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The determination of association constants of aqueous cadmium complexes by a chelate solvent extraction method
J. Inorg.Nucl,Chem.,1965,Vol.27. pp. 99 to 104. PersamonPren Ltd. Printedin Northern]rebind
THE DETERMINATION OF ASSOCIATION CONSTANTS OF AQUEOUS CADMIUM COMPLEXES BY A CHELATE SOLVENT EXTRACTION METHOD H. E. HeLLW~E and G. K. S ~ Departments of Chemistry,Rollins College,Winter Park, Florida, and Universityof Tennessee,Knoxville,Tennessee (Received 18 March 1964; in revised form 19 May 1964) AiMazet--The extraction of cadmium (H) from aqueous solution in the absence and presence of compiexing agents into chloroform containing oxine has been carried out under suitable conditions such that idmtiflcations of the aqueous complex specks and estimations of their association constants could be realized. The use of fifteen different aqueous complexing agents has lead to the estimation of over thirty association constants.
IN recent years, increasing use has been made of metal chelate solvent extraction
systems for the investigation of complex equilibria in aqueous solutions. The results and techniques up through 1958 have been reviewed by ZOZULYAand Pmmcow,. (I) Some additional results have been reported in the biennial surveys of Moaltmos and F l t m ~ . (z) This study was undertaken to expand this technique by investigating the utility of the extraction of cadmium from aqueous solutions without and with complexing agents into chloroform containing oxine for characterizing aqueous complexes of cadmium. THEORY In the extractionof cadnnum (II)from an aqueous phase containing a complexing agent X in a concentration [X] into a chloroform phase contaim\ng oxine H R in a concentration [HR]~ the most fikely extracting organic species can often be represented as C d I ~ H R ) , and the most likely aqueous species as CdR,(OH)hX r These assumptions seem reasonable when one observes the experimental results on similar systems and considers the low concentration of HR in the aqueous phase. When experiments are conducted to ascertain the organic-aqueous distribution coemcient of the total cadmium D, it is generally desirable to determine D as a function of three variables: the pH, [HR]~ and IX]. The data are then plotted as curves of log D against each of the variables (expressed as pH, log. [HR]~ or log [X D, the other two variables having been held constant. These curves ofttimes show regions of constant slope and regions of changing slope, the constant-slopexegious generally representing conditions under which a single species predominates in each phase. The value D i n a constant-slope region of an experimental curve may be approximated by the following relationship: D = [Cdl~(HR),]0/[CdRr(OH)hX~], where the subscript "0" indicates the organic phase and the unsubscripted brackets signify t h e aqueous phase. Charges have been omitted for simplicity. By the substitution of c1~A. P. Z o z ~ ' a and V. M. Pmmwvx, Russ. Chem. Rw. (Engl. Trans.) 29, 101 (1962). cl~ 0 . H. MovcarsoN and H. Famm~, Analyt. Chem. 30, 632 (1958); 32, 37R (1960); 34, 64R (1962); 36, 93R (i964). 99
100
H.E. H~rJwme and G. K. ~ z i m
appropriate association constants and partition constants, the following results: D = K,P,[HR]0V-'+'/K,~-'P~-'+aC,~K,h[H]2-'-~[X] ~,
( 1)
where K. is the association constant of CdRa(HR) a, Pa is the partition constant of C d I ~ ( H R ) . , / ~ is the acid association constant of HR, P; is the partition constant of HR, C,~ is the association constant of CdR,(OH)~X,, and Kw is the ion product of water. In numerous previous systems of this type, the assumption that both Pa and P, remain constant has been shown to be justified, cl~ It will be noted from this equation that the slope of a log D-against-log-pH plot at constant [HR]o and [X] will be 2--r--h, the slope of a log D-against-log-[HR] 0 plot at constant [H] and IX] will be 2--r--a, and the slope of a log D-against-log-IX] plot at constant [HR]o and [HI will be --x. These relationships allow decisions as to possible predominating species on the constant-slope portions of the experimental curves, and then the involved constants can be calculated in many cases. Regions of the experimental curves with changing slopes usually reflect that several species are involved in one of the phases, that is, that a species transformation is occurring. Such regions can often be represented by the sum of several terms of the type #oven above, r or a or x or h differing in the successive terms. By proper slope analysis and curve fitti/lg, the terms needed to write the complete equation for a total system can be ascertained and usually many of the constants (K,, P~, C,~=) can be estimated. A more detailed treatment of this sort of a'theoretical approach has been presented in a previous paper. ~a~ EXPERIMENTAL PROCEDURES Cadmiom-115min nitric acid, as obtained from Oak Ridge National Laboratory, was converted to the perchlorate by successiveevaporations with perchloric acid. All chemicals used were reagent grade, and all solventswer~purifiedby double distillation. Using 30 ml glass bottles, 10 mi portions of the aqueous phase were stirred to equilibriumwith 10-mlportions of the chloroform phase containing HR at 30-0 4- 0.5°. In all cases, the originalcadmium concentrationinthe aqueousphasewas lO-"VM, and the ionic strength was made up to the desired value with sodium perchlorate. The complexing anions were introduced into the aqueous phase as sodium salts. Adjustments of pH were made with perchlorio acid and sodium hydroxide solutions, and pH measurements were conducted with a Beckman Model 76 Meter equipped with a Beckman Combination Electrode. The instrument was calibrated freqmmtlywith Coleman buffers at pH values of 2.00, 4.00, 7,00, 9.00 and 11.00. After a givensystemhad reached eqnih'brium,a 150 pl. pipette was used to sampleeach phase. The samples were placed onto planchets, dried, counted under a Tracerlab Beta Scintillation Counter, and corrected for background and self-absorption. RESULTS AND DISCUSSION In Table 1 are presented extraction data for a number of systems in which log D was determined as a function of pH or log [HR]0 or log [X] with the other two variables being held constant. These data were plotted and regions of constant slope were identified. The slope values are generally accurate within 4-0.3 slope units. Non-complexed systent¢
Systetns 1--4 indicate the influence of pH on log D at four different concentrations of H R . in all cases the curves rise with a slope of 2, then plateau to a slope of 0, then fall with a slope of --1. These values correspond to the exponent of [H] in cs~G. K. Sc~wexrzn, Analyt. CMm. Acta 30, 68 (1964).
