Badoni, V. N.

Sarai, R.

English

NOPR

Indian Journal of ChemistryVol. ISA. August 1977. pp, 731-733Spectrophotometric Determination of Formation Constants ofMolecular ComplexesR. SARAI* & V. N. BADONIDepartment of Chemistry, V.S.S.D. College, Kanpur 208002Received 13. October 1976; accepted 25 March 1977A new model has been suggested for the determination of equitlbrtum constants, K" andextinction coefficient, E, of fairly strong 1: 1 molecular complexes. The model involves theassumptton : AIC~ = K,C~E/(1+K,C~)-KiAI(1+K,C~)2, where A is the absorbance of the corn-plex, and C~ and C~ are the initial conce~tration of the acceptor and donor respectively.SEVERAL graphical approaches exist for eva-luating the equilibrium constant (K1) andextinction coefficient (£) of 1: 1 molecularcomplexes from spectrophotometric data in inertsolvents>". Inherent, in all the derivations, is theassumption that if C~~C~>CAD (where C~ and C~represent the initial concentrations of acceptor, A,and donor, D, respectively, and CAD is the equilibriumconcentration of the complex) then CAD can beneglected in the term (C~-CAD)' in the expressionfor equilibrium constant (Eq. 2). However, thisis not always a valid assumption. It has beennoticed that this approximation fails in the case ofstrong molecular complexes, when C~~ CAD4. Insuch cases, neglecting the term CAD will lead toerroneous equilibrium constants and other relatedthermodynamic data. We suggest a more adequatemodel than the ones presently used for the deter-mination of Kl and E of fairly strong molecularcomplexes.TheoreticalUnder the conditions of equilibrium for 1:1complex, AD, we haveA+D~AD; K = KIKy; Ky =YAD/YAYD ... (1)andCADK, = -(C---U-- 0 ••• (2)A-CAD) (CD-CAD)where Y. is the Raoult activity coefficient of speciesi. In general, Kl and Ky are not constants butare functions of concentrations of the reactantsand products. Since in most spectrophotometricmeasurements, we keep C1 constant and vary C~,it is convenient to define a set of dimensionless quan-tities as follows:K~=KIC~; Co~=C~/C~; C~D=CAD/C~In terms of these dimensionless quantities, Eq. (2)becomes• CA"DKl = (1-c" )(CO" C" ) ... (3)AD D- AD*To whom all the correspondence should be addressed.Solving for C~D from Eq. 3 yieldsC~D = 1/2(1+C~· + l/K~) -1/2[(1 +C~· +1/K~)2_4C~']lCD (2k-2) C~-k= 2 ~(k-1)! (1+C~-+1!K;)2k-lk=l 'co- [ co- ]= (I+C~- ~l/K~) 1+ (I+C~- ~1/K~)2 +. (4)Eq. (4) indicates that when C~-~ l/K~ C~D varieslinearly with C~·. Fig. 1 shows the theoretical plotsbetween C~D and Co~for different K; values. Theseplots indicate that the linear relation betweenC~Dand C~· holds only up to K~ = 10-3•o-sFig.10 20 30 it a 50 60CDO*1 - Theoretical plot of C;A (= A *)different values of K~versus C~O for70 90 100731INDIAN ]. CHEM .. VOL. 15A. AUGUST 1977The Beer-Lambert law can be stated as A = dC,w(where A is the absorbance. e is the molar extinctioncoecffiient and I is the path length). Assumingthat I = 1 em. we haveC' D = ~ = A* ... (5)A eVAEq. 5 indicates that C~D is proportional to A·.Th us. if we draw a theroetical plot of log A· (or logC~D) versus log cO; for various values of K~, then bysuperimposing on it an experimental plot of log Aversus log C~ we can determine K~ and hence K1.Eq. 5 shows that A is always smaller than eC~. Sub-stitution of Eq. (5) into Eq. (3) gives Eq. (6).• A' A'/C~'Kl = (l-A')(C~*-A") = (I-A")(l-A*/C~") ... (6)If we choose C~"~1 (i.e. cO; ~C~), then A"/C~".c{l,and Eq. 6, after neglecting A" /C~", reduces to Eq. 7,A"/Co;=K~(l-A") ... (7)which is of the same form as Benesi-Hildebrand(BH)l, Scott2 or Foster-Hammick-Wardley (FHW)3equations.To find out the exact linear relation betweenA"/~' and A", we rewrite Eq. (6) as Eq. (8)·" 0" K~(l-A") - (A") (8)A ICD = (l+K~)[I-(K~A"/l+K;)] - Y1 •••Expanding Y1(A") in terms of A" by Taylor'sexpansion gives,"ICO" - ~ -~ A"+R (A") (9)A D - 1+K~ - (1+K~)2 . 