Proton-fluoride association in sodium perchlorate media

J Inorg.Nucl.Chem., 1964,Vol.26, pp. 1959to 1965. PergamonPressI_td. Printedin Northern Ireland

P R O T O N - F L U O R I D E ASSOCIATION IN SODIUM PERCHLORATE M E D I A H. N. FARRER a n d F. J. C. ROSSOTTI Inorganic Chemistry Laboratory, Oxford University, England and Department of Chemistry, Edinburgh University, Scotland (Received 31 March 1964)

Abstract--The formation functions ~ (log h)A of hydrofluoric acid in 1 and 3 M sodium (perchlorate) media at 25°C have an isohydric point and midpoint symmetry. Consequently, proton-fluoride complexes higher than HF2-, which are considered to exist in concentrated acid fluoride solutions, cannot be detected at the fluoride concentrations employed ( < 1 M). Values of the formation constants of HF and HF2- are reported and their dependence on ionic strength is discussed. PICK (1) suggested in 1912 t h a t the c o n d u c t i v i t y o f a q u e o u s hydrofluoric acid is consistent with the equilibria H + -:,- F - ::: H F

/k~l

HF+

A],~

and F - ± H F 2-

Values o f K l l a n d KlZ have s u b s e q u e n t l y been d e t e r m i n e d by a variety o f experimental methods.(2, 3) H o w e v e r , the a g r e e m e n t between values o b t a i n e d u n d e r the same e x p e r i m e n t a l c o n d i t i o n s is n o t good. M o r e o v e r , in none o f these investigations were the c o n c e n t r a t i o n variables altered widely e n o u g h , n o r were the d a t a subjected to sufficiently r i g o r o u s m a t h e m a t i c a l analysis to exclude the possibility t h a t other species are formed. T h e existence o f higher complexes H~Fq (p > 1, q > 2) in c o n c e n t r a t e d acidic fluoride solutions has recently been inferred f r o m studies o f infra-red ~4) and nuclear m a g n e t i c r e s o n a n c e spectra, (5) a n d f r o m the kinetics o f d e p o l y m e r i z a t i o n o f trioxan. ~6) T h e ion H2Fa- has been identified c r y s t a l l o g r a p h i c a l l y in the solid state, (v~ a n d n u m e r o u s p h a s e - r u l e studies (8) are consistent with the existence o f H3F a- and H4Fs-. M u l t i m e r i z a t i o n o f H F occurs in the gas phase, (9) in organic solvents (1°) a n d (1~ H. PICK, Nernst Festsehrift, p. 360, Halle (1912). (2~ Mellor's Comprehensive Treatise on Inorganic and Theoretical Chemistry, Suppl. II, Part 1, p. 111. Longmans, London (1956). (a~ Stability Constants, Part H: Inorganic Ligands, p. 88. Chem. Soc., London (1958). ~4~L. H. JONESand R. A. PENNEMAN,J. Chem. Phys. 22, 781 (1954). (a) p. M. BORODIN and F. I. SKRIPOV,Izvest, Vysshikh. Uehets. Zavedenii, Radiofiz. 1, 37 (1958). (~ R. P. BELL, K. N. BASCOMBEand J. C. McCouBREY, J. Chem. Soc. 1286 (1956). ~') J. D. FORRESTER, M. E. SENNO, A. ZALKINand D. H. TEMPLETON,Aeta Cryst. 16, 58 (1963). (s) j. p. BUETTNERand A. W. JACHE, Inorg. Chem. 2, 19 (1963); J. S. MORRmONand A. W. JACHE, J. Amer. Chem. Soc. 81, 1821 (1959). ~'~ J. N. MACLEAN,F. J. C. ROSSOTTIand H. S. ROSSOTTI,J. Inorg. Nucl. Chem. 24, 1549 (1962). ~0~ R. M. ADAMSand J. J. KATZ, J. Mol. Spectr. 1, 306 (1957); M. L. JOSlEN, P. GRANGEand J. LASCO~BE, C. R. Aead. Sci., Paris 246, 3339 (1958). 1959