The determination of association constants of aqueous cadmium complexes
IO1
TAIIt£ 1.--Ex-rlt~crloN DATA System number-Experimental ~ t e r s * - D a t a 1. 0.03 M HR and 0.1 M perchlorate: pHOog D), 4.5(-2.47)' 5.2(-1.42)' 5.9(-0.23)' 6.4(0.21)' 6.7(0-67), 7.1(I.23), 7.3(1-27)' 7.4(i.27); slopes 2,0 2. 0.1 M HR and 0-1 M perchlorate: pH0og D), 4-1(-1-66)' 4.4(--1.24)' 4.5(-1.03)' 4.6(-0-96)' 5.0(-O.II), 5;5(0.39). 6-1(!.06), 5.7(!.61), 6-8(1.68)' 7.0(1.93), 7.1(!.94)' 7.4(1.85)' 7.7(1-80), 8.6(!-65), 9.5(I.22), 9.8(0.99), 1I.!(0"42), 12.0(-0-60); slopes 2, O, - 1 3. 0.3 M HR and 0.1 M perchlorate: pH(log D), 3.1(-1.80), 3.4(-1.24), 3.7(-0-74), 3.9(-0-211), 4.4(0.45), 4.9(I.0(0, 5.4(I.79), 5.8(I.96), 6.4(2.18), 7.0(2.49)' 7.1(2.50)' 7.6(2.~), 11.2(2.29)' 8-7(2.13), 9.0(1.94)0 9.4(1.93), 10.0(1.78): slopes, 2, O, - 1 4. 1.0 M HR and 0.1 M perchlorate: pH0og D)° 2"0(-2"53)' 2.4(-2.10), 2.6(--1,20), 3"1(-0.21)' 3.6(0-78), 3.7(I.i I), 3-9(I.67), 4.8(2-09), 5.5(2-70), 5-'7(2.71), 6.2(2.70), 6.3(2.75), S.*¢2.SO), 7"2(2.85), 8-0(2.73), 8.8(2.51), 9-0(2.54), 9.4(2.34), 9.8(2"09); slopes 2, O, " 1 5. varying HR and 0.1 M perchlorate at pH 4"1 : log [Hit], (log D), --1.5(--3"00), --i.0(--1.511) -0.5(-0-15), 0.0(I.28): slope 3 6. varying HR and O.! M perchlorate at pH !1.0: log [HR.], (log D), -34~t~dl)' -2~(14)O)' - 1.2(I.38), - 1.0(I.46), -0.5(I.94), -0.2(2.27)' 04)(2.52) slope 1 7. 0.1 M Hit and 3.0 M perchlorate: pH(log D), 3~(-2.28)' 3.5(--1.34)' 4.0(-o.a0), 4.4(0.35)' 4.9(i.18)' 5-4(1..62), 5.8(2.07), 6.2(2.35), 6.3(2.43)' 6.6(2.56)' 7.2(2.55), 8~(2.49), 9,3(2.11)' 1o.4, (!.50), 11.0(o-96)' 11.1(o.77); slopes 2, 0, - 1 8. 0.1 M Hit: pH(log D), 4.0(-0.96), 4"5(-0"35), 5"1(0.64)' 5"5(1"06), 6'0(1"30), 6-3(1"49), 6.6(!'60)' 7-0(1"76), 7"1(1"82), 7"4(!'82), 7.8(1"80), 9"1(1"32), 9"3(1"29)' 9"7(1"1T)' 10"3(!-00); slopes 2, o, - ! 9. 0.1 M HK and minimum perchlorate: pH(Iog D), 4.4(- 1-77), 4.6(- 1.03)' 4.9(-0-7~, $.3(O4N), 5.9(0.89), 6.8(1.58), 7-1(1.90)' 7.4(1.89)' 7.9(I-86), 9.1(1.43)' 9'4(1.17)' 10.0(0-76)' i14(O4flg); slopes 2, O, --1 10. 0.1 M Hit and varying chloride at pH 6.0: log IX] 0og. D): -3~0(1.51), -2.52(I.56), -2.00(1.46), - 1.52(!.48)' - 1.00(1.06)' -0.52(0-62)' 0.00('0"_42); slopes O, - 1, - 2 11. 0.1 M Hit and varying bromide at pH 6.0: log IX] (log D), -3~0(1.40)' -2.52(1.39)' - 2 ~ 0 (1.38), - 1.52(1.20)' - 1.00(0.90)' -0.52(0.00)' 0410(- l.t 1) slopu O, - 1, - 2 1 2 . O-1 M Hit and varying iodide at pH 6.0: log IX] (log D)' -3.00(1-43)' --2.52(1.47), -2.22(143), -2~0(1.35)' --1.70(1.25)' -1.52(!.08)' --1~0(0.00)' --0.52(-1.23), 0.00(--2.32); slopes O, -1, -2 13. 0.1 M HR and various fluoride at pH 6-0: log IX] (log D)' --3.00(1.37)' -2.52(1.26)' -24X}(1.23) - 1.52(1.35), - 1"00(1.39), --0.52(1.15), -0-22(0-65)' 0.00(-0"15); slopes O, -- 1, --2 14. 0.1 M Hit and varying cyanideT at pH 6.0: log IX] (log D)' --5.52(1.22)' -5"00(1.18), --4.00(!.16)' 3.52(1.18)' -3.00(1.23), -2.52(1.10), -2.00(0-5"/), -1.52(-0.28)'-|.00(--1.31); O, -I, - 2
15. 0.1 M HR and varying thio~anate at pH 6.0: log [Xl (log D)' -3~0(1.31)' -2.52(t.30)' -2.00(1.31), --1.52(1.20), -1.00(1.17), -0.52(0.63)' 0.00(-0.28); slopes O, - i , - 2 16. 0.1 M Hit and varying acetate at pH 5.2: log IX] (log D)' -3~0(1.41), --2-52(1.$1)" --2qM)(1.44), - t.52(1.48), -- 1.00(1.21), -0.52(0.85), 0.OO(--0.2O); slopes O, -- 1, --2 17. O.1 M HR and varying nitrate:g at pH 5.0: log IX] (log D), -- 1.52(2"51), -0.92(2.55)' --0.52(2-31) -0-22(2.25)' -0-05(2.11), 0~(2.10), 0.32(1.74), 0-48(1.34); slzpes O, --1, --2 18. 0.1 M HR and varying oxalatet at pH 6~: log IX] (log D)' --4~0(1.20)' --3-52(14B), -3.00(0.90), -2.52(0-63), -2-00(O~4)' --1.52(-0-66)' --1.00(--1.77); slopes O, --1, --2 19. 0.1 M HR and varying thiosulphateT at pH 5.9: log IX] (log D)' -4.00(0-99)' -3.'/g~O-Wt)' -3.52(0.94)' --3.22(0-82), -3.00(0.78)' -2.52(0.41), -2.00(-0-10)' -1.52(-1.00)' ~1.00(-2.28); slopes O, - 1 , - 2 20. O-1 M Hit. and varying sulfate at pH 6.O~:: log PC] (log D), --3.O0(2.14)' --2.00(2.14)' --1-Y2(2.17), --1.22(2"10), --1-00(2-17), --0.70(2.12), --0.52(!-86), --0.22(1.39)' 0.00(O'13); slops O, --1, --2
