Association equilibrium in the system Ni2+H3PO3H2O at 25°C

J. inorg, nucl.Chem., 1970,Vol. 32. pp. 967 to 976. PergamonPress. Printedin Great Britain

ASSOCIATION

EQUILIBRIUM IN THE Ni2+-H3PO3-H20 AT 25°C

SYSTEM

M. E B E R T and J. E Y S S E L T O V A D e p a r t m e n t of Inorganic C h e m i s t r y of the Faculty of Science, Charles University, Prague. Czechoslovakia

(First received 12 May 1969; in revised fi~rm 18 August 1969) A b s t r a c t - T h e equilibrium between the nickel cation and phosphite anion was studied on the basis of potentiometric p H m e a s u r e m e n t in a q u e o u s solution. T h e p r o c e d u r e selected to s t u d y the equilibria was subjected to statistical analysis, from which the experimental and calculatory conditions of its applicability were concluded. T h e association c o n s t a n t for the p a n i c l e NiH2PO:~ + was found to be K, = 28 _+6, for the particle N i H PO:~ this is K2 = (3.6 ± 2.6) . 103. INTRODUCTION

THE SYSTEMS bivalent metal-phosphite were studied in dilute aqueous solutions by means of potentiometric pH measurement in the case of bivalent zinc[l], vanadium[2] and vanadyl[3]. In the case of vanadium and zinc, the pH of mixtures with a preselected ratio of the respective metal, phosphorous and perchloric acids or of sodium hydroxide was measured, while in the case of vanadyl, potentiometric titration of a solution of phosphorous acid containing vanadyl ions with sodium hydroxide was involved. The selection of complex particles for calculating the constants is governed in these studies by the general scheme reported by Frei [4]. The procedure involved in the calculation has only been described in the case of zinc phosphites [1], being based on a system of relations designed for analytical concentrations of individual components of the system, dissociation constants of phosphorous acid and association constants of the ion pairs considered. None of the cited studies present a statistical assessment of the experimental and calculatory conditions of the procedure selected to study the association equilibria. The importance of such an analysis for judging the reliability and accuracy of association constants is confirmed by work of Rydberg e t aL[5-8], especially in the case where a complicated method of calculation is used and a large number of particles are considered. The most important one of these studies is an analysis by Rydberg[5] of results obtained with a number of systems from extraction equilibria by means of the ligand number method, Leden method and 1. 2. 3. 4. 5. 6. 7. 8.

V. Frei, J. Podlahovfi and J. Podlaha, Zh. neorg. Khim. 10, 1690 (1965). J. Podlaha, Colin Czech. Chem. Commun. 31, 7 (1966). J. P o d l a h a and J. Silha, Colin Czech. Chem. Commun. 32, 3760 (1967). V. Frei, Z. phys. Chem. (Leipzig) 223,289 (1963). J. Rydberg,,4cta chem. scand. 14, 157 (1960). J. R y d b e r g a n d J . C. Sullivan, Acta chem. scand. 13, 2057 (1959). J. C. Sullivan, J. R y d b e r g and W. F. Miller, Acta chem. scand. 13, 2023 (1959). J. Rydberg, Acta chem. scand. 15, 1723 ( 1961). 967

968

M. EBERT and J. EYSSELTOV,~

the two-parameter method [9, 10]. Although all the consecutive stability constants of these systems were calculated by means of these methods and the results agreed well with one another, Rydberg proved by using the least squares method [6] that in the majority of cases, only the products of two and sometimes of three of these consecutive constants but not their individual values may be regarded as being reliable. The criterion of reliability of the constants obtained is the condition

a--~(a) > 0

(1)

where a is either the required constant proper or an auxilliary parameter, related to the value of this constant by means of a simple functional relationship, sO(a) is the error of this quantity. In the present study we wish to determine the association constants of the particles NiH2POa + and NiHPO3 in an aqueous solution on the basis of pH measurements at the titration of phosphorous acid by sodium hydroxide in the presence of nickel(| |)-ions and to carry out a statistical analysis of the procedure used. EXPERIMENTAL

