This dissertation has been 63-2552 microfilmed exactly as received
SIMONAITIS, Richard Ambrose, 1930- THE STABILITY AND NATURE OF COMPLEXES OF MERCURY WITH HIGHER PHOSPHATES.
The Ohio State University, Ph.D., 1962 Chemistry, analytical
University Microfilms, Inc., Ann Arbor, Michigan THE STABILITY AND HATHRE OF COMPLEXES OF MERCURY
WITH HIGHER PHOSPHATES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Richard Ambrose Simonaitis, B.S., M.Sc.
The Ohio State University 1962
Approved by
A dviser ipartment of Chemistry ACKNOWLEDGMENTS
The author wishes to express his great appreciation to his adviser. Professor James I. Watters, for h lB great interest, under standing and guidance in all phases of this work.
He also wishes to thank his wife, Vera, for her aid in the preparation of this manuscript.
i i CONTENTS
CHAPTER Page
I INTRODUCTION ...... 1
II METHOD...... 21
III THE COMPLEXES OF MERCURY(I) WITH PYROPHOSPHATE . . 31
Experimental ...... 31
Experimental Results and Discussion ...... 33
IV THE COMPLEXES OF MERCURY(I) WITH TRIPHOSPHATE . . . 6l
Experimental ...... 6 l
The Acidity Constants of Triphosphoric Acid in the Presence of 1 M Sodium and Potassium Ions ...... 62
The Complexity Constants of Mercury(l) with Triphosphate ...... 63
V THE COMPLEXES OF HERCURY(I) WITH TETRAPHOSPHATE . 86
Experimental ...... 86
Experimental Determination of Acidity Constants ...... 88
Experimental Determination of Complexity Constants ...... 90
VI SUMMARY...... 115
AUTOBIOGRAPHY...... 12h
i i i TABLES
Table Page
1 Potential Data of Pyrophosphate-Mercury( I) System in the Presence of 1 M Sodium Io n ...... 4-8
2 Contributions of Various Complex Species to Fj .... 5®
3 Potential Data of Pyrophosphate-Mercury(I) System in the Presence of 1 M Potassium Io n ...... 52
U Contributions of Various Complex Species to P^ ----- 5^
5 Complexity Constants for Pyrophosphate-Mercury(l) S y s te m ...... 60
6 Potential Data of Triphosphate-Mercury(I) System in the Presence of 1 M Sodium Ion at High pH Range 70
7 Potential Data of Triphosphate-Mercury(I) System in the Presence of 1 M Sodium Ion at Low pH Range .... 72
s Contributions of Various Complex Species to . . . . 73
9 Potential Data of Triphosphate-Mercury(I) System in the Presence of 1.0.M Potassium Io n ...... j6
10 Contributions of Various Complex Species to F^ •••• 78
11 Complexity Constants for Triphosphate~Mercury(I) S y s te m ...... 85
12 Potential Data of Tetrapbosphate-Mercury(I) System in the Presence of 1.0 M Sodium Io n ...... 100
13 Contributions of Various Complex Species to P^ .... 103
lU Potential Data of Tetraphosphate-Mercury(I) System in the Presence of 1.0 M Potassium Io n ...... 106
iv TABLES (contd.)
Table Page
15 Contributions of Various Complex Species to Pi .... 108
16 Complexity Constants for Tetraphosphate-Mercury(I) S y s te m ...... 110
17 Summary o f Com plexity C onstants fo r M ercury(l) Polyphosphate System ...... 117
v FIGURES
Figure Page
1 Survey Polarogrem of the Mercury Pyrophosphate Sys t e m ...... 3^
2 Potentiometric Potential Shifts as a Function of pH for the Mercury(l) Pyrophosphate System ...... JS
3 Graphic Determination of /^Oll an<^ /^012 ^or t^ae Mercury(l) Pyrophosphate System in the Presence of 1.0 M Sodium Ion ...... ^1
!+ Graphical Determination of ^010 *-n Presence of Potassium Io n ...... UU
5 Percentage Distribution of Mercury(l) Pyrophosphate Complex Species as a Function of pH in the Presence of Sodium Io n ......
6 Percentage Distribution of Mercury(l) Pyrophosphate Complex Species as a Function of pH in the Presence of Potassium Io n ...... 5^
7 Potentiometric Potential Shifts as a Function of pH for the Mercury(l) Triphosphate System ...... 6U
8 Graphic Determination of /^ o il /^012 ^or Triphosphate System in the Presence of Potassium I o n ...... 67
9 Percentage Distribution of Mercury(l) Triphosphate Complex Species in the Presence of 1.0 M Sodium Ions ...... SO
10 Percentage Distribution of Mercury(l) Triphosphate Complex Species in the Presence of 1.0 M Potassium Ions as a Function of pH ...... 82
vi FIGURES (con td .)
Figure Page
11 Potentiometric Potential Shifts as a Function of pH for the Mercury(l) Tetraphosphate System .... 91
12 Graphic Determination of /^oil /^012 ^or Tetraphosphate System in the Presence of Sodium Ion ...... 93
13 Graphic Determination of /^oiO for tlle Tetraphosphate System in the Presence of Potassium Io n ...... 98
lU Percentage Distribution of Mercury(l) Tetraphosphate Complex Species in the Presence of 1.0 M Sodium Ions as a Function of pH ...... I l l
15 Percentage Distribution of Mercury(l) Tetraphosphate Complex Species in the Presence of 1.0 M Potassium Ions as a Function of pH ...... 113
v ii CHAPTER I
IHTRODUCTION
Until recently, it was generally assumed that mercury(I) complexes were unstable with, respect to disproportionatlon to form the more
stable mercury(Il) complex and free mercury. In contrast, the equi
librium constant for the formation of aquomereuxy(l) ion from ele mentary mercury and aquomercuxy(Il) ion is 130 in 0 .5 M NaClOty,. ^ The
XS. Hietanen and L. G. Sillen, Arki▼ Kemi, 10, IO 3 ( 1956 ).
reaction is readibly reversible.
On the basis of potentiometric evidence, Sillen and his co- workers ’ have suggested weak complexes of mercury(l) ion formed by
2G. Infeldt and L. G. Sillen, Svensk. Chem. Tidskr., ( 19 U6). nitrate, sulfate and perchlorate anions due to ion-pair association with formation constants of:
2 .5 M*1 (Hg2H03^), 0.5 M~2 (Hg2(N03)2) t 20 M“l (Hg2S0h),
250 IT 2 (Hg2(S 0^)22") and 0 .9 IT 1 (Hg2C10l / ) .
1 However, during the nin eteenth century, Stromeyer^ and then
3y. Stromeyer, Schweigger's Journal, 38, 130 ( 1830 ); as reported in J. V. Mel lor "A Comprehensive Treatise on Inorganic and Theoretical Chemistry," Vol. IT, Longman, Greens & Co., London, 1923. P* 100 3.
Brand^ reported that a white precipitate forms and then redissolves in
**Brand, Z. anal. Chen., 28, 592 (1889). excess of reagent when sodium pyrophosphate solution is added to a mercury(l) solution which suggests the formation of a strong, stable complex.
R ecently, Yamane and Davidson^ confirmed th ese o b serv atio n s and
^T. Yamane and N. Davidson, J. Am. Chem. Soc., 82, 2123 (i 960 ). also reported stable mercury(l) complexes with tripolyphosphate, oxalate, oC-Dimethylmalonate and succinate anions. They employed a potentiometric method on a buffered solution in the present of 0.75 **
NaHOj a t 27.^ £ 0.1°C and reported the principle complexes as
HggLg^-^)" and HggL(OH) (o.“l)"i where L^“ is the anion. The overall complexity constant for HggfPg^g”^Wa8 found to ( 2.h / 0 . 6) 10^
M“ 2j Hg2(0H)Pg0y"3 was (h.h / 0 . 6) 10*5 g-2 in a pg -ange 0f
7.^9-55. for Hg2 (P3Oio)2"S it was (1.7 £ 0.3)l0U ; and for
Hg2(0H)P301Q'"14, i t was (1.0 / 0 . 2) 10*5 in the pH range 7*18 to 9*00.
Expressions for these constants will be presented later. 3
Many investigators have studied the acidity constants of pyro- phosphoric acid. Abbott and Bray,^ in a conductivity study of the
6&. A. Abbott and W. C. Bray, J. An. Chem. Soc., 2 1 * 1 * 3 U909) • hydrolysis, of ammonium salts of pyrophosphoric acid By a distribution method at 18°C obtained the values E^ » l.U x 10“*; E 2 = I *1 x 10"2S
Kj 3 2.9 x 10“7; and Kjj. * 3*6 x 10"9 at sero ionic strength. Eolthoff and BosclJ applied the Debye-Suckle relationship to data obtained from
^1. M. Kolthoff and W. Bosch, Rec. trav. chim., Uj., 826 (1928). a hydrogen electrode at 18°C extrapolated to infinite dilution and obtained the values, K 3 - 2 .1 x 10**7 and E^ = M-.06 x 10""*®. Horton®
®C. Morton, J . Chem. Soc. (London), 1928. 1U01. obtained the values E3 = I .98 x 10“ 7 and E 14. = I .32 x 10"10 a t 30°C and also noted complex formation with alkali metal and alkaline earth salts. In a hydrolysis study. Me Gil very and Crowther,9 determined the
^J. D. McGilvery and J. P. Crowther, Can. J. Chem., 3 2 * ^7^ ( 195*0. acid dissociation constants at 65.5°^. Substituting the data obtained by electrometric titrations into the basic stoichimetric equations by a series of approximations, they obtained the values, Ej = 0 . 107,
Eg = 7.58 x 10“ 2, E3 = 1.U5 x 10”6, and El* - 9 .8 x 10*9. Monk*® studied pyrophosphoric add by means of conductance measurements
10C. B. Monk, J. Chem. Soc., lqUq. U23. a t 25°C and calculated the dissociation constant for the NaPj^^" complex. From pH measurements of solutions of the sodium salts and the acid he was able to calculate the acid dissociation constants of pyrophosphoric acid at u * o as K 3 s 2 .7 x 10” 7 and E^ = 2.U x 10"*® after taking the association between sodium ions and pyrophosphate ions in to consideration. Lambert and Watters*'* determined the a c id ity
**S. M. Lambert and J . I . Watters, J. Am. Chem. S oc., 2$, h262 (1957). constants extrapolated to infinite dilution as pE^ = > 00 , pE2 = 2.6H; pE^ = 6 . 76; pE^ ■ 9*^2. Huhn and Beck*^ a lso calcu lated the d lssoci~ ation constants of pyrophosphoric acid.
*^P. Huhn and M. T. Beck, Acta Univ. Szegediensis, Acta Phys. et Chem. (N .S .), *£, 45 (I 95 S).
The tendency of pyrophosphate to form complexes with many metals through chelate ring formation has been the subject of many studies.
In a polarographic study, Eolthoff and Watters*3 determined the
*3l. M. Eolthoff and J. I. Watters, Ind. Eng. Chem., Anal. Ed., 15, g (19^3)• diffusion coefficients of the complex manganipyrophosphoric acid ion with the aid of the Ilkovic equation. Prom the relation between the diffusion coefficient and the molecular weights compared to CoCC^^)^
they calculated the approximate molecular weight and postulated the
formula as Rogers and Reynolds1** used potentiometric
^L . B. Rogers and C. A. Reynolds, J. Am. Chem. Soc., Jl, 2081 (19^9).
and conductometric measurements to study complexes of pyrophosphate.
They found that the complex, M(ll)(P20^) ” was formed by cadmium,
cobalt, copper, lead, magnesium, nickel and sine; M(II)(P20y)2^~ was
formed by copper and zinc; and M(II)(P 20y)1- and M(III)(P 207) 2^”
formed by aluminum and iron. Polarographic studies were made by Tan
Wazer and Campanella1^ on aqueous solutions of barium or sodium with
^ J . R. Tan Wazer and D. Campanella, J. Am. Chem. Soc., J 2 , 655 (1950).
the tetramethylammonium salt of pyrophosphoric acid. These studies
showed that the coordination number of barium is four and that of
sodium is two in the complexes. They reported the dissociation
constant of sodium as approximately lO"^ and of barium of about 10"9*5
based on the concentration of pairs of phosphorus atoms. In addition,
they presented the effect of twenty metal ions on the pH titration
curves of polyphospheric acids and interpreted them in terms of com* pi exion formation, which they divided into the following groups: (l) quaternary ammonium ions, which form no complexes, (2) alkali metal
and similar cations forming weak complexes and ( 3) the other metals which form strong complexes. This complex formation was ascribed to chelate ring structures formed along the polyphosphate chain. Souchay
and faucherre^ In a discussion of the relations that enable a calcu-
Souchay and J. Faucherre, Bull. soc. chim. France, 19*47. 529.
lation of the coordination numbers and the equilibrium constants of
complexes from the displacement of polarographic potentials found that
the coordination number of cadmium pyrophosphate is two and that the
equilibrium constant was 1.5 x 10^. Watters and Kolthoff1? reported
I . Watters and I . M. K olthoff, J. Am. Chem. S o c., 20.* 2*455 (19*46).
that both manganese(Il) and manganese(III) coordinate three dlhydrogen
pyrophosphate ions at zero pH. In a polarographic study of sodium
pyrophosphate-ferric chloride solutions, Eriksson^-® found that there
Eriksson, Kgl. Lantbruks Hogsko. Ann, 16, 39 * 72 ( 19*49) • was a dipryo-ferric complex in weakly acid solutions and a dihydroxy-
monopyrophosphate-ferric complex in neutral and slightly alkaline
solutions. He reported the coriplexity constant for CuPjjOy in solu-
r -lU tions of pH more alkaline than 11 to be 6 x 10 . Syrokomski and
A v i l o v * 9 in their studies found the ferric ion also forms a 1:1 complex
with pyrophosphate ion.
s. Syrokomski and V. B. Avilov, Zavodskaya Labo, l 6, 11 (1950). 7
From thermometric titration curves, transport experiments and pH titration of sodium pyrophosphate against a ferric chloride, Banerjee end Mltra2® formulated the complexes Fe(P 20y )2^” and Fe(P 20y )1- and
20s. Banerjee and S. K. Hitra, Science and Culture, l 6 , 530 (1 9 5 D . reported an instability constant of 2.8 x 10”^ for the FeCP^y^^” pT_pli complex from photometric measurements. Haidar studied pyrophos-
21B. C. Haidar, ibid.. lU, 3^0 (19^9). 22B. C. Haidar, Nature, 166, 7bh (1950).
2h . C. Haidar, Current Sci. (India), 1^, 2b4 (1950).