102
H. E. I-ImJW~e and G. K.
Txm.z I. (Contd.)
21. 0"1 M HR and varying tartrate at pH 5.9: log IX] (log D), --2.52(1.40), --2.00(1.44), --1.22(1.14), --1.00(~88), --0.70(0.38) --0.52(0.05), 04}0(--1.90); slopes0, --1, --2, --4 22. 0.1 M HR and varying n i t r ~ t e at pH 6.0: log IX] (log D), --5.52(0-92), --5.00(0.60), -4.52(0-15),--4.00(--0.36),--3.52(--1.15),--3.00(-2.62); slopes--1,--2 23. 0.1 M HR and varying ethylenediaminetetra-acetateat pH 6.2: essentiallyno extraction for IX] > 10-H M 24. 0-1 M HR and varyingpyrophosphateat pH 6.0: log IX] (log D), --4.00(0-9~), -3.52(1.03), --3.00(0.64), --2.52(0~)8), --2.00(--0-70), --1.52(--1.54), --1.00(--2.72); slopes 0, --1, - 2 25. ~1 M HR and varyingcitrate at pH 6.2: log IX] (log D), --4.00(1.62), --3.52(1.63), -3.00(1.52), --2.52(1.20), --2.00(1.01), --1.52(~57), --1.00(-0.3S); slopes0, --1, --2 * All aqueousphas~ we~ I0-~'v M in cadmiumperchlorateand weremade up to anionicstrength of 1.0 with ,~lium l~rchlorate unless otherwiseindicated.
t Ionic m~ngth 0.I. :~Ionic strmgth 3.0. equation one (2--r--h) and would indicate an organic species of CclR~(HR)~ with the aqueous species changing from Cd I+ to CdR + to CdR~ to CdRs- as the pH rises. Systems .5-6 show the dependence of log D on the HR concentration, The indications are that 2--r~-a equals 3 at low pH values and equals 1 at high pH values, corresponding to-an organic species of CdR~.HR in all cases. The data of systems 1-6 may be adequately represented by writing D = [CdR4'HR]o/([Cd] + [CdR] + CdRj] + [CdRs]) or lID = [Cd]/[CdRz'HR]o + [CdR]/[CdR~.HR]o + [CdI~]/[CdR~.HR]o -/[CdR~]/[CdI~.HR]0 -~ I(.rsP~[H]S/KIPI[HR]os + I(rPrZ[H]C~o/KIPI[HR]o s + PrCi0o/ KIPI[HR]o + I(.r-I[I'I]-IC~KIPI. Using values of l o g / ~ and log Pr of 9"7 and 2"6 as given by HELLWEORand SCHW~TZl~,(4) curve-fitting techniques yielded log KIPI equal to 20.7, log C1oe 7.9, log Cz0o 15.3, and log CNo 18.4. These data compare favourably with results for the zinc-oxine-chloroform system,c6) but disagree with previous identifications of CdP~(HR)z as the extracting species.~4,s) It is suspected that the latter conclusion was arrived at on the basis of too few HR concentration data. To ascertain the effects of ionic strength on log D, the extractions indicated in systems 2, 7-10 were run. Fairly marked effects were noted, a displacement of as much as 1.0 pH unit occurring for a change in ionic strength from 0.1 to 3.0. In view of this, all extractions with complexing agents (with a few exceptions) were carried out at an ionic strength of 1.0. Complexed systems
Systems 11-25 indicate data gathered when various complexing agents in a series of concentrations were added to the aqueous phase. The information in each system was plotted, slopes were identified, suitable equations were written, and curve fitting procedures were employed to give estimates of the association constants of the involved aqueous complexes. In general, all these complexing systems could be treated by writing an equation of the type D = [CdR2.HR]0/([Cd] @ [CdX] I'IXLLW~Eand G. K. SCHW~Z~, Analyt. Chits. Acta 28, 236 (1963). m O. K. ~ z B x and W. V. Wn~LrJ,Analyt. Chlm. Acts 30, 114 (1964). c,) j. STAY,Analyt. Chtm. Acta 28, 132 (1963). t.) H. E.
