pp. 3602to 3604. PergamonPress. Printedin Great Britain
The boric acid-borate-mannitoi system* (Received 16 December 1970) A l~VIEW of the literature on the boric acid-mannitol system indicates that definitive work remains to be done. All of the studies have either gone astray in interpretation or are deficient in one or more of the experimental requirements of calibration of the hydrogen ion concentration, temperature and ionic strength control, and accuracy. Nickerson, for example, has recently attributed the pH effects of mannitol in boric acid solutions and titration results to the formation o f a 1 : 1 borate-mannitol complex with the boric acid existing as a dimeric species [1]. Campbell has criticized the treatment and contends that the data are consistent with the formation of a 1:2 complex [2]. Nickerson has published additional titration results at higher concentration, which he claims support the evidence at lower pH in favor of a 1 : 1 complex [3]. The dimeric boric acid was not mentioned. The present note will support Campbell's critique so far as it goes but will also direct attention to a real difficulty which exists for the system. The question at issue is the relative importance of two equilibria which may be written, neglecting the role of water, as HB+P = BP-+H ÷
(1)
HB+2P = BP~-+H +
(2)
where HB is boric acid and P is mannitol. The origin of Nickerson's error in interpreting his low pH data has been correctly identified by Campbell[2]. It may be added that writing the "reactions" or "equilibrium constants" which imply the reactions [ 1,3] HB + nP = BPnHB + nP = H + is disastrous to the interpretation. Neither mass nor charge is conserved and any attempt to correlate observation with equilibrium constants for these inequalities is meaningless. Another example of misinterpretation is recent work by Nazarenko and Ermak, who postulate a large dependence of the dielectric constant on mannitol concentration which they remove by an erroneous extrapolation, forgetting that the mannitol is a reactant in the equilibrium [4]. The literature data for the system may be grouped into two sets in which Reaction (1) appears (I) *Based on work performed under the auspices of the U.S. Atomic Energy Commission. 1. R. F. Nickerson, J. inorg, nucl. Chem. 30, 1447 (1968). 2. G.W. Campbell, Jr.,J. inorg, nucl. Chem. 31, 2625 (1969). 3. R. F. Nickerson, J. inorg, nucL Chem. 32, 1400 (1970).
Notes
3603
to be, or (II) not to be, negligible. The existence of reaction (2) and approximate values for equilibrium quotients are well established. Set !. If Reaction (2) is the only reaction, the hydrogen ion concentration is equal to the concentration of the anion, BP2-, in solutions of mannitoi and boric acid (no other acid) and the equilibrium concentrations will conform to the relation log Ks = 2 log [H +] -- log [HB] - n log [P]
(3)
where brackets denote molarity, n is 2, and the value of K~ includes the activity coefficients. The equilibrium is far to the left and the concentration of HB and P are essentially unchanged by reaction. If the acid species HBP exists, it does not affect the correlation when the boric acid and mannitol concentrations are less th n 0"1 M[5]. All the d a t a [ l , 6 - 8 ] in which [HB] or [P] were constant and the pH was less than 5.4 were placed on composite plots of log [H ÷] vs. log [P] or log [HB]. The observed values of n were close to 2 or slightly larger. Displacements in log [H ÷] between independent studies indicated large inconsistencies in the methods of [H ÷] scale calibration. There was no evidence for appreciable concentrations of the acid species, HBP2 [9]. From these data alone one would conclude that the value of K2 at low ionic strength (< 10 -3) is in the range 5-9 x 10-5 at temperatures presumed to be somewhere near 25°. There was no evidence for Reaction (1) with the exception of Nickerson's data[I] which show deviations (n less than two) at low mannitol concentrations corresponding to a value for K1 of ca. 3 × 10-7. Set !I. Other workers claim that reaction (1) contributes significantly to [H+]. Antikainen has given values for K~ and K2 of 6.05 x 10~ and 4-38 x 10-5, respectively, at zero ionic strength[10]. His computational method seems not to be correct for the resolution of two constants, however, since the values proved to be inconsistent with Antikainen's own observation that the average value of n (Equation 3) is 1.81. Plots of log [H ÷] vs. log [P] at constant [HB] calculated with these constants are markedly curved, deviating widely from those of Set I. Antikainen's single value (Kn,o) [ 11] taken to be K2, gives fair agreement with the data of Mehta and Kantak [8] in the high P concentration range (0.11.0 M). If indeed the average value of n is about 1.8, one may derive K~ and K2 values of 5.9 x 10-r and 4-3 x 10-5 from Antikainen's single value (pKn,o) of 4.303[11]. The H ÷ concentrations calculated with these constants are again not in agreement with Set I values at low concentrations of P. The most credible work On the system has been done by Vermaas who derived values of ca. 2.5 x 10-e and 1.1 × 10-4 for K~ and Kz near 18° from titrations with KBO2 [5]. No corrections were applied for ionic strength (0-025-0.095). Assuming heats of reaction o f - 1 4 . 