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Independent determination of equilibrium constant and molar extinction coefficient of molecular complexes from spectrophotometric data by a graphical method
0584-8539/82/020289-04$03.00/0 @ 1982Pergamon Press Ltd
Spectrochimica Ada, Vol. 38A.No. 2, pp.289-292, 1982 Printedin Great Britain.
Independent determination of equilibrium constant and molar extinction coefficient of molecular complexes from spectrophotometric data by a graphical method B. K. SEAL and H. SIL Department of Chemistry, Burdwan University, W. Bengal, India
and D. C. MUKHERJEE Department of Chemistry, University of Calcutta, 92, Acharya Prafulla Chandra Road, Calcutta-700009, India (Receioed 6 September 1981) Abstract-The Benesi-Hildebrand equation and its modified forms have been rearranged to give equations which enable independent evaluation of K and Q of molecular complexes from spectrophotometric data by graphical procedure. The equations have been tested with data on several 1: 1 complexes. The results agree fairly well with those determined by other well-known procedures.
INTRODUCTION After the important observation of BENESI and HILDEBRAND PI and the subsequent interpretation of the phenomenon by MULLIKEN[~], several
equations [l, 3-61 have been derived and tested for the evaluation of equilibrium constants (K) and molar extinction coefficients (E) of molecular complexes from spectrophotometric data. In all these equations one single parameter, either K or E and the product Ke appear either in the slope or in the intercept. Therefore, only one parameter can be evaluated independently of the other which is obtained from the product KE. The reported values of K and c while showing fair constancy among the values obtained by different investigators for strong complexes deviate widely for weak complexes. Various explanations [7-181 have been suggested to account for the observed discrepancies. It has been pointed out by many that, although the product KE can be obtained with relative ease, difficulties and ambiguities arise, particularly for weak molecular complexes, when attempts are made to separate these two parameters. Although criteria for meaningful separation of K and l from the product Ke have been discussed by PERSON[T], DERANLEAU[lg], and by LABUDDE and TAMRES [20], necessary equations for independent evaluation of K and E ‘have not been suggested. Recently we have been successful in rearranging the Benesi-Hildebrand equation and its modified forms into suitable forms to evaluate K and l independently of each other by graphical procedure. In the present communication we report the results of our investigations in this connection.
PRINCIPLE For a 1: 1 complex (AD) formed between an acceptor (A) and a donor (D) according to the
scheme A + D G AD equation is
the
Benesi-Hildebrand
where the terms have their usual significance. A simple rearrangement of the Eqn. (1) yields d = C:el-e
d
(2)
wherein the product KE is absent and both K and l have been separated from each other. Thus the two parameters can be determined independently of each other by a graphical plot of the necessary functions. Equations (2) and (3) are the limiting cases of the following more general Eqns (4) and (5), when c: 4 c:. d = C:cl - dKC,
289
(4)
B.K.
290
which have been obtained lowing equation[21]
c;cgr d
by rearranging
the fol-
_ 1 +(c:+G)
KE
SEAL et al.
(6)
l
Equations (4) and (5) may be used in place of Eqns (2) and (3) to obtain independently the equilibrium constant and the molar extinction coefficient of the complexes under the condition of constant Ci. For the purpose of verifying the principles outlined above, we have used the Eqns (2) and (5) respectively. However, the other equations can likewise be used. RESULTS AND DISCUSSIONS