The determination of association constants of aqueous cadmium complexes
103
[CAXt] + [CdX,]) or 1/9 ffi [Cd]/[Cdl~.mt]e + [CAX]/[C.~I~.HIt]e + [CdXt]/[Cdlte.HR]e + [CdX,]/[CdRe.HR]e ffi K,sp,t[H]t/£tPI[HR],s + K,sPetCm[H]a[X]/KiPl~lt~a + g,'I~JC~p[X?IKIP~IR~ * + x, s P , ~ P l r ~ x U ~ * . values o f l o g / ~ , log P,, and log XIPx are available from the previo~ work on the non-
complexed systems, thus the values of Coo, are readily obtai._nable. These ettimated values are presented in Table 2, along with some previotudy determined values. For all these complexed systems log D was also determined as a fanction of log [l'IR]e at several values of IX] and at the pH values indicated for the systems in Table I. In each case, the slopes were 3, giving confidence that the extracting species remained CdRs.HR. Log D was further determined as a function of log [X] at a pH of 9.5 and [HR]o equal to 0.1 M. Changes in log D were observed only with cyanide, thiosulphate, nitrilotriacetate, and ethylenedraminetetra-acetate. Tiffs indicates that only these complexing agents are strong enough to break the CdRe- complex. Examination of Table 2 indicates good agreement between w..ines reported here and those reported in the literature, especially when differences in ionic streogths TABLE2.~A,q~X~ATIONCON~rAN'~OF Complexing Agent Fluoride Chloride Bromide Iodide Cyanide Nitrate Acetate Thiocyanate Sulfate Thiosulfate Oxalate Tartrate Citrate Nitrilotfiacetate Pyrophosphate
Log C,,x, Coos,Coo,* 0.3, 0.5, 1.2, 1.8 1.4, 1.9, 1.4, 2.7, 5.8, I1.1 0.1, 0.1 0-7, 1.4 0.7, 1.5 0.1, 1.0, 3.2, 5.0 3.0, "4.7 1.1, 2.2, 2.6, 3.6 9.2 4.0, 6.3
1.2 2.2 4.2
1.7 2.4
Lit. Log Crux,Cm, Cml' 0.5, 0.6 1.3, 2.2, 2.4 1.6, 2.0, 2.3 1.8, 2.7, 4.2 5.5, 10.6, 15.2 0.1 1.3, 2.3 1.4, 2.0, 2.6 0.9 2.7, 5.2 3.5, 5.3 3.2 3.4, 5.0 9.5 5.6
KefeINmee (7) (8) (9) (10) (7) (7) (7) (11) (12) (13) (14) (15) (16) (17) (18)
* Values estimated in this research; accuracy approximately -4-0.2. ? Some previously reported values. ~T~I. l.J~s, Doctoral Dissertation, Lurid (1943). c,) E. L. KIN<),J. Amer. Chem. $o¢. 71, 319 (1949). c,~ p. KrVALO and P. Er,~x, Suomen Kern. 30B, 116 (1957). (x0)M. QuIm~ and S. PltLL~R, J. Chim. Phys. $3, 226 (1956); C.R. Acad. $¢1., Paris 24~ 768 (1956). ~xx~I. Lm>eN,Z. Phys. Chem. 188, 160 (1941). cxa~I. L w ~ , Acta Chem. Scared. 6, 971 (1952). ~x,)K. B. YAlmmasg.uand L. V. Gus'KOVA,Zh. ~,org. Khim. 2, 2039 (1957). (x,) W. J. CLAYTONand W. C. Vosatmos, ?. Amer, Chem. Soc. m , 2414 (1937). cx,~I. V. l~ArNrrsgJI, Zh. A~lyt. KAtm. 6, 119 (1951). cx,) p. K. MIOALand A. Y. SYcH~, Zh. Neorg. Xhim. 3, 314 (1958). (1,~ G. SCh'WAIgZENBACH and E. Flun'rAO,Helv. CAlm. Aeta 28, 1492 (1945). ~1,~G. SARTORI, Gazzetta 64, 3 (1934).
104
:[. E. ~ w l o m
and O. K. S a / w m ' r m
are recol~zed. Ionic strens~h effects seem to be especially critical in the evaluation of the first cumulative association constant Com. The data in the last column of Table 2 are not meant to be compared directly with the values obtained in this work' since in m0st cases the conditions d/IE,r somewhat, but they are illustrative values Oven only to indicate general agreement. Acksm~/ddS,Imat.--The ass/stance of a fellowsh/p granted by the Nat/onal S¢/eoce Foundation to
m~ ,- ~ a X y
w,knowledpd.