9 and --19.4 kcal for Reactions (1) and (2), respectively (i.e. - 4 . 5 kcal mole -~ mannitol reacting with borate ion)HI, and a 12 per cent ionic strength effect[12], one obtains 1.2× 10-e and 4-4x 10-s for K~ and K2 at 25 ° and infinite dilution. The latter value falls near the range of Set I values but a plot according to Equation (3) is not linear because of the large contribution of [H ÷] from Reaction (1) at low concentrations of mannitol. The average value of n is about 1.5 in the range 0.01-0.1 M mannitol. A n uncertainty of an order of magnitude thus exists in the value of K1 from the two sets of data. If Reaction (I) is important, it will be evident at low mannitol concentration and Nickerson's titration data [3] become of interest. We consider in detail his solution at pH 8 containing 0"910 mole N a O H / mole boric acid, 1M total boric acid, and 1 M total mannitol. The appreciable concentrations of polyborate ions expected under these conditions are calculable with the constants given by Ingri [ 13]. An 4. 5. 6. 7. 8. 9.
10. 11. 12. 13.
V . A . Nazarenko and L. D. Ermak, Zh. neorg. Khim. 12, 643 (1967); ibid. 12,2051 (1967). N. Vermaas, Recl. tray. chim. 51, 67 (1932). H . Z . Schafer, Z. anorg, allg. Chem. 247, 96 (1941). S. D. Ross and A. J. Catotti, J. Am. chem. Soc. 71, 3563 (1949). S. M. Mehta and K. V. Kantak, J. Am. chem. Soc. 74, 3470 (1952). In reviewing this Note, Dr. G. W. Campbell, Jr. pointed out the independent nmr evidence against appreciable concentrations of HBP2 obtained by T. P. Onak, H. Landesman, R. E. Williams and I. Shapiro, J. phys. Chem. 63, 1533 (1959). P.J. Antikainen, Acta chem. scand. 9, 1008 (1955). P. J. Antikainen, Ann. acad. Sci, Fennicae A II, 8 (1954). C.W. Davies, lonAssociation Chap. 3. Butterworth, Washington, D.C. (1962). N. Ingri, Acta chem. scand. 16, 439 (1962).
3604
Notes
approximation to [OH-] of 1.4 x 10-OM is obtained by assuming the H + activity to be antiiog ( - p H ) , a H + activity coefficient of 0.8114], and an ionization constant for water of I '74 × 10-~4[15]. By itemtion with an initial guess for the boric acid concentration, the Ingri constants give the following concentrations for the important boron species other than those containing mannitoi: 0.0640M B(OH)s, 0.0166M B(OH)4-, 0-0116M B3Os(OH)4- and 0-0013 M B4Os(OH)42-. The total acid equivalence remaining in these ions is 0.09 M as required by the titration. The total molarity of excess electrons (charge x molarity) in the anions is 0.03, leaving 0'88 M to be accounted for by borate-mannitol anions, We see, as did Nickerson [3], that the ion BP2- could account for 0"5 M at most, if all the mannitol reacted with B(OH)C. Another borate-mannitol anion is required. If the ion is BP-, its concentration must be consistent with the following: [P] + [BP-] + 2[BPc] = 1 M [BP-] + [BPz-] = 0.88 M [H+] [BP2 - ] K~---- [ H a ] [ p ] 2 . The equations are solved by introducing the [H ÷] and [HB] values from above and the approximate value from Vermaas[5] for Ks, corrected to 6.65 x 10-5 for ionic strength 0.9111]. The resulting concentrations are 0.020M P, 0.740M BP- and 0-140M BP2-. The value of K, calculable from these data is 4.6 x 10-e or 3"0 × 10-e at infinite dilution which, considering the uncertainties, is not far from the value of 1-2 x 10-8 estimated from Vermaas' data. The discrepancy could possibly be explained by a combination of factors: (1) carbon dioxide was not excluded from the titration; (2) the large heat of reaction was not removed; (3) H + concentration is not related in the assumed manner to the pH reading; (4) the activity coefficients do not conform to the empirical estimates; and (5) there may be a large salt effect on the mannil~oi. In conclusion, Nickerson's titration could be consistent with Vermaas' values for the constants, but there remains a serious disagreement between the data of Sets I and II and a more thorough study is needed.
