SHELDON M. LAMBERT AND JAMES I. \TATTERS
4262
[CONTRIBUTIOS FROM hfCPHERSON CHEMICAL
LABORATORY, THEOHIO
Vol. $9
STATE UNIVERSITY]
The Complexes of Pyrophosphate Ion with Alkali Metal Ions BY SHELDON AI. LAMBERT' AXD RECEIVED hIARCH
J A ~ I E SI.
\ 5 7 ~ % ~ ~ ~ ~ ~ 2
18, 1957
The stabilities of the complexes of pyrophosphate ion with sodium, potassium and lithium ions have been calculated from t h e pH lowering during the titration of pyrophosphate ion with hydrogen ion. The acidity constants of pyrophosphoric acid have been obtained in the absence of alkali metal ions arid compared with those of ortho- and triphosphoric acid. T h e following complexes and their corresponding complexit>- constants were obtained a t 26' using tetramethylammoniunl 10J.8J O . O f i . Xa(P20i)3-, K K ~ ,=, ~1O1.O0 * " . 0 6 ; Lichloride t o adjust the ionic strength t o unity. K(P20;)3-, K I ~ !=, ~ ( P 2 0 r ) 3 - , KLipy - 102.3n=0.u6.Only lithium ions formed an acidic complex with the ligand ( H P 2 0 i 3 - ) ; Li(HP20i)2-, KLiHpy = 101.03 0.06. The successive acidity constants of pj-rophosphoric acid a t 25' and unity ionic strength were 10°.82, 101.81, l O f i . I 3 , S o complexes of the alkali metal ions with orthophosphate ion were detected.
*
*
Introduction This is the third paper of a series on the acidity and complexes of p o l y p h ~ s p h a t e s . ~ ~ ~ The existence of alkali metal complexes with pyrophosphate ion was not considered before Monk,j during a conductance study of the acidity of pyrophosphoric acid, found evidence of complex formation with sodium ion and calculated a dissociation constant of for the complex, KaP&&-. Complex formation of pyrophosphate with alkali metal ion is of considerable importance since alkali metal ions usually are added to adjust ionic strength or as a source of pyrophosphates. The classic conductivity measurements of Xbbott and Bray6 yielded reliable values for the acidity constants of pyrophosphoric acid, particularly t h e first and second constants, while Kolthoff and Bosch7 obtained excellent values for the third and fourth ionization constants extrapolated to infinite dilution. The tendency of pyrophosphate to form complexes with many metals through chelate ring formation has been the subject of numerous In the present study the acidity constants of pyrophosphoric acid were evaluated a t various ionic strengths in the presence of tetramethylammonium chloride with alkali metal ions absent. As in the second paper of this series4 on triphosphate complexes with alkali metal ions the lowering of the apparent acidity constants of pyrophos(1) 4 b s t r a c t e d from t h e P h . D . thesis of Sheldon hL. L a m b e r t submitted in partial fulfillment of t h e requirements for t h e P h . D . degre?, T h e Ohio S t a t e University, 1957. ( 2 ) T o whom communications should be directed. (3) J . I . Watters, E D Loughran and S . R I . 1,ambert. THISJ O U R N A I , , 78, 48.53 (195l;). (IJ) . I. W a t t e r s , S. 11. 1,ambert and E. D. Loughran, i b i , i , 79, R1i5l ( 1 9 5 7 ) . (.5) C. B. AIonk, J . Che7n. SOC.,1'23 ( 1 9 4 9 ) . i f i ) C . A. A h b o t t and 11'. C . Bray, T H I S J O U R N 31, A L 7'20 , (1909). ( 7 ) I. I f . Kolthoff and W .Bosch, Rcc-.f T u % ' , chiin , 47, 821'1 (1928) 18) 1. XI. Kolthoff and J . I. \Tatters, I i i d . E n # . C h e i n . . A i i i i i . E L , 16, 8 ( 1 9 4 3 ) . (9) J . I . \Tatters and A . Aaron, THISJ O U R N A L , 75, 011 (19.53). (10)L . B . Rogers a n d C . .4. Reynolds, i b i d 71, 2081 (19403. (11) A . E. Martell and G . Schwarzenbach, Efelu. Chiin. A c t o , 39,653 (1936). (1'2) H A. Laitinen and E:. I. O n s t o t t , THISJ O E R N A I . , 72, 4729 (1950) (131 E A Ukshe a n d A . I. L e v i n . Zhiir. Obshchri K h i m . , 24, 775 (1934) (14) J R . Van Wazer and D. Campanella, T H I S JOURX.AI., 72, G55 (1930). (13) RT Bohtelsky and S . Kertes, J . A O p . C h e i i i . ( I ~ d u ? i ) 4, , 410 ( 19.54 1 . ( I f ; ) J . 4 . Davis, Dissertation Abstracts, Vol. X V , N o 12. '2403 ( 1Ti ;7 .5 )