Reagents and analytical methods Phosphorous acid HzPOa was prepared by hydrolysing bidistilled phosphorous chloride (Lachema, purity not declared). The product contained, by analysis, 98-99 per cent HaPOz. Nickel perchlorate Ni(CIO4)~. 5H20 was prepared by dissolving excess basic nickel carbonate (pure, Lachema) in 40 per cent HCIO4 (reagent-grade, Xenon Lodz). After filtration to remove the excess carbonate the product was recrystallised and contained 99.0 to 99.5 per cent Ni(ClO4)2.5H20. The substances prepared were analysed by gravimetric means, the concentration of solution used in titrations was checked by volumetric methods. Nickel was determined by titration with complexone 111 using murexide as indicator[l 1], its gravimetric analysis was performed by means of electroanalysis [12]. Phosphorus was determined by manganometric titration[13] and by a gravimetric procedure after separating the metal in the form of Ni(OH)z and oxidation to phosphate, the product weighed being MgzP2OT[12]. Perchlorate was quantitatively determined by a gravimetric method in the form of nitrone perchlorate [ 14]. The 0.! N sodium hydroxide solution used for the titrations was prepared in the conventional manner [ 12] from sodium hydroxide (reagent-grade, Lachema), boiled bidistilled water and perchloric acid (reagent-grade, Xenon Lodz) so as to make the solution 0'2 M in NaClO4 at the same time. Its exact concentration was checked by titration of oxalic acid (reagent-grade, Lachema).

pH measurement Potentiometric pH measurements were carried out with an instrument made by the Radiometer Co., Copenhagen, with a cell consisting of a high-resistance glass and saturated calomel electrode. The 9. F. J. C. Rossotti and H. Rossotti, The Determination of Stability Constants and Other Equilibrium Constants in Solution. McGraw-Hill, New York (1961). 10. S. Fronaeus, The Determination of Formation Constants of Complexes, In Technique of Inorganic Chemistry (Edited by H. B. Jonassen and A. Weissberger), Vol. 1. lnterscience, New York (1963). 11. R. P~ibil, Komplexony v chemick6 analyse (Complexones in Chemical,4nalysis), N(~SAV, Praha (1957). 12. O. Tomi6ek, Kvantitativnianalysa(Quantitative,4nalysis), SZN, Praha (1958). 13. J. Nassler, Colin Czech. Chem. Commun. 28, 3424 (1963). 14. A. Jilek and J. Kota, Vfi2kovfi analysa a elektroanalysa (Gravimetric Analysis and Electroanalysis) III., S N T L Praha (1956).

Equilibrium Ni2+-H.~POa-H20

969

cell was calibrated with a c o m m e r c i a l buffer made by the R a d i o m e t e r Co., C o p e n h a g e n IpH = 6.458) and a s a t u r a t e d p o t a s s i u m h y d r o g e n tartarate solution (pH = 3.555). T h e solutions w e re titrated in a special double-wall vessel t e m p e r e d by m e a n s of the H i i p p l e r ultrathermostat. All m e a s u r e m e n t s were carried out at an ionic strength c o r r e s p o n d i n g to 0-2 M NaC104. Solutions titrated were 5. 10 -~ M Ni(CIO4)2 + 5 . 10 -3 M H3PO.~ (A), I . 10 -2 M NitCIO4)., + 5 . 10-:~ M H:~PO:~ (B) and 5. 10 -:~ M H:,PO~ (C). The results are s u m m a r i z e d in Ta bl e I. Table 1. Titrations A, B, C [ I t ] (mol. I ') c.~a • 10 4 (tool. l -l)

A

B

0"00 3.98 7.94 11-9 15.7 19.6 23-4 27.2 31 "0 34.7 38.5 42.1 45.8 49.4 53.0 56-6 60.2 63.7 67'2 70.6 74.1 77.5 80.9 84.2 87.6 90.9 94.2 97.5 101 104 107

6 . 1 0 . 1 0 -3 4-49 3"67 3.02 2.95 2.24 2.00 1.46 1.07 6.46. 10-4 2.57 5 . 0 8 . 1 0 -'~ 2.07 1.20 7-36. 10-6 5.37 4.07 3.02 2.24 1.79 1.35 9.55. 10-7 6.92 4.79 2.88 2.02 1.38 1.15 1-01 8.91 . 10 -s 8.51

4"37. 10- 3 3"96 3"61 3"22 2'90 2'58 2"19 1 "82 1 "53 1'18 8 " 7 5 . 1 0 -4 4'08 1 "09 1"12. 10 r, 5"62 10 6 3"23 2"29 1"57 1"18 8"22 10-7 6"31 4"41 2"88 1 "90 1 "00 3-80 10 -x 2.29

METHOD

OF

1-90 1.70 1.66 1.62

C 3"98 . 10 -a

3'82 3"51 3"24 3"16 2'79 2'29 1'86 1'41 I '05 6"38. 10-4 2"90 2"90. 10-~ 6"10. 10-" 3"09 I "95 1"38 1 "02 7"41 . 10-7 5"76 4"47 3"24 2"46 1"70 1"10 5' 52. 10 -~ I "44 1"53.10 -' ° 4"47. 10-" 2'48 1 '78