Chemistry Division Argonne National Laboratory Argonne, Illinois 60439 U.S~4 .
L. B. M A G N U S S O N
14. H. S. Harned and B, B. Owen, The Physical Chemistry of Electrolytic Solutions 2nd Edn. p. 547 Reinhold, New York (1950). 15. Ref. [14]. p. 487.,
J. inorg,nucl.Chem.,1971,Vol.33, pp. 3604to 3608. PergamonPress. PrintedinGreat Britain
Hydrated oxalates of the yttrium group rare earth elements and scandium (First received 15 January 1971 ; in revised form 18 March 1971) THE EXISTENCEof rare earth oxalates with various numbers of waters of hydration have been clarified through numerous synthesis studies and thermal analysis. However, in the ordinary procedure for precipitating rare earth oxalates, the temperature usually was not kept constant and the crystallization process did not proceed without considerable changes in concentrations of both reagent anffprecipitant and as a result, oxalates prepared by usual procedures were, in most cases, mixtures. The poor reproducibility of various physicochemical measurements undoubtedly results from the use of impure materials thus obtained. In the present study, a method was introduced whereby precipitation proceeds slowly at constant temperatures. This is accomplished through the use of a two phase system.
Notes
Acknowledgement-Our thanks are due to the Ministry of Education, Government of India, for the grant of Research Scholarship to one of us (U.S.C.) and to Principal R. M. Advani for providing research facilities.
Department of Chemistry Molariya Regional Engineering College Jaipur India
R. S. S A X E N A U. S. C H A T U R V E D I
J. inorg,nucl.Chem.,1971,Vol.33, pp. 3602to 3604. PergamonPress. Printedin Great Britain
The boric acid-borate-mannitoi system* (Received 16 December 1970) A l~VIEW of the literature on the boric acid-mannitol system indicates that definitive work remains to be done. All of the studies have either gone astray in interpretation or are deficient in one or more of the experimental requirements of calibration of the hydrogen ion concentration, temperature and ionic strength control, and accuracy. Nickerson, for example, has recently attributed the pH effects of mannitol in boric acid solutions and titration results to the formation o f a 1 : 1 borate-mannitol complex with the boric acid existing as a dimeric species [1]. Campbell has criticized the treatment and contends that the data are consistent with the formation of a 1:2 complex [2]. Nickerson has published additional titration results at higher concentration, which he claims support the evidence at lower pH in favor of a 1 : 1 complex [3]. The dimeric boric acid was not mentioned. The present note will support Campbell's critique so far as it goes but will also direct attention to a real difficulty which exists for the system. The question at issue is the relative importance of two equilibria which may be written, neglecting the role of water, as HB+P = BP-+H ÷
(1)
HB+2P = BP~-+H +
(2)
where HB is boric acid and P is mannitol. The origin of Nickerson's error in interpreting his low pH data has been correctly identified by Campbell[2]. It may be added that writing the "reactions" or "equilibrium constants" which imply the reactions [ 1,3] HB + nP = BPnHB + nP = H + is disastrous to the interpretation. Neither mass nor charge is conserved and any attempt to correlate observation with equilibrium constants for these inequalities is meaningless. Another example of misinterpretation is recent work by Nazarenko and Ermak, who postulate a large dependence of the dielectric constant on mannitol concentration which they remove by an erroneous extrapolation, forgetting that the mannitol is a reactant in the equilibrium [4]. The literature data for the system may be grouped into two sets in which Reaction (1) appears (I) *Based on work performed under the auspices of the U.S. Atomic Energy Commission. 1. R. F. Nickerson, J. inorg, nucl. Chem. 30, 1447 (1968). 2. G.W. Campbell, Jr.,J. inorg, nucl. Chem. 31, 2625 (1969). 3. R. F. Nickerson, J. inorg, nucL Chem. 32, 1400 (1970).