THE DETERMINATION OF ASSOCIATION CONSTANTS OF AQUEOUS CADMIUM COMPLEXES BY A CHELATE SOLVENT EXTRACTION METHOD H. E. HeLLW~E and G. K. S ~ Departments of Chemistry,Rollins College,Winter Park, Florida, and Universityof Tennessee,Knoxville,Tennessee (Received 18 March 1964; in revised form 19 May 1964) AiMazet--The extraction of cadmium (H) from aqueous solution in the absence and presence of compiexing agents into chloroform containing oxine has been carried out under suitable conditions such that idmtiflcations of the aqueous complex specks and estimations of their association constants could be realized. The use of fifteen different aqueous complexing agents has lead to the estimation of over thirty association constants.
IN recent years, increasing use has been made of metal chelate solvent extraction
systems for the investigation of complex equilibria in aqueous solutions. The results and techniques up through 1958 have been reviewed by ZOZULYAand Pmmcow,. (I) Some additional results have been reported in the biennial surveys of Moaltmos and F l t m ~ . (z) This study was undertaken to expand this technique by investigating the utility of the extraction of cadmium from aqueous solutions without and with complexing agents into chloroform containing oxine for characterizing aqueous complexes of cadmium. THEORY In the extractionof cadnnum (II)from an aqueous phase containing a complexing agent X in a concentration [X] into a chloroform phase contaim\ng oxine H R in a concentration [HR]~ the most fikely extracting organic species can often be represented as C d I ~ H R ) , and the most likely aqueous species as CdR,(OH)hX r These assumptions seem reasonable when one observes the experimental results on similar systems and considers the low concentration of HR in the aqueous phase. When experiments are conducted to ascertain the organic-aqueous distribution coemcient of the total cadmium D, it is generally desirable to determine D as a function of three variables: the pH, [HR]~ and IX]. The data are then plotted as curves of log D against each of the variables (expressed as pH, log. [HR]~ or log [X D, the other two variables having been held constant. These curves ofttimes show regions of constant slope and regions of changing slope, the constant-slopexegious generally representing conditions under which a single species predominates in each phase. The value D i n a constant-slope region of an experimental curve may be approximated by the following relationship: D = [Cdl~(HR),]0/[CdRr(OH)hX~], where the subscript "0" indicates the organic phase and the unsubscripted brackets signify t h e aqueous phase. Charges have been omitted for simplicity. By the substitution of c1~A. P. Z o z ~ ' a and V. M. Pmmwvx, Russ. Chem. Rw. (Engl. Trans.) 29, 101 (1962). cl~ 0 . H. MovcarsoN and H. Famm~, Analyt. Chem. 30, 632 (1958); 32, 37R (1960); 34, 64R (1962); 36, 93R (i964). 99
100
H.E. H~rJwme and G. K. ~ z i m
appropriate association constants and partition constants, the following results: D = K,P,[HR]0V-'+'/K,~-'P~-'+aC,~K,h[H]2-'-~[X] ~,
( 1)
where K. is the association constant of CdRa(HR) a, Pa is the partition constant of C d I ~ ( H R ) . , / ~ is the acid association constant of HR, P; is the partition constant of HR, C,~ is the association constant of CdR,(OH)~X,, and Kw is the ion product of water. In numerous previous systems of this type, the assumption that both Pa and P, remain constant has been shown to be justified, cl~ It will be noted from this equation that the slope of a log D-against-log-pH plot at constant [HR]o and [X] will be 2--r--h, the slope of a log D-against-log-[HR] 0 plot at constant [H] and IX] will be 2--r--a, and the slope of a log D-against-log-IX] plot at constant [HR]o and [HI will be --x. These relationships allow decisions as to possible predominating species on the constant-slope portions of the experimental curves, and then the involved constants can be calculated in many cases. Regions of the experimental curves with changing slopes usually reflect that several species are involved in one of the phases, that is, that a species transformation is occurring. Such regions can often be represented by the sum of several terms of the type #oven above, r or a or x or h differing in the successive terms. By proper slope analysis and curve fitti/lg, the terms needed to write the complete equation for a total system can be ascertained and usually many of the constants (K,, P~, C,~=) can be estimated. A more detailed treatment of this sort of a'theoretical approach has been presented in a previous paper. ~a~ EXPERIMENTAL PROCEDURES Cadmiom-115min nitric acid, as obtained from Oak Ridge National Laboratory, was converted to the perchlorate by successiveevaporations with perchloric acid. All chemicals used were reagent grade, and all solventswer~purifiedby double distillation. Using 30 ml glass bottles, 10 mi portions of the aqueous phase were stirred to equilibriumwith 10-mlportions of the chloroform phase containing HR at 30-0 4- 0.5°. In all cases, the originalcadmium concentrationinthe aqueousphasewas lO-"VM, and the ionic strength was made up to the desired value with sodium perchlorate. The complexing anions were introduced into the aqueous phase as sodium salts. Adjustments of pH were made with perchlorio acid and sodium hydroxide solutions, and pH measurements were conducted with a Beckman Model 76 Meter equipped with a Beckman Combination Electrode. The instrument was calibrated freqmmtlywith Coleman buffers at pH values of 2.00, 4.00, 7,00, 9.00 and 11.00. After a givensystemhad reached eqnih'brium,a 150 pl. pipette was used to sampleeach phase. The samples were placed onto planchets, dried, counted under a Tracerlab Beta Scintillation Counter, and corrected for background and self-absorption. RESULTS AND DISCUSSION In Table 1 are presented extraction data for a number of systems in which log D was determined as a function of pH or log [HR]0 or log [X] with the other two variables being held constant. These data were plotted and regions of constant slope were identified. The slope values are generally accurate within 4-0.3 slope units. Non-complexed systent¢
Systetns 1--4 indicate the influence of pH on log D at four different concentrations of H R . in all cases the curves rise with a slope of 2, then plateau to a slope of 0, then fall with a slope of --1. These values correspond to the exponent of [H] in cs~G. K. Sc~wexrzn, Analyt. CMm. Acta 30, 68 (1964).
