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Determination of the stability constants of MgF+ and CaF+ using a fluoride ion selective electrode
J. inorg, nucl,Chem., 1970.Vol. 32, pp. 937 to 944. PergamonPress. Printedin Great Britain
DETERMINATION OF THE STABILITY CONSTANTS OF MgF + AND CaF ÷ USING A FLUORIDE ION SELECTIVE ELECTRODE BENGT ELGQUIST D e p a r t m e n t of Analytical Chemistry, University of GiSteborg, Kemig~rden 3 , 4 0 2 20 G6teborg. Sweden
(Received 10 July 1969) A b s t r a c t - T h e stability c o n s t a n t s of M g F + and C a P have been determined at 25°C in a q u e o u s solutions of ionic strength 0.1, 0.4, 0-7 and 1.0M held constant by m e a n s of NaCI. N o buffering agents were used but the pH was in the range 5.5-6.0. A n Orion fluoride ion selective electrode, model 94-09, was used to m e a s u r e the fluoride ion activity with a saturated calomel electrode as reference. T h e complexation of fluoride in sea water is calculated on the basis of the m e a s u r e m e n t s . INTRODUCTION
THE DEVELOPMENT of the fluoride ion selective e l e c t r o d e [ I - 5 ] seems to have opened new possibilities in the determination of fluoride by means of titration [1, 6, 7]. This method of following the fluoride ion activity ought also to be suitable for the determination of stability constants of fluoride complexes [8]. Since it is likely that considerable part of the fluoride present in sea water exists in the form of the complexes MgF ÷ and CaF +, the determination of the stability constants of these complexes was considered to be of interest since, once these constants are known, it is possible to calculate the amounts of MgF ÷ and CaF ÷ present at different salinities. EXPERIMENTAl,
Reagents. Stock solutions I - I V were prepared as follows: I. 0.09955 M N a F . 20.9057 g N a F (Merck p.a.), recrystallized once and dried for 24 hr at 120°C, was dissolved in water to give 5.000 I. 11. 0.4993 M MgCI2.0-5 mol. pure m a g n e s i u m ( B D H , rain. 99.7% Mg) was dissolved in water containing 1 mol. HC1 ( p H - T a m m , from an ampoule). A slight e x c e s s of m a g n e s i u m was added and the solution was stirred for 72 hr, filtered and the v o l u m e of the filtrate adjusted to 1.0001. T h e pH was 6-0 and [Mg 2+] was determined by m e a n s of titration with N a O H according to Jagner[9]. 1. 2. 3. 4. 5. 6. 7. 8. 9.
J . J . Lingane, A nalyt. Chem. 39, 881 (1967). R. A. D u r s t and J. K. Taylor, Analyt. Chem. 39, 1483 (1967). R. E. Mesmer,.4 nalyt. Chem. 4 0 , 4 4 3 (1968). K. Srinivasan and G. A. Rechnitz, A nalyt. Chem. 40, 613 (1968). A. M. G. Macdonald and K. Toth, A nalytica, chim. A cta 41, 99 (1968). J.J. Lingane, A nalyt. Chem. 40, 935 (1968). T. Anf~ilt, D. D y r s s e n and D. Jagner, Analytica. chim. Acta 43,487 (1968). C. F. Baes Jr., lnorg. Chem. 8 , 6 1 8 (1969). D. Jagner, Report on the Chemistry o f Sea Water-111. Dept. of Analytical C h e m i s t r y , University of G o t h e n b u r g (1967). 937
938
B. E L G Q U I S T
III. 0.4821 M CaClz. 73.510 g CaClz(H20)2 (Merck p.a.) was dissolved in water to give 1.0001. The pH was 5-5 and [CI-] was determined by ing. Kerstin Ar6n by means of potentiometric titration with silver nitrate[10, 11]. IV. 2,00 M NaCI. NaC1 (Merck p.a.) was recrystallized once, dried 24 hr at 120°C and dissolved in water. The water used for I - I V was distilled twice, and the solutions were stored in polyethylene bottles. The stock solutions were used to prepare the following solutions.