Equations (2) and (5) have been tested by using the experimental data of different investigators from existing literature. A number of systems have been studied. These include (i) 1,3$tricyanobenzene-TMPD [223, (ii) chloranil-indole [23], (iii) 1,3,5-trinitrobenzene--diphenylamine[24], (iv) fluoranil-HMB [25], (v) iodine-tetramethyl urea [26], (vi) iodine-methylacetate[26], (vii) iodinemethylthioacetate[26], (viii) iodinemonochloridedioxane [27], (ix) TCPA-naphthalene [28], (x) TCPA-stilbene [28], (xi) TCPA-biphenyl[28], (xii) TCPA-phenanthrene [28], (xiii) TCPAanthracene [28], (xiv) TCPA-quinoline [29] and (xv) TCPA-2-methylquinoline[29]. The results are recorded in Table 1 and some typical plots are shown in Figs. 1 and 2 respectively. As expected Eqns (2) and (5) yield good linear plots. The scattering is much less with the Eqn. (5)
Table 1. Independent
determination
than with Eqn. (2). An advantage of using the Eqn. (2) over the Benesi-Hildebrand equation (1) is that c is more accurately estimated by it since E appears as a product of Cl1 and the value of the product Ciel is usually much greater than l/e which appears in the intercept of the BH equation. Often the BH plot has a low value of the intercept introducing large uncertainties in the estimated value of l and hence in the value of K evaluated from the product KE obtained from the slope of the equation. The BH equation, as observed, has certain other demerits. Sometimes the BH plot passes through the origin or sometimes it leads to a negative intercept, in both the cases the value of E is an absurd quantity. Equation (2), like the BH equation, requires an extrapolation to concentrated solutions for the evaluation of E independent of K which is evaluated directly from the gradient of the line without recourse to an extrapolated intercept. A disadvantage experienced in using Eqn. (2) is that for some of the systems studied by us the span in the values of d/CA is small while that in d is quite marked. As already mentioned the association constant and the extinction coefficient of the complex may be obtained independently of each other by using Eqn. (5) which, unlike the Eqn. (2), does not require extrapolation to concentrated solutions. This equation enables one to obtain E from the gradient and K-’ from the negative intercept of the linear plot of (Ci+ CL) vs CiCA/d. Good linear plots have been obtained for the various systems studied in the present investigation. However, for many systems the function CxCL/d
of association constant and molar extinction coefficient of some molecular complexes by graphical method Reported
Eqn. (5)
Eqn. (2) f
System
mol. 1-l
1 . mol-’ . cm-’
1,3,5-TricyanobenzeneTMPD Chloranil-indole 1,3,5-Trinitrobenzenediphenylamine Fluoranil-HMB Iodine--tetramethyl urea Iodine-methylthioacetate Iodine-methylacetate Iodinemonochloride-dioxane TCPA-naphthalene TCPA-stilbene TCPA-biphenyl TCPA-phenanthrene TCPA-anthracene TCPA-quinoline TCPA-2-methylquinoline
4.04
355
4.04
356
4.0
354
2.90
1498
2.94
1486
2.86
1510
0.5 13.56 5.98 0.73 0.55 22.80 2.27 5.98 2.73 7.78 8.75 26.84 13.70
1395 4030 701 -405 -455 813 1190 401 525 739 1161 134 219
0.50 11.76 6.33 0.75 0.52 22.2 2.27 6.76 2.69 7.52 8.47 26.32 13.2
1395 3041 685 -386 -477 819 1200 400 533 6% 1184 136 229
0.40 6: 0.72 0.52 23.86 2.8 5.5 2.9 7.3 10.3 26 15
1390 677 -410 -478 830 1000 476 500 714 1000 132 226
benzene;
TCPA-t&a-
TMPD-N, N, N’, N’--tetramethyl chlorophthalic anhydride.
K
c
E
K
K
mol * 1-l 1 . mol-’ . cm-’ mol
p-phenylenediamine;
HMB-hexamethyl
1-l 1 . mol.’ . cm-’
Equilibrium constant and molar extinction coefficient
291
d.IO'
I-
I\
F
\
I
0.9 -
I
%O
I\
I
I_ 14
40.7 20.5 I 2
0 a30
I 5
IO
I5
20
25
35
40
d/c;
Fig. 1. Plot of d vs d/C; for (A) chloranil-indole, (B) I*tetramethyl urea, (C) Kl-dioxane and (D) TCPA-phenanthrene systems.
Fig. 2. Plot of (CX+ Cfi) vs CiCg l/d for (A) chloranil-indole, ICMioxane (365 nm) and (D) TCPA-phenanthrene
(365 mm)
(B) &tetramethylurea, systems.
(C)