1960

H . N . FARRER and F. J. C. ROSSOTTI

in t h e solid p h a s e , m) C o n s e q u e n t l y , a c a r e f u l r e i n v e s t i g a t i o n o f t h e e q u i l i b r i a in a q u e o u s s o l u t i o n has b e e n c a r r i e d o u t . T h r e e o t h e r e q u i l i b r i u m studies h a v e a p p e a r e d ~1~-14) since t h e p r e l i m i n a r y c o m m u n i c a t i o n o f o u r o w n findings. (aS) EXPERIMENTAL Potentiometric titrations with a quinhydrone electrode have been used to measure the hydrogen ion concentration h of a series of hydrofluoric acid-sodium fluoride buffers as a function of total fluoride concentration A at 25°C. The variation of activity coefficients was minimised by adding sodium perchlorate to make the sodium ion concentration 1 M and 3 M in two independent series of measurements. The measurements covered the ranges 5 > -- log h > 1.5, and 0"005 < A < 0.9 M in the 3 M ionic medium, and A < 0-6 M in the I M medium. Apparatus A modified form of the cell described by FORSLING et al. ~18~was used containing the following solutions. AMHF 0'01 M AgC104 -- Ag, AgCI 3 M NaC104 x M NaOH Q, H~Q Pt+ 2"99 M NaC104 (3 -- x) M NaCIOa (Specific details here and elsewhere refer to the 3 M ionic medium). The glass tube terminating in the J-shaped liquid junction was replaced by a similarly-shaped polythene tube, and a multiplenecked polythene pot was used as the titration vessel. The cell was kept in a thermostat at 25 :k 0.05°C within a room at 25 :k 0'5°C. Potentials were measured to 4-0"1 mV using a Radiometer valve potentiometer p H M 4, which had been calibrated against a Cambridge precision potentiometer. The silver reference electrode was prepared by Brown's method/17~ The inert electrodes consisted of 1 cm ~ platinum foils with platinum leads sealed into polythene tubes, After igniting these electrodes in an alcohol flame, it was necessary to immerse them in water for about a day before steady and equal potentials were obtained. Pairs of platinum electrodes were used in the potentiometric titrations: their potentials were invariably identical. Procedure First, it was shown by titrating perchloric acid with sodium hydroxide in a 3 M sodium ionic medium that the measured mV potentials conformed to the Nernst equation E = E0 + 59.15 logh

(1)

in the range h < 0'025 M. Here, h is the hydrogen ion concentration, and the composite parameter E0 includes constant liquid junction potential and activity coefficient terms. Thereafter, E0 was determined by immersing the electrode in two dilute, standard solutions of perchloric acid in 3 M sodium perchlorate. The value of Eo was always the same within ±0.1 mV. Each buffer was treated as follows: stock buffer solution was run out of a polythene burette into 20.0 ml of 3 M sodium perchlorate, contained in the polythene titration vessel, to make A ~ 0,005 M. This solution was saturated with recrystallized AnalaR quinhydrone while E0 was being determined. The two inert electrodes were transferred to the titration vessel and left for 10 min. to equilibrate. After measuring E(A), Eo was rechecked and the electrodes transferred to a second titration vessel containing undiluted stock buffer solution. This was now diluted stepwise by addition of 3 M sodium perchlorate. In this way, E(A) was determined over the maximum possible range, consistent t11~ M. ATOJI and W. N. LISCOMB,Aeta Cryst. 7, 173 (1954). t12) A. J. ELLIS, J. Chem. Soc. 4300 (1963). cas~ T. ERDEv-GROz, T. MAJTI-mNYand E. KtrGLER, Aeta Chim. Aead. Sci. Hung. 37, 393 (1963). t~4~ L. CIAVATTA,Arkiv.Kemi. 21, 129 (1963). ~5~ H. N. FARRER,J. N. MACLEAN,F. J. C. ROSSOTn and H. S. Rossox'rIProeeedings 7th International Conference on Co-ordinate Chemistry p. 197. Almqvist and Wiksell, Uppsala (1962). cxe~W. FORSLrNG, S. Hn~rANEN and L. G. SILL~N, Aeta. Chem. Seand. 6, 901 (1952). ~1~ A. S. BROWN, J. Amer. Chem. Soe. 56, 646 (1934).