Solution 9.955 mM N a F 4.993 mM MgCI2 0-1991 mM N a F %.42 mM CaC12
Stock solution used I and 11 and I and 11I and
IV IV IV IV
Molar ionic strength 0.1 0.1
0-4 0.4 0.4 0.4
0.7 0.7 0.7 0-7
1.0 1.0 1-0 1.0
Instrumental equipment. Solartron LM 1867 and Dynamco 2006 digital volt meters and a Dosimat automatic buret were used. Procedure. 50 ml of a solution of NaF was titrated with about 20 ml of MCIz (M = Mg or Ca) at constant temperature and under constant stirring. For the determination of KMgr*, 9'55 mM NaF and 4-993 mM MgCI z were used, producing an E M F difference between the first and last readings of approximately 16 mV. Kcar÷ was determined with 0.1991 mM NaF and %.42 mM CaClz giving a corresponding EMF difference of approximately 10 mV. [F-] was followed by measuring the EMF of an Orion fluoride ion selective electrode, model 94-09, (solid state) relative to a saturated calomel electrode (SCE, Radiometer type K401). The E M F was measured with a digital voltmeter with a resolution of 10/,~V and the electrode system was calibrated in the fluoride ion solution before the addition of MCI~. Because the complexes to be measured were expected to be rather weak [ 12], the solution was not buffered but the pH was always approximately 5.5 to 6.0 which is far enough from the pKa of H F (ca. 2.9112]) for [HF] to be negligible. The ionic strength was kept constant by means of NaCI, and any decrease in the ionic strength caused by the reaction M~++ F - ~ MF + was neglected. The formation of chloride complexes of Mg 2+ and Ca z÷ was also assumed to be negligible [ 12]. The number of titration points were usually 12-20 and about ten titrations were carried out for each value of the ionic strength for both Mg and Ca. The electrodes were allowed to stabilize in the titrant solution before calibration but the titration time was kept below 15 mirt in order to minimise errors due to changes in E ° with time. This was accomplished simply by containing the stirring while the EMF was measured (the streaming potential is very low in solutions of such ionic strengths). The titrations were performed at 25 + I°C, but the temperature was held constant to --- 0.05°C in each titration. CALCULATIONS
AND RESULTS
T h e e l e c t r o d e s . T h e O r i o n f l u o r i d e e l e c t r o d e f o l l o w s a c c o r d i n g t o M e s m e r [3] a n d o t h e r s t h e N e r n s t r e l a t i o n w i t h r e s p e c t t o [ F - ] i n t h e r a n g e 10 -1 t o 10 -5 M . This has been confirmed by the present investigation. Moreover, the electrode has been found to have a short response time in the linear range, from almost immedi a t e r e s p o n s e i n 10 -2 M f l u o r i d e t o a b o u t 3 0 s e c i n 10 -4 M s o l u t i o n s (I = 0 . 1 - 1 . 0 M , rapid stirring). Mesmer[3] also points out that the sensitivity of fluoride over c h l o r i d e is g r e a t e r t h a n 103 , a n d i n t h i s i n v e s t i g a t i o n it w a s n o t p o s s i b l e t o d e t e c t any response to chloride, other than that due to the effect of on the ionic strength 10. D. Dyrssen and D. J agner, A nalytica, chim. A cta 35,407 (1966). 11. D. Dyrssen et al. Progress Report on Potentiometric Titrations o f Alkalinity and Chlorinity o f Sea Water, Report on the Chemistry o f Sea Water-II, GiSteborg (1966). 12. L. G. Sill6n and A. E. Martell, Stability Constants, 2nd Edn. The Chemical Society, London (1964).
Determination of stability constants
939
and thus on the activity factor of the fluoride ion. Response to O H - could be neglected as the p H was 5.5-6.0 so that [ O H - ] was negligible c o m p a r e d with [F-]. T h e fluoride electrode can thus be a s s u m e d to follow the N e r n s t equation R T In l0
E r = E °'
-
F
log av
( 1)
and the m e a s u r e d E M F can be e x p r e s s e d as E = E v - - EscE = E °' -- EscE--A log av=
(2)
Since EscE is constant, E = E . . . . A log av-.