292
B. K. SEAL et al.
[8] P. H. EMSLIE, R. FOSTER, C. A. FYFE and I. HORMAN, Tetrahedron 21,2843 (1965). [9] S. CARTER, J. Chem. Sot.(A), 404 (1%8). [lo] S. D. Ross and M. M. LABES, I. Am. Chem. Sot. 79, 76 (1957). [l l] G. D. JOHNSONand R. E. BOWEN, I. Am. Chem. Sot. 87, 1655 (1%5). [12] S. CARTER, J. N. MURREL and E. J. ROSCH, J. Chem. Sot. 2048 (1%5). [13] D. W. TANNERand T. C. BRLJICE,J. Phys. Chem. 70, 3816 (1966). [14] J. D. CHILDS, S. D. CHRISTIANand J. GRUNDNES,J. Am. Chem. Sot. 94, 5657 (1972). [15] R. FOSTER, Organic Charge-tr&sfer Complexes, pp. 16&165 and 171-173. Academic Press, London and New York, (1%9). [16] S. D. CHRISTIANand E. E. JUCKER,J. Phys. Chem. 74, 214 (1970). [17] R. S. MULLIKEN and W. B. PERSON, Molecular Complexes, pp. 92-100. Wiley Interscience, New York (1969). [18] G. BRIEGLEB, Elektronen-LIonator-AcceptorKomplexe. Springer-Verlag, Berlin, 1961. 1191 _ _ D. A. DERANLEAU, J. Am. Chem. Sot. 91, 4044 (1964). [20] R. A. LABUDDE and M. TAMRES, J. Phys. Chem. 74, 4009 (1970). [21] M. TAMRES and J. YARWOOD, Spectroscopy and Structure of Molecular Complexes, Ch. 3, p. 221. Acknowledgement-Sincere thanks are due to Prof. R. Plenum Press, London and New York (1973). FOSTER, Dept. of Chemistry, University of Dundee, for [22] R. FOSTERand J. J. THOMPSON,Trans. Faraday Sac. supplying the raw data on the floranil-HMB system. 59, 2287 (1%3). [23] R. FOSTERand P. HANSON, Trans. Faraday Sot. 60, REFERENCES 2189 (1%4). [24] R. FOSTER,D. LL. HAMMICKand A. A. WARDLEY, J. [l] H. A. BENESIand J. H. HILDERBRAND,J. Am. Chem. Chem. Sot. 3817 (1953). Sot. 71, 2703 (1949). [25] B. DODSON, R. FOSTER, A. A. S. BRIGHT, M. I. [2] R. S. MULLIKEN, J. Am. Chem. Sot. 74, 811 (1952). FOREMAN and J. GORTON, J. Chem. Sot. B, 1283 [3] J. A. A. KETELAAR,C. VANDE STOLPE,A. GOLJDSMIT (1971). and W. DZCUBAS, Reel. Trav. Chim. Pays-Bas Belg. [26] R. L. MIDDAUGH, R. S. DRAGO and R. J. NIED71, 1104 (1952). ZIELSKI,J. Am. Chem. Sot. 86, 388 (1964). [4] R. S. Scorr, Reel. Trav. Chim. Pays-Bas [27] A. I. POPOV, C. C. Brsr and W. B. PER&N, J. Phys. Belg. 75, 787 (1956). Chem. 64, 691 (l%O). [5] R. FOSTER,J. Chem. Sot. 5098 (1957). [28] M. CHOWDHURYand S. BASU, Trans. Faraday Sot. [6] N. J. ROSE and R. S. DRAGO, J. Am. Chem. Sot. 81, 56, 355 (1960). 6138 (1959). [29] M. CHOWDHURY,J. Phys. Chem. 65, 1899 (1961). [7] W. B. PERSON,J. Am. Chem. Sot. 87, 167 (1965).
shows appreciable fluctuations which make the application of Eqn. (5) difficult for these systems. The values of K and E for various systems evaluated with the help of the Eqns. (2) and (5) agree (as seen from Table 1) in most cases among themselves and also with those evaluated by other well known procedures. The noted differences in some cases may be due to the different approach of the methods. While Eqns (2) and (5) evaluate K and e independent of each other, the other methods require the separation of K and E, through the intercept and slope of linear plots, from the product Kc, occurring in the derived equations. The system fluoranil-hexamethyl benzene has been treated by us as a 1: 1 complex while FOSTER [25] treated it as a mixture of 1: 1 and 1: 2 complexes. For this system the plot of d vs d/CD0 according to Eqn. (12) shows appreciable scatter of data points while Eqn. (5) yields a good straight line.
Spectrochimica Ada, Vol. 38A.No. 2, pp.289-292, 1982 Printedin Great Britain.
Independent determination of equilibrium constant and molar extinction coefficient of molecular complexes from spectrophotometric data by a graphical method B. K. SEAL and H. SIL Department of Chemistry, Burdwan University, W. Bengal, India
and D. C. MUKHERJEE Department of Chemistry, University of Calcutta, 92, Acharya Prafulla Chandra Road, Calcutta-700009, India (Receioed 6 September 1981) Abstract-The Benesi-Hildebrand equation and its modified forms have been rearranged to give equations which enable independent evaluation of K and Q of molecular complexes from spectrophotometric data by graphical procedure. The equations have been tested with data on several 1: 1 complexes. The results agree fairly well with those determined by other well-known procedures.