phoric acid in the presence of an excess of various alkali metal ions was used as a means of evaluating the extent of complex formation. Theoretical If an acid can be titrated in the presence of a relatively large excess of metal ion without precipitate formation, i t is possible to investigate complex formation by the lowering of t h e pH. When the inflections a t the various equivalence points persist for the stepwise addition or removal of hydrogen ions, the calculations are greatly simplified. I n this case, i t is evident t h a t each ligand adds one hydrogen ion in a stepwise manner even though the ligand may also be bound to a metal ion. Under these conditions i t is expedient t o define a function which is called the apparent acidity for this stepwise addition of hyconstant," drogen ion as
where m, n and q indicate the number of metal, hydrogen and pyrophosphate ions in any particular species. I n this paper parentheses indicate concentrations and brackets indicate activities. The number of bound hydrogen ions, n, has a single value from zero to four if the addition of hydrogen ion is stepwise while m and q may have several values if several complex species, and the uncomplexed ligand, as well, are in equilibrium. The general equation for t h e stepwise addition of hydrogen ion t o pyrophosphate ion and the corresponding acidity constant are H+
+ H,,P~o+-'L)-
~ , , ~ ~ ? 0 ~ 1 3 - ' 1 ! -
The general equation for the formation of any complex ion and the corresponding complexity constant, PAI,,H,L,,are ?&I+
+ (IH,,P~O;O"-'~!-
M,,(H,,P,0i),(9'4-"'-"
-
where the subscript L indicates the ligand PlOi'-. The equations used to calculate the complex formation constants were derived by substituting equations having the forms of (2) and (3) into (1) with m and q assumed to be equal to unity.
Aug. 20, 1957
COMPLEXES OF PYROPHOSPHATE IONWITH ALKALIMETALIONS
K 3 and K 4 are the acidity constants of pyrophosphoric acid, while K M Land KMHL are the formation constants for the complexes M(P207)3- and AT(HPZOi)'-. From these equations it follows t h a t the apparent acidity constants are constants if the concentration of unbound metal ion is constant, provided precautions are taken to avoid changes in activity coefficients. X high concentration of an essentially non-complexing electrolyte and relatively low concentrations of metal ion and pyrophosphate ion were used for this purpose. For the titration of pyrophosphate ion with hydrogen ion in the absence of metal ions the acidity constants can be calculated by the following form of eq. 1. is calculated by In the presence of metal ions the same equation
4263
of 0.02968 M((CH3)4N)4P207with a solution containing 0.2805 M HC1 and the same concentration of H4P207as the solution titrated. Curve 5 , Fig. 1, was obtained for the titration of 0.04524 ill H4P207 with 0.08901 M (CH3)kNOH. All solutions contained sufficient (CH3)4NC1to produce an ionic strength of unity. The ordinate "a" is the number of equivalents of acid or base added per mole of
I
PH.
(6)
where a is the number of moles of hydrogen ion per mole of pyrophosphate ion present in any form. The symbol f indicates the activity coefficient of a univalent ion. If the acid is not too dilute the constants have the same value as the $H a t a = n 1/2. Experimental
+
T h e source of pyrophosphate ion for most of the experiments was Na4PnOi.10H20, hlallinckrodt analytical reagent grade. The pyrophosphoric acid was prepared from sodium pyrophosphate by the use of the acid form of the ionexchange resin Dowex 50-X12, 100-200 mesh, low porosity in a manner exactly analogous t o t h a t described for the preparation of triphosphoric acid.3 Potassium pyrophosphate was prepared by heating anhydrous dipotassium hydrogen phosphate a t 500 to 700" for 3 hr.* Lithium pyrophosphate was prepared in the same manner as lithium triphosphate in the previous study using the exchange resin Dowex 50-Xl2 charged with lithium ions. All other reagents and the general experimental procedure are described in the previous paper.* The titrations were performed in an aqueous thermostat adjusted to 25 f 0.1' using the Beckman model G p H meter equipped with a "general purpose" glass electrode. The H4P207or (( CHo)*X)dP207solutions obtained from the columns were tested for removal of sodium ion.3 The extent of hydrolysis of ((CHa)aS)aPnOiwas tested by titrations and found to be negligible after periods of one week if the solution was stored in a freezer a t - 15". Crowther and his c o - ~ o r k e r s studied ~ ~ ~ ~ *the hydrolysis of pyrophosphoric acid and found it t o be acid catalyzed b u t not base catalyzed. In the present study no appreciable hydrolysis was observed if the tetramethylammonium pyrophosphate solution was left at room temperature for one hour.