(3)
If the activity coefficient of F - is denoted b y f av- = f [ F - ]
w h e r e f i s defined so thatf---~ 1 when [F-] ~ (0.1 to0-1 M). E = E°"--A Iogf-A
(4) 0 at the constant ionic strength used
log [F-] = E ° - - A log [F-]
E = E°+ApF.
(5) (6)
A rather curious p h e n o m e n o n was o b s e r v e d in that the calculated values for the stability constants were 1 0 - 2 0 per cent too high for the first titration points ( 1 - 4 ml) of e v e r y titration. T h e s e points were excluded in the subsequent calculations. It has not, h o w e v e r , been possible to arrive at plausible explanation for this "electrode s h o c k " phenomenon.
CALCULATIONS T h e calculations were p e r f o r m e d on a S A A B D21 c o m p u t e r using an A L G O L 60 program ( M g F +) and on an I B M 360/50H c o m p u t e r using a program written in F O R T R A N 1V ( M g F + and CaF+). Input data are the n u m b e r of titration points, the concentrations of fluoride and metal used, the temperature, a " s t e p " p a r a m e t e r used in the refinement and the titrand volume Vo, followed by the volumes, V, of titrant added and corresponding E M F values recorded. T h e N e r n s t coefficient is first calculated according to RTln
A - -
F
10
(7)
after which E ° is derived from E ° = E(at V = 0 ml) - - A p F o
(8)
940
B. E L G Q U I S T
where pFo is calculated from the composition of the initial titrand solution. The free fluoride concentration can then be calculated from [F-] = 10 exp
((E°--E)/A).
(9)
Since the analytical (total) concentrations of fluoride and metal are known the stability constant can be calculated according to [MF +] [F-]tot-- [F-] K~F+ = [M2+] [F-] = ([M2+]tot-- [F-]tot+ [ F - ] ) [ F - ] "
(10)
A value of the constant is thus derived for each titration point. The mean value of K ~ + is then calculated together with its standard deviation, and from this mean value a titration curve is derived which can be compared with the experimental one. With the exception of the first titration points (see above) no trend was observed in the differences. There is thus no drift in the E ° of the electrode system. A refined value of the constant was then obtained by varying the mean value so as to minimise the summation (Ecalc-Eobs) 2, i.e. the discrepancy between calculated and observed titration curves. RESULTS Table 1. Determination o f K ~ r ÷ Ionic strength (M)
Mean value of K Standard (M -1) deviation
Numberof titrations
0.1
28.7
-+ 1.7
6
0.4 0.7 1.0
22.0 18-8 18.6
-4-1.6 ---0.7 -+0.8
6 10 8
Table 2. Determination of Kcar + lonicstrength (M)
Mean value o f K (M -1)
Standard deviation
Numberof titrations
0.4 0.7 1.0
5.01 4.22 3.85
--+0.16 -----0-067 -----0.079
I0 12 12
Only in a very few cases did the standard deviation for single titrations exceed 0-1. The primary data and examples of some titration curves will be published in "Report on the Chemistry of Sea W a t e r - V I I " [13]. The results agree well with those of Connick and Tsao [14], who used a Pt/Fe 3÷, 13. B. Elgquist, Report on the Chemistry o f Sea W a t e r - V I I . Dept. of Analytical Chemistry, University of Gothenburg (1969). 14. R. E. Connick and M. S. Tsao, J . A m . chem. Soc. 76, 5311 (1954).