Proton-fluoride association in sodium perchlorate media

1961

with the limited solubility of sodium fluoride, and reversibility of the equilibria was checked. Finally E0 was again determined: the value seldom shifted by as much as 0'1 mV throughout the study of one buffer. Each complete run was duplicated with a reproducibility of ±0'1 inV. Chemicals"

Buffer solutions were prepared by mixing appropriate quantities of ~5 M solutions of AnalaR hydrofluoric acid, carbonate-free sodium hydroxide and recrystallized sodium perchlorate, all of which had been standardized by weight. The stock solution of hydrofluoric acid was standardized by titration with sodium hydroxide, using phenolphthalein as indicator. The total hydrogen ion concentration (A -- x) in each buffer was checked similarly. Silver perchlorate was prepared and analysed as described elsewhere? TM Alkaline and fluoride solutions were stored in polythene vessels. CALCULATIONS The average n u m b e r of b o u n d protons per fluoride ion was calculated for each point using the equation -

A --x--h

(2)

A

These values are summarised in Table 1. F o r m a t i o n curves 1i (log h)~ were plotted and transformed by interpolation to the curves log A (log h)~ shown in Fig. 1. The system provides the simplest possible example of an isohydric point. {.9) The midpoint symmetry o f all the formation curves, and their a p p r o a c h to the shape of the m o n o nuclear m o n o p r o t o n a t i o n curve with decreasing values of A, are consistent with the formation of H F and H F z- alone. C o m p a r i s o n of the data log A (log h),~ with appropriate normalized curves is necessary to exclude the possibility that the polynuclear species is a multimer of H F 2- and to determine the relevant formation constants. Substitution of the normalized variables h -- KHh

{3)

A = K~2A

(4)

and a --

K12a

into the mass balance equations A -: a ~ Kllha + 2KllKl~ha 2

and A~ = K u h a 4- KuK12ha ~

for the system containing H F and H F 2-, yields A=a-~ha+2ha

2

and A~ :

ha :- ha 2

Elimination o f a gives (1 - - h ) [ ~ - - h ( l A --

h ( 1 - - 2if) 2

-- ~)] (5)

(1st F. J. C. ROSSOTTIand H. S. ROSSOTTI, Acta Chem. Scan& 9, 1177 (1955). ~x~}j. D. E. CARSONand F. J. C. ROSSOTTLAdvances in the Chemistry qfthe Co-ordination Compounds (Edited by S. KmSCHNrR) p. 180. Macmillan, New York (1961); F. J. C. ROSSOTTIand H. S. RossoTrJ, The Determination of Stability Constants Chap. 17. McGraw-Hill, New York (1961). 13

1962

H . N . FARRER and F. J. C. ROSSOTTI TABLE 1.--EXPERIMENTAL DATA /~ (LOG h)x IN 3 M Na(C104)

