Bag, Saswati P.

Chakrabarti, Anil K.

English

NOPR

Indian Journal of ChemistryVol. 15A, August 1977, pp. 724-727The Concept of Theoretical Molar Absorptivity forPhotometric Determination of Trace Amount of Metal &Thermodynamic Formation Constants of Mo(VI) Complexes withDisodium cis-I,2-Dicyanoethylene-I,2-dithiolate*SASWATI P. BAG & ANIL K. CHAKRABARTIDepartment of Chemistry, ]adavpur University, Calcutta 700032Received 27 November 1976; accepted 10 February 1977A new concept on theoretical molar absorptivity for the Mo-MNT complex has been glvenutfliztng photometr-ic law and free-Hgand concentrations. Also, a new photornetrfc methodhas been described for the evaluation of stepwise and successive forrnation constants for the1: 4 metal-Iigand system. The overall formatlon constant can be termed as therrnodynamlcstability constant for a 10-4M solution of rriolybdenurrr-M'N'I' chelate complex, Different photo-rnetrtc procedures have been included for the calculation of overall formatton constants Includingthat of extrapolation of log K values agalnst II and COIn pared with each other. Log kI' Iog k2•Iog k3• lo~ k. and log II. have been found to be 4'46, 2'68, 2·91. 2·72 and 12·75 respectively. TheIog K values from Harvey-Mannlng'a equation. mole-r-atio plot and extrapolation methojj arefound to be 15·85. 15·85 and 18·25 respectively at 25°± 0.1°. The theoretical molar absorptivity(TMA) and the calculated molar absorptivity values are 5·80 x 103 and 5·87 x 103 litre mole'< crrr+respectively. The free energy change for the reaction comes out to be -17·5 kcal mote-t(lo~ K = 12-75) at 25°.D ISODIUM cis-l ,2-dicyanoethylene-l ,2-dithio-late (Na2MNT) has been found to formcoloured complexes with rnolybdenumfv I) ,tungstenfV.l). vanadiumfV] and many platinumgroun metals in 50% acetonitrile-water mixed sol-vent.'. Previously, a ~;reen complex of molybdenumin tile mixed solvent (Arnax, 665 nrn) has been utilizedfor a selective photometric estimation of the metalin 2.11oy steels''. In the present investigation, anew concept on theoretical molar absorptivity (TMA)has been evaluated on the basis of photometric law,composition and graphical extrapolation method.The metal to Iigand ratio from both the continuousvariation and mole-ratio methods has been found1:4 with varied metal ion concentrations.pH-metric methods for formation constants areoften applied in many metal-chelate systems givingrarely unusual and abnormal results. However,with Mo(VI) chelates some unusual behaviour isoften encountered due to redox reactions andHvbcnding. Further, Mo(VI) complexes are sup-posed to be reduced to Mo(V) by thiols and thedetermination of stepwise formation constants isinvariably difficult, and more so in case of high dis-sociation. Previously, it has been observed thata same degree of accuracy is achieved by twodistinctly different photometric procedures whenapplied to Mo(VI)-thiol chelate with high metal-ligand ratios. In the present investigation withmolybdenum-MNT system the degree of complexformation function and subsidiary functions hasbeen considered because of greater accuracy claimedin the method. The log J{ (K = overall formation• A part of the contribution made during the tenure inCSIR Pool, India.724constant) values obtained emj-loying subsidiaryfunctions, Harvey-Manning's equation, mole-ratio plotand ext raj olat ion met hocs was found to differ bylogarithmic units. The results obtained by differentmethods have been compared and discussed. Thesuccessive formation constants (~l' ~2' ~3 14) havebeen obtained from intercepts p;iYcn by photometricmethod of extrapolation. The'Y functions are plot-ted against and extrapolated to zero free-ligand [L].Materials and MethodsMolybdenum solutions (4'168xlO-3M] were ob-tained by proper dilution of the stock solution ofknown strength. Reagent solutions of equimolarstrength were jrepared from extremely rue formof Na2MNT, to study the effect of varying metalto ligand ratio", For this reason the reagent waspurified three times from ethanol-ether mixture.Higher