Determination of stability constants
941
Fe 2+ redox electrode. They obtained for an ionic strength of 0.5 M KMgv+ = 20 and Kcav+ ~< 3"2. DISCUSSION
An attempt to calculate the stability constants of MgF2 and CaFz was not successful. The stability constants for the second step are probably quite low. Furthermore, due to the rather low solubilities of MgFz and CaF2, the product [M2+][F-] 2 = [MF2]/fi2 cannot be increased sufficiently. The determination of Kcav+ was carried out at a lower concentration of fluoride and a higher concentration of metal than that used for the determination of KM~+ in order to obtain comparable EMF differences with the weak CaF + and the stronger MgF +. A metal concentration much higher than 96.42 mM is not feasible with an ionic strength of 0.4 M and at fluoride concentrations lower than 10-4 M it is possible than one may enter the nonlinear range of the fluoride electrode. The equilibria studied were, as expected, instantaneous (no change of E MF with time was observed). N o r was there visible precipitation of MgF~ or CaF~. Absence of precipitates was further confirmed from the titration curves which would have shown discontinuities at the beginning of precipitation. Furthermore, the computer values of the constant would not have converged since no solid phases were included in the program. The liquid potential of the SCE was assumed to be constant because ionic strength, temperature and stirring were all constant, and its value was therefore included in E °.
T H E C O M P L E X A T I O N O F F L U O R I D E IN SEA W A T E R
The stability constants determined may be plotted against the ionic strength and the corresponding salinity of sea water[15] as in Fig. 1. The amount of fluoride in the form of F-, MgF ÷ and C a P can then be calculated and the results are given in Tables 3 and 4 and plotted in Fig. 2. In this calculation the ionic strength and the concentrations of magnesium and calcium in normal sea water (S = 35 o/oo) have been taken from Dyrssen[15] Fable 3 Ionic strength Salinity Density [Mg] (m) (o/oo) (25°C) (mol/kg) 0-1 0.2 0.4 0.6 0.7 0.8 1.0
5 10 20 30 35 40 50
1.00087 1.00462 1.01210 1"01960 1-02336 1-02714 1.03464"
0-00759 0.01519 0.03037 0-04556 0.05315 0-06074 0-07593
[Ca] (mol/kg)
[Mg] (M)
[Ca] (M)
KMgv + (M -1)
Kcav+ (M-')
0.00147 0.00294 0.00588 0.00882 0"01029 0.01176 0-01470
0.00760 0.01526 0.03074 0-04645 0.05439 0-06239 0.07856
0.00147 0'00295 0-00595 0"00899 0.01053 0-01208 0.01521
28.7 26.0 22.0 19.6 18.8 18.7 18.6
6.6 5.9 5.01 4.4 4.22 4.1 3.85
*Extrapol. 15. D. Dyrssen, In Chemical Oceanography,An Introduction, Chap. i II. To be published.
942
B. ELGQUIST
6666666
6666666
[-.
7
6666666
q~ q~ 6 6 6 6 ~
.u 0
Determination of stability constants
943
I-5
1.0 o
o5
,
,
,
,
I0
15
20
25
,
•
,
30
35
40
-
45
50
,
O'G
Oq
08
0'9
I
5% 0 I
0"2
0 $
04
0 5
IM
Fig. 1. Logarithms of stability of MgF + (circles) and C a F ~ tsquares) as a function of the salinity of sea water. tOO
75
50
25
0 5
I0
15
~ 20
25
30
35
40
45
50
s%
Fig. 2. The amounts of F - (open circles). MgF + (filled circles) and C a F ÷ (squares) in per cent of the total amount of fluoride as a function of the salinity of sea water.
944
B. E L G Q U I S T
(0.05315 and 0.01029 mol. per kg, respectively). The density of sea water at different salinities has been taken from Cox [ 16]. mol/i. = (density) x (mol/kg).
(11)
Thus any complexation with magnesium and calcium other than with fluoride has been neglected and as an approximation the following fluoride mass balance has been used: [ F - ] t o t -----[MgF +] +
[CaF +] + [F-].
(12)
[F-]tot_ [MgF +] [F-] [F-]
[CaF +] ~- 1. [F-]
(13)
Hence
Finally
[MgF +] [F-]tot
[MgF +] [F-]tot [F-]
[F-]
(14)
[ C a F + / [ F - ] t o t c a n be obtained in a similar manner. These values are given in Table 4 and plotted in Fig. 2.
Acknowledgements-I wish to thank the head of this department, Professor David Dyrssen, for suggesting this investigation and discussing the results and their presentation with me. I also wish to thank Dr. Susan Jagner for revising the English text of this paper. Our work on the chemistry of sea water is supported by the Swedish Natural Science Council. 16. R. A. Cox, In Chemical Oceanography (Edited by Riley and Skirrow), p. 103. Academic Press, New York (1965).