2l4B. C. Haidar, ibid., ]£, 283 (1950). phate complexes with copper, nickel, cobalt, lead and sine by thermo metric, transport, conductometric, pH, magnetic and cryoscopic measurements in saturated Na 2S0^. solutions. He found that the formulas for the complexes formed was M(P20y)2^” and M(P 20y)2~, where M indi cates the metal ion. From polarographic data, Laitinen and 0nstott25
25h. A. Laitinen and E. I. Onstott, J. Am. Chem. Soc., J 2 , k J 2 S (1950). showed that copper(Il) ion coordinated with two HP^y-^" ions in solu tions haring more than one fold excess of the complexing ion, and that one HF 20y3~ ion was coordinated when less than one-fold excess of the complexing ion was present in the pH range of } .6 to 5*3* They also gave evidence for the exLstance of Cu(HP 20y)(PgOy)^” and/or Cu(P 20y )2^~ in the pH range of 7 to 10, and that Cu(OH)(P 2O7)existed in strongly alkaline solution. From polarographic data they calculated the dis
sociation constant of bismonohydrogenpyrophosphate-cuprate(II) as 1 x
10"*®, monohydrogenpyrophosphate-cuprate(II) as U x 10" 7 and. hydroxopyrophosphate-cuprate(Il) as 2 x 10"*^. Mayer and Schwartz2^
p A S. W. Mayer and D. Schwartz, ibid., 5106 (1950)* measured the distribution of cerium(lll) between ion-exchange resin
Dowex 50 and solutions of pyrophosphoric acid and calculated the as
sociation constant for CeP^y*" to be l.k x 10* 7 . Lingane and M eites27
^ J . J. Lingane and L. Meites, ibid.. 73. 2165 (1951)* reported that they obtained data on the half-wave potentials and dif fusion-current constants of the waves of vanadium(II), and vanadium(ll) in pyrophosphate solutions but did not discuss the complex formulas.
In a polarographic study of Thallium pyrophosphate complexes, Senise and Delahay2® found that the species TlCPgOy)^" was predominant in the
2gP. Senise and P. Delahey, ibid.. f k , 6128 (1952). neighborhood of pH 13 but that complexes of a higher order also existed. However, their formation constants could only be determined in a very approximate manner by the polarograph method. Watters and
Aaron2^ found that copper(Il) and pyrophosphate ion give complexes
^ J. I. Watters and A. Aaron, ibid.. 75. 6l l (1953)* having ratios of 1: 2, 1: 1, 2: 1, and U :1 in solutions containing the corresponding ratios of copper to pyrophosphate ion. The last two species were detected only in very dilute solutions. They found that th e 1:2 ratio was predominant in solutions containing a moderate excess of pyrophosphate ion in the pH range of 10 to J and that the equili- brium shifted to form more of the 1:1 complex at lower concentrations of pyrophosphate ion or in weakly acidic solution. At an ionic strength of one, they reported the stepwise dissociation constants of the 1:2 complex as 2 x 10” ^ and 2 x 10“*.
From equilibrium potential and conductivity measurements, Ukshe and Levin^O calculated the instability constants for CuCPgOy)and
A. Ukshe and A. I . le v in , Zfanr. P is. Khim., 2£, 139^ (1953)*
CuCPpOy)^" as O.63 x 10“6 and 0.5 x 10“*®, respectively. Bobtelsky and Kertes^*’^ investigated pyrophosphate complexes of calcium,
3*M. Bobtelsky and S. Kertes, J. A ppl. Chem. (London), *£, Ul9
( 195^ ) •
32M. Bobtelsky and S. Kertes, ibid.. 5 , 675 (1955). strontium, barium, magnesium, manganese, nickel, cobalt and copper by heterometric, potentiometric, pH and conductivity titration. They found that all the cations gave complexes of the type MtPgOy)2* and, in addition, copper and nickel gave the complexes CuXPgO-^^”,
Cu(P207)310“ and H i^PgO ^2". 10
Yateimirskii and Va8ilev33.3^ in a solubility study of pyrophos-
33k . B. Yateimirskii and V. P. Vasilev, Zhur. Fiz, Khim., TO. 901 (1956).
3**K. B. Yatsimirskii and V. P. Vasilev, Zhur. Anal. Khim., 11, 536 (1956). phate salts reported complexes and their dissociation constants of
CUP2O72" , 2.0 x 10"7; Cu(P 20y )2^” , 1 x 10~9 . ^(PgOy)2', 1 .5 x 10“ ^*
NitPgOy)2^*, 6.5 x 10“g . They a lso found th e complexes ZnCPgOyJg^”
and Pb(P 207) 2^” but did not report any dissociation constants.
Vasilev35*36 determined by means of colorimetric pH measurements, the
35y. P. Vasilev, Zhur. Piz. Khim., 31, 692 (1957).
3 ^. p. Vasilev, Zhur. Heorg. Khim., 2, 6O5 (1957).
instability complexes of MtPgOy) “, where M indicates magnesium,
strontium, or barium to be 5 x lO- ^, 2.2 x 10~5 and 2.3 x 10* 3,
respectively. Subrahmanya3^“39 studied the polarographic behavior of
37r. S. Subrahmanya, J. Indian Inst. Scl., ^ 8A. 87 (195^).
3%. S. Subrahmanya, ibid.. ^ 8 A. 163 ( 1956 ).
^H. S. Subrahmanya, Anal. Chim. Acta, 22, U 95 ( i 960)•
complexes o f pyrophosphate ion w ith iro n , lead , cadmium, bism uth,
titanuim and niobium at various pH values. He determined the lead p pyrophosphate complex formula as Pb(P 20y) but was unable to ascertain
the nature of the other complexes due to the irreversibility of their polarographic waves. By means of amperometric and visual titration, 11 and polarographic and solubility methods, Yakshova too established the
^P . I. Yakshova, Trudy Voronesh. Univ., U2, No, 2, 63 (1956)* existance of FeCHPgOy^^* In aqueous solutions containing pyrophosphate and iron(IIl) ions at pH of 6 to 9 . 6. He reported the dissociation constant of the ion to be 6 .5 x 10"^. Lambert and W atters^ calcu-
^S. M. Lambert and J. I. Watters, J. Am. Chem. Soc., 5^08 (1957)- lated the stabilities of the complexes of pyrophosphate ion with magnesium(Il) ion from pH lowering during titration with hydrogen ion a t 25°, ionic strength of unity, to be MggPgOy = 10^* 55^ MgPgOy2” = lO^*^ and MgCHPgOy)1* = 10^*°^. Yaid and Bama Char *2 used potentio-
U2 J. Yaid and T. L. Rama Char, Bull. India Sect. Electrochem. S oc., I , 5 (1958). metric, conductometric and spectrophotometric methods to study complex formation between pyrophosphate ion and copper, zinc, tin, lead, nickel and cobalt ions. They found that a complex of the tjrpe (MPgOy)2*’, where M indicates the metal ion, was formed by all the ions and that the instability constants of the complexes were Sn, ( 2 .2 - 2 .5) x 10“ ^ ;
Zn, ( 2 . 2- 3. 7) x 10"7; Cu (0.8 x 10“l0); Pb, ( 6. 8 - 8 .7) x 10-11;
Ni, 2.U x 10”**; and Co, 9*5 * 10“**. They also reported that complexes of the type HtPgOy^^" was formed by copper, nickel, cobalt and zinc but gave no instability constants. Copper and zinc pyrophosphates 12 were studied potentionmetrically ‘by Persiantseva and Titov. ^3 They
^3v. P. Persiantseva and P. S. Titov, Nauch. Doklady Vysehei Shkoly, Khim. i Khim. Tekhnol., 1958. No. 3, 584. also found complexes of the type M(P 20y)and MPgOy2" and reported the dissociation constants at 25° to be K^ * 6.8 x 10“9 and. Kg - 1.02 x 10’ 9 for the copper complex and K^ = 8.0 x 10“ ' and Kg = 8.06 x 10 for the zinc complex. Tarayan and his coworkers1^*"^ used polarography
^ 7 . M. Tarayan, M. G. Ekimyan and A. I. Kochoryan, Irvest. Akad. Nauk Armyan. S.S.H., Ser. Khia. Nauki, 10, No. 2, 105 (1957)*
**5v. M. Tarayan and M. G. Ekimyan, ibid. . 11, No. 1, 23 (1958). ^V. M. Tarayan, L. A. Eliazyan and 0. A. Darbiryan, ibid., 12, 333 (1959). and potentiometry to study pyrophosphate complexes with cerium and magnesium ion. They reported the complex Mn(HgPgOy ) - ^ r to be the pre dominant species at a pH of 4.25 and that Mn(HPg0y)g3" was the pre dominant species above that pH. In the case of the cerium complex they found that the complex had the form CeCHgPgOy)at a pH of 4.25 and th a t Ce(HPg0 7)g2“ was the species at a pH of 7*5* Calcium com plexes of pyrophosphate ion were studied at 25° and unit ionic strength by Watters and Lambert^ using a pH titration procedure. The complexes
^ J . I. Watters and S. M. Lambert, J. Am. Chem. Soc., 81, 3201 (1959). they found and their respective complexity constants were CaPgOy ,
10^'95 and Ca(HP207) 1' , 102 *3°* Triphosphoric acid titration curves were first published by Budy
and Schloesser*® but, due to complex formation, no attempt was made to
**SH. Budy and H. Schloesser, B er., ]£, 1*8** (I 9 H0 ).
n calculate the acidity constants. By application of the Debye-Huckel
equation to data obtained in the titration of triphosphoric acid with potassium hydroxide, Beukenkamp, Bieman and Lindenbaum^ were able to
^ J . Beukenkamp, W. Bieman and L. Lindenbaum, Anal. Chem., 26, 505 (195*0-
report the values pK-j = 2*79. pKty. = 6.1*7 and pK^ = 9 . 2U. Watters,
Loughran and Lambert-*® reported pK's for a c id ity constants at an io n ic
5®J. I. W atters, E. D. Loughran and S. M. Lambert, J. Am. Chem. S o c., J8, U855 (1956).
strength of unity and temperature 25° as pK2 - 1 .0 6 , pK-j = 2 .1 1 , pKh =* 5 -83t and pK^ = 8 .8 1 .
The tendency of triphosphate ion to form complexes with many metals has been studied by many investigators. Van Wazer and Campa-
nella*5 in polarographic studies on aqueous solutions of barium or
sodium w ith tetramethylammonium s a lts o f acids obtained from several
condensed phosphates showed that the coordination number of barium is
four and that of sodium is two in the polyphosphate complexes. They
found that the sodium reduction was completely reversible and the dissociation constant was approximately 10“ 3 (based on concentration
of pairs of phosphorus atoms) and that the barium reduction was 1U somewhat irreversible giving a calculated constant of approximately
10"9-5. The constants they calculated were independent of the poly phosphate molecular weight. In addition, they reported the effect of twenty metal ions on the pH titration curves of the polyphosphoric acids and interpreted them in terms of complex-ion formation, which was ascribed to chelate ring structures formed along the polyphosphate chain. Monk1® employed conductance to determine the sodium triphos phate complexity constant. Rudy and coworkers51-52 observed the
51h . Rudy, Angew. Chem., kkj ( lg H l) .
5%. Rudy, H. Schloesser and R. Watzel, Angew. Chem., 53 ( I m possibility of a calcium complex by means of pH lowering during a study of lime soaps. Prankenthal53 observed that the addition of
53l. Frankenthal, J. Am. Chem. Soc., 66, 212k (1944). magnesium chloride to sodium triphosphate caused a depression o f pH that depended on the concentration of the magnesium chloride, and that mixtures w ith a high magnesium chloride content had an even lower pH than magnesium chloride alone at the same concentration. The same results were observed in the presence of aluminum ion. Monnier,
Bonnet and Brard.5^ briefly discussed the formation of calcium
5Hi. M. Monnier, V. Bonnet and R. Brard, Arch. Intern, Physiol., 5 H, lgg ( I 9 I+6 ). 15 complexes with triphosphate Ion in "body fluid. Boh tel sky and
Kertes^1’^ studied alkaline earth metals, manganese, cohalt, nickel, and copper complexes hy heterometric, turbidity, pH, potentiometry, and conductivity measurements. In the presence of triphosphate ion thqy found that in all cases a soluble salt of the formula MPjOio*^- , where M indicates metal ion, was formed, and in addition, soluble salts of the complex were obtained with nickel and cobalt and o f M^PjOio)with copper. By means o f an acid titr a tio n method,
M artell and Schwarzenbach55 a lso found that magnesium and calcium forms
55a. E. Martell and G. Schwarzenbach, Helv. Chim. Acta, 39» 653 (1956). complexes with triphosphate ion of the formula MP^Oio^- . Kobayashi5^*57
5%i. Kobayashi, J. Chem. Soc. Japan, Pure Chem. Sect., 793 (1955).
57m. Kobayashi, Nippon Kagaku Zasehi, jS, 1023 (1955)* studied complexes o f sodium triphosphate with n ic k e l, lead and cadmium by means of amperometric titrations. He found that the predominant species for all three ions present was MPjOiq '*”, where M indicates the metal ion.
The stability of complexes of triphosphate ion with sodium, po tassium and lithium from pH lowering during titrations of triphosphate ion with hydrogen ion were reported by Watters, Lambert and Loughran5g
5gJ. I. W atters, S. M. Lambert and E. D. Loughran, J. Am. Chem. S o c., 2 2 , 3651 (1957)- at 25° in 1 M methylammonium chloride. The formulas of the complexes and the values of their formation constants they found were: KP jP i q * ~ , lO1*^; NaPjOiQ1*”. lO1*^; LiP^io*4-, 102’87; Na(HP-j0 10) 1 0 ° ' 77{ and Li(HPjO-Lo)^“>t 10^*88. W atters and Lambert ***1*7 also studied com plexes of triphosphate ion with calcium and magnesium ions by a pH
titration method. The complexes and the complexity constants they
found a t 25° in one molar tetramethylammonium chloride were:
107 *96; MgPjOlO3” , 105*83; Mg(HP 3010) 2' . lO3' 3**; CaP 30103' ,
1q5 * ^ ; and. Ca(HP 3O^Q)103’^. Pamfilov, Lopreshanskaya and Gusel^
59a. V. Pamfilov, A. I. Lopreshanskaya and E. B. Gusel, Ukran. Khim. Zhur., 2^, 297 (1957). reported that the triphosphate complexes of lead and cadmium were of
the type M ^P^iq)^11*", the coordination number of the metals were
four. They obtained the dissociation constants as 3 X 10"5 and 9 x
10“ for the lead and cadmium complexes, respectively. Subbaraman and his coworkers^*^ used polarography to study uranyl and also lead,
^®P. R. Subbaraman, N. R. Joshi and J . Gupta, A nal. Chim. Acta, 2 0 , 89 (1959).
6lP. R. Subbaraman, P. S. Shetty, ibid.. £2, U95 ( i 960 ). bismuth, titanium and niobium complexes. They reported that all of the polarographic waves except those for lead at pH 5 were irreversible but gave no discussion of any complexity formulas. Ion-exchange
experiments were made on solutions of sodium and copper triphosphate complexes "by Heitner-Wirguin, Salmon and Mayer.They found no
62C. Heitner-Wirguin, J. E. Salmon and E. Mayer, J. Chem. Soc., I 960 . U60. evidence of complexes containing more than two triphosphate ligande.
In the presence of chloride ion a 1:1 complex was found that was more strongly sorbed in competition with other lone than complexes formed in the absence of choride ion which they ascribed to the formation of a mixed chlorophosphate complex. Wolhoff and Overbeek^ studied com-
63j. A. Wolhoff and J. Th. G. Overbeek, Rec. trav. chim., ][ 8 , 759 (1959). plex formation by means of a pH lowering method. They found that both pyro- and triphosphoric acids had the same acid dissociation constants, namely, 10"9*52 at 250. They also found that triphosphate had some what stronger complexing properties than pyrophosphate and listed the formation constants for lithium, sodium, potassium, cesium, magnesium, calcium , stro n tiu m , barium , zinc, and cadmium io n s.