Results and Discussion The Acidity of Pyrophosphoric Acid.-Since all previous studies of the acidity of pyrophosphoric acid a t large ionic strength were made in the presence of alkali metal ions, the acidity constants were re-evaluated using tetramethylammonium chloride to adjust the ionic strength but with alkali metal ions absent. Curve 1, Fig. 1, was obtained for the titration (17) J. D. Crowthrr and A. E. R. Westman, Can. J . Chem., 32, 42 (1954). (18) J . D. McGilvery and 1.P. Crowther, ibid., 32, 174 (1954).
I I
I 2
I
3
I 4
1
0 .
Fig. 1.-Curves for the titration of pyrophosphate ion with hydrochloric acid and the titration of pyrophosphoric acid with tetramethylammonium hydroxide. A comparison of the effects of potassium, sodium and lithium ion on the titration curve of pyrophosphate ion with hydrochloric acid. Curve 1, 0.02968 M ((CH3)aS)aP20i titrated with a solution 0.2805 N in HC1 and 0 02968 M in HdPzO;; curve 2, similar to curve 1, but 0 12 JI in K + ; curve 3, 0.12 dl in K a + ; curve 4,0.12 111 in I d i f + ; curve 5 , 0.04524 -11H4P107 titrated with a solution 0.08901 A 1 (CH3)aXOH. All s o h tions adjusted to # = 1 with ( CH3)4SC1.
pyrophosphate present in any form. The titration curves for pyrophosphoric acid indicate that the first two hydrogen ions are highly dissociated and that the values for their ionization constants are not widely separated. Therefore, Bjerrum's method was used to evaluate these constants in the same manner as for triphosphoric acid.3 The expression for the stepwise complexity constants is
where parentheses indicate concentrations and brackets indicate activities. Due to the absence of appreciable concentrations of the species Pz07'- and HP2073- a t p H values below 3 the simultaneous solution of Bjerrum's formation equation3 for Pa and p 4 in groups of two yielded the values of log P3 = 1.81 f 0.03 and log P 4 = 2.63 f 0.05. Converting to the usual stepwise acidity constants the values are pK2 = 1.81 j= 0.05 and pK1 = 0.82 j= 0.05, Table I shows the
TABLE
I
The titratiiin of 20 1x11. of a solution of 0.iJ2968 -11 ((CH3)4S)IP?O; with a solution 0.2805 d l in HC1 and 0,02968 111 in HaP.0;. Both solutions contained sufficient (CHa)rSC1 t o produce a n ionic strength of 1.0. 0
9H
2.10 2.24 2.37 2 , 50 2 . ti3 3 OR :3.41 3 . 7-5 4 , ox 4.93
2.93 2.61 -.I. 1 2 2 ,25 2 . 13 1.89 1 .7:3
5,x4
1.15
2.00 2,l-I-
j i Ki
pK
. . .
.)
-.). - -Q.1
PA-.,
- . .9.)
d-
-.I . - I.9()
2 :i5 2 ,j:3 2 . (i4 2 7.5 2 x:3 3 Oil 3 03
1 .32 1.31
,
2.3% 2 31 2.51 2,W 2 79 2.8X 3 . 00 3.11
agreement between ??experimental and fitheuretical, where fi is the mean number of bound H+ions per pyrophosphate ion. The acidity constants also were evaluated a t infinite dilution. In the previous study of triphosphoric acid an excess of (CHa)?SC1was present in the dilution solution in order to substitute the known ionic strength of the latter for the less certain effect of the larger dispersed ionic charge of the triphosphate ion. U-hen attempts were made to obtain similar data for pyrophosphoric acid with excess (CH:()JCl present to adjust the ionic strength, as was done in the previous study, the graphed data did not approach a straight line before the electrode became poorly poised. Consequently the data were obtained without the extraneous electrolyte, and the ionic strength was calculated on the basis of total pyrophosphate ionic charge. The values of KO, K j and Ki a t concentrations approaching infinite dilution were calculated using eq. (i which contains terms for the degree of hydrolysis and dissociation. The activity coeficients of Harned and EhlerslYwere used. The p values of Z