DETERMINATION OF THE STABILITY CONSTANTS OF MgF + AND CaF ÷ USING A FLUORIDE ION SELECTIVE ELECTRODE BENGT ELGQUIST D e p a r t m e n t of Analytical Chemistry, University of GiSteborg, Kemig~rden 3 , 4 0 2 20 G6teborg. Sweden
(Received 10 July 1969) A b s t r a c t - T h e stability c o n s t a n t s of M g F + and C a P have been determined at 25°C in a q u e o u s solutions of ionic strength 0.1, 0.4, 0-7 and 1.0M held constant by m e a n s of NaCI. N o buffering agents were used but the pH was in the range 5.5-6.0. A n Orion fluoride ion selective electrode, model 94-09, was used to m e a s u r e the fluoride ion activity with a saturated calomel electrode as reference. T h e complexation of fluoride in sea water is calculated on the basis of the m e a s u r e m e n t s . INTRODUCTION
THE DEVELOPMENT of the fluoride ion selective e l e c t r o d e [ I - 5 ] seems to have opened new possibilities in the determination of fluoride by means of titration [1, 6, 7]. This method of following the fluoride ion activity ought also to be suitable for the determination of stability constants of fluoride complexes [8]. Since it is likely that considerable part of the fluoride present in sea water exists in the form of the complexes MgF ÷ and CaF +, the determination of the stability constants of these complexes was considered to be of interest since, once these constants are known, it is possible to calculate the amounts of MgF ÷ and CaF ÷ present at different salinities. EXPERIMENTAl,
Reagents. Stock solutions I - I V were prepared as follows: I. 0.09955 M N a F . 20.9057 g N a F (Merck p.a.), recrystallized once and dried for 24 hr at 120°C, was dissolved in water to give 5.000 I. 11. 0.4993 M MgCI2.0-5 mol. pure m a g n e s i u m ( B D H , rain. 99.7% Mg) was dissolved in water containing 1 mol. HC1 ( p H - T a m m , from an ampoule). A slight e x c e s s of m a g n e s i u m was added and the solution was stirred for 72 hr, filtered and the v o l u m e of the filtrate adjusted to 1.0001. T h e pH was 6-0 and [Mg 2+] was determined by m e a n s of titration with N a O H according to Jagner[9]. 1. 2. 3. 4. 5. 6. 7. 8. 9.
J . J . Lingane, A nalyt. Chem. 39, 881 (1967). R. A. D u r s t and J. K. Taylor, Analyt. Chem. 39, 1483 (1967). R. E. Mesmer,.4 nalyt. Chem. 4 0 , 4 4 3 (1968). K. Srinivasan and G. A. Rechnitz, A nalyt. Chem. 40, 613 (1968). A. M. G. Macdonald and K. Toth, A nalytica, chim. A cta 41, 99 (1968). J.J. Lingane, A nalyt. Chem. 40, 935 (1968). T. Anf~ilt, D. D y r s s e n and D. Jagner, Analytica. chim. Acta 43,487 (1968). C. F. Baes Jr., lnorg. Chem. 8 , 6 1 8 (1969). D. Jagner, Report on the Chemistry o f Sea Water-111. Dept. of Analytical C h e m i s t r y , University of G o t h e n b u r g (1967). 937
938
B. E L G Q U I S T
III. 0.4821 M CaClz. 73.510 g CaClz(H20)2 (Merck p.a.) was dissolved in water to give 1.0001. The pH was 5-5 and [CI-] was determined by ing. Kerstin Ar6n by means of potentiometric titration with silver nitrate[10, 11]. IV. 2,00 M NaCI. NaC1 (Merck p.a.) was recrystallized once, dried 24 hr at 120°C and dissolved in water. The water used for I - I V was distilled twice, and the solutions were stored in polyethylene bottles. The stock solutions were used to prepare the following solutions.