Eleitmann and Henneberg^ first claimed the preparation of sodium
^Fleitmann and W. Henneberg, Liebigs Ann. Chem., 6^ , 32^ (18^8). tetraphosphate by a fusion of sodium metaphosphate with sodium pyrophos phate in a 2:1 ratio. Schwarz^ claimed to prepare Eleitmann and
Schwarz, Zeit. anorg. Chem., g., 2^9 (1895)* IS
Henneberg ’8 acid tetraphosphate, Nai|B2P4£l3 the salt, Na2H2P2®7
by the removal of the water of cyrstallisation. Strange^ stated that
Strange, Z. anorg. allg. Chem., 12, W* (I896 ).
he was able to confirm this. Later, however, three sets of workers67“’69
67 k . R. Andress and K. W urst, Z. anorg. a llg . Chem., 237. 113 (1938). 6®P. Bonneman-Bemia, Ann. Chim., l 6, 395 (19^1).
69 e . p . Partridge, V. Hicks and Q-. W. Smith, J. Am. Chem. Soc., £ l. k 5 k (19^1).
contradicted the existence of the compound by means of x-ray studies.
In 19^9, Thilo ani Rat *70 prepared sodium tetraphosphate by mild
7°E. Thilo and R. Ratz, Z. anorg. chem., 260, 255 (19^9).
alkaline hydrolysis of sodium metaphosphate at 1+0°. They obtained a
colorless, viscous oil which they were unable to crystallize although
they were able to obtain insoluble calcium, silver and zinc tetraphos- phates which were amorphous to x-rays. The existence of the tetraphos phate ion was confirmed by the use of chromatography by Westman and
Scott7^ and also by Ebel,72*73 tut they also failed to succeed in
7xA. E. R. Westman and A. E. S c o tt, N ature, l 6g. 7^0 (1951)* 7 2 j. P. E bel, Compt. re n d ., 23U, 6 2 1 (1 9 5 2 ). 73j. P. Ebel, Bull. soc. chim. France, 1953. IO 89 . isolating a crystalline tetraphosphate. Quimby,7^ in a study on
7*0. T. Quimby, J . Phys. Chem., ^ 8 , 603 (l9 5 h ).
soluble crystalline polyphosphates succeeded in crystallizing the
hexaguanidine tetraphosphate from a formamide rich solution which was purified to 95"99 P©r cent and confirmed by means of x-ray diffraction.
By heating appropriate mixtures of PbtHgPOiPg and PbHPOij. to
constant weight at 550°» Osterheld and Langguth,75 were able to fora
75a. K. Osterheld and H. P. Langguth, J. Phys. Chem., 22.» 76 (1955).
lead tetraphosphate which they confirmed by means of x-ray diffraction.
Schulz7^ also prepared lead tetraphosphate and also bismuth tetraphos-
7^1. Schulz, Z. anorg. u . allgem . Chem., 287. 106 ( 1956 ). phate which he analyzed by x-ray diffraction and paper chromatography,
showing the former to be the same salt as prepared by Osterheld and
Langguth. Schulz was unable to prepare anhydrous tetraphosphates of
zinc, cadmium o r lith iu m and reached th e conclusion the anhydrous
crystalline tetraphosphates exist only for elements with relatively high atomic number and large ionic radius.
Tetraphosphate complexes with cadmium, lead and zinc were studied by Pamfilov, Lopushanskaya and M andel'eil77 using polarography. They
77 a . V. Pamfilov, A. I. Lopushanskaya and A. M. Mandel'eil, U krain, Khim. Z hur., 26, h i ( i 960 ). found that the tetraphosphate complexes gave irreversible waves and that the specific velocity of reduction of zinc, cadmium and lead tetraphorphates did not depend on the pH or the temperature. CHAPTER II
METHOD
Leden's?® method was used for the evaluation of the equilibrium
7 8 I . Leden, Z. Physik. Chem., 188A. l 6o (1941).
constants. He showed how the several complex species which exist
simultaneously in solution can be considered in potentiometric stu
d ie s .
The general expression for the equilibria of the aquo metal ion
with several ligands, assuming only mononuclear complexes are formed
and the overall formation constant for the reaction is
M / iA I JB / kC^MAiBjCk; /*ijk = (l) (M)(A)i (B)«)(C)k where i, j, and k may vary from zero to N, the maximum number of co
ordinated groups but their sum cannot exceed N. Rearranging equation
(l) and summing the equations for all species of M, yields
1 - K j - ffi k - N«1 2___ ) ) ^MAiBJCk^ i - O j = 0 k = 0 ( 2) (M) s ------i =- N j = k = J ' ' _ > ZZ. AjkCAj^BjJCOk i = o j = o k = o
21 22
The Nernst equation for the simple aquo metal ion is
E^ » Ef / S log (M)rp 3 ( ) where S is 2.303 RT/nF, E is the measured electrode potential versus the standard hydrogen electrode and Ef is the formal potential for the electrode reaction of the aquo metal ion.
The Uern8t equation for the complex ion is given hy
i * N 1 = N' k =* N " x z z z x z r (MAiBjCk) i = O j = O k = O E c * E f / S log ------(U) i_U j = N* k = N" 4 .4 v > XZ XZ /Sijk(A)1(B )J(C)k iro j-o k - 0
The equation for conservation of the metal ion is expressed aB
i = N j = N* k = N " (M )t = XZ XZ > ' (MAfBjCfc) ( 5) i ^ o j r O k-.iO
If the concentration of the metal ion is kept constant, and a constant large excess of supporting electrolyte is present, substituting equation ( 5) into equation (U) and subtracting from equation ( 3), y ie ld s
Eaq-Ec =Slog ^ 1Jk(A)i(B)j(c)k (g)
Rearranging equation (6) and by definition of the function F0,
(Eaq " Ec) i a K .1 = N» k = I 11 F0 = antilog ( § ) = Z ^____ Z i 2 f__ zX ------X Z 2 (7) i = 0 j = 0 k = 0
/* i,p C(A) 1(B).)(C)k When only one type of ligand Is completed, equation ( 7 ) expands to
r0 . 1 //*!<*> / /32(A)2 / ... /S„(A)» (S) which can he rearranged to
Ti - / ^ 2(A) / ... ^ n(A)n'X (g)
I f th e successive ^3 »8 a r e sufficiently separated, the constants can he determined hy a graphical plot of F-^ versus (A). A straight line will he obtained with an intercept equal to^3 j_ and a slope equal to
^ 2 ' After the first constant has been determined, higher F functions can he used to obtain the higher constants.
^ / A ( a ) / . . . ^ n( a)”-2 (1 0 )
In general,
^ »/?,/ (I D
If only a single complex exists over a large range of (A) values, the
F function will remain constant and can he determined directly. The
F function will also remain constant if all the other complex species present in the particular range of (A) values are known and the ap propriate values can he subtracted from the function.
In conqplicated situations such as those in which many complex species are formed with one type of ligand throughout the entire con centration range of study so that at no time is one species the pre dominant one or if complexes can form with more than one ligand or if complexes can form with two variable ligands at the same time, it is 2k necessary to solve for the constants by use of simultaneous equations.
The use of determinants for the calculations of stability constants has been discussed by Hindman and S u l l i v a n . 79 Procedures fo r mixed
7 9 j. c. Hindman and J . C. S u lliv an , J . Am. Chem., S oc., 2itt 6091 ( 1952 ). complexes and those associating with hydrogen ions have been developed in this laboratory.®® For the case of a metal ion complexing with two
8 ®0 . E. Schupp, P. E. Sturrock and J. I. Watters, Inorg. Chem. Aug. (in press). ligands, the equations take the form of
r l = f * 10 t ^ 2 0 ^ t y^OlClI / ^pg(B) 2 / h (B ) ( 12)
Complexes containing hydrogen ions can be treated in this way if one considers the hydrogen ion and the ligand bound to the metal ion rather than the hydrogen ion bound to the ligand as is normally con sidered. Thus, the equilibrium would be written as
M / iA / jB / kC ^ MAiBjCfc. ( 13) and the complexity constant would be expressed as
' (lU) where iA, jB, and kC in equation ( 13) indicates the number of hydrogen ions, polyphosphate ions and hydroxyl ion in the complex, rather than as normally expressed
M / iAB / kC ^ M(AB)1Ck ( 15) and its complexity constant, (M(AB)i pfc) ik ■(M)(AB)i (C)k (16)
One can convert ijk to the more generally accepted ik form from the acid dissociation equation
AiBj ^ iA i S B (17) and the dissociation constant
K , (A)*(B)J a ^AiBj^ (18)
Multiplying equation (lU) hy equation (18) one obtains equation (l 6) .
Thus,
(MAjBjOk) t (A)l (B)J a (MAiB.iCk) (M)(A) (B)^(C)k (AiBj) ‘ (M)(AiBj)(c)k (19)
The true concentration of hydrogen and hydroaqrl ions are actually not known, hut rather their activities, since a pH meter standardized against buffers of known hydrogen ion activity, is used in studies of this type. However, by use of hybrid acidity constants determined at the same ionic strength one can convert the hybrid complexity constants to the true complexity constant.
After the complexity constants have been determined, either by use of determinants or by means of graphical interpretation, the ap propriate substitution of these values and the ligand concentrations into equations of the type of equation ( 12) allows the calculation of a theoretical at the various experimental values based on potential
shift. A much smaller value of the experimentally determined Fi than the theoretical F^ would indicate the existence of a conqjlex species 26 which was not taken into consideration, while agreement between the
two values is a good indication of the accuracy of the calculated
complexity constants as well as an indication that the proper species were assumed to be present.
The hybrid acidity constants of the polyphosphoric acids were
calculated from a titration of the acid. Using pyrophosphoric acid,
as an example, the stepwise dissociations and corresponding hybrid
constants are
HhPy^h d / HjPy1' kx = | V ] (HjPy1") ( 2 0 ) (% Py) H-jPy1' d / HgPy2" k2 ( 21 ) (HjPy1")
H2Py2" ^ / HPy> k3 id ■ ( 22) (H2Py2^)
HPy5" d / Py^~ = L d j (Py1^ (23) (BPy3“ ) where Py indicates the pyrophosphate ion, brackets indicate activities,
and parentheses indicate concentrations.
Let b equal the number of millimoles of hydroxide added per
millimole of pyrophosphoric acid orriginally present and Cp equal the
molarity of pyrophosphoric acid present in any solution. Then, for
the conservation of pyrophosphate in all forms, Cp = (HtyPy) / (HjPy^“)
/ (H2Py2“ ) i (H Py>) / (Py1*") (2h)
and for the conservation of sodium ions,
bCp = (Ha/) (25) The equation for conservation of neutrality is
(Na^) / (h/) = (HjPy1-) / 2(H2Py2**) / 3(HPy3“) / ^Py*") i (OS’ ) (26)
When b Is appreciably less than 1, the only forms of the pyro- phosphate which need to be considered are HtyPy and H-jPy^". The others can be neglected since there is a negligible secondary ionisation or hydrolysis of an acid or base for which the ionization constants differ by 100 fold. Thus, equations (2h) and ( 25) reduce to
Cp - (E^Py) / (H-jPy1” ) (27) and,
bCp / (H/) = (HjPy1") /(OH-) (28)
Subtracting equation (27) from equation (28), yields
(HuPy) = (l-a)C p - (h /) / (o ir ) ( 29 )
Solving equation ( 27) for the (HjPy^“) species, yields,
(H3Py1-)- a Cp / (H/) - (OH") (30)
Substituting equations ( 29 ) and ( 30) into (20) yields,
ki - uL^J .rJ I*0? f ------/ (3 1 N) ( 1-b)C p-(HT) / (OH")
By definition of hydrogen ion activity,
[h/J = f(H/) ( 32) and, from the ionization of water,
(o ir ) = ( 33)
Solving equation ( 31) in terms of hydrogen ion activity,
W h < W * - bdl/fm rd J (3*0 .H / J / KW f 7 W 777 28
to hen the value of b is between 1 and 2, the species o f oyro- phosphoric acid which need to be considered are (^Py^-) and (HgPy^- ).
In this case, equations (2U) and ( 25) reduce to
Cp = (HjjPy1” ) / (H2Py2“ ) (35)
and bCp / V ) = ( H-jPy1-) / 2(H2Py2") / (OH") ( 36)
Subtracting the above two equations yields,
(HgPy2' ) = (b -l)C p / V ) - (O D (37)
Solving fo r (H^Py^“ ) y ie ld s,
(HjPy1-) =• (2-b)Cp - V ) / )0 r) (38)
Substituting equations (37). (38). (3^) and (33) (21) yields
IV] f (b-l)Cp / _£§£ - _Kw. 1 L J L t k2 = M L ! ± J (39) (2-b)Cp - Ce/J _ Kw
f ( h/// f
To solve for k 3 the value for b between the values 2 and 3 where
the species I^Py2- and HPy3“ predominant needs to be considered. In
this situation equation ( 2U) is written as
Cp = (H2Py2~) / (HPy3*) (UO)
and equation ( 25) is written as
bCp / (h /) = 2(H2Py2" ) / 3(HPy3“ ) / (CH") (M-l)
Solving equations (Uo) and (U-l) fo r (H Py3") y ie ld s
(H Py3*) = (b-2)Cp / ( h/ ) - (OH") (1*2)
Solving for (H 2Py2_) yields
(H2Py2" ) * (3-b)C p - (h/) / (OH") (1*3) Substituting ( 32) , ( 33), (42), and (43) into (22) yields
t3 = W [ ('-e,c> m
(3“*)Cp - / Br f [ b/J /f
Similarly, is solved in the region where b lies "between the values
3 and 4. In this region, the species which need to be considered are
(H P y3~) and (Py1*"). Therefore, equation (24) reduces to
Cp = (HPy>) / (Py1^) (45)
and equation ( 23) reduces to
bCp / (H/) = 3(HPy3~) / 4(P yM / (0H“) (46)
Solving the above two equations for (Py^“) yields
(Py4-) - (b-3)Cp / (H/) - (0H-) (47)
and, (HPy3“) i s given by t h e equation
(H P y3-) =■ (4-b) Cp - ( h/) / (OH') (48)
Substituting equations ( 32), (33)» (47). and (48) into ( 23) y ie ld s
(4-b) Cf, - ML*. Ew f [h / 7/ f
Similar derivations were made for triphosphoric and tetraphosphoric
acids. In general, the dissociation constants of the acid are given
by the equation
k, ( 5 0 ) (n-b)Cp - h t i p - - I —1 % . * f ru1X7It r If the acid is not too dilute and the constants are between 10“ 5 and 10‘9 constants are given by the equation
a t b 3 iH r (51)
To solve for the free concentration of the alkaline polyphosphate ion the following derivation was made using pyrophosphate ion as an example.
The stepwise dissociation of pyrophosphoric acid was given by equations (20) through ( 23) . Solving these equations in terms of
(Py*~) and substituting into equation ( 2U) y ie ld s
Cp * -M l 4 4 -h£L 4 i l cpy“-) (52) P [_kl k 2k3kh kgk-jk]^ kjkl^ converting to a common denominator and solving for (Py^“) yields,
(Py1*-) = ______„ ______^ ( 53)
S ince j s / j can be measured by a pH meter and the acid dissociation constants were previously determined, the concentration of free poly phosphate ion is readily calculated.