The determination of association constants of aqueous cadmium complexes
IO1
TAIIt£ 1.--Ex-rlt~crloN DATA System number-Experimental ~ t e r s * - D a t a 1. 0.03 M HR and 0.1 M perchlorate: pHOog D), 4.5(-2.47)' 5.2(-1.42)' 5.9(-0.23)' 6.4(0.21)' 6.7(0-67), 7.1(I.23), 7.3(1-27)' 7.4(i.27); slopes 2,0 2. 0.1 M HR and 0-1 M perchlorate: pH0og D), 4-1(-1-66)' 4.4(--1.24)' 4.5(-1.03)' 4.6(-0-96)' 5.0(-O.II), 5;5(0.39). 6-1(!.06), 5.7(!.61), 6-8(1.68)' 7.0(1.93), 7.1(!.94)' 7.4(1.85)' 7.7(1-80), 8.6(!-65), 9.5(I.22), 9.8(0.99), 1I.!(0"42), 12.0(-0-60); slopes 2, O, - 1 3. 0.3 M HR and 0.1 M perchlorate: pH(log D), 3.1(-1.80), 3.4(-1.24), 3.7(-0-74), 3.9(-0-211), 4.4(0.45), 4.9(I.0(0, 5.4(I.79), 5.8(I.96), 6.4(2.18), 7.0(2.49)' 7.1(2.50)' 7.6(2.~), 11.2(2.29)' 8-7(2.13), 9.0(1.94)0 9.4(1.93), 10.0(1.78): slopes, 2, O, - 1 4. 1.0 M HR and 0.1 M perchlorate: pH0og D)° 2"0(-2"53)' 2.4(-2.10), 2.6(--1,20), 3"1(-0.21)' 3.6(0-78), 3.7(I.i I), 3-9(I.67), 4.8(2-09), 5.5(2-70), 5-'7(2.71), 6.2(2.70), 6.3(2.75), S.*¢2.SO), 7"2(2.85), 8-0(2.73), 8.8(2.51), 9-0(2.54), 9.4(2.34), 9.8(2"09); slopes 2, O, " 1 5. varying HR and 0.1 M perchlorate at pH 4"1 : log [Hit], (log D), --1.5(--3"00), --i.0(--1.511) -0.5(-0-15), 0.0(I.28): slope 3 6. varying HR and O.! M perchlorate at pH !1.0: log [HR.], (log D), -34~t~dl)' -2~(14)O)' - 1.2(I.38), - 1.0(I.46), -0.5(I.94), -0.2(2.27)' 04)(2.52) slope 1 7. 0.1 M Hit and 3.0 M perchlorate: pH(log D), 3~(-2.28)' 3.5(--1.34)' 4.0(-o.a0), 4.4(0.35)' 4.9(i.18)' 5-4(1..62), 5.8(2.07), 6.2(2.35), 6.3(2.43)' 6.6(2.56)' 7.2(2.55), 8~(2.49), 9,3(2.11)' 1o.4, (!.50), 11.0(o-96)' 11.1(o.77); slopes 2, 0, - 1 8. 0.1 M Hit: pH(log D), 4.0(-0.96), 4"5(-0"35), 5"1(0.64)' 5"5(1"06), 6'0(1"30), 6-3(1"49), 6.6(!'60)' 7-0(1"76), 7"1(1"82), 7"4(!'82), 7.8(1"80), 9"1(1"32), 9"3(1"29)' 9"7(1"1T)' 10"3(!-00); slopes 2, o, - ! 9. 0.1 M HK and minimum perchlorate: pH(Iog D), 4.4(- 1-77), 4.6(- 1.03)' 4.9(-0-7~, $.3(O4N), 5.9(0.89), 6.8(1.58), 7-1(1.90)' 7.4(1.89)' 7.9(I-86), 9.1(1.43)' 9'4(1.17)' 10.0(0-76)' i14(O4flg); slopes 2, O, --1 10. 0.1 M Hit and varying chloride at pH 6.0: log IX] 0og. D): -3~0(1.51), -2.52(I.56), -2.00(1.46), - 1.52(!.48)' - 1.00(1.06)' -0.52(0-62)' 0.00('0"_42); slopes O, - 1, - 2 11. 0.1 M Hit and varying bromide at pH 6.0: log IX] (log D), -3~0(1.40)' -2.52(1.39)' - 2 ~ 0 (1.38), - 1.52(1.20)' - 1.00(0.90)' -0.52(0.00)' 0410(- l.t 1) slopu O, - 1, - 2 1 2 . O-1 M Hit and varying iodide at pH 6.0: log IX] (log D)' -3.00(1-43)' --2.52(1.47), -2.22(143), -2~0(1.35)' --1.70(1.25)' -1.52(!.08)' --1~0(0.00)' --0.52(-1.23), 0.00(--2.32); slopes O, -1, -2 13. 0.1 M HR and various fluoride at pH 6-0: log IX] (log D)' --3.00(1.37)' -2.52(1.26)' -24X}(1.23) - 1.52(1.35), - 1"00(1.39), --0.52(1.15), -0-22(0-65)' 0.00(-0"15); slopes O, -- 1, --2 14. 0.1 M Hit and varying cyanideT at pH 6.0: log IX] (log D)' --5.52(1.22)' -5"00(1.18), --4.00(!.16)' 3.52(1.18)' -3.00(1.23), -2.52(1.10), -2.00(0-5"/), -1.52(-0.28)'-|.00(--1.31); O, -I, - 2
15. 0.1 M HR and varying thio~anate at pH 6.0: log [Xl (log D)' -3~0(1.31)' -2.52(t.30)' -2.00(1.31), --1.52(1.20), -1.00(1.17), -0.52(0.63)' 0.00(-0.28); slopes O, - i , - 2 16. 0.1 M Hit and varying acetate at pH 5.2: log IX] (log D)' -3~0(1.41), --2-52(1.$1)" --2qM)(1.44), - t.52(1.48), -- 1.00(1.21), -0.52(0.85), 0.OO(--0.2O); slopes O, -- 1, --2 17. O.1 M HR and varying nitrate:g at pH 5.0: log IX] (log D), -- 1.52(2"51), -0.92(2.55)' --0.52(2-31) -0-22(2.25)' -0-05(2.11), 0~(2.10), 0.32(1.74), 0-48(1.34); slzpes O, --1, --2 18. 0.1 M HR and varying oxalatet at pH 6~: log IX] (log D)' --4~0(1.20)' --3-52(14B), -3.00(0.90), -2.52(0-63), -2-00(O~4)' --1.52(-0-66)' --1.00(--1.77); slopes O, --1, --2 19. 0.1 M HR and varying thiosulphateT at pH 5.9: log IX] (log D)' -4.00(0-99)' -3.'/g~O-Wt)' -3.52(0.94)' --3.22(0-82), -3.00(0.78)' -2.52(0.41), -2.00(-0-10)' -1.52(-1.00)' ~1.00(-2.28); slopes O, - 1 , - 2 20. O-1 M Hit. and varying sulfate at pH 6.O~:: log PC] (log D), --3.O0(2.14)' --2.00(2.14)' --1-Y2(2.17), --1.22(2"10), --1-00(2-17), --0.70(2.12), --0.52(!-86), --0.22(1.39)' 0.00(O'13); slops O, --1, --2