CALCULATION

Factors of importance to the calculation of association constants of particles in a specified system include choosing of the method of calculation which is bestsuited under the experimental conditions studied, selection of possible ion pairs under the respective experimental conditions and statistical evaluation of the error involved in the calculation procedure employed. By evaluation of the titration A the treatment reported by Schwarzenbach

970

M. E B E R T and J. E Y S S E L T O V A

et ai.[15-17] was used. The titration curve is described by means of two so called apparent dissociation constants here, for which the following relations apply in the case under consideration:

[H] ( [NiH2PO3] + [H2PO3] ) fff~ ---[H3PO3]

~

[H] ([NiHPO3] + [HPO3]) = [NiH2PO3] + [H2POz]

(2) (3)

(ion charges have been omitted for the sake of clarity, square brackets indicate the concentrations of the respective particles). The basic prerequisite for application of this calcultion procedure is a constant concentration of the metal ion. We used the linear regression technique[18] which, differing from the graphical procedure used by Schwarzenbach's school [ 16, 17], permits the errors of the parameters required to be determined, in order to calculate the dissociation constants of phosphorous acid [H] [H2PO3] [HaPO3]

(4)

[H] [HPO3] 5g'~2= [H2PO3]

(5)

~1

=

and

from the titration C and the apparent dissociation constants ~'1, ~ ' from the titration A; to this purpose the relation

1 1 y = --~-~1x + ~,~2resp. y = -- X---~x+ ~Z~

(6)

where y=

X~

[H] (ca-- (cNa+ [ H ] ) )

2Cp-- (CNa+ [HI) [H]2(CNa+ [HI) 2Cv-- (cNa + [H] )

(Ca is the analytical concentration of the phosphite, CNais the analytical concentration of the hydroxide added) was used. The procedure of calculating the dissociation constants from pH-metric titration excludes in principle the possibility of satisfying the demand of constant metal ion concentration, since in general this concentration varies with any interaction 15. 16. 17. 18.

G. G. G. A.

Schwarzenbach, Heir. chim. Acta 33, 947 (1950). Schwarzenbach, A. Willi and R. O. Bach, Heir. chim.Acta 31, 1303 (1947). Schwarzenbach and H. Ackermann, Helv. chim. Acta 31, 1029 (1948). Hald, Statistical Theory with EngineeringApplications. Interscience, New York (1952).

Equilibrium Ni2÷-H.~PO~-H~O

971

taking place in the system studied. Evidently the true metal ion concentration varies in the course of the titration within the limits given by the conditions [Ni] = cNi

(7)

(cNi is the analytical concentration of the nickel) and [Ni] = cNi - Cp

(8)

which are used as approximation to this value by Schwarzenbach et al.[16, 17] and Saini et al.[ 19], respectively, when a final metal excess is used (scheme 1). In principle, however, validity of the relation (7) could be achieved during the entire titration only with an infinite metal excess, when the relation (8) would be satisfied at the same time. Therefore, the metal ion concentration cannot be calculated accurately with a finite metal excess and a suitable approximation to this value and its error must be selected. The Schwarzenbach approximation (7) approximation.

--T

__

(7)

i

(9)

(8)

probable course of frue me#a/ ion concentrahon

fixation cour~

Scheme 1, explaining the approximation to the nickelous ion concentration [Ni] and its errors in the calculation of association constants.

will be better suited to the calculation, the greater the metal excess employed. Likewise the Saini approximation (8) can be used in this case, since the difference of metal ion concentration employed is small compared with the overall metal concentration. With respect to the final value of equilibrium constants, differing from zero, we believe that the most suitable approximation for the metal ion concentration is the condition [Ni] --

2CNi - -

Cp

2

19. G. Saini, G. Ostacoli, E. Campi and N. Cibrario, Gazz. chim. ital. 41,242 ( 1961 ).

(9)

972

Charge dispersion studies I0¢

13Ocs

5-0 A

Z p¢J hi

o

0 ~ I '0

0.5

zo

3b

J

=

40

50

PROTON

60

70

80

ENERGY (MeV)

Fig. 1. Excitation functions of 129Cs and 13°Cs.