Solution 9.955 mM N a F 4.993 mM MgCI2 0-1991 mM N a F %.42 mM CaC12
Stock solution used I and 11 and I and 11I and
IV IV IV IV
Molar ionic strength 0.1 0.1
0-4 0.4 0.4 0.4
0.7 0.7 0.7 0-7
1.0 1.0 1-0 1.0
Instrumental equipment. Solartron LM 1867 and Dynamco 2006 digital volt meters and a Dosimat automatic buret were used. Procedure. 50 ml of a solution of NaF was titrated with about 20 ml of MCIz (M = Mg or Ca) at constant temperature and under constant stirring. For the determination of KMgr*, 9'55 mM NaF and 4-993 mM MgCI z were used, producing an E M F difference between the first and last readings of approximately 16 mV. Kcar÷ was determined with 0.1991 mM NaF and %.42 mM CaClz giving a corresponding EMF difference of approximately 10 mV. [F-] was followed by measuring the EMF of an Orion fluoride ion selective electrode, model 94-09, (solid state) relative to a saturated calomel electrode (SCE, Radiometer type K401). The E M F was measured with a digital voltmeter with a resolution of 10/,~V and the electrode system was calibrated in the fluoride ion solution before the addition of MCI~. Because the complexes to be measured were expected to be rather weak [ 12], the solution was not buffered but the pH was always approximately 5.5 to 6.0 which is far enough from the pKa of H F (ca. 2.9112]) for [HF] to be negligible. The ionic strength was kept constant by means of NaCI, and any decrease in the ionic strength caused by the reaction M~++ F - ~ MF + was neglected. The formation of chloride complexes of Mg 2+ and Ca z÷ was also assumed to be negligible [ 12]. The number of titration points were usually 12-20 and about ten titrations were carried out for each value of the ionic strength for both Mg and Ca. The electrodes were allowed to stabilize in the titrant solution before calibration but the titration time was kept below 15 mirt in order to minimise errors due to changes in E ° with time. This was accomplished simply by containing the stirring while the EMF was measured (the streaming potential is very low in solutions of such ionic strengths). The titrations were performed at 25 + I°C, but the temperature was held constant to --- 0.05°C in each titration. CALCULATIONS
AND RESULTS
T h e e l e c t r o d e s . T h e O r i o n f l u o r i d e e l e c t r o d e f o l l o w s a c c o r d i n g t o M e s m e r [3] a n d o t h e r s t h e N e r n s t r e l a t i o n w i t h r e s p e c t t o [ F - ] i n t h e r a n g e 10 -1 t o 10 -5 M . This has been confirmed by the present investigation. Moreover, the electrode has been found to have a short response time in the linear range, from almost immedi a t e r e s p o n s e i n 10 -2 M f l u o r i d e t o a b o u t 3 0 s e c i n 10 -4 M s o l u t i o n s (I = 0 . 1 - 1 . 0 M , rapid stirring). Mesmer[3] also points out that the sensitivity of fluoride over c h l o r i d e is g r e a t e r t h a n 103 , a n d i n t h i s i n v e s t i g a t i o n it w a s n o t p o s s i b l e t o d e t e c t any response to chloride, other than that due to the effect of on the ionic strength 10. D. Dyrssen and D. J agner, A nalytica, chim. A cta 35,407 (1966). 11. D. Dyrssen et al. Progress Report on Potentiometric Titrations o f Alkalinity and Chlorinity o f Sea Water, Report on the Chemistry o f Sea Water-II, GiSteborg (1966). 12. L. G. Sill6n and A. E. Martell, Stability Constants, 2nd Edn. The Chemical Society, London (1964).
Determination of stability constants
939
and thus on the activity factor of the fluoride ion. Response to O H - could be neglected as the p H was 5.5-6.0 so that [ O H - ] was negligible c o m p a r e d with [F-]. T h e fluoride electrode can thus be a s s u m e d to follow the N e r n s t equation R T In l0
E r = E °'
-
F
log av
( 1)
and the m e a s u r e d E M F can be e x p r e s s e d as E = E v - - EscE = E °' -- EscE--A log av=
(2)
Since EscE is constant, E = E . . . . A log av-.