The amount of complexed ligand can be neglected if the concen tration of free alkaline polyshosphate is much greater than that of the metal ion. At lower ligand concentrations, a correction must be applied for the amount of ligand present in the complex. CHAPTER III
THE COMPLEXES OF MERCUBY(l) WITH PYROPHOSPHATE
Experimental
« Following the procedure of Pugh,*** a stock solution of mercury(l)
« ¥ . Pugh, J. Chem. Soc.,182U (1937).
nitrate was prepared "by shaking red mercury(Il) oxide, mercury and
nitric acid until after the addition of sodium chloride, a filtered
aliquot gave no test for mercury(II) ion upon testing with H 2S. I t was then standardized hy titration versus a standard sodium chloride
solution using O.Oh per cent bromophenol blue as the indicator.
Mercury(Il) nitrate was prepared by dissolving metallic mercury with freshly boiled concentrated nitric acid and diluting. The mercury(Il) nitrate solution was standardized against standard
thiocyanate using ferric alum indicator following the method of
Kolthoff and Sandell . 82
®^I. M. Kolthoff and E. B. Sandel, "Testbook of Quantitative Inorganic Analysis," 3r<* Ed., The Macmillan Co., New York, 1952, p. 5US).
31 32
Throughout this thesis, Cgg2 indicate the molar concentration o f H§2^ ions which is equal to £ the molar concentration of mercury(l) atom s.
The sodium pyrophosphate (Baker analyzed reagent grade) was ti trated with nitric acid to ascertain its purity and concentration.
Potassium pyrophosphate was prepared following the method of
Kolthoff and W atters^ "by heating dibasic potassium phosphate (Baker analyzed reagent grade) for 3 hours at 500- 700°C. After dissolving the salt in distilled water, an aliquot was titrated with standard n i t r i c acid using a Beckman Model G pH m eter to determ ine th e concen tration and the apparent acidity constants in the presence of 1 molar potassium ion.
The potential of the aquo solution of mercury(l) mercury was measured at pH I .90 in the presence of sodium ions and 3*07 *n the presence of potassium ion. These pH's were used because the potential and the pH of the solutions varied with time and were very slow to reach an equilibrium potential.
Potentials were measured with a Rubicon Model 2760 potentiometer.
Most of the polarograms were made with a manual polarogram designed by Watters.®3 However, some survey work was done using a Sargent-
8 3 j. 1. W atters, Rev. S c i. I n s t r ., 2 2 . 851 (1951)*
Heyrovsky Model XII Polarograph. A Beckman Model G pH meter equipped with a "general purpose" glass electrode was used for all pH measure m ents.
All experiments were performed in a constant temperature water hath maintained at 25/O.I degrees centigrade. In all experiments the alkaline pyrophosphate solution was used for the highest pH values and
the lower pH values were obtained by making stock solutions containing
varying amounts of nitric acid. In the studies made in the presence of alkali metals the saturated calomel half-cell and the dropping
electrode half-cell were connected by means of two 3 P*r cent agar- agar bridges of 11 mm inner diameter containing 1 M KNOy dipping into
an intermediate beaker containing 1 H O O y
Experimental Results and Discussion
Preliminary polarograms of pyrophosphate complexes with both mercury(l) and mercury(ll) obtained by means of a Sargent-Heyrovsky
Model XII Polarograph are shown in Figure 1. Both mercury(l) and mercury(Il) solutions yielded the same spontaneous potential but the mercury(Il) aquo ion has a diffusion current which is somewhat lower.
However, it was noted that in the presence of pyrophosphate ion the polarographic waves of both mercury(ll) and mercury(l) exactly coin
cided. The addition of chloride ion indicated the presence of mercury(l) ion in the mercury(Il) pyrophosphate solution, while the mercury(I) pyrophosphate solution showed no evidence of mercury(II) ion after precipitation of mercury(l) chloride, filtration and the addition of hydrogen sulfide to the filtrate. These results indicate Figure 1. Surrey Polarogreun of the Mercury Pyrophosphate System
Curve 1 1.22 i 10“ 3m Hg2(1 *03)2 5 x 10“ ^M Na^Py 0.0005^ Methyl Red
1.23 x 10“ 3m Hg(N0 3) 2 5 x 10"^M Nai|.Py O.OOO556 Methyl Red
Curve 2 1.22 x 10“ 3m Hg2(lK>3)2 1 M NaNO-j 0.0005^ Methyl Red
Curve 3 1 .2 3 x 10“ 3m HgCHOj) 2 1 M NaKC'3 0.000556 Methyl Red
Curve k 5 x 10“ ^ M Hai+Py O.OOO556 Methyl Red 35
ID o - 1" * I »---- 1---1 ■ I__ I__ L_ I I I <0 t W o w ^ <0 • » I + + + that a stable mercury(l) pyrophosphate complex Is formed. Furthermore, after mixing a solution of mercury(II) pyrophosphate with elementary mercury for one hour, exactly two moles of mercury(l) were precipitated for each mole of mercury(II) originally present. These observations were also made by Yamone and Davidson.5
A polarographic study of millimolar mercury(l) pyrophosphate was begun using the manual polarograph. However, it was soon noted that a very limited range of pH was available due to precipitation of the mercury(l) pyrophosphate. The concentration of mercury(l) ion was then reduced to 10"5 M and it was noted that the polarographic waves practically coincided with the residual current wave. The spontaneous potential was determined primarily by the residual or charging current of the dropping mercury electrode. Therefore, it was decided to use a quiet mercury pool similar to that used by Mason0^ in his studies of
0. Mason, Ph. D. doctoral dissertation, The Ohio State University (1955)* J. I. Watters, J. 0. Mason and 0. E. Schupp, J. Am. Chem. Soc., 28, 5782, 1956. the complexes of mercury(Il) with ethylenediamine tetraacetate.
The hybrid acidity constants for pyrophosphoric acid were ob tained using equation ( 50) on data obtained by titrating the salt in the presence of one molar alkali metal with standard nitric acid.
In the presence of one molar sodium ion, the constants obtained were pKlj. - 7.^8 and pKj = while in the presence of one molar potassium ion the values obtained were 7-89 and 5*66, respectively. It was found that the first and second hydrogen ion, corresponding to Ki and K2 were not associated sufficiently to have effect on the calculation of the free pyrophosphate ion. Thus, equation (53) reduces to
(Py> ° Kjku * * * ?/ •''k iW3 [ e r t j /i T£ h i/J n 2 <*>
For the mercury(l) pyrophosphate system in the presence of one molar sodium ion it was found that the data were consistent with the assumption that Hg2Py, HggPy . Hg2PyOH, and Hg2Py(0H)2- Thus equation
(7) can he written as
To - antilog „ y3010(p y) ^ yS020(Py)2 / ^ Q l l W (O D
/ ^ 012
It then follows that
Fl " fpyT - f 0 1 0 ^ ^ 020(Py) / / W ® - ) / ^ 012^0H"^2 ^ ^
A series of F^ terms were calculated from the shift of electrode potential by varying the pH of a stock solution containing mercury(l) ion and pyrophosphate ion in the presence of one molar sodium ion.
These potential shifts as a function of pH are shown in Figure 2. It was found that F^ had a constant value of 10^°*®3 in the pH range of
5. 29 - h . 56. This value corresponds to ^ 010.
H g ^ / P20y“ Hg2(P207) 2- ; 010 = _ 1Q10.g3 (H g| )(P207l4~) (in the presence of 1.0 M NaT.) 38
Figure 2. Potentiometric Potential Shifts as a Junction of pH for the Mercury(l) Pyrophosphate System.
Cjig = 1.22 x 10"5 M
Cpy = 3.88 x 10~2 M
Curve 1: In the presence of 1.0 M Sodium Ion.
Curve 2i In the presence of 1.0 M Potassium Ion. v= TT oq o 0.20 0.05 0.25 0.35 Q30 0.10 0.15 Pyrophosphate pH 39 Uo
To solve for y^ggO’ a ki&^er r function was obtained.
Is = n - A>io _ „ . g (OH-) . ( o r ) 2 ( 1 7) r 020 / r 011 ' ° 01 t * t ( 58 )
Again a pH region was found where F2 was constant. This range was from a pH of 8.32 to 5*73* Thus
* e f / 2P2o!f- ^ Ee2(P207) 6 - . « 020 = (ag2(P2o7) |') _ ,.1 1 .7 2 ' (B^XPjO*-)2 (in the presence of 1.0 M Na^). (59)
To solve for the complex species containing hydroxyl ion a new fu n ctio n was w ritte n as
*1 * PoiO -pOttM R r2 a = ------"(orj------= f 0 1 1 i foizioir) (6 0 )
The above equation was solved graphically in Figure 3* A plot of F2a versus hydroxyl ion concentration yielded a slope equal toy^Q12
Hg|V P20^ / 20H -^ Hg2(P207)(0H)^; (*01g = (^ (^ K O ^ g D
(H g ^ )(P 20 ^ )(0 H “ )
- io 20,1*1 (in the presence of 1.0 M Nar). (6l) and an intercept equal to ^ g i l
Hg|^ / P20^" / OH* ^ Hg2(P207)(0H)3-; y3Qn . ) (0H)3~). _ (H g ^ )(P 20 ^ )(0 IT )
, iol 5-07 (in the presence of 1.0 M Na^). (62)
The value obtained for y3 012 Was b rib er checked by the equation
F3a - F2a- f a l l , (01f ) ’ f012 (63) F igure 3* Graphic Determination of /^oil ^012 *or Mercury(l)
Pyrophosphate System in the Presence of 1.0 M Sodium Ion
CS g £ = 1.22 x 10-5 M
Cpy = 0.05 M
CNa = 1.0 M -IS 20 X 20 10 f Mercurous Mercurous Pyrophosphate in 1.0 £i N at - 6 x O (HO) and a constant value for was obtained of lO^O.^O wkiCh agrees very well with that obtained graphically.
The potentiometric potential shifts as a function of pH for the mercury(l) pyrophosphate system in the presence of one molar potassium ion is also shown in Figure 2. In solving equation ( 56) for F]_ it was found that F^ never assumed a constant value but decreased with de creasing pH and then increased as pH continued to decrease. It was then postulated that a (Hg 2HPy) complex e x is te d a t low pH v a lu e s and eq u atio n ( 56) was rewritten as
* i = = ^110 ^^-//bio/y^oso^ ^oh(oh-) //^oigtoa- ) 2 ( $ 0
Consequently, QIO was determined by plotting the free pyrophosphate ion concentration versus the F^ term in the pH range were F]_ decreased with decreasing pH in Figure U. The intercept was taken for the^AoiO v alu e
(Hg2(P207) 2-)
(H g ^ )(P20^ ) (in the presence of 1.0 M k/). and the slope was 0 q20
H g |/ / 2P2o ! f - ^ Hg2 (P207) i - ; - 101 2 ,2 5 (Hel^CPgoif- ) 2 ( i n th e p resen ce o f 1 .0 M K^) (66)
To solve for rilO equation (l9)-was used Figure U. Graphical Determination of qio in the Presence of
Potassium Ion.
Cug2 = 1.22 x 10*5 M;
Cpy * 3.88 X 10“2 M;
Cjj = 1 .0 M o eg
v (Py)
& in <3 * ro cvj — o
6- 0 ' * 'J U6
The three logarithm values of (F^ - ^010 ) / E^ 7 were found to "be
13.83, 13*72 and- 13.88 at pH's U. 99 . U.8U and It-.63 resp e c tiv e ly . Thus,
He§^ / HP20^- ^ HgjEPJ07"
/S 110 = i lig§g1>e0 7~>..._ r io^-SJ X io-T-89 = 105-91* (67) 1 (Hgf‘)(HP2075-)
The complex sp ecies Hg2HPy was found to "be n e g lig ib le in the a c id ity range where the species Hg2Py2, HggPyCH and Hg2Py( 0H)2 ex isted .
Therefore, the graphical determination of ^ QIO ^ ^ 020 was val i d and equations (58), (60) and (63) used in the presence of sodium ion could also be used when potassium ion was present. The values ob tained were
(Hg2(P2 07) j b * w 7) f - ; / s 020 = = “ 12-27 (6e)
(in the presence of 1.0 M k /)
(Hg2(P2O7) ( 0H )> ) Hgg * ^ - Hg 2(P207)( 0H)3- ; pQ11 s =
1015*85 (in the presence of 1.0 M k/) (69)
(Hg2(P2 07) ( 0H)^") _ Hg| ^ P2°7 * Hg2(P2C7)(0H)^; p Q 1 2 (Eg2/j(poU-)(o ^ !
1020.05 (in the presence of 1.0 M &/) (70) In Tables 1 and 3 are listed the potential data for the mercury(l) pyrophosphate system in the presence o f one molar sodium and potassium ions, respectively, along with the logarithm terms for the concentra tion of free alkaline pyrophosphate ion and the various F functions. The logarithm contributions of the various complex species to Fi are listed in Tables 2 and U for the system in the presence of one molar sodium and potassium ion s, resp ectiv ely . Prom th ese tab les the percentage distribution of the complex species as a function of pH shown in Pigures 5 an(^ 6 was calcu lated .
The summary of the complexity constants found is given in Table 4g
Ta"ble 1
Potential Data of Pyrophosphate-Mercury( I) System in the Presence of 1 M Sodium Ion cEg 2 » 1.22 x 10-•5 M, CBy * 0.05 M; Cjfe » l.OM; = 0.3852 ▼. v s. S.C.E.
pH ^aq^c -lo g (Py) log Pi log Pg log P2a lo g P3,
9.62 0.3086 1.30 11.71 13.01 16.07 20.40
9.58 O.3065 1.30 II.65 12.95 16.04 20.41
9-53 0.3035 1.30 11.55 12.85 15.99 20.40
9.39 0.296h 1.31 11.32 12.63 15.87 20.43
9.1 6 0.2860 1.31 10.97 12.28 15.67 20.38
9 .oh 0.2822 1.31 10.84 12.15 15.60 20.40 g.g6 O.2763 1.31 10.66 11.97 15.45 20.35 g.72 0.2739 1.31 10.57 11.88 15.36 20.32 s. 69 0.2731 1.32 10.56 11.88 15.38 19.97
8.58 0.2722 1*33 10.53 11.85 15.31 20.34 g.32 0.2675 I.3 6 10.40 11.75 s.1 3 0.2648 1-39 10.34 11.72 g.02 0.2640 1.41 10.33 11.72
7.70 0.2580 1.51 10.23 11.72
7.50 O.2539 1.59 10.17 11.74
7-31 0.2478 1.70 10.07 11.74
7.12 0.2403 1.82 9.9^ 11.72
6.96 0.2332 1.94 9.82 11.71
6-73 0.2226 2.14 9.64 11.71 1+9
Table 1 (contd.)
pH Ifed-Bc “l0« W l«e Fi log P2 l0«r 2a lo g
6.53 0.2125 2.32 9 . 1+8 11.67
6.30 0.2001+ 2.56 9.33 11.73
5.93 0.1819 2.97 9.12 11.67
5.79 0. 173^ 3. 1U 9-00 11.67
5.73 0.1701 3.22 8.96 11.59
5.29 0. 11+82 3.85 8.86
5.11 O.I396 1+.11+ 8.86
5.03 O.I3U9 1+.27 8.83
1+.79 0.1219 1+.70 8.82
1+.60 0.1128 5.01+ 8.85
1+.56 O.IO98 5.12 8.83
Ave. 8.83 11.72 50
Table 2
Contributions of Verious Complex Species to F^
CHg2 " 1.22 x 10'•5 Mi = O.05 M; Cjja = 1.0 M; Eaq = 0.3852 ▼. v s . S.C.E.