concentrations of freshly jrejared solutionsof reagent were utilized for mixing incornplernentaryproportions (6 ml). Pure acetonitrile (Ricc'el) wasfurther purified by distillation over P20S'All spectral measurements were made with aUnicam SP600 spectrophotometer in 1 cm glass cells.Determination of the metal-ligand composition-The composition of the molybdenum-MNT complexin mixed solvent was determined by method of conti-nuous variation" and verified by mole-ratio method".Equimolar solutions of metal and reagent were uti-lized in the final volume of 25 ml and mixed in com-plementary proportions (6 ml). After addition ofrequired amount of acid (HCl), reagent solutions ofhigher concentrations were added and acidity wasmaintained at 3M HCI. The curves have been ob-tained by plotting absorbances (measured at 665 nm)BAG & CHAKRABARTI: THEORETICAL MOLAR ABSORPTIVITY & DETERMINATION OF Mo(VI)against mole fraction of metal. For constant metalion (2·084xI0-3M and 4·I64xI0-3M), mole-ratioplot indicated the composition to be 1:4 (molyb-denum: MNT).Photometric procedure - A suitable aliquot ofMo(VI) solution was taken and to this was addedvarying amounts of reagent solutions and hydro-chloric acid so as to maintain acidity at 3M Helin a total volume of 25 ml. The turbidity ofsolution was removed by adding 12'5 ml of purifiedacetonitrile. After thorough mixing the solutionwas allowed to attain normal room temperature.The absorbances measured at 665 nrn were plottedagainst mole fraction of molybdenum. The photo-metric titration data (Table 1) have been utilizedfor evaluation of formation constants as well astheoretical absorbance.Calculations - The theoretical molar absorptivity(TMA) of complex species was evaluated fromphotometric titration results", A series of ab-sorbance values were determined considering amountof metal complexed from Beer's law. Since molyb-denum species absorbed strongly at wavelengthmaxima the different absorptivities were expressedas e = absorbanceCj, and the average valuewas found for solution comprising only singlecoloured species. Principle of the method of ob-taining TMA of the complex involved extrapolationof absorptivities at several points in photometrictitration curve. The e values were plotted againstY where Y stands for inverse of free-ligand concen-tration [L]. The intercept gives TMA at almostinfinite amount of free-ligand concentrations, i.e. inthe presence of large excess of ligand (Na2MNT).Successive and stepwise formation constants ofmolybdenum-MNT complex species were obtainedconsidering the equation M+nL~MLn (n = 4).Since overall concentration of metal in solution(CM) is sum of the concentrations of complexes, itfollows thatcp= f~= I+ML]+~2[LJ2+~a[LJa+~4[LJ4where ~l> ~2' e, and ~4 are the successive formationTABLE 1- ABSORBANCE, FREE-LIGANDCONCENTRATIONS AND THEMOLAR ABSORPTIVITY VALUES OFMOLYBDENUM-MNT SYSTEM IN50% AQUEOUS ACETONITRILE AT 25°±0'1°[M = R = H68xl0-sM]Totalligandcone.(CL X 10·, M)Absor- Free-ligand Molar Y = 1/[L]bance conc. absorptivity (x 10-3)([L] x 10·, M) litremole'? em'?(exl0-S)6·601 0·760 1·285 4·559 7·7828·337 0'860 2·321 5·159 4·3089·870 0·885 3-678 5'309 2·71811'672 0·920 5·228 5·520 1-91313'339 0'925 6·867 5'549 1'45615·007 0'930 8·495 5'580 1·17716·674 0'930 10·162 5'580 0'98418'341 0·930 11·830 5·580 0'84520·009 0·930 130497 5·580 0·740constants''. The degree of complex formation fune-tion (cp) has been calculated on the basis that thecomposition was 1:4 even in the presence of insuffi-cient ligand concentration. In this procedure aseries of subsidiary functions were constructed andextrapolated to zero value of the variable [L]. Thefunction h can be constructed and defined asfollows:cp-1 . . cp-1h= [LJ and Lim IJil= Lirn [LJ = ~1[L]--?O [L]--?OL··1. I . h-~l ~ k k[~j:b2= [tbo [LJ = ~2 = 12L· .r, L' 1Ji2-~2 ~ k k[~]~b3 = [L]:o[I] = ~3 = 12k3L' .r, L' 1Ji3--~3 kim '1'4 = irn -[L) = ~4 = kl 2k3k,[L)--?O [LJ--?OIn general, Lim IJin= Lim IJin-l-~n-l = ~n[LJ--?O [LJ--?O [LJ(where n = 2, 3, 4 and kl' k2' k3' k4 = stepwise