A

0"005

0.01

0'015

ti

--log h

~

--log h

~

--log h

~

--log h

0"695 0"682 0.641 0"572 0"513 0-407 0"266 0"191 0'114 0.041

2"905 2'971 3"052 3-181 3"281 3'466 3.754 3-940 4'242 4.718

0"765 0"743 0"699 0"622 0'555 0.437 0-282 0"202 0.120 0.043

2'748 2.820 2.926 3.078 3-198 3.411 3.719 3-913 4.207 4-727

0'799 0.771 0'725 0"644 0"572 0.449 0-288 0"206 0.122 0.044

2"664 2"734 2-859 3'032 3.161 3"389 3"712 3"908 4"203 4"724

0.818 0"790 0"740 0.656 0.582 0"455 0.291 0-208 0'123 0-044

2"601 2'681 2"813 3"001 3"139 3'378 3"709 3'909 4"204 4'730

A

0.03

0'840 0-811 0'758 0.670 0"593 0'462 0.295 0-210 0'124 0"045

2.509 2"602 2.753 2"964 3.112 3-367 3'710 3'917 4.213 4"744

A

0.10

0'883 0'851 0.791 0-692 0"609 0"471 0'299 0"213 0-125 0"045

2.219 2'360 2-570 2"853 3'042 3"353 3'752 3.989 4'305 4"857

A

0"20

0'897 0"862 0'799 0"697 0'613 0.473 0"300 0"213 0,126

2"024 2"192 2'442 2-770 2"994 3"356 3.809 4.073 4-418

0"899 0.865 0-801 0'698 0"614 0.474 0.301

0"045

4.986

0"906

0.04 0"854 0'823 0"769 0"677 0.598 0-465 0"296 0.211 0.124 0"045

0.06 2-444 2.546 2-711 2-937 3-096 3.362 3.715 3.927 4-226 4.760

0'870 0-838 0"780 0-685 0'604 0"468 0-298 0.212 0"125 0.045

0.12 0'888 0"855 0-793 0'693 0'611 0"472 0"300 0.213 0-126 0"045

0.02 M

0'08 M 2-351 2"466 2"651 2-901 3"074 3-358 3"727 3'948 4-254 4"793

0.878 0'845 0-787 0"689 0.607 0"470 0"299 0.212 0-125 0"045

0.15 2.174 2.317 2,542 2.833 3'030 3.352 3.764 4.007 4.329 4.886

0-892 0-858 0"796 0'695 0-612 0'473 0"300 0.213 0.126 0'045

0'25

0.175 M 2.110 2'265 2"499 2"806 3.015 3'353 3"781 4'033 4.363 4-925

0-895 0.860 0.798 0.696 0-613 0'473 0.300 0.213 0.126 0"045

0"30 1.955 2"131 2.393 2'740 2.977 3.359 3.836

0-901 0-867 0'803

1.644

0"903 0"868 0"804

A 0,40

1'843 2"032 2.311 A 0.50

1-794 2-276

0-905 0-805

1'554

0.907

A 0.75 0"907

2.065 2.226 2-468 2.788 3-003 3"354 3.795 4.053 4.392 4.958 0'35 M

1-892 2-078 2"349

0-904 0.804

A 0"60

2'279 2"409 2-608 2,874 3"058 3-354 3.739 3"969 4.278 4-825

1.713 2.214 A 0-9 M 1.480

Proton-fluoride association in sodium perchlorate media

1963

from which the normalised curves log A (log h)~ may be calculated. These are shown in Fig. 1 superimposed on the experimental data in the position of best fit. The excellence of this fit, and the failure to find an acceptable fit with analogous normalised curves calculated for a multimer of HF2-, support the choice of species. Values of log/{11 and log Klz, together with their limits of error, were obtained by solving Equations (3) and (4). The parameters so obtained, and those obtained from analogous measurements using a 1M sodium ionic medium, are given in Table 2. log h -5

-4

-3

-2

I

I

I

1

/ I

!

-I

-2

•0 5

0'1

0.2

I

0'3

0.4 0.5 0.6 0.7

I

0"8

-

I 0

<[

o~

0"9

I

-2

log h

log A (log h)~ superimposed in the position of best fit on the experimental data log A (log h)~ for the 3 M Na(CIO~) medium.