I0.0

132Cs

E Z

_o I,t~l ([}

0n,tj

i31Cs

1.0

0.1

2~)

~o

,io

r;o

do

~

do

~o

I00

PROTON ENERGY (MeV)

Fig. 2. Excitation functions for ~31Cs and '3zCs.

by these authors, the maxima of the excitation functions of different products have been plotted against their neutron-to-proton ratios, N[Z, in Fig. 7. Also included in the figure are results for zasU [6], and 2ZZTh[7] and 233U[9]. As can be seen from Fig. 7, the energies at which the maxima of the excitation functions of various products are reached increase with decreasing N/Z values of the products. It is further noted that the variation of these energies with the neutron-to-proton ratio of the products is not the same for all targets. Although no unique correlation can yet be established for data from different targets, it is obvious that the peak of the excitation function of a given product occurs at a lower energy for a target of lower N/Z. This is further verification of this trend pointed out by Tomita and Yaffe [9].

973

Equilibrium N i 2 + - H a P O 3 - H 2 0

tions studied as ionic associates[27] and thus cannot form structures more complicated than binary ones [28]. T h e calculation of the errors involved was based on the law of error additivity [ 18]: when the quantity y is a function of n variables x~, x2. . . . . x, y = F ( X l , x2 . . . . .

(12)

xn)

the following applies to its error: n

s~(Y)=

E

/OF,, 2

)1/2

~xi) sC2(x')J'

(13)

i=l

where s~(x~) is the error of the quantity x~ expressed in the same manner as the error ~:(y). RESULTS

T h e dissociation constants of phosphorous acid X~ and Y{2 and the apparent dissociation constants from the titration A ~ and Yt~ as well as their standard deviations are presented in Table 2. This table also includes correlation coefficients r which prove the justification of utilisation of the linear regression technique [ 18]. Table 2. Dissociation c o n s t a n t s and correlation coefficients Titration A C

~ 1 , Yt~'l

Y2, ~

r

(6.3--+0.3).10 -2 ( 2 . 1 + 1 ) . 1 0 6 0.92 (2-6---0.3) . 10 -z (3.0-+ 1.8) . 10 -7 0.87

F r o m data obtained in titration A, the association constants for the particles NiH2PO~ + and N i H P O 3 were calculated as K1 = 28-2-_6 (log K1 = 1.5-+0. I) and K2 = (3"6-+2"6). 103(log K2 = 3-6-+0-3). DISCUSSION

Values of the calculated association constants indicate, that the attractive forces responsible for forming the respective ion pairs are weak, similarly as in the case of zinc phosphites [1], vanadium phosphites[2] and vanadyl phosphites [3], in as far as we take into account the validity of the order, although the authors reported the association constants to two decimals in these studies. T h e reason is, besides the fact that in these studies statistical assesment of the errors of the constants calculated was not carried out and the selection of the assumed particles is not substantiated sufficiently, there also appear other doubtful points. E.G. with vanadyl phosphite[3], the authors tried to prove the existence of the assumed 27. J. F. D u n c a n and D. L. Kepert, A q u o - l o n s and Ion Pairs In The Structure of Electrolytic Solutions (Edited by J. W. H a m e r ) , p. 380. Wiley, N e w York (1959). 28. R. M. F u o s s and F. Accascina, Electrolytic Conductance, pp. 207, 225, 249. Interscience, N e w York (1959).