for-mation constants).Thus, the values for ~h ~2' ~3 and ~4 are obtainedby plotting the functions 1Ji1>1Ji2'lJia' 1Ji4against thevariable and extrapolated to zero free-ligand con-centration [LJ. Knowing the metal-ligand composi-tion, the free-metal and free-ligand concentrationsfor each of the solutions are calculated from Beer'slaw data. The metal is bound to Iigand in 1:4 ratioeven in the absence of sufficient amount of equimolarreagent concentrations. So, once the amount ofmetal complexed is known the free-metal can becalculated. Also, the free-ligand concentration isobtained considering amount of ligand complexedin the complex species. The successive formationconstants have been found directly from interceptvalues.The free-energy change for the reaction has beencalculated from the equationAP =-RT In K=-17·5 kcal mole"! (log K-12'75) at 25°Results and DiscussionIn Fig. 1, e values with different free-ligandconcentrations have been plotted against y, i.e.If[LJ. The curve is extrapolated to y tending to-wards zero and the intercept gave for TMA a valueof 5·80 X loa litre mole+ crrr? (5'87 X 103 litre mole=cm+, d. Beer's law). In the presence of sufficientreagent in excess Mo-MNT complex appeared tobe a strong one. TMA obtained by extrapolationmethod (5'80x 103) was almost similar to that givenby Beer's law data (5'87x 103) and lies withinhighest experimental accuracy as revealed by thedata in Table 1. The concept of TMA has alreadybeen followed with different metal-ligand ratios.Since absorbance corresponds directly to the amountof molybdenum complex formed, [LJ is found usingestablished composition and r.hotometric law. Tl-eTMA concept appeared to be important. Becausethe actual. analytical concentration of metal ioninvolved for high dissociating complexes can be7257INDIAN J. CHEM., VOL. 15A, AUGUST 19775o -)(••432~ __~ -L ~ __~~ __~ ~~o 0'5 2'5 3'0'·0 "5 2·0Y X 10-3Fig. 1 - Average molar absorptivity e as a function of thereciprocal of the free-ligand concentrationaccurately evaluated from theoretical absorbance.In the present system, the concentration of molyb-denum obtained from observed absorbance andtheoretical absorbance (d. TMA) are tl-e same.From Fig. 1 the immediate conclusion regardingnature of complex species is that four to five timesequimolar excess of MNT solution was enough toform a strong complex with negligible degree ofdissociation. Utilizing TMA it would be possibleto design and choose a sensitive and selectivereagent for a particular metal ion system in aparticular solvent. The concept of TMA is usefulfor molybdenum-MNT system for accuracy involvedduring selective determination of trace quantityof the metal. Also, since the intercept gives TMAat excess of free-ligand degree of dissociation (ex) isminimum lowest possible.Figs. 2 and 3 illustrate the plots of '¥ functionagainst free-ligand [L]. In the range of reagentconcentrations employed between 8'337 X 1Q-4M and15·01 X 1O-4M in the final volume the different sub-sidiary functions have been constructed. Thefunctions near the vicinity of 1:4 metal to ligandratio were most suitable to give intercepts that areaccurate and reproducible. From Table 2 it isevident that the cp value increases with decreasein free-metal (uncomplexed). A general trend hasbeen maintained with 'l' functions plotted against5 oe-10XN~,Fig. 2 - Subsidiary functions 'Y1, 'Y. as a function of free-ligand concentration [L]4320fJ~ 2 0 10'~ ~HXIO =/33~... --~---=-- 1 58 X10 = 13,.. 