Notes
3603
to be, or (II) not to be, negligible. The existence of reaction (2) and approximate values for equilibrium quotients are well established. Set !. If Reaction (2) is the only reaction, the hydrogen ion concentration is equal to the concentration of the anion, BP2-, in solutions of mannitoi and boric acid (no other acid) and the equilibrium concentrations will conform to the relation log Ks = 2 log [H +] -- log [HB] - n log [P]
(3)
where brackets denote molarity, n is 2, and the value of K~ includes the activity coefficients. The equilibrium is far to the left and the concentration of HB and P are essentially unchanged by reaction. If the acid species HBP exists, it does not affect the correlation when the boric acid and mannitol concentrations are less th n 0"1 M[5]. All the d a t a [ l , 6 - 8 ] in which [HB] or [P] were constant and the pH was less than 5.4 were placed on composite plots of log [H ÷] vs. log [P] or log [HB]. The observed values of n were close to 2 or slightly larger. Displacements in log [H ÷] between independent studies indicated large inconsistencies in the methods of [H ÷] scale calibration. There was no evidence for appreciable concentrations of the acid species, HBP2 [9]. From these data alone one would conclude that the value of K2 at low ionic strength (< 10 -3) is in the range 5-9 x 10-5 at temperatures presumed to be somewhere near 25°. There was no evidence for Reaction (1) with the exception of Nickerson's data[I] which show deviations (n less than two) at low mannitol concentrations corresponding to a value for K1 of ca. 3 × 10-7. Set !I. Other workers claim that reaction (1) contributes significantly to [H+]. Antikainen has given values for K~ and K2 of 6.05 x 10~ and 4-38 x 10-5, respectively, at zero ionic strength[10]. His computational method seems not to be correct for the resolution of two constants, however, since the values proved to be inconsistent with Antikainen's own observation that the average value of n (Equation 3) is 1.81. Plots of log [H ÷] vs. log [P] at constant [HB] calculated with these constants are markedly curved, deviating widely from those of Set I. Antikainen's single value (Kn,o) [ 11] taken to be K2, gives fair agreement with the data of Mehta and Kantak [8] in the high P concentration range (0.11.0 M). If indeed the average value of n is about 1.8, one may derive K~ and K2 values of 5.9 x 10-r and 4-3 x 10-5 from Antikainen's single value (pKn,o) of 4.303[11]. The H ÷ concentrations calculated with these constants are again not in agreement with Set I values at low concentrations of P. The most credible work On the system has been done by Vermaas who derived values of ca. 2.5 x 10-e and 1.1 × 10-4 for K~ and Kz near 18° from titrations with KBO2 [5]. No corrections were applied for ionic strength (0-025-0.095). Assuming heats of reaction o f - 1 4 . 9 and --19.4 kcal for Reactions (1) and (2), respectively (i.e. - 4 . 5 kcal mole -~ mannitol reacting with borate ion)HI, and a 12 per cent ionic strength effect[12], one obtains 1.2× 10-e and 4-4x 10-s for K~ and K2 at 25 ° and infinite dilution. The latter value falls near the range of Set I values but a plot according to Equation (3) is not linear because of the large contribution of [H ÷] from Reaction (1) at low concentrations of mannitol. The average value of n is about 1.5 in the range 0.01-0.1 M mannitol. A n uncertainty of an order of magnitude thus exists in the value of K1 from the two sets of data. If Reaction (I) is important, it will be evident at low mannitol concentration and Nickerson's titration data [3] become of interest. We consider in detail his solution at pH 8 containing 0"910 mole N a O H / mole boric acid, 1M total boric acid, and 1 M total mannitol. The appreciable concentrations of polyborate ions expected under these conditions are calculable with the constants given by Ingri [ 13]. An 4. 5. 6. 7. 8. 9.
10. 11. 12. 13.