Exp. Contributions to F^ by Various Species CalcdL. pH lo g FI Hg2py HggPyg Hg2Py0H Hg2Py(0H) 2 lo g Fi
9.62 11.71 10.41 10.70 11.66 11.73
9.58 II.65 10.41 10.66 11.58 11.66
9.53 11.55 10.41 10.61 11.4s 11-57
9-39 11.32 10.40 10.47 11.20 11.33
9.16 10.97 g.g3 10.40 10.24 10.74 10.99
9.04 10. gu g.g3 10.40 10.12 10.50 10. S5
8.86 10.66 S .S3 10.39 9 . 9^ 10.14 10.6s g.72 10.57 g.g3 IO.39 9.80 9.86 10.59 g.69 10.56 s.g3 10.3S 9.77 9-80 10.57
8 . 5s 10.53 g.S3 10.3S 9.66 9.58 10.52 g.32 10. to S .S3 IO.35 9.40 9.06 10.43 g .13 10. 31* g .83 IO.32 9.21 8.6s 10.37 g.02 10.33 g.g3 10.30 9.10 S.46 10.35
7.70 10.23 S .S3 10.20 g.78 7.82 10.24
7.50 10.17 g.g3 10.12 S.5S 7.42 10.15
7.31 10.07 g.g3 10.01 8.39 7.04 10.05
7.12 9.94 g.S3 9-89 S. 20 6.66 9-93
6.96 9.g2 S. S3 9.77 g.04 9.82
6.73 9.64 g.S3 9-57 7. s i 9.65 51
Table 2 (contd.)
Contributions to Fi by Various Species Calcd. pH log n Hg2Py HggPy 2 Hg2PyOH HggPy(OH)g lo g Vi
6.53 9.48 8.83 9-39 9.50
6.30 9.33 8.83 9.15 9-32
5-93 9.12 8.83 8.74 9.09
5-79 9.00 8.83 8.57 9.02
5.73 8.96 8.83 8.49 8.99
5.29 8.86 8.83 7.86 8.87
5.11 8.86 8.83 7.57 8.85
5.03 8.83 8.83 7. 41+ 8.85
4.79 8.82 8.83 7.01 8.84
4.60 8.85 8.83 6.67 8.83
4.56 8.83 8.83 6.59 8.83 52
Tahle 3
Potential Data of Pyrophoephate-Mercury(l) System in the Presence of 1 M Potassium Ion o 1 3 CVJ 1.22 x 10"•5 Mi Cpy = 3.88 x 10- ’2 H; CK * 1.0 M; Eaq = 0 - 37! v. v s. S.C
pH -log(P y) log Pi lo g Pg log p2a lo g F3j
10.00 0.3223 l . 4l 12.30 13.71 16.28 20.08
9.90 0.3173 l . 4l 12.13 13. 5* 16.21 20.06
9.87 O.316O l . 4l 12.09 13.50 16.19 20.05
9.84 0.3144 l . 4l 12.03 13.44 16.16 20.03
9.81 0.3135 1.42 12.01 13.^3 16.17 20.08
9.69 0.3082 1.42 11.83 13.25 16.09 20.03
9.63 0.3060 1.42 11.76 13.18 16.07 20.04
9.59 0.3043 1.42 11.70 13.12 16.04 20.00
9.40 0.2978 1.42 11.48 12.90 15.96 19.62
9.36 0.2947 1.42 11.47 12.79 15.85
9.21 0.2911 1.43 U .3 6 12.69 15.83
8.95 0.2863 1.45 11.12 12.56 15.85
8.78 0.2830 1.47 11.03 12.49 15.85
8.60 0.2802 1.49 IO.96 12.44 15.87
8.39 0.2731 1-53 10.86 12.28 8.20 0.2701 1.58 10.81 12.27
8.00 O.2652 1.66 10.72 12.26
7.83 0.2610 1. 7^ 10.60 12.28 53
Table 3 (contd.)
pH ®aq“®c -log(P y) lo g ?! log ? 2
.7.63 0.2539 1.86 10.1*9 12.27
7-^7 0.21*78 1.97 10.31* 12.27
7.26 0.2383 2.11* 10.19 12.27
7.01* 0.2276 2.33 10.02 12.27
6. 61* 0.2075 2.72 9.73 12.27
6.25 0.1891 3.16 9.55
5.91 0.1721 3-59 9.1*0
5^ 3 0 . 11*81 U.30 9.30
5.32 0 . ll*18 1*. 1*8 9.37
M 9 0.1288 5.06 9.1*1
1+.8I* 0.1213 5. 3^ 9.1*1*
U.63 0.1132 5.7!+ 9.56
Ave. 9.25 12.27 15.85 20.05 5^
Tattle 1+
Contributions of Various Complex Species to P]_
CHg2 = 1*22 x 10“5 °Py = 3-8S x 10“2 M; % = 1.0 M; Eaq = O .3753 v. vs. S.C.E.
Exp Contributions to P|_ ty Various Species Calcd. pH lo g ’?! Hg2py Hg2(HPy) H g ^ Hg2PyOH Hg2Py( 0H)2 log Fi
10.00 12.30 10.26 11.85 12.05 12.28
9.90 12.13 10.86 11.75 11.85 12.13
9.87 12.09 10.86 11.72 11.79 12.08
9.81+ 12.03 9.25 10.86 11.69 11.73 12.01+
9.81 12.01 9.25 10.85 11.66 11.67 12.00
9.69 11.83 9.25 IO.85 11.5!+ 11. 1+3 11.81+
9.63 11.76 9.25 10.85 11.1+8 11.31 11.76
9.59 11.70 9-25 10.25 11.1+1+ 11.23 11.71
9.U0 11.1+8 9.25 . 10.85 11.25 10.85 11.51
9.36 11. 1+7 9.25 10.85 11.21 10.77 11. 1+7
9.21 II.36 9.25 10.8U 11.06 10.1+7 11.33
8.95 11.12 9.25 10.82 10.80 9.95 11.15
8.78 11.03 9.25 10.80 10.63 9.61 11.05
8.60 IO.96 9.25 10.78 10.1+5 9.25 IO.96
8.39 10.26 9.25 IO.7I+ 10.21+ 8.83 10.87
8.20 10.21 9.25 IO.69 10.05 s.1+5 10.79
2.00 10.72 9.25 10.61 9.85 8.05 10.70
7.83 10.60 9.25 10.53 9.68 7.71 10.61 55
Table 1+ (contd.)
Exp. Contributions to Fi by Various Species Calcd. pH log J1! Hg2Py Hg2(HPy) Hg2Py2 Hg2PyOH Hg2Py(CH)2 log
7.63 10. 1+9 9.25 10.1+1 9 . 1+8 IO.1+9
7.*+7 10.31+ 9.25 10.30 9.32 IO.38
7.26 10.19 9.25 10.13 9.11 10.22
7.0U 10.02 9.25 9.91+ 8.89 10.05
6. 61+ 9-73 9.25 9.55 8.1+9 9-75
6.25 9-55 9.25 9.11 8.10 9 . 1+0
5.91 9.1+0 9.25 7.92 8.68 7.76 9.37
5.1+3 9.30 9.25 g.1+0 7.97 9.32
5.32 9.37 9.25 8.51 7.79 9.33
1+.99 9.1+1 9-25 8.SH 7.21 9.39
1+.84 9.1+1+ 9.25 8 .99 6.93 9 . 1+1+
I+.63 9.56 9.25 9.20 6.53 9.52 56
Figure 5 * Percentage Distribution of Mercury(l) Pyrophosphate
Complex Species as a Function of pH in the Presence of Sodium Ion.
Cjjgg = 1.22 x 10-5 M
Cpy = 0 .0 5 M
Cua = 1.0 M
Complex Species
Curve 1 HgpPy
Curve 2 HggPyg
Curve 3 Hg2IV0H
Curve U Hg2Py(0H) 2 Percentage Distribution of Complex Species 100 40 20 80 60 4.0 opee o Mruos yohsht i te rsne f . M oim Ions. Sodium M 1.0 of Presence the in Pyrophosphate Mercurous of Complexes 5.0 6.0 7.0 pH &0 ( 2 ) (3) 9.0 (4) 10.0 Figure 6. Percentage Distribution of Mercury(I) Pyrophosphate
Complex Species as a Function o f pH in the Presence o f Potassium Ion.
= 1.22 M
Cpy = 0.0U- M
Cjj = 1.0 M
Complex Species
Curve 1 Hg 2(HPy)
Curve 2 % 2Py
Curve 3 Hg2Py2
Curve 14- Hg2PyOH
Cur ve 5 Hg 2Py( 0H) 2 Percent Distribution of Complex Species 100 0 6 80 40 20 . 5.0 4.0 opee o Mruos yohsht i te rsne f . Ptsim o. VD Ion. Potassium 1.0M of Presence the in Pyrophosphate Mercurous of Complexes ( 2 ) 6.0 pH 7.0 8.0 (3) 9.0 (4) (5) 10.0 6o
Table 5
Complexity Constants for Pyrophosphate-Mercury(l) System
Logarithm of Complexity Constants Alkali metal concentration 110 010 020 O il 012
1.0 M Sodium S. 83 11.71 15.08 20.1+2
1.0 M Potassium 5.93 9.25 12.27 15.85 20.05 CHAPTER IV
THE COMPLEXES OF MERCURY(I) WITH TRIPHOSPHATE
Experimental
The experimental procedures and equipment were the seme as for the pyrophosphate study. The sodium triphosphate was purified before use by the procedure described by 7/a tter s, Loughran and Lambert. 5®
For brevity the triphosphate ion w ill sometimes be indicated by the symbol, Tp.
Potassium triphosphate was prepared by means o f ion-exchange chromatography. A 100 cm. by b cm. Pyrex column filled to a. height o f 60 cm. with Dowex 5Q~xl2 cation exchange resin, 100-200 mesh, low p o ro sity , supported on a Pyrex g la ss wool plug was used. This column was fitted with a Pyrex water jacket through which ice water could be circulated to decrease the extent of hydrolysis. The column was initially charged by means of a 15 per cent solution of hydrochloric acid. A 10 per cent solution of potassium chloride containing just enough potassium hydroxide to make the solution slightly basic was then passed through the column. The inclusion of base insured the complete replacement of hydrogen ion. Next a 15 per cent solution of potassium chloride was passed through the column, after which it was rinsed overnight with d is t ille d water. Then, a solu tion o f sodium triphosphate of approximately twice the desired concentration was 62 passed, through. The first 5 per cent of effluent, which yielded a flame test for potassium, was collected and discarded, after which,
85 Per cent of effluent was collected and used immediately. Con tinual flame tests for sodium were negative throughout the period of collection. The solutions used on the column were transferred to a separatory funnel which was then tightly stoppered. The stem was inserted into the column at the desired liquid level and, once set, this feed mechanism automatically maintained the desired level of liq u id a/bove thp resin .
The Acidity Constants of Triphosphoric Acid in the Presence of 1 M Sodium and Potassium Ions
Prom the results of a titration of 0.05 molar sodium triphosphate adjusted to 1.0 molar sodium ion w ith sodium n itra te versus O.96 molar nitric acid containing 1.0 molar sodium n itr a te the a cid ity constants for triphosphoric acid, in the presence of 1.0 molar sodium io n , were determined to he, pk^ * 7.00 and pk^ = U.83 "by use of equation (50).
To determine the constants in the presence of potassium ions, a prelim inary titr a tio n o f the efflu en t from the ion-exchange column was performed to determine the correct amount of potassium ion to he added to bring the total concentration of potassium ion up to 1.0 molar. After a similar titration as in the case in the presence of sodium ion the acidity constants for triphosphoric acid in the presence of 1.0 molar potassium ion were determined to he pkij = 7* 3^ and pkh 3 U.96. 63
The calculation of the concentration of free triphosphate ion was made by use of equations similar to equation ( 53)* As in the situation of pyrophosphate, only the last two acidity constants were reauired to make this calculation.
The Complexity Constants of Mercury(l) with Triphosphate
The experimentally determined potentiometric potential shifts as a function of pH are shown in Figure J. I t was p o ssib le to measure the potential shift in the presence of sodium ion down to a pH of U.
However, in the presence of potassium ion, the difference in potential remained constant as the pH was decreased "below a pH of 6. 75*
The complexity constants for the mercury(I) triphosphate system in the presence of 1.0 molar sodium ion were obtained from equation
(56) by use of determinants and the complexity constants were
2->
( 71)
( H g - ^ o ) 5-)
/*oio= (*§f)(, o£> : l o 7 " ( 72)
,/ (%2(P30i0)f-) Hg2/ 4 2P ,o 5~ Hg (P 0 ) 8“ * r ------— ~ = 10 3 10 'V'V-w'z ' r 020 (Bg|/ ) ( p 3o 5j ) 2 ( 73) 61+
Figure J. Potentioraetric Potential Shifts as a Function of pH for the Mercury(I) Triphosphate System.
Curve 1: 3 1.22 x 10“5 m
clp = 3-5s x 10-2 M
Cjr 9 1.0 M
Curve 2: ^Hg 2 = x ^
cTp = 5-0 * 10 “2 M .
°Ha = 1*° M TToq -TTc 0.30 0.20 0.25 0.35 0.05 0.10 0.15 Triphosphate pH ( 2 ) 65 (HggCP^^COH)1^) Hgf^ / P3OJ5 / 0H -^H g2(P3010)(CH)U-;y% n (H e ^ )(P 3o ^ ) ( o r ) 1013*65
m
(H e2 P3o 10) ( 0 H ) |- ) s4 ‘f * P3°10 * 20H -^ H g2(P3 010) ( 0H)5-./ 3012 = (H g|^)(P30 5 -)(0 iT ) 2 l 0 2O.O5
(75) These results are summarized, in Table 11.
A slightly different procedure was used to calculate the com plexity constants for the mercury(l) triphosphate system in the presence of 1.0 molar potassium ion. In this case, the problem was solved starting from the higher pH values. Equation (56) was modified to
(76)
The graph of the above equation shown in Figure S, gave a nearly straight line for the more basic solutions with an intercept of /^oil
= 10^*31 and a slope o f ^012 = 102®*35. Tke use of determinants confirmed that the predominant complexes present in this range of acidity were HggTpOH and Hg2Tp( 0H)2 , and the values for ^ Q ll and-
P 012 obtained were
(Hg^PjO-LoKOH)14") / p3° 5o / 0H -?iH g2(P30l o ) ( 0H )^ ; f$01{ (Hg| 6 (P30^ )(O lT ) lOlH.22 67
Figure 8 . Graphic Determination of /^oil / 012 ^or
Triphosphate System in the Presence of Potassium Ion. 9 68 8 7 6 5 4 (OH) (OH) X 10® and J3|Z for Triphosphate in Potassium System ,, 3 3 / 2 Graphic Determination of 0 2 6 0 4 6 16 10 12 14 (HC' (Hg2(P3 010)(C H )|p t P3CS , • -p— r
= iq 20.35 (in the presence of 1 M d) ( 78 )
A fter y^Qll ^ 012 were determined, equation (56) was rewritten as
*1 " - / W 0 ir >2 = /^OlO / y^020^Tp^ ( 79 )
Equation ( 79 ) was solved "by means o f determinants and the values ob
tained in the presence of 1 M id were
. (HgP(P , 0lo ) 3-) Hef / P3°S ^ %2(p3Oio^ * /010 - / % (%r)(r3 »fe) (so)
^ ^ 2^ 3^10^ 2 ^ ^ f*020 Z = 10 9 7 ( 81 )
These complexity constants are summarized in Table 11.