(3)
If the activity coefficient of F - is denoted b y f av- = f [ F - ]
w h e r e f i s defined so thatf---~ 1 when [F-] ~ (0.1 to0-1 M). E = E°"--A Iogf-A
(4) 0 at the constant ionic strength used
log [F-] = E ° - - A log [F-]
E = E°+ApF.
(5) (6)
A rather curious p h e n o m e n o n was o b s e r v e d in that the calculated values for the stability constants were 1 0 - 2 0 per cent too high for the first titration points ( 1 - 4 ml) of e v e r y titration. T h e s e points were excluded in the subsequent calculations. It has not, h o w e v e r , been possible to arrive at plausible explanation for this "electrode s h o c k " phenomenon.
CALCULATIONS T h e calculations were p e r f o r m e d on a S A A B D21 c o m p u t e r using an A L G O L 60 program ( M g F +) and on an I B M 360/50H c o m p u t e r using a program written in F O R T R A N 1V ( M g F + and CaF+). Input data are the n u m b e r of titration points, the concentrations of fluoride and metal used, the temperature, a " s t e p " p a r a m e t e r used in the refinement and the titrand volume Vo, followed by the volumes, V, of titrant added and corresponding E M F values recorded. T h e N e r n s t coefficient is first calculated according to RTln
A - -
F
10
(7)
after which E ° is derived from E ° = E(at V = 0 ml) - - A p F o
(8)
940
B. E L G Q U I S T
where pFo is calculated from the composition of the initial titrand solution. The free fluoride concentration can then be calculated from [F-] = 10 exp
((E°--E)/A).
(9)
Since the analytical (total) concentrations of fluoride and metal are known the stability constant can be calculated according to [MF +] [F-]tot-- [F-] K~F+ = [M2+] [F-] = ([M2+]tot-- [F-]tot+ [ F - ] ) [ F - ] "
(10)
A value of the constant is thus derived for each titration point. The mean value of K ~ + is then calculated together with its standard deviation, and from this mean value a titration curve is derived which can be compared with the experimental one. With the exception of the first titration points (see above) no trend was observed in the differences. There is thus no drift in the E ° of the electrode system. A refined value of the constant was then obtained by varying the mean value so as to minimise the summation (Ecalc-Eobs) 2, i.e. the discrepancy between calculated and observed titration curves. RESULTS Table 1. Determination o f K ~ r ÷ Ionic strength (M)
Mean value of K Standard (M -1) deviation
Numberof titrations
0.1
28.7
-+ 1.7
6
0.4 0.7 1.0
22.0 18-8 18.6
-4-1.6 ---0.7 -+0.8
6 10 8
Table 2. Determination of Kcar + lonicstrength (M)
Mean value o f K (M -1)
Standard deviation
Numberof titrations
0.4 0.7 1.0
5.01 4.22 3.85
--+0.16 -----0-067 -----0.079
I0 12 12
Only in a very few cases did the standard deviation for single titrations exceed 0-1. The primary data and examples of some titration curves will be published in "Report on the Chemistry of Sea W a t e r - V I I " [13]. The results agree well with those of Connick and Tsao [14], who used a Pt/Fe 3÷, 13. B. Elgquist, Report on the Chemistry o f Sea W a t e r - V I I . Dept. of Analytical Chemistry, University of Gothenburg (1969). 14. R. E. Connick and M. S. Tsao, J . A m . chem. Soc. 76, 5311 (1954).
Determination of stability constants
941
Fe 2+ redox electrode. They obtained for an ionic strength of 0.5 M KMgv+ = 20 and Kcav+ ~< 3"2. DISCUSSION
An attempt to calculate the stability constants of MgF2 and CaFz was not successful. The stability constants for the second step are probably quite low. Furthermore, due to the rather low solubilities of MgFz and CaF2, the product [M2+][F-] 2 = [MF2]/fi2 cannot be increased sufficiently. The determination of Kcav+ was carried out at a lower concentration of fluoride and a higher concentration of metal than that used for the determination of KM~+ in order to obtain comparable EMF differences with the weak CaF + and the stronger MgF +. A metal concentration much higher than 96.42 mM is not feasible with an ionic strength of 0.4 M and at fluoride concentrations lower than 10-4 M it is possible than one may enter the nonlinear range of the fluoride electrode. The equilibria studied were, as expected, instantaneous (no change of E MF with time was observed). N o r was there visible precipitation of MgF~ or CaF~. Absence of precipitates was further confirmed from the titration curves which would have shown discontinuities at the beginning of precipitation. Furthermore, the computer values of the constant would not have converged since no solid phases were included in the program. The liquid potential of the SCE was assumed to be constant because ionic strength, temperature and stirring were all constant, and its value was therefore included in E °.