8• •I120 ~?x-.A-JoOOL8----~2----~4----~6~--~--~I~OOCL 1 X 10,1, MFig. 3 - Subsidiary functions 'Y •• 'Y4 as a function of free-ligand concentration [L][LJ. However, log kl (4'46) > log k3 (2'91) >log k4 (2'72) and log kl > log k2 (2'68?) < log k3·Overall foi mat ion constant (K) has been calculatedconsidering TMA as absoi bance maximum. ex fromthe relation, ex = TMA -- ".bsorbancf'stoicbiometric!TMA was found to be 0·1827. Thus, log K utilizingHarvey-Manning's method" comes out to be 15·85.The log K evaluated by photometric method is foundTABLE 2 - ABSORBANCE.FREE-LIGAND CONCENTRATIONSAND DEGREE OF COMPLEXFORMATIONFUNCTIONSOFMOLYBDENUM-MNTSYSTEM IN 50% AQUEOUSACETONITRILEAT 250 ± 0.10[M = R = 4-168 x 10-3M; final volume = 25 ml]Total Absorbance Equilb. Equilb. Cone. of Degree of q,1 q,. h q,4ligand ligand metal metal complex (x 10-') (x10-7) (x 10-1°) (x 10-12)cone. cone. cone. complexes formation(CLX 10', M) ([LJ x 10', ([MJX 105, (x10', M) function.M) M) 'P =CM /[M]6·601 0·760 1'285 3'384 1'329 4·926 3·056 1·603 1·97 67·708·337 0'860 2'321 1'634 1'504 10·20 3'964 4·794 14'86 593'19·869 0'885 3-678 1-194 1·548 13·96 3·523 1·829 1'30 5·43711'672 0'920 5'228 0·574 1·610 29·04 5'363 4·806 6·61 105·413'39 0'925 6'867 0·494 1·618 33·75 4·769 2·801 1-48 5·53515-007 0'930 8'485 0'394 1'628 42'31 4'863 2'369 1·71 7·063726BAG & CHAKRABARTI: THEORETICAL MOLAR ABSORPTIVITY & DETERMINATION OF Mo(VI)to be 12·75. The overall stability constant hasalso been calculated employing extrapolated curvein mole-ratio plot. The basis for the procedure isthat the ratio of true absorbance to the extrapolatedabsorbance in mole-ratio plot is mole fraction oftile molybdenum complex actually formed (absstoich!absextrapt= MLf.!CM). The value of ot has beenconsidered further to be 0·1383 (ot = absextrapt-absstoicb!absextrapt)for Harvey-Manning's equation.Thus, log K (average) from mole-ratio plot is foundto be 15·85 (CM = 1·667x10-'M).In extrapolation method, ot values obtained frompoints above stoichiometric break are found to be0'1162, 0,1412, 0·1739, 0·1783 and 0·1827. log Kvalues from corresponding ot in titration curve wasfound to give an increasing trend with ot. The plotis linear having a negative slope. It increasessharply with more of free-ligand, indicating somedissociation of Mo-MNT complex around equalmolar proportions of reagent. log K (= 18·25)obtained by extrapolation to zero ot was found toto differ from that given directly by Harvey-Manning's method (15·85).Difference in log K by several units, photometric12'75 ;Harvey-Manning 15·85 ;mole-ratio plot 15'85andgraphscal extrapolation 18·25 supported a dissociativenature of molybdenum thiolate complex in the absenceof sufficient amount of reagent. In the presence ofexcess of reagent the dissociation is checked and com-plete formation of the complex is ensured. In photo-metric method evaluation of !p involved lower concen-tration of the coloured species which contributeda value much lower than theoretical absorbance.On the other hand, ot has been calculated consi-dering the complete formation of the species. Withvery dilute solutions of 10-'M molybdenum andMNT, both ionic strength and the salt effect in theacetonitrile-water solvent have not necessarily beenconsidered. Actually, the formation constant canbe termed thermodynamic stability constant.References1. CHAKRABARTI, A. K., Complexes of less-common metals(Studies on formation constants and analytical applica-tions), Ph.D. thesis, Jadavpur University, 1971.2. CHAKRABARTI, A. K. & BAG, S. P., Talanta, 19 (1972),1187.3. BAG, S. P. & CHAKRABARTI, A. K., J. Indian chem. Soc.,51 (1974), 474.4. DAVISON, A. & HOLM, R. H., Inorganic syntheses, Vol. 10(McGraw-Hill, New York), 1967, 11..5. VOSBURGH, W. C. & COOPER, G. R., J. Am. chem. Soc.,63 (1941), 437.6. YOE, J. H. & JONES, A. L., Ind. Engng Chem. (Anal.edn) , 16 (1944), 111.7. CHAKRABARTI, A. K. & BAG, S. P., Talanta, 23 (1976),736.8. BAG, S. P. & CHAKRABARTI, A. K., J. Indian chem. s»;52 (1975), 492.9. HARVEY, A. E. & MANNING, D. L., J. Am. chem. Soc.,72 (1950), 4488; 74 (1952), 4744.727

The Concept of Theoretical Molar Absorptivity for Photometric Determination of Trace Amount of Metal & Thermodynamic Formation Constants of Mo(VI) Complexes with Disodium cis-1,2-Dicyanoethylene-1,2-dithiolate

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The Concept of Theoretical Molar Absorptivity for Photometric Determination of Trace Amount of Metal & Thermodynamic Formation Constants of Mo(VI) Complexes with Disodium cis-1,2-Dicyanoethylene-1,2-dithiolate

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