102
H. E. I-ImJW~e and G. K.
Txm.z I. (Contd.)
21. 0"1 M HR and varying tartrate at pH 5.9: log IX] (log D), --2.52(1.40), --2.00(1.44), --1.22(1.14), --1.00(~88), --0.70(0.38) --0.52(0.05), 04}0(--1.90); slopes0, --1, --2, --4 22. 0.1 M HR and varying n i t r ~ t e at pH 6.0: log IX] (log D), --5.52(0-92), --5.00(0.60), -4.52(0-15),--4.00(--0.36),--3.52(--1.15),--3.00(-2.62); slopes--1,--2 23. 0.1 M HR and varying ethylenediaminetetra-acetateat pH 6.2: essentiallyno extraction for IX] > 10-H M 24. 0-1 M HR and varyingpyrophosphateat pH 6.0: log IX] (log D), --4.00(0-9~), -3.52(1.03), --3.00(0.64), --2.52(0~)8), --2.00(--0-70), --1.52(--1.54), --1.00(--2.72); slopes 0, --1, - 2 25. ~1 M HR and varyingcitrate at pH 6.2: log IX] (log D), --4.00(1.62), --3.52(1.63), -3.00(1.52), --2.52(1.20), --2.00(1.01), --1.52(~57), --1.00(-0.3S); slopes0, --1, --2 * All aqueousphas~ we~ I0-~'v M in cadmiumperchlorateand weremade up to anionicstrength of 1.0 with ,~lium l~rchlorate unless otherwiseindicated.
t Ionic m~ngth 0.I. :~Ionic strmgth 3.0. equation one (2--r--h) and would indicate an organic species of CclR~(HR)~ with the aqueous species changing from Cd I+ to CdR + to CdR~ to CdRs- as the pH rises. Systems .5-6 show the dependence of log D on the HR concentration, The indications are that 2--r~-a equals 3 at low pH values and equals 1 at high pH values, corresponding to-an organic species of CdR~.HR in all cases. The data of systems 1-6 may be adequately represented by writing D = [CdR4'HR]o/([Cd] + [CdR] + CdRj] + [CdRs]) or lID = [Cd]/[CdRz'HR]o + [CdR]/[CdR~.HR]o + [CdI~]/[CdR~.HR]o -/[CdR~]/[CdI~.HR]0 -~ I(.rsP~[H]S/KIPI[HR]os + I(rPrZ[H]C~o/KIPI[HR]o s + PrCi0o/ KIPI[HR]o + I(.r-I[I'I]-IC~KIPI. Using values of l o g / ~ and log Pr of 9"7 and 2"6 as given by HELLWEORand SCHW~TZl~,(4) curve-fitting techniques yielded log KIPI equal to 20.7, log C1oe 7.9, log Cz0o 15.3, and log CNo 18.4. These data compare favourably with results for the zinc-oxine-chloroform system,c6) but disagree with previous identifications of CdP~(HR)z as the extracting species.~4,s) It is suspected that the latter conclusion was arrived at on the basis of too few HR concentration data. To ascertain the effects of ionic strength on log D, the extractions indicated in systems 2, 7-10 were run. Fairly marked effects were noted, a displacement of as much as 1.0 pH unit occurring for a change in ionic strength from 0.1 to 3.0. In view of this, all extractions with complexing agents (with a few exceptions) were carried out at an ionic strength of 1.0. Complexed systems
Systems 11-25 indicate data gathered when various complexing agents in a series of concentrations were added to the aqueous phase. The information in each system was plotted, slopes were identified, suitable equations were written, and curve fitting procedures were employed to give estimates of the association constants of the involved aqueous complexes. In general, all these complexing systems could be treated by writing an equation of the type D = [CdR2.HR]0/([Cd] @ [CdX] I'IXLLW~Eand G. K. SCHW~Z~, Analyt. Chits. Acta 28, 236 (1963). m O. K. ~ z B x and W. V. Wn~LrJ,Analyt. Chlm. Acts 30, 114 (1964). c,) j. STAY,Analyt. Chtm. Acta 28, 132 (1963). t.) H. E.