1 ...where° 1 ( KiA" )2RI(A ) = -1+K~-K~A" l+K~ ... (10)RI(A)" represents the higher order correction terms.It should be noticed that Eq. (9) reduces to Eq. (7)only when KI<{1. From the above derivation,we can see that the linear relation given by Eq. (9)represents the tangent to the curve A" ICo; versusA" at A* = O.From Eq. (8) it is clear that as long as K~(the product of the equilibrium constant and theinitial concentration of acceptor) is kept small sothat (KiA*/(1+Ki)2 is within the experimentalaccuracy (smaller than unity), a good linearrelation between A"IC~* and A* is expected to holdregardless of the donor concentration used. Fig. 2shows the theoretical relation between A '/C~" andA* for different Ki values. An analysis of theseplots indicates that the linear relation between A "IC~*and A" holds only up to Ki::::: 0,02. above which theplot starts deviating from linearity at lower concen-tration of the complex as observed previously also inour NMR investigations. but linearity is observedat higher concentration of the complex (Fig. 2).To compare the best theoretical linear relationbetween AO/C~oand A" with the conventional linearrelation between A °lCO; and A". we write Eq. 7 asAorC~*= Ki(l-AO)+R1H(A") ... (11)732~Ir-------------------------~0·9~--- __oo0·' 01 a·) 0'4- O'S 0-6 0'7 0-8 os 10COA* lcA"')Fig. 2 - Theoretical plots of A * /C~" against A * for differentvalues of K~where the correction term R1H(A*) IS given byEq. (12).RIH(A*) = -KW-A*)(A*/C~*) ... (12)orRIH(A*)/(A·IC~*) = -KW-A*) ... (13)which should be compared withR1H(A*) K~ ( A* )2A/COo* = -1-A* l+K~ ... (14)Thus. from Eqs. (13) and (14) we can determinethe errors introduced by the BH. Scott or FHWmodels and by the exact linear relation.It can easily be shown that the linear relationgiven by Eq. (11) actually represents the tangent tothe curve represen ting plot of A * /Co; versus A *. atA* = 1, if we notice that YW) = -K!, and A*/Cr;equals zero at A* = 1. A theoretical comparisonof the relation between A*/Cr; and A*, generated byEqs. (7), (8) and (9) for different K~ values is shownin Fig. 3. It may be seen from this figure that theFHW equation and the exact linear relation behavein a similar manner and are in good agreement withthe exact theoretical relation only when K! issma.Her than 0,01. As K! increases. both plotsdeviate from the exact theoretical plot. and it canbe noticed that in the FHW model Eq. (11) representsthe tangent to the curve representing the plot ofI 0"A* CD versus A*, at A*= 1. Eq. (9) represents thetangent at A * = 0 as shown above.Results and DiscussionSpectrophotometric equilibrium data based onB~ m<;>delfO.rs0IIl:e fairly strong molecular complexesof IOdine WIth different donors8-11 are summarizedin Table 1. The data obtained using our model(Eq. 15) and the percentage error introduced ineach case have also been shown in Table 1. It isSAHAI & BADON!: MOLECULAR COMPLEXESTABLE 1 - COMPARISONOF SPECTROPHOTOMETRICEQUILIBRIUMDATA FOR SO!llE STRONG1: 1 MOLECULARCOMPLEXESOFIODINE* WITH DIFFERENT DONORSDonor Literature values Calc. values from Eq. 15 Percentage errorK Emu Ref. [((litre mole=) (litre mole=)N,N-Dimethy1aniline 18·8 7 19·8 5·05Methylamine 530·0 8 551'8 3·95Ethylamine 720·0 8 762·1 5·50Tri-u-propylamine 1390·0 8 1560'5 10'90Tri-a-butylamine 1600·0 8 1820·8 11·02Triethylamine 6320·0 9 15369·0 58·80.Dimethylamine 6800·0 8 22495·0 69·70Phthalazine 346'7 10 574·5 39·60Diethylsulphide 210·0 11 235'8 10'90Pyridine 269·0 12 302·7 11'12Be (acacj , 10·1 2718 5 12·4 2729 18·50 0·40Sctacac); 20·0 25770 5 21·8 2604Q 8·25 1·04Altacac); 76·1 6410 5 81·3 6627 6·30 3·20Hexamethylbenzene 148·0 4780 13 164·2 4806 9·08 0·54N,N-Dimethylacetamide 2·6 760 14 2'7 779 4·40 2'45Th(acac). 