T H E C O M P L E X A T I O N O F F L U O R I D E IN SEA W A T E R
The stability constants determined may be plotted against the ionic strength and the corresponding salinity of sea water[15] as in Fig. 1. The amount of fluoride in the form of F-, MgF ÷ and C a P can then be calculated and the results are given in Tables 3 and 4 and plotted in Fig. 2. In this calculation the ionic strength and the concentrations of magnesium and calcium in normal sea water (S = 35 o/oo) have been taken from Dyrssen[15] Fable 3 Ionic strength Salinity Density [Mg] (m) (o/oo) (25°C) (mol/kg) 0-1 0.2 0.4 0.6 0.7 0.8 1.0
5 10 20 30 35 40 50
1.00087 1.00462 1.01210 1"01960 1-02336 1-02714 1.03464"
0-00759 0.01519 0.03037 0-04556 0.05315 0-06074 0-07593
[Ca] (mol/kg)
[Mg] (M)
[Ca] (M)
KMgv + (M -1)
Kcav+ (M-')
0.00147 0.00294 0.00588 0.00882 0"01029 0.01176 0-01470
0.00760 0.01526 0.03074 0-04645 0.05439 0-06239 0.07856
0.00147 0'00295 0-00595 0"00899 0.01053 0-01208 0.01521
28.7 26.0 22.0 19.6 18.8 18.7 18.6
6.6 5.9 5.01 4.4 4.22 4.1 3.85
*Extrapol. 15. D. Dyrssen, In Chemical Oceanography,An Introduction, Chap. i II. To be published.
942
B. ELGQUIST
6666666
6666666
[-.
7
6666666
q~ q~ 6 6 6 6 ~
.u 0
Determination of stability constants
943
I-5
1.0 o
o5
,
,
,
,
I0
15
20
25
,
•
,
30
35
40
-
45
50
,
O'G
Oq
08
0'9
I
5% 0 I
0"2
0 $
04
0 5
IM
Fig. 1. Logarithms of stability of MgF + (circles) and C a F ~ tsquares) as a function of the salinity of sea water. tOO
75
50
25
0 5
I0
15
~ 20
25
30
35
40
45
50
s%
Fig. 2. The amounts of F - (open circles). MgF + (filled circles) and C a F ÷ (squares) in per cent of the total amount of fluoride as a function of the salinity of sea water.
944
B. E L G Q U I S T
(0.05315 and 0.01029 mol. per kg, respectively). The density of sea water at different salinities has been taken from Cox [ 16]. mol/i. = (density) x (mol/kg).
(11)
Thus any complexation with magnesium and calcium other than with fluoride has been neglected and as an approximation the following fluoride mass balance has been used: [ F - ] t o t -----[MgF +] +
[CaF +] + [F-].
(12)
[F-]tot_ [MgF +] [F-] [F-]
[CaF +] ~- 1. [F-]
(13)
Hence
Finally
[MgF +] [F-]tot
[MgF +] [F-]tot [F-]
[F-]
(14)
[ C a F + / [ F - ] t o t c a n be obtained in a similar manner. These values are given in Table 4 and plotted in Fig. 2.
Acknowledgements-I wish to thank the head of this department, Professor David Dyrssen, for suggesting this investigation and discussing the results and their presentation with me. I also wish to thank Dr. Susan Jagner for revising the English text of this paper. Our work on the chemistry of sea water is supported by the Swedish Natural Science Council. 16. R. A. Cox, In Chemical Oceanography (Edited by Riley and Skirrow), p. 103. Academic Press, New York (1965).