The determination of association constants of aqueous cadmium complexes
103
[CAXt] + [CdX,]) or 1/9 ffi [Cd]/[Cdl~.mt]e + [CAX]/[C.~I~.HIt]e + [CdXt]/[Cdlte.HR]e + [CdX,]/[CdRe.HR]e ffi K,sp,t[H]t/£tPI[HR],s + K,sPetCm[H]a[X]/KiPl~lt~a + g,'I~JC~p[X?IKIP~IR~ * + x, s P , ~ P l r ~ x U ~ * . values o f l o g / ~ , log P,, and log XIPx are available from the previo~ work on the non-
complexed systems, thus the values of Coo, are readily obtai._nable. These ettimated values are presented in Table 2, along with some previotudy determined values. For all these complexed systems log D was also determined as a fanction of log [l'IR]e at several values of IX] and at the pH values indicated for the systems in Table I. In each case, the slopes were 3, giving confidence that the extracting species remained CdRs.HR. Log D was further determined as a function of log [X] at a pH of 9.5 and [HR]o equal to 0.1 M. Changes in log D were observed only with cyanide, thiosulphate, nitrilotriacetate, and ethylenedraminetetra-acetate. Tiffs indicates that only these complexing agents are strong enough to break the CdRe- complex. Examination of Table 2 indicates good agreement between w..ines reported here and those reported in the literature, especially when differences in ionic streogths TABLE2.~A,q~X~ATIONCON~rAN'~OF Complexing Agent Fluoride Chloride Bromide Iodide Cyanide Nitrate Acetate Thiocyanate Sulfate Thiosulfate Oxalate Tartrate Citrate Nitrilotfiacetate Pyrophosphate
Log C,,x, Coos,Coo,* 0.3, 0.5, 1.2, 1.8 1.4, 1.9, 1.4, 2.7, 5.8, I1.1 0.1, 0.1 0-7, 1.4 0.7, 1.5 0.1, 1.0, 3.2, 5.0 3.0, "4.7 1.1, 2.2, 2.6, 3.6 9.2 4.0, 6.3
1.2 2.2 4.2
1.7 2.4
Lit. Log Crux,Cm, Cml' 0.5, 0.6 1.3, 2.2, 2.4 1.6, 2.0, 2.3 1.8, 2.7, 4.2 5.5, 10.6, 15.2 0.1 1.3, 2.3 1.4, 2.0, 2.6 0.9 2.7, 5.2 3.5, 5.3 3.2 3.4, 5.0 9.5 5.6
KefeINmee (7) (8) (9) (10) (7) (7) (7) (11) (12) (13) (14) (15) (16) (17) (18)
* Values estimated in this research; accuracy approximately -4-0.2. ? Some previously reported values. ~T~I. l.J~s, Doctoral Dissertation, Lurid (1943). c,) E. L. KIN<),J. Amer. Chem. $o¢. 71, 319 (1949). c,~ p. KrVALO and P. Er,~x, Suomen Kern. 30B, 116 (1957). (x0)M. QuIm~ and S. PltLL~R, J. Chim. Phys. $3, 226 (1956); C.R. Acad. $¢1., Paris 24~ 768 (1956). ~xx~I. Lm>eN,Z. Phys. Chem. 188, 160 (1941). cxa~I. L w ~ , Acta Chem. Scared. 6, 971 (1952). ~x,)K. B. YAlmmasg.uand L. V. Gus'KOVA,Zh. ~,org. Khim. 2, 2039 (1957). (x,) W. J. CLAYTONand W. C. Vosatmos, ?. Amer, Chem. Soc. m , 2414 (1937). cx,~I. V. l~ArNrrsgJI, Zh. A~lyt. KAtm. 6, 119 (1951). cx,) p. K. MIOALand A. Y. SYcH~, Zh. Neorg. Xhim. 3, 314 (1958). (1,~ G. SCh'WAIgZENBACH and E. Flun'rAO,Helv. CAlm. Aeta 28, 1492 (1945). ~1,~G. SARTORI, Gazzetta 64, 3 (1934).
104
:[. E. ~ w l o m
and O. K. S a / w m ' r m
are recol~zed. Ionic strens~h effects seem to be especially critical in the evaluation of the first cumulative association constant Com. The data in the last column of Table 2 are not meant to be compared directly with the values obtained in this work' since in m0st cases the conditions d/IE,r somewhat, but they are illustrative values Oven only to indicate general agreement. Acksm~/ddS,Imat.--The ass/stance of a fellowsh/p granted by the Nat/onal S¢/eoce Foundation to
m~ ,- ~ a X y
w,knowledpd.