FrG. ].---The normalised curves

DISCUSSION The calculation of hydrogen ion concentrations in relatively concentrated fluoride buffers by means of Equation (1) rests upon the assumptions that neither the addition of neutral H F to the ionic medium, nor the exchange of F - for C104- at constant sodium ion concentrations, affects the constancy of the liquid junction potential and activity coefficient terms contained within the parameter E 0. The addition of undissociated H F to 3 M sodium perchlorate at 25°C appears to increase E o linearly by + 3-4 mV per mole of acid, but we have been unable to measure the effect of exchanging the anions. Our experience with carboxylate equilibria 120) suggests that the latter effect may be of opposite sign, and unless the observed midpoint symmetry in the formation functions is fortuitous, the two effects are likely to be equal and opposite within the experimental error. Correction for the effect of H F alone on E 0 shifts the isohydric point from 0-490 _~ 0"005 to 0.500 :~: 0"005 and slightly improves the lit with the normalised curves. The deduction that H F 2- is the sole polyacidic species detectable does not rest ~0~ H. N. FARP,ER and F. J. C. ROSSOTrl,Acta Chem. Scand. 17, 1824 (1963).

1964

H . N . FARRER and F. J. C. ROSSOTTI

upon the position of the isohydric point alone. It has been shown previously(19~that when the species HA, HA 2- and H2A2 coexist, the ratio of the protonation constant K22 of HA2- to that of A- is given by /(22

2fi-

Kn

1

2fi

Hence, a value of K22 in the range 0 < K22/Kn < 0.02 would still give an isohydric point within the experimental error of ~i = 0.5. The position of the isohydric point will be an even less sensitive criterion of the existence of H2A3-, since an increase in the value of the equilibrium constant for the reaction

HA~- 4- HA ~- H2A3 from zero to infinity would only shift the (pseudo-) isohydric point from ti = 0.50 to 0"67. Consequently, the mid-point symmetry of the formation functions over a wide concentration range is more significant than the mere position of the isohydric point. Assignments of species made in other polynuclear systems(21) from the position of the isohydric point alone require substantiation. TABLE 2.--AssoCIATION

NaCIO4 I at 25°C

CONSTANTS IN

MEDIA OF IONIC STRENGTH

1

013~

0"5 c~l

1"0

3'0 M

log KI1 log K12

3"17 0"59

2"91 --

2"95 :k 0"01 0"58 ~ 0"1

3"29 ~ 0"01 0"86 :k 0"02

Our values of log Kll are in good agreement with comparable values. 13,14~ Their dependence on the formal ionic strength I in sodium perchlorate media has been obtained by utilising two additional values (3) of log Kll. The four values listed in Table 2 conform to the Debye-HiJckel equation log Kll = 3.17

1.0221½ 1 4- 1"3321½+ 0-218I

within the experimental error. The rather wide limits of error for our value of log K12 in the 1M medium span scattered comparable values. TM However, the discrepancy between the value for the 3 M medium and Ciavatta's value (14) of 1.06 + 0.05 exceeds the combined limits of errors. If the increase in log K12 with the concentration of sodium perchlorate is predominantly due to the increase in log )'HF (where 7~F is the activity coefficient of HF), then log K12 will increase linearly as the electrolyte concentration, with a slope equal to the salting-out coefficient k of hydrogen fluoride by sodium perchlorate. Combination of our values with those for lower ionic strengths(3, ~2J is consistent with k ~-~ 0.1, whereas CIAVATTA'Shigher value would require the less likelyt2~ value of k ~ 0"2. CIAVATTAhas reported a value of log K~ = 0.74 4- 0.i in a 3 M potassium (chloride) medium at 25°C. This value also suggests that his value for the perchlorate tZl) G. CARPENI,Annales Facultd Sciences de Marseille 30, 3 (1960). c22~F. A. LONG and W. F. McDEVlT, Chem. Rev. 51, 119 (1952).

Proton-fluoride association in sodium perchlorate media

1965

m e d i u m is a b n o r m a l l y high. T h e r e a s o n for the d i s a p p o i n t i n g a g r e e m e n t between o u r own a n d CIAVATTA'S value o f KI~ is obscure. It stems f r o m discrepancies between the two sets o f p r i m a r y data. Y e t b o t h sets o f f o r m a t i o n functions show m i d p o i n t symmetry.

Acknowledgements--We are grateful to the Commonwealth Scholarship Commission for an award to H. N. F., and to the Earl of Moray Endowment Committee and to Imperial Chemical Industries Ltd., for the loan of equipment.