The potential data for the mercury(l) triphosphate system along with the logarithm term for the concentration of free alkaline
triphosphate ion and the various F functions in the presence of one molar sodium ion are lis te d in Tables 6, 7. snd 8 , while the data in
the presence of one molar potassium ion are listed in Tables 9 &nd 10. 70
Table 6
Potential Data of Triphosphate-Mercury(I) System in the Presence of 1 M Sodium Ion at High pH Range
1.22 x 10“■5 M; CTp = o.05x10”2 1.0 M; Ea(l = 0.3852 % 2 = M* °IIa = V. vs. S.C.E.
pH Eaq.-Ec -log Tp log Pi log F2 log P2a log Pja
9-3U 0.2791 1.31 10.7U 12.05 15.Uo 20.05
9.22 0.2762 1.31 10.6U 11.95 15.36 20.07
9-17 0.2703 1.31 10.UU 11.75 15-27 20.09
9.03 0.2617 1.31 IO.15 11. U6 15.12 20.07
8.88 O.253I 1.31 9.86 11.17 1U.9S 20.08
8.80 0.2U72 1.31 9.66 10.97 lU.85 20.03
8.68 0.2U15 1.31 9.U7 10.78 lU.78 20.07
8.65 0.2389 1.31 9.38 10.69 1U.72 20.03 s.53 O.233O 1.32 9.19 10.51 1U.65 20.07 8.U8 O.2303 1.32 9.10 10. ui 1U.60 20.07
8.38 0.2250 1.32 8.92 10.23 1U.51 20.07
8.35 0.2226 1.32 8.SU 10.15 1U.U6 20.03
8.23 0.2173 1.33 8.67 9-99 lU.39 20.07
8.1U 0.2125 1.33 8.51 9.82 1U.29 20. OU 8.07 0.2092 1. 3U 8.U1 9.72 1U.2U 20.05
7.90 0.2021 I.36 8.19 9.51 1U.12 20.05
7-78 0.1980 1-37 8.06 9-37 1U.0U 20. OU
7.71 O.I96O 1.38 8.00 9-31 lU.Ol 20.05 71
Tafcle 6 (contd.)
pH Eaq"Ec “log Tp log Fx log Fg log F2a lo£ E3a
7.60 O.I927 1.1+0 7-91 9.22 13.95 20.01+
7.1+8 O.I89I+ 1.1+3 7 .S3 9.15 13.89 20.OU
7.39 0.1873 1.1+5 7 .7 s 9 .H 13.85 20.01+
7.32 O.IS59 1.^7 7.75 9.09 13-85
7.26 0.181+1+ 1.1+9 7.72 9.07 13.83
6.83 0.1729 1.70 7.5U 9.00 13.80
6.73 O.1696 1.76 7.1+9 S.97 13.68
6.58 O.16U5 1.87 7-^3 S.95
6. 4s 0 .l6 ll 1.9U 7.3S 8.91
6.38 O.1578 2.02 7.35 8.90
6.23 O.1527 2.15 7.30 8.90
6.03 0.11+60 2.3I+ 7.27 8.90 5.88 0.1U09 2.1+9 7.25 8.90
5-S3 0.1393 2.51+ 7.25 8.9U
5.73 0.1359 2.61+ 7.23 8.82
5-53 0.1292 2.86 7.23
5.1+3 0.1258 2.98 7.23
5-33 0.1221+ 3.10 7.21+
5.28 0.1207 3.16 7.21+
Ave. 8.9O 13.65 20.05 72
T able 7
Potential Data of Triphosphate-Mercury(l) System in the Presence of 1 M Sodium Ion at Low pH Range
1 .0 M; = O.3852 v. CHg£ = 1.22 x 10“5 m; Cjp = 5^10''2 = v s . S.C .E.
pH Eaq."Ec -lo g Tp log l0£ /^no l0e f2
5.os 0. 11U0 3.42 7.27 11.69
4.93 0.1089 3.63 7.31 11.70
4 .8 3 O.IO56 3-77 7. 3^ 11.70
4 .6 8 0.1005 4 .0 0 7.39 11.68
4.53 0.0955 4 .2 5 7.48 11.70
4.38 0 . 090 U 4.50 7-55 11.70
4.2 8 0.0871 4.68 7.62 11.71
4 .2 3 0.0854 4.77 7.65 11.71
4 .1 8 0.O837 4 .s 6 7.69 11.72
U.13 0.0820 4.9 5 7-72 11.71
4.0 8 O.O8O3 5.04 7-75 11.70
4.03 0.0786 5-13 7-79 11.70
Ave. 11.70 73
Table g
Contributions of Various Complex Species to Pi
CHg 2 = 1,22 x 10"5 M; CTp = 5 x 10"2 K; °Ka = ^ M; Eaq. = 0.3852 v. vs. S.C.E.
Exp. Contributions to Pi by Various Species Calcd. pH log Pi Hg 2Tp Hg 2(Tp) 2 Hg2TpOH Hg 2Tp(0H)2 Hg 2HTp lo g Pi
9-34 10.74 7.16 7-59 S .99 10.73 10.74
9.28 10.64 7.16 7-59 8.93 10.61 10.62
9-17 10.44 7.16 7-59 8.82 10.39 10.40
9.03 IO.15 7.16 7-59 8.68 10.11 10.13
8.88 9.86 7.16 7.59 8.53 9.81 9.84
8.80 9.66 7.16 7.59 8.45 9.65 9.68
8.68 9.47 7.16 7-59 8.33 9.41 9.45
8.65 9.38 7.16 7-59 8.3O 9-35 9-40
S. 53 9.19 7.16 7-58 8.18 9.11 9.17
8 . 1*8 9.10 7.16 7.58 8.13 9.01 9.08
8.38 8.92 7.16 7.58 8.03 8.81 8.91
8.35 8.84 7.16 7-58 8.00 8.75 8.85
8.23 8.67 7.16 7-57 7.88 8.51 8.65
8.14 8.51 7.16 7-57 7-79 8.83 8.51
8.07 8.41 7-16 7.56 7.72 8.19 3.63 8.41
7.90 8.19 7.16 7.54 7.55 7.85 3.80 8.19
7.78 8.06 7.16 7-53 7.43 7.61 3.92 8.06
7.71 8.00 7.16 7.52 7.36 7.47 3-99 8.00 1+.93 .8 .7 .6 5.1+8 7.16 7.27 5.08 6.36 7.16 7.25 6.56 7.16 5.83 6.75 7.27 7.16 7.31 6.03 6.23 6 5.28 .0i+5.28 6 7.16 7.23 5.53 6.1+1 7.16 7.25 5.88 6.58 7.39 .+ 72 71 5.92 7.16 7.23 5.1+3 5-73 6.1+8 7.20 7.16 7.5I+ 6.83 .6 .2 .6 7.1+1 . 6-73 7.16 7.72 7.26 7.32 7.5O 7.16 7.16 7.83 7.9I 7.1+8 7.60 H og' H2p g(p2 Hg2Tp Hg2(Tp)2 Hg2Tp ! '? g lo pH
07• . 33 3 S
-3 .6 6.26 7.16 7-23 7.21+
x. otiuin t F. y aiu Seis Calcd. Species Various by F]. to Contributions Exp. 7.31 7 7 7 7.75 7-35 7-33 7 . - . - 21 1+3 7 1+9 S + 7.03 7-16
7.16 7.16 7.16 7.16 7.16 7.16 7-16 7-16 7.16 7.16 6.88 6.96
5.27 5.go 5 7 J.lk 7 7 ab e (contd.) 8Ta"ble . - - - 7 1+3 1+5 1+7 !+ I I 1+.93 1+-73 5.08 6.91 6 5.18 5.33 5-53 7.13 7 6.97 .81+.51 5.68 5.88 6.38 5.1+8 6.03 7.25 .35.21 6.13 6.23 +.98 +.58 . . 01 1+8 0 + Hg2Tp( H .15.87 3.71 1 1+.11 3.81 7.01 5 .2 7 6.83 6.69 6.57 5-71 5.01 5.51 +. 8 0 ) H2T lg Ej. log Hg2HTp H)2 I 6.77 6.62 6 .77.25 6.37 6.27 6.17 1+.87 1+.31 I+. 1 1+.97 5.67 5.32 5-97 5-82 5.22 1+.22 i+.io 5.12 5.1+7 +. . 1+2 1 3 + 1 S + 7.28 7.32 7.25 7-21+ 7.21+ 7.25 7.28 7.21+ 7.26 7.33 7.37 7 7-75 7-78 7.72 7.1+9 7.53 7 7.83 7.91 .U . 1 + 0 1 + 7*+ 75
Ta"ble 8 (contd.)
Exp. ContritJutions to Ei l)y Various Species Calcd. pH log EX HggTp Hg 2(Tp)2 Hg 2Tp0H Hg 2Tp(0H)2 Hg 2HTp lo g Ex
U.83 7.3U 7.16 5-13 U.U8 6.87 7 .3U
U.68 7.39 7.16 U.90 U.33 7.02 7-UO
U.53 7.us 7.16 U.65 U.18 7.17 7 -U7
U.38 7-55 7.16 u.uo U.03 7.32 7-55
U.28 7.62 7.16 U.22 3.93 7.U2 7.61
U.23 7.65 7.16 U.13 3.88 7 -U7 7.6U
U.18 7.69 7.16 U.oU 3.83 7.52 7.68
4.13 7.72 7.16 3.95 3.78 7.57 7-71
U.OS 7.75 7.16 3.86 3-73 7.62 7-75
U.03 7.79 7.16 3-77 3.6s 7.67 7-79 76
Table 9
Potential Data of Triphosphate-Mercury(l) System in the Presence of 1.0 M Potassium Ion cHg2 = 1.22 X 10-5 M; Cjp = 3.58 x 10- ’2 M; CK = 1.0 Mi Eaq = 0 .3 7 1 V. vs 1. S.C.:
pH Eaq“Ec -lo g (Tp) log Pj log F2 log P2a log Pjj
9.88 0.3157 1.1+6 12.13 13.59 16.25 20.37 9.81 0.3112 1.1+6 11.98 13. 1+1+ 16.17 20.36
9-71 O.3056 1.1+6 11.78 13.21+ 16.07 20.35
9.52 O.2938 1.1+6 11.39 12.85 15.87 20.34
9.1+0 0.2877 1.1+6 11.18 12. 61+ 15.78 20.37
9 .1 s 0.271+1 1.47 10.73 12.20 15.55 20.35
9.01 0.2639 1.47 10.39 11.86 15.38 20.34
3. 9 U 0.2601+ 1. 1+7 10.27 11.7!+ 15.33 20.35
8.90 0.2579 1.1+7 10.18 II.6 5 15.28 20.34
8.84 0.251+9 1. 1+7 10.08 11.55 15. 21+ 20.35
8.81 0.2522 1. 1+7 9.99 11.1+6 15.18 20.31
8.7!+ 0.21+97 1.1+8 9.92 11.1+0 15.17 20.39 s . 71 0.21+63 1.1+8 9.80 11.28 15.03 20.31
8.66 0.21+1+0 1.1+8 9.72 11.20 15.01+ 20.31
8.59 0.21+03 1.1+8 9.60 11.07 14.99 20.32
8.52 0.2351 1. 1+9 9 * 1+3 10.91 14.88
8.1+8 0.2329 1.1+9 9.36 10.81+ 14.85
8.U1 0.2302 1. 1+9 9.27 10.74 14.82
8.35 0.2261 1.50 9 . 11+ 10.62 14.74 77
Table 9 (contcL.)
pH Eaq“Ec -lo g (Tp) log Fj log F2 log F 2a l0 £ F3a
2.29 0.2232 1.51 9.O5 10.53 lU.69
8.20 0.2203 1.52 8.96 IO.U5 11+.6S
8.09 0.2156 1-53 8.81 10.29 ll+.60
7-97 0.2105 1.55 8.66 10.14 11+.51
7.87 0.2068 1-57 8.56 10.04 11+.1+6
7.69 0.2019 1.62 8.44 9.93 11+.U1+
7.52 O.I968 1.68 8.33 9.81+ 1U.1+0
7.40 O.I927 1-73 8.24 9-75 11+.30
7.28 O.I895 1.79 8.19 9.72 11+.30
7.0k 0.1821 1.91+ 8.O9 9.67 11+.26
6.92 0.1790 2.02 8.07 9.70 lU.38
6.60 0.1682 2.28 7.96 9.62 11+.21 78 Table 10
Contributions of Various Complex Species to
CHg2 3 1.22 x 10"5 M; C-pp = 3-58 x 10“2 M; Pk = 1.0 M; JSaqL = 0 . 375. v. vs. S.C.E
Exp. Contributions to Fi by Various Species Calcd. pH log ?i Hg2Tp Hg2Tp2 Hg2Tp 0H Hg2Tp( 0H)2 log Ei
9 -gS 12.13 7. 81+ 8.01 10.10 12.11 12.11
9.81 11.98 7 . 81+ 8.01 10.03 11.97 11.98
9-71 11.78 7. 81+ 8.01 9.93 11.77 11.78
9.52 11.39 7. 81+ 8.01 9.71+ 11.39 11.1+0
9.1+0 11.18 7 . 8’4 8.01 9.62 11.15 11.16
9 .1 s 10.73 7.8U 8.00 9 . 1+0 10.71 10.73
9.01 10.39 7 . 81+ 8.00 9.23 10.37 10.1+0 8.91+ 10.27 7. 81+ 8.00 9.16 10.23 10.27 to g.90 10.18 • 8.00 9.12 10.15 10.19
8.gi+ 10.08 7 . 81+ 8.00 9.06 10.03 10.08
8.81 9.99 7. 81+ 8.00 9.03 9-97 10.02
8.7!+ 9.92 7. 81+ 7.99 8.96 9-83 9 .89
8 .71 9.80 7 . 8'4 7-99 8.93 9.77 9 . 81+
8.66 9-72 7. 81+ 7.99 8.88 9.67 9-75
8.59 9.60 7 . 81+ 7.99 8.81 9-53 9.62 s . 52 9 . 1+3 7. 81+ 7.98 8.7I+ 9-39 9.50
8 . 1+8 9.36 7. 81+ 7 .9 s 8 .70 9.31 9 . 1+3
8 . 1+1 9.27 7. 81+ 7.98 8.63 9-17 9.32
8.35 9 . 11+ 7. 81+ 7.97 8.57 9.05 9.22 79
Table 10 (contd.)