V . A . Nazarenko and L. D. Ermak, Zh. neorg. Khim. 12, 643 (1967); ibid. 12,2051 (1967). N. Vermaas, Recl. tray. chim. 51, 67 (1932). H . Z . Schafer, Z. anorg, allg. Chem. 247, 96 (1941). S. D. Ross and A. J. Catotti, J. Am. chem. Soc. 71, 3563 (1949). S. M. Mehta and K. V. Kantak, J. Am. chem. Soc. 74, 3470 (1952). In reviewing this Note, Dr. G. W. Campbell, Jr. pointed out the independent nmr evidence against appreciable concentrations of HBP2 obtained by T. P. Onak, H. Landesman, R. E. Williams and I. Shapiro, J. phys. Chem. 63, 1533 (1959). P.J. Antikainen, Acta chem. scand. 9, 1008 (1955). P. J. Antikainen, Ann. acad. Sci, Fennicae A II, 8 (1954). C.W. Davies, lonAssociation Chap. 3. Butterworth, Washington, D.C. (1962). N. Ingri, Acta chem. scand. 16, 439 (1962).
3604
Notes
approximation to [OH-] of 1.4 x 10-OM is obtained by assuming the H + activity to be antiiog ( - p H ) , a H + activity coefficient of 0.8114], and an ionization constant for water of I '74 × 10-~4[15]. By itemtion with an initial guess for the boric acid concentration, the Ingri constants give the following concentrations for the important boron species other than those containing mannitoi: 0.0640M B(OH)s, 0.0166M B(OH)4-, 0-0116M B3Os(OH)4- and 0-0013 M B4Os(OH)42-. The total acid equivalence remaining in these ions is 0.09 M as required by the titration. The total molarity of excess electrons (charge x molarity) in the anions is 0.03, leaving 0'88 M to be accounted for by borate-mannitol anions, We see, as did Nickerson [3], that the ion BP2- could account for 0"5 M at most, if all the mannitol reacted with B(OH)C. Another borate-mannitol anion is required. If the ion is BP-, its concentration must be consistent with the following: [P] + [BP-] + 2[BPc] = 1 M [BP-] + [BPz-] = 0.88 M [H+] [BP2 - ] K~---- [ H a ] [ p ] 2 . The equations are solved by introducing the [H ÷] and [HB] values from above and the approximate value from Vermaas[5] for Ks, corrected to 6.65 x 10-5 for ionic strength 0.9111]. The resulting concentrations are 0.020M P, 0.740M BP- and 0-140M BP2-. The value of K, calculable from these data is 4.6 x 10-e or 3"0 × 10-e at infinite dilution which, considering the uncertainties, is not far from the value of 1-2 x 10-8 estimated from Vermaas' data. The discrepancy could possibly be explained by a combination of factors: (1) carbon dioxide was not excluded from the titration; (2) the large heat of reaction was not removed; (3) H + concentration is not related in the assumed manner to the pH reading; (4) the activity coefficients do not conform to the empirical estimates; and (5) there may be a large salt effect on the mannil~oi. In conclusion, Nickerson's titration could be consistent with Vermaas' values for the constants, but there remains a serious disagreement between the data of Sets I and II and a more thorough study is needed.
Chemistry Division Argonne National Laboratory Argonne, Illinois 60439 U.S~4 .
L. B. M A G N U S S O N
14. H. S. Harned and B, B. Owen, The Physical Chemistry of Electrolytic Solutions 2nd Edn. p. 547 Reinhold, New York (1950). 15. Ref. [14]. p. 487.,
J. inorg,nucl.Chem.,1971,Vol.33, pp. 3604to 3608. PergamonPress. PrintedinGreat Britain
Hydrated oxalates of the yttrium group rare earth elements and scandium (First received 15 January 1971 ; in revised form 18 March 1971) THE EXISTENCEof rare earth oxalates with various numbers of waters of hydration have been clarified through numerous synthesis studies and thermal analysis. However, in the ordinary procedure for precipitating rare earth oxalates, the temperature usually was not kept constant and the crystallization process did not proceed without considerable changes in concentrations of both reagent anffprecipitant and as a result, oxalates prepared by usual procedures were, in most cases, mixtures. The poor reproducibility of various physicochemical measurements undoubtedly results from the use of impure materials thus obtained. In the present study, a method was introduced whereby precipitation proceeds slowly at constant temperatures. This is accomplished through the use of a two phase system.