974

M. E B E R T and J. EYSSELTOV,/~

particles experimentally by means of an isomolar series, although these results are not applied in selecting particles for calculating the constants, no definite explanation being given: the results are only dismissed with no justification by general reference to the monographs [9] and [10]. In the same study, the authors mention the dissociation constant K~ = [VOHPO3] [H3PO3]/[VO(H2PO3)2] = = 1.61.10 -3, pK~ = 2-79, obtained by measuring the solubility of vanadyl phosphite in phosphorous acid. Setting out from their concept of the study [3], the value of the constant K~ may be calculated as K~ = K1K3~z/KJt~I = 7.08.10 -5, pK'3 = 4.15, using the definitions and values of constants K1, K2, K3 (Table 4 in Ref. [3]) and the dissociation constants of phosphorous acidY{~ and Y{2 (Table 2). Similarly the explanation of the difference between values of the dissociation constants KznHPO3 and KznH2PO3+ calculated from potentiometric measurements with metal and glass electrodes can be contradicted on the basis of the starting points proper of the work on zinc phosphites [1]. This explanation is based on the existence of the ion pair ZnCIO4 +. Provided the principles of the study [4] are accepted and measured values of zinc and hydrogen ion concentrations are included in the calculation at the same time, it becomes possible to use a scheme similar to scheme A in [1] to calculate the constants Kznu~Poa + a s well as the constant Kznoo+ = [Zn] [CIO4]/[ZnCIO4]. In a number of mixtures with different ratios of CZn: Cp: CHthe Kznclo,+ value is found to be negative, which is a contradiction of the existence of the ion pair ZnC104 + in terms of criterion reported by Frei and Solcov~ [29]. Comparing the association constants of NiHPO3 with NiSO4 [30-33] on the basis of similar behaviour of the phosphite and sulphate ion in aqueous solution [33, 24-26] we find that according to Duncan and Kepert [27] the ion pair formed belongs to the category of that formed by hydrated ions. In the case of the titration B (CNi:Cp----2) the difference CNi--Cp represents 50 per cent of the total metal concentration (cf. scheme l) and thus the metal excess is clearly insufficient for the use of apparent dissociation constants. This titration was evaluated by solution of the system of relations reported by Schwarzenbach and Ackermann [17] for the unknown concentrations of all the particles present. Consecutive calculation of the individual concentrations and their errors (Table 3) indicated, that no experimental points can be found in which the inequality (1) would be satisfied for individual concentrations of NiH2PO3 + alone. This means that the condition (1) is satisfied in none of the points of this titration nor for the calculated constant K2, the error of the constant exceeds the value of the constant itself and the calculated constant is devoid of any sense. This depreciation of the experimental results is a consequence of the law of additivity of errors (l 3) according to which the errors of dependent variables rise with the rising number of mathematical operations. Thus, procedures cannot be recommended, in which a solution of the system studied is obtained with the use of 29. V. Frei and A. Solcov~, Colin Czech. Chem. Commun. 30, 961 (1965). 30. C. W. Davies, Incomplete dissociation in Aqueous Salt Solutions, In The Structure o f Electrolyte Solutions (Edited by J. W. Hamer), p. 19. Wiley, New York (1959). 31. R.W. Money and C. W. Davies Trans. Faraday Soc. 28, 609 (1932). 32. V. S. K. Nair and G. H. Nancollas, J. chem. Soc. 3934 (1959). 33. A. P. Ruckov, Zh. Fiz. Khim. 28, 402 (1954).

975

Equilibrium Ni2+-H3PO3-HzO Table 3. Evaluation of the titration B [H2PO3] (mol. l - q 3-6.1~ 3 3.6 3.6 3.6 3.6 3-6 3.7 3.7 3.7 3-7 3-7 3-8 3-8 3.7 3.6 3.5 2.9 2.7 2.2 1-9 1.6 1-2 9-3.10 4 6.4 3.1

~([H2PO3I) (mol. I-q 1.7. 10-3 1.7 1-7 1.7 1-7 1.7 1.7 1.7 1"7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1-7 1-7 1.7 1-3 1.3 0'6 0'5 0.3 0.2

[NiH2PO3] (mol. 1 ~) 8.9. 10 4 9.0 9-3 8.9 9.2 10.7 9.6 9-1 9-2 9-2 9.7 9.3 10.6 9.1 6.7 5.1 3.0 4.4 3.7 2.2 2.0 1.8 1.0 1.0 0-5

~([NiH2PO3]) (mol. 1-1) 2.3. 10-3 2.2 2-2 2-2 2.1 2.0 2.0 1.9 1-9 1.9 1.8 1-8 1.7 1.7 1-7 1-7 1.7 1.7 1.5 7.0.10 4 6.5 6.0 4.8 3.3 1.9

a maximum number of particles at the expense of an increase in the number of variables and equations [4]. It is likewise impossible to select the particles in the system by calculating their equilibrium constants [29] since the unreal character of these constants may be caused by the mathematical procedure proper. The experimental conditions, under which the error of the constant required will not be greater than the constant itself, might be searched for in general by solving the inequality (l) by means of consecutive substitution and modification of the solution, e.g. in the form of

f(CMe, CA) > g(c~'q~l, Gq('~2,~ l p ~'~t2, K,, Kz, sc(Y{,), ~( , 2), ((SV'l),

~(K,), ~(K.,)). More detailed knowledge of the relationships between the individual variables and their errors, however, is needed for the practical application of this inequality. There follows from the above considerations that the choice of the experimental procedure and of the particles formed in the system must be based on preliminary experimental studies. The method of calculation should be as simple as possible, especially in the case where a large number of ion pairs will probably

976

M. EBERT and J, EYSSELTOV,~,

b e i n v o l v e d , s o m e t i m e s e v e n at the p r i c e that a n o t h e r e x p e r i m e n t a l t e c h n i q u e will h a v e to b e e m p l o y e d .

Acknowledgements-In concluding we should like to thank Professor RNDr. PhMr. Stanislav ~kramovsk~,, DrSc., and Assistant Professor lng. Frantigek Fabi/m, CSc., for their interest and discussions, which inspired us in our work.