Exp. Contributions to Pi by Various Species Calcd. pH log Ei Hg2Tp Hg2Tp2 Bg2Tp0H Hg2Tp( 0H)2 log Ti
8.29 9.05 7.8U 7.96 s . 51 8.93 9.13
8.20 3.96 7.8U 7-95 8.U2 8.75 8.99
8.O9 8.81 7.8U 7.9^ 8 .3I 8.53 8.8^
7-97 8.66 l.Sk 7.92 8.19 8.29 8.70
7*87 8.56 l.zb 7.90 8.09 s . 09 8.60
7.69 8 .UU l.zk 7-85 7.91 7-73 8 . 1+H
7.52 8.33 7.8H 7-79 7- 7H 7.39 8.32
7.U0 8 . 21+ 7.8U 7. 7^ 7.62 7.15 s. 26
7.28 8.19 7.8H 7.68 7.50 6.91 8.20
7. 01+ 8.09 7.8U 7.53 7.26 6.U3 8.09
6.92 8.07 7.8I+ 7A 5 1.1k 6.19 8.O5
6.60 7.96 l.zk 7.19 6.82 5*55 7.96 go
Figure 9 * Percentage Distribution of Mercury(l) Triphosphate Complex
Species in the Presence of 1.0 M Sodium Ions.
cHg2 * 1,22 x 10~5' 2
CTp = M 5 x lO"2 M
°Sa = i -0 H
Curve Complex Species
1 HggHEp
2 % 2Tp
3 h§2t P2
U Hg2 TpOH
5 Hg2Tp(0H)2
6 Percentage Distribution of Complex Species 100 0 6 80 40 20 opee o Mruos rpopae n h Peec o 1 M oim Ion. Sodium M 10 0 of 5 Presence the in Triphosphate Mercurous of Complexes 0 4 ( 2 ) 0 6 pH 7.0 (3) 8.0 .(4) (5) 9.0 10.0 Figure 10. Percentage Distribution of Mercury(l) Triphosphate
Complex Species in the Presence of 1.0 M Potassium Ions as a
Function of pH.
cHg2 = 1,22 * 10"5 -
CTp » 3.5S x 10~2 M
Cg = 1 .0 M
Curve Complex Species
1 Hg2Tp
2 Hg2Tp2
3 Hg2TpOH
H Hg2Tp(0H)2 Percentage Distribution of Complex Species 100 80 60 40 20 opee o Mruos rpopae n h Peec o 10 Ptsim Ion. Potassium M 1.0 of Presence the in Triphosphate Mercurous of Complexes 7.0 ( 2 ) 7.5 8.0 (3) (4) pH . 9.0 8.5 9.5 100 Prom Tables 8 and. 10 the percentage distribution of the complex species as a function of pH was calculated and is shown in Figures 9 and 10 in the presence of one molar sodium ion and potassium ion, respectively.
The logarithms of the complexity constants for the Mercury(l) triphosphate in the presence of 1 molar concentrations of these two alkali metals that were determined are listed in Table 11. 85
Table 11
Complexity Constants for Triphosphate-Mercury(I) System
Logarithm of Complexity Constants Alkali metal concentration ^02q /^oil folZ
1.0 M Sodium U.3U 7-16 8.90 13.65 20.05
1.0 M Potassium l.zb 9.U7 1U.22 20.35 CHAPTER V
THE COMPLEXES OE MERCURY( I) WITH TETRAPHOSPHATE
Experimental
The experimental procedures and equipment were the same as for the pyrophosphate and triphosphate studies. Tetraphosphate ion was prepared, according to a slight modification of a procedure "by Quimby and his coworkers®5 hy opening the cyclic 4 member ring in tetrame-
T. Qpimby and F. P. Kraus, Inorganic Synthesis (McGraw- Hill Book Co., Inc., Sew York, N. Y.), 5, 97-102 (1957). taphosphate by hydrolysis in alkaline solution. Hexaguanidine tetraphosphate was crystallized from the solution to separate tetraphosphate from other hydrolysis products. Subsequent studies indicated that guanidine forms a complex with tetraphosphate. Conse- I quently, the acidity constants and the complexity constants obtained were in the presence of 0.15 molar guanidine. The source of the tetrametaphosphate was a commercial product "Cyclophos" manufactured by the Victor Chemical Co., 155 W&cker Dr., Chicago 6, Illinois.
In th is procedure, 300 grams o f crude HaiiPiiPig.UHgO was d isso lv e d in 2 liters of water at room temperature and filtered. Ethanol was added in a steady small stream until precipitation began, after which, the rate was reduced so that the remainder of one liter of ethanol was
86 added over a period of at least one hour, the solution "being stirred
vigorously throughout the addition. The solution was filtered and washed twice, first with 300 ml. of 50 cent ethanol, then with 300 ml. o f 35 per cent ethanol. The crystals were redissolved and re precipitated as before with a total of 1 ml. of ethanol for each 2 ml. of water used.
A 10-15 per cent solu tion o f Na^P^O^ was prepared and, a fte r
cooling, mixed with sufficient cold concentrated NaOH to yield a 8.5-
10 per cent solution of Na^P^Oj^ anc^ three moles NaOH per mole of
Na^P^O^* without allowing the temperature to exceed UO°C. This
solution was stored at a constant temperature of 32°C until two moles
o f NaOH had been consumed, as shown by periodic titr a tio n s o f the
excess NaOH to a pH of about 10. The time required was three weeks.
A more concentrated solution was prepared by mixing an equal
volume of ethanol with the above solution of NagP^D^ and allowing it
to stand until clear liquid layers forned. The lower layer, which was
a syrupy liquid containing about per cent NagP^D-j^* w&s separated
by means of a separatory funnel. Further purification was effected
by adding three volumes of water to one volume of the Ud- per cent
solution, mixing well, then adding four volumes of ethanol and
separating as before.
To 100 grams o f the syrupy liq u id (ca. g. or O.O9U moles
NagP^O^-j) 121 grams o f guanidinium chloride (h ereafter ind icated as
(GuH)Cl) (Eastman Organic Chemicals) in 121 ml. water was added. To
the aqueous solution at 25- 28 °C, formamide was gradually added with vigorous stirring until the solution became faintly turbid and farther small additions were periodically made until the turbidity persisted.
This required about J00 ml. o f formamide. Upon the addition o f 5 a l. of water, crystallization began. Stirring was continued for one hour after which the crystals were filtered off on a sintered glass filter and washed three times with 50 ml. portions of anhydrous ethanol.
The crystals were air-dried to constant weight at 25- 2g°C and a r e l ative humidity of 50 per cent. The yield of air-dried porduct was about 75 Per cent.
For higher purity, the crystals were recrystallized by dissolving h5 grams o f (GuE)3H2O and 5 grams o f (GuK)Cl in 75 ml* water and d ilu ted gradually w ith s u ffic ie n t formamide (about JO m l.) to produce a permanent turbidity. The crystals were filtered off and washed as above. About S 5 per cent of the hexaguanidinium tetraphos phate was recovered.
Experimental Determination of Acidity Constants
Since a titration of O.25 molar hexaguanidinium tetraphosphate in the presence of 10 molar alkali metal ion with 0.200 molar hydro chloric acid containing 1.0 molar alkali metal ion gave only a very slight inflection at the point where one equivalent of acid had been added per equivalent o f the s a lt titra ted , Bjerrum's method was ap p lied in a manner applied by W atters, Loughran and Lambert^ in th eir studies of the acidity constants of triphosphoric acid. It was necessary to use this method as the constants have values which do not
differ greatly. The constants are expressed as stepwise complexity
constants, thus
( 82 )
where parentheses again indicate concentrations and brackets indicate
activities. The symbol Pa w ill be used to indicate the tetraphosphate
ion.
Bjerrum's formation function is written in the form
.n = (1- n ) | V J / (2 -n )/3 2 |V J 2 / ( 3-n)yS 3 [ ^ j 3 /
| V j 4 / < 5-n ) p 5 5 / ( 6-n) ^ [W j 6
It was found that in the range of interest only the first two terms
on the right side of equation (83) were required to calculate the
first two acidity constants. To calculate n, the average number of
bound hydrogen ions per tetraphosphate ion, the total number of moles
of hydrogen and tetraphosphate ion were obtained from the titration
data, the concentrations of free hydrogen ions are assumed to be equal
to the known concentration of hydrochloric acid having the seme pH in
the presence of the same concentration of indifferent electrolyte.
These PcH values were found to be 0.10 / 0.02 units smaller than the measured pH values giving a corresponding activity coefficient of 0.80 which is consistant with the results of Hamed and Ehlers^ and with
s . Earned and R. W. Ehlers, J . Am. Chem. S oc., 55, 2179 ( 1933 ). 90
W atters, Loughran and. Lambert. 5^ The simultaneous solution of equations (83) "by use of determinants yielded the results for the stepw ise a cid ity constants as pkg ■ 6-535 P^5 = ^* 97 ; i-n the presence o f 1 M sodium ion; 0.15 M guanidinuim ion and pkg = 6.92 and pk^ =
5.22 in the presence of 1 M potassium ion and 0.15 M guanidinium ion.
Experimental Determination of Complexity Constants
Solutions containing 1.22 x 10"5 M HggCHO^^, 2.5 x 10" ^ M
(OuH^Ity^. 1.0 M NaEO^ and varying amounts o f MO3 were prepared.
One of the solutions was then added to a half-cell of the potentio- metric apparatus, mercury was introduced and electrical connection made hy means o f a platinum wire which was to t a lly immersed in the mercury layer. After the potential versus the saturated ce.lamel electrode was read, the pH was taken hy means of a Beckman Model G pH meter. Acid variations were made hy the addition of solutions of different acidity than the first.
In the presence of one molar potassium ion the ahove procedure was repeated with the exception that 1.0 M KNO3 replaced the 1.0 M
HaHO'j.
The experimentally determined potential shifts as a function of pH are shown in Figure 11. As was the case for mercury(l) triphos phate in the presence of 1.0 molar potassium ion, the difference in potentials remained constant helow a pH of ahout 6.
Equation (76), the graph of which is shown in Figure 12 was used to calculate Foil ani A )12 for mercury( I) tetraphosphate system 91
Figure 11. Potentiometric Potential Shifts as a Function of pH for
the Mercury(l) Tetraphosphate System.
Cjjgg = 1.22 x 10“5 m
Cp = 2. 5 0 x 10~ 2 M
Curve 1: In the presence of 1.0 M Sodium Ion.
Curve 2s In the presence of 1.0 M Potassium Ion. Eoq — Ec 0.30 0.24 0.26 0.28 0.20 0.22 0.18 0.16 5
6 pH 7
( 2 ) 8
9 93
Figure 12. Graphic Determination of ^ o il an^ /^ 012 ^or
Tetrephosphate System in the Presence of Sodium Ion. 9^
20
18
16
14
l?
10
8
6
4
2
0 I 4 r b t 8 9
F| -16 (Ohi x 10 3phic Determination of /3M and / 3 , 2 in the Tetraphosphute .'odium System. 95
in the presence of 1.0 molar sodium ion. A straight line was obtained
in the more alkaline region. The results obtained were (He2)p^o13)(OH)5-) *4 4 V f c 4 Cr # H g2(P,C13)(OH,5-;A n . (Hei/)(p|t0f y (o ir i ■
1015.91 (in the presence of 1.0 M Ka• and 0 .1 5 M guanidinuim ion) (8U)
and,
(Hg2(Pu013)(0 H )|“ ) Hg2 / i / 20H-^ Hg2(P4C13)2(0H)6-; = (Hg|/)(Puo^)(O ir)2 1022.6H
(in the presence of 1.0 M Ua/ and 0.15 M guanidinuim ion) ( 85 )
After the above results were found equation (79) was solved by means
of determinants to find ^QIO ant* ^ 0 2 0 results obtained were
b (Hg2(Pl+013)1+-) % r / * 4° 13 ^ H g2(PU013) ^ ; f 0 1 Q = = 106 -9g
(in the presence of 1.0 M Na^ and O .15 M guanidinuim ion) (86)
and,
(Hg2(Pl+°13) 2° T 4 f a - ^
(in the presence of 1.0 H Na/ and 0.15 M guanidinuim ion) ( 87 )
These results are summarized in Table l6 .
The use of determinants on equations of the type of equation ( 76)
gave the values of (Hg2 (PU0 1 3 )( 0 H )5" ) 3# 4 ^ 4 or^CP^HoH,*-, Au = =
1015*26 (in the presence of 1.0 M yJ" end. 0.15 M guanidinuim ion) ( 88 ) and,
(Hg2(P1+Oi3) ( ° H) | “ ) a # t t 20B-^^(V l,X0E)2 : Al2 . (He|/)(P|)06--AHip =
1012.U5
(in the presence of 1.0 M yJ" and 0.15 M guanidinuim ion) (89) in the presence of one molar potassium ion. Then, equation ( 79 ) was used to solve for ^QIO and graPhically as shown in Figure
13. The results obtained were
(Hg 2(P1^013)l4~)
/ W = 10?' 32
(in the presence of 1.0 M end 0.15 M guanidinuim ion) (90) and,
(Hg 2(P^013) f - ) xef 4 ppuo 6- V V x j 1^ A » * ( h^ k'f ^ p = 1 0 9 ' SS
(in the presence of 1.0 M id" and 0.15 M guanidinuim ion) ( 91 )
These resu lts are also summarized in Table l 6.