3472 5 7264 52·20Zrtacacl , 3390 5 6728 49·60N,N-Dimethylpropionamide 704 15 719 2·08Dioxane 937 16 946 0·97Triethylamine 2560 9 304Q 15'78*C?t = 3'64xl0-"M for SI No. 1-7, 14,20; 5'Ox10-<M for SI No.8; 2'51xl0-4M for 51 No.9, 10; 4'Oxl0'-M for Ll,13, 16, 17; 9·2 x 10-aM for SI No. 15.smax [( £max,·o..-----,::------"'"-------,r--,\ 1O·9r----L~___ \---- .. - .. - ..--\. ;_.- .. -_····-_ .._ ..-_L. \\\\\'i'I080·7o·"""--'"-!l! .•. ;;-...j K·/'+K .~... ,, .03(}201 0·'oo 0·' 0·2 0') 0·4. 0·5 (}6 a·'COA*=A*Fig.3 - Comparison of theoretical relationship betweenA *'Co; and A· for different values ofKI* using different models[Continuous line. exact linear equation; broken line, Foster-Hammick-Ward ley equation; dotted line, present equation]apparent from these data that the percentage errorbecomes larger when the product of K, and C~ be-comes more pronounced compared to unity, as is evi-dent fromEq. (9) which maybe represented after neg-lecting the higher order correction terms as follows:AICb=KIC~E/(l +KIC~)-KIAI(l +KIC~)2 ... (15)Adoption of the present model (Eq. 15) introduceserrors varying from 4- to 70% in Kl and from 1to 50% in E for the present complexes. In the case-of fairly strong triethylamine-iodine complex,approximately 10% error in K, was introduced bythe equation suggested by Nagakurat, For thisparticular system 58'8% error in K, is observed onthe basis of present model (Table 1). ThoughLaBxdde and Tamres'? have proposed a means ofestimating the errors introduced by dropping termsthrough linear regression model, our model (Eq. 15)would be helpful to calculate the errors introduced inBH. Scott or FHW equations and further it will pro-vide a con venien t graphical approach for determiningK, and E of molecular complexes in general and thoseof fairly strong molecular complexes in particular.References1. BENES!. H. A. & HILDEBRAND, J. H., J. Am. chem,Soc., 71 (1949), 2703.2. SCOTT, R L.. Reel. Trav. chim. Pays-Bas. Belg., 75(1956), 787.3. FOSTER, R, HAMMICK, D. LL. & WARDLEY, A. A.,J. chem. Soc., (1953), 3817.4. MULLIKEN,R S. & PEARSON•• V. B., Molecular complexes- a lecture and reprint volume (J. Wiley & Sons, NewYork). 1969. Ch. 7, 81; FOSTER, R, Molecular com-plexes, Vol. 2 (Paul Elek Ltd, London), 1974. 107 andreferences cited therein.5. SAHAI, R, LOPER, G. L., LIN, S. H. & ERYING, H.,Proc. natn. A cad. Sci., 71 (1974), 1499.6. SINGH, P. R & SAHAI.R. Aust. J. cu«; 23 (1970). 269.7. TSUBOMURA.H., J. Am. chem, Soc .. 82 (1960). 40.8. YADA, H .. TANAKA, J. & NAGAKURA, 5.• Bull. chem,Soc. Japan, 33 (1960), 1660.9. NAGAKURA,S.• J. Am. chem, Soc., 80 (1958), 520.10. SAHAI, R, unpublished result.11. GOODENOW,J. M. & TAMRES, M., J. chem, Phys., 43(1965), 3393.12. Popov, A. I. & RVGG. R H., J. Am. chem, Soc., 79(1957), 462213. STRONG,R L. & PERA:'IO. J., J. A m. chem. Soc., 83(1961), 2843.14. DRAFA, R. S.. BOLLES, T. F. & NIEDZIELSKI. R J.. J.Am. chem, Soc .. 88 (1966). 2717.15. DRAGO.R 5 .. WENZ, D. A. & CARLSON,R L., f. Am.chem. Soc., 84 (1962), 1106. .16. DRAGO, R S. & ROSE, N. J., J. Am. chem. Soc., 81(1959), 6141.17. LABuDDE, R A. & TAMRES, M.. J. phys. Chern .• 74(1970), 4009.733

Spectrophotometric Determination of Formation Constants of Molecular Complexes

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Spectrophotometric Determination of Formation Constants of Molecular Complexes

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