The potential data for the mercury(l) tetraphosphate system in the presence of one molar sodium or potassium ions along with the logarithm terms for the concentration of free alkaline tetraphosphate ion and the various F functions are listed in Tables 12 and 1^, respectively. Tables 13 end 15 list the logarithm contributions of the various complex species found and also the calculated log F^ value. The data from Tables 13 and 15 were then used to calculate the percentage distribution of the various complex species as a function of pH which i s shown in Figures 14- and 15. 98
Figure 13. Graphic Determination ^ 010 f°r the Tetraphosphate
System in the Presence of Potassium Ion. 99
12
10
8
6
4
2
0 0 2 3
[f , - / 3 m (0H) — /3,2(OH)2] X I0 '8
Graphic Determination of y3, in the Tetraphosphate Potassium System. 100
Table 12
Potential Data of Tetraphosphate-Mercury(I) System in the Presence of 1.0 M Sodium Ion
CHg2 = 1.22 x 10''5 M; Cpq = 2.491 x 10‘ “ i = 1.0 M; Eaq = 9 *: v. v s. S.i
pH Eaq~Ec -lo g (Pa) log Pi log ]?2 log P2a lo e p 3a
8.31 0.2863 1.62 11.29 12.91 16.98 22.63
8.24 0.2824 1.62 11.16 12.78 16.92 22.63
8.14 0.2768 1.62 IO.97 12.59 16.83 22.63
8.O9 0.2740 1.63 10.89 12.52 16.80 22.65
8.O3 0.2706 1.63 10.77 12.40 16.74 22.64
7. 9 S 0.2678 1.64 IO.69 12.33 16.71 22.64
7.91 0.2639 1.64 IO.56 12.20 16.65 22.65
7-84 0.2b00 1.65 10.43 12.08 16.59 22.65
7.79 0.2572 1.65 10.34 11.99 I6.55 22.65
7.72 0.2533 1.66 10.22 11.88 16.50 22.65
7.63 0.2483 1.68 10.07 11.75 16.44 22.65 7.60 0.2466 1.68 10.01 II.6 9 16.41 22.64
7-51 0.2416 1.70 9.86 11.56 16.35 22.64 7.49 0.2404 1.70 9.82 11.52 lc .3 3 22.63
7.45 0.2382 1.71 9-75 11.46 16.30 22.61 0 CT\ 7.39 » 1-73 9-67 11.40 16.27 22.66
7.35 0.2326 1. 7^ 9.60 11.34 16.24 22.62
7-33 0.2315 1.74 9.56 11.30 16.22 22.60
7.29 0.2293 1.76 9.51 II.2 7 16.21 22.62 101
T atle 12 (contd.)
pH Eaq-Ec -lo g (Pq) log log I2 log *2a log F3a
7.24 0.2265 1.77 9.42 11.19 16.17 22.59
7-22 0.2254 1.78 9.40 11.18 16.17 22.61
- 7.18 0.2250 1.79 9-39 11.18 16.20 22.61
7.14 0.2223 1.81 9.32 11.13 16.17 22.68
7.11 0.2209 1.82 9.28 11.10 16.16 22^69
7.07 0.2192 1.84 9.24 11.08 l6 .l6 22.63
7-03 0.2170 1.85 9.18 11.03 16.14 22.72
7.00 0.2148 1.87 9-13 11.00 16.12 22.69
6.96 0.2130 1.89 9.09 IO.98 l 6 . l l 22.73
6.90 0.2089 1.92 8.98 10.90 16.06 22.63
6.87 0.2075 1-93 8.94 10.87 16.05 22.62
6.80 0.2042 1-97 8.87 IO.83 16.05 22.68
6.75 0.2019 2.00 8.82 10.81 16.05 22.72 6.71 0.1991 2.03 8.76 10.78 16.02 22.67
6.66 O.I969 2.06 8.71 IO.76 16.02 22.72
6.62 0.1941 2.09 8.65 10.73 16.08 22.65
6.58 0.1918 2.12 8.60 10.71 15.99 22.62
6.54 O.I896 2.15 8.56 10.70 15.9s 22.64
6.50 0.1874 2.18 8 .5 I 10.68 15-97 22.60
6.48 0.1864 2.20 s.50 IO.69 15.98 22.69
6. 4l 0.1826 2.25 8.42 IO.65 15-97 22.65
6.37 0.1801 2.29 8.37 10.64 15.96 22.58 102
Table 12 (contd.)
pH Eaq"Ec ~log loe Fi l°g *2 log P2a log ? 3a
6.34 0.1779 2.31 8.32 10.61 15.93
6.27 0. 17^7 2.38 8.28 10.64 15.96
6.22 0.1723 2.42 8.24 10.64 15.97
6.18 O.I695 2.46 8.19 10.62 15.95
5. 9 S 0.1578 2.66 7.99 10.61 15.9^ 103
Table 13
Contributions of Various Complex Species to F^
cHg 2 = 1.22 x 10“5 M; Cpq = 2 .1+9 x 10-2 M; Cjja = 1.0 M; Eaq = O.38 v. vs. S.C.
Exp. Contributions to F^ by Various Species Calcd. pH log Fx HggPq. HggPq^ HggPqOH H 2Pq.(0H) 2 log Fi
s . 31 11.29 6.98 7.80 10.22 11.26 11.30
S. 2k 11.16 6.98 7.80 10.15 11.12 11.16
S. Ik 10.97 6.9 S 7.80 10.05 10.92 IO.98
8.09 10.89 6.98 7.79 10.00 10.82 10.88
2.03 10.77 6.98 7-79 9.9!+ 10.70 10.77
7.98 10.69 6.98 7.78 9-89 10.60 10.68
7.91 10.56 6.98 7-78 9-82 10.1+6 10.55
7.8k 10.1+3 6.98 7-77 9.75 IO.32 10.1+2
7-79 10.31+ 6.98 7-77 9-70 10.22 IO.3U
7.72 10.22 6.98 7.76 9.63 10.08 10.21
7.63 10.07 6.98 7. 71+ 9.5!+ 9.90 10.06
7.60 10.01 6.98 7. 71+ 9.51 9 . 81+ 10.01
7-51 9.86 6.98 7.72 9 .1+2 9.66 9.86
7.^9 9.82 6.98 7.72 9.1+0 9.62 9-83
7.U5 9-75 6.98 7.71 9.36 9.5!+ 9.76
7-39 9.67 6.98 7.69 9.30 9 .1+2 9.67
7.35 9.60 6.98 7.68 9.26 9.3!+ 9.61
7.33 9.56 6.98 7.68 9 . 21+ 9.30 9.58
7.29 9.51 6.98 7.66 9.20 9.22 9.52 7. 21+ 9.1+2 6.98 7.65 9.15 9.12 9 .1+1+ 104
Table 13 (contd.)
Exp. Contributions to F]_ by Various Species Calcd. pH log Fi HggPq. HggPq^ HggPqOH H2Pq_(0H) 2 log F^
7.22 9.40 6.98 7.64 9-13 9.08 9.42
7.18 9.39 6.98 7.63 9.09 9.00 9.36
7.14 9.32 6.98 7.61 9.05 8.92 9.30
7.11 9.28 6.98 7.60 9.02 8.86 9.26
7.07 9.24 6.98 7-58 8 .9 s 8 . 7? 9.21
7.03 9.18 6.98 7-57 8.94 8.70 9.15
7.00 9.13 6.98 7.55 8.91 8.64 9.11
6.96 9.09 6.98 7-53 8.87 S .56 9.06
6.90 8.98 6.98 7.50 8.81 8.44 8.98
6.87 8.94 6.98 7.49 8.78 8.38 8.95
6.80 8.87 6.98 7.45 8.71 8.24 8.86
6.75 8.82 6.9S 7.42 8.66 8.14 8.80
6.71 8.76 6.98 7-39 8.62 8.06 8.75
6.66 8.71 6.98 7.36 8.57 7.96 8.69
6.62 8.65 6.98 7-33 8.53 7.88 8.65
6.58 8.60 6.98 7.30 8.49 7.80 8.60
6.54 8.56 6.98 7.27 8.45 7.72 8.56
6.50 8.5I 6.98 7.24 8.41 7.64 8.5I
6.48 8.50 6.9S 7.22 8.39 7.60 8.49
6. 4l 8.42 6.98 7.!7 8.32 7.46 8.42
6.37 8.37 6.98 7.13 8.28 7-38 8.37
6.34 8.32 6.98 7.11 8.25 7.32 8.35 105
T atle 13 (contd.)
Exp. Contrit>utions to $1 "by Various Species Calcd. pH log F Hg2Pq. Hg2?a_2 Hg2PqOH H2Pq( 0H)2 log Ei
6.27 8.28 6.9 8 7.04 8.18 1.18 8.27
6.22 8 .2k 6.98 7.00 8.13 1.08 8.22
6.1S 8.19 6.98 6.96 8.09 1.00 8.18
5-98 7-99 6 .9 s 6.76 7-89 6.60 7-99 io6
Table lU
Potential Dpta of Tetraphosphate-Mercury(I) System in the Presence of 1.0 M Potassium Ion
cHg2 = 1.22 x 10“■5 M; Cpq_ = 2.1+81+ x 10' N; % = 1.0 M; Eaq * 0. 37! v. vs. S.C.!
pH % r s c -lo g (Pd) log F]_ log F2 r2a log F3a
8.61 0.2980 1.61 11.68 13.29 17.07 22.U5
8.55 0.291+8 1 .6 l 11.6l 13.22 17.06 22.50
8 . 1*5 0.2885 1.6l II.36 12.97 16.91 22. U5
8.»+l 0.2856 1.6l 11.26 12.87 16.85 22. U3
8.35 0. 282 U 1.62 11.16 12.78 16.81 22. U5
8.27 0.2772 1.62 10.99 12.61 16.72 22. U3
8.20 O.2733 1.62 10.86 12. US 16.66 22.UU
8.15 0.2703 1.62 10.75 12.37 16.60 22. U3
8.09 0.2662 I.63 10.62 12.25 16.51 22. Ul
8.00 0.2612 I.63 10.1+5 12.08 16. U5 22. U2
7 .9 ^ O.2575 1. 61+ 10.31+ 12.00 16.UO 22. U2
7.90 O.2553 1. 61+ 10.26 11.90 16.36 22. U2
7-83 0.2521 1.65 10.17 11.82 16.33 22. U7
7.80 0.21+97 1.65 10.09 11.7U 16.28 22.UU
7* 7*+ 0.21+63 1.66 9.98 11.6U 16.23 22. UU
7.70 0.21+1+2 1.67 9.92 11.59 16.21 22. U6
7 .6U 0.21+09 1.68 9.82 II.50 16.17 22.U7
7.60 0.2385 1.68 9 . 71+ 11.Uo l 6 . l l 22.UU
7.52 0.231+6 1.70 9.63 11.33 16.09 22.50 107
Table lH (contd.)
pH Eaq-E c -lo g (Pq) log log Fg log r2a log l j a
7-50 O.2330 1.70 9-57 11.26 16. OH 22. H6
7 -^7 0.2302 1.71 9.51 11.22 16.02 22. H6
7.HO 0.227H 1.72 9.Ho 11.12 15.97 22. H8
7-35 O.22H5 1 .7 H 9.32 11.06 15.9H 22. H8
7.2 9 0.2213 1.76 9.2H 10.99 15.91 22.51
7 .2 5 0.2182 1.77 9.16 10.92 15.86 22. H9
7 .1 9 0.2151 1-79 9.06 10.8H 15.81 22.H8
7 .1 5 0.2133 1.80 9.01 10.80 15.80 22.50
7 .0 9 0.2097 1.83 8.91 10.73 15.7 H 22. H8
7.00 0.2051 1.87 8.80 10.66 15.71 22.51
6.93 0.2016 1.90 8 .71 10.59 15.67 22.52
6.25 0.1923 1. 9H 8.6H 10.56 15.67 22.60
6.21 O.I951 1.97 8.56 10.50 15.61 22.5H
6.75 O.I913 2.00 8.H6 10. H3 15.53 22. H5 6.68 0.1277 2.05 8.39 10.HO 15.52 22 M
6.65 0.1252 2.07 8.35 10.38 15. H9 22 M 6.60 0.1230 2.11 8.29 10.35 15. H6 22. H3 6.52 0.1790 2.16 8.21 IO.31 15.H3 22. Hi 6.Ho 0.1729 2.26 8.10 10.28 15.Ho 22.HH
6.30 0.1672 2 .3H 8.01 10.23 15.37 22. Hi
6.25 O.I65O 2.39 7-97 10.25 15.37 22. H5
6.20 0.1628 2.H3 7.93 10. 2H 15.36 22. H5
6.15 0.1600 2.H8 7.89 10.23 15.35 22. H6 108
Table 15
Contributions of Various Complex Species to F^
* 1-22 x 10' 5 M; Cpq = 2.1+SU x 10"2 M; {fc = 1.0 M; Eaa = 0.3753 v. vs. S.C.E.
Exp. Contributions to Fi by Various Species Calcd. pH log Fp HgpPq HggPqp HgpPoCH Hg 2Pq(0H)g log Fj.
8.61 11.68 7.32 8.27 9.87 11.67 11.68
8.55 11.61 7.32 8.27 9.81 11.55 11.56
8.45 11.36 7.32 8.27 9.71 11-35 11.36
8.41 11.26 7-32 8.27 9-67 11.27 11.28
8.35 11.16 7.32 8.26 9.61 11.15 11.16
8.27 10.99 7.32 8.26 9-53 10.99 11.00
8.20 10.86 7.32 8.26 9.46 IO .85 10.87
8.15 10.75 7.32 8.26 9.41 10.75 10.77
8.09 10.62 7.32 8.25 9-35 IO.63 IO.65
8.00 10.45 7.32 8.25 9.26 10.45 10.48
7.9^ 10.34 7.32 8.24 9.20 10.33 IO.36
7.90 10.26 7.32 8.24 9.16 IO.25 10,29
7-83 10.17 7.32 8.23 9.09 10.11 10.16
7.so 10.09 7-32 8.23 9.06 10.05 10.10
7.74 9.9S 7.32 8.22 9.00 9.93 9-99
7.70 9.92 7.32 8.21 8.96 9.85 9.91
7.64 9.82 7.32 8.20 8.90 9.73 9.80
7.60 9.74 7.32 8.20 8.86 9.65 9.73
7.52 9.63 7.32 8.18 8.78 9.49 9.59 109
Table 15 (contd.)
Exp. Contributions to by Various Species Calcd. pH log Fj_ HggPq. Hg2Pq2 HggPqOH HgPq^OHjg log %
7.50 9*57 7.32 8.18 8.76 9 . 1+5 9.55
7. 1+7 9.51 7.32 8.17 8.73 9-39 9.50
7. 1+0 9.U0 7.32 8.16 8.66 9.25 9-38
7.35 9.32 7.32 8.11+ 8.61 9.15 9.30 7.29 9.21+ 7.32 8.12 8.55 9.03 9.20
7.25 9.16 7.32 8.11 8.51 8.95 9.11+
7.19 9.06 7.32 8 .O9 8 .1+5 8.83 9.01+
7.15 9.01 7.32 8.08 8 . 1+1 8.75 8.98 7.09 8 .9 I 7.32 8 .O5 8.35 8.63 8.89
7.00 8.80 7.32 8.01 8.26 8.1+5 8.77
6.93 8.71 7.32 7-98 8.19 8.31 8.68
6.85 8.61+ 7.32 7.9H 8.11 8.15 8.58
6.81 8.56 7.32 7.91 8.07 8.07 8.53
6.75 8.1+6 7.32 7.88 8.01 7.95 8 . 1+6
6.68 8.39 7.32 7.83 7-9>+ 7.81 8.38
6.65 8.35 7-32 7.81 7.91 7.75 8.35
6.60 8.29 7.32 7.77 7.86 7.65 8.29
6.52 8.21 7.32 7.72 7-78 7.1+9 8.21
5. 1+O 8.10 7.32 7.62 7.66 7.25 8.10
6.30 8.01 7.32 7.5^ 7.56 7.05 8.01
6.25 7.97 7.32 7.1+9 7.51 6.95 7.97
6.20 7.93 7.32 7.1+5 7. 1+6 6.85 7-93
6.15 7.89 7.32 7.1+0 7-1+1 6.75 7.89 110
Tahle 16
Complexity Constants for Tetraphosphate-Mercury(I) System
Logarithm o f Complexity Constants Alkali metal concentration /^OlO /*020 J 3®!! ^ 0 1 2
1.0 M Sodium 6.gg 9.1*2 15.91 22.61*
1.0 M Potassium 7.32 9.88 15.26 22.1*5 I l l
Figure lh. Percentage Distribution of Mercury(I) Tetraphosphate
Complex Species in the Presence of 1.0 M Sodium Ions as a Function o f pH.
CKg2 = 1.22 x 10“5 M
Cpq = 2.U91 x 10-2 M
%a = i -0 M
Curve Complex Species
1 Hg2PqOH
2 Hg2P q (0H)2
3 Hg 2Pq2
4 Hg2Pq Percent Distribution of Complex Species
r\> 100 OO o> 00 o o o o