INTRODUCTION After the important observation of BENESI and HILDEBRAND PI and the subsequent interpretation of the phenomenon by MULLIKEN[~], several
equations [l, 3-61 have been derived and tested for the evaluation of equilibrium constants (K) and molar extinction coefficients (E) of molecular complexes from spectrophotometric data. In all these equations one single parameter, either K or E and the product Ke appear either in the slope or in the intercept. Therefore, only one parameter can be evaluated independently of the other which is obtained from the product KE. The reported values of K and c while showing fair constancy among the values obtained by different investigators for strong complexes deviate widely for weak complexes. Various explanations [7-181 have been suggested to account for the observed discrepancies. It has been pointed out by many that, although the product KE can be obtained with relative ease, difficulties and ambiguities arise, particularly for weak molecular complexes, when attempts are made to separate these two parameters. Although criteria for meaningful separation of K and l from the product Ke have been discussed by PERSON[T], DERANLEAU[lg], and by LABUDDE and TAMRES [20], necessary equations for independent evaluation of K and E ‘have not been suggested. Recently we have been successful in rearranging the Benesi-Hildebrand equation and its modified forms into suitable forms to evaluate K and l independently of each other by graphical procedure. In the present communication we report the results of our investigations in this connection.
PRINCIPLE For a 1: 1 complex (AD) formed between an acceptor (A) and a donor (D) according to the
scheme A + D G AD equation is
the
Benesi-Hildebrand
where the terms have their usual significance. A simple rearrangement of the Eqn. (1) yields d = C:el-e
d
(2)
wherein the product KE is absent and both K and l have been separated from each other. Thus the two parameters can be determined independently of each other by a graphical plot of the necessary functions. Equations (2) and (3) are the limiting cases of the following more general Eqns (4) and (5), when c: 4 c:. d = C:cl - dKC,
289
(4)
B.K.
290
which have been obtained lowing equation[21]
c;cgr d
by rearranging
the fol-
_ 1 +(c:+G)
KE
SEAL et al.
(6)
l
Equations (4) and (5) may be used in place of Eqns (2) and (3) to obtain independently the equilibrium constant and the molar extinction coefficient of the complexes under the condition of constant Ci. For the purpose of verifying the principles outlined above, we have used the Eqns (2) and (5) respectively. However, the other equations can likewise be used. RESULTS AND DISCUSSIONS
Equations (2) and (5) have been tested by using the experimental data of different investigators from existing literature. A number of systems have been studied. These include (i) 1,3$tricyanobenzene-TMPD [223, (ii) chloranil-indole [23], (iii) 1,3,5-trinitrobenzene--diphenylamine[24], (iv) fluoranil-HMB [25], (v) iodine-tetramethyl urea [26], (vi) iodine-methylacetate[26], (vii) iodinemethylthioacetate[26], (viii) iodinemonochloridedioxane [27], (ix) TCPA-naphthalene [28], (x) TCPA-stilbene [28], (xi) TCPA-biphenyl[28], (xii) TCPA-phenanthrene [28], (xiii) TCPAanthracene [28], (xiv) TCPA-quinoline [29] and (xv) TCPA-2-methylquinoline[29]. The results are recorded in Table 1 and some typical plots are shown in Figs. 1 and 2 respectively. As expected Eqns (2) and (5) yield good linear plots. The scattering is much less with the Eqn. (5)
Table 1. Independent
determination
than with Eqn. (2). An advantage of using the Eqn. (2) over the Benesi-Hildebrand equation (1) is that c is more accurately estimated by it since E appears as a product of Cl1 and the value of the product Ciel is usually much greater than l/e which appears in the intercept of the BH equation. Often the BH plot has a low value of the intercept introducing large uncertainties in the estimated value of l and hence in the value of K evaluated from the product KE obtained from the slope of the equation. The BH equation, as observed, has certain other demerits. Sometimes the BH plot passes through the origin or sometimes it leads to a negative intercept, in both the cases the value of E is an absurd quantity. Equation (2), like the BH equation, requires an extrapolation to concentrated solutions for the evaluation of E independent of K which is evaluated directly from the gradient of the line without recourse to an extrapolated intercept. A disadvantage experienced in using Eqn. (2) is that for some of the systems studied by us the span in the values of d/CA is small while that in d is quite marked. As already mentioned the association constant and the extinction coefficient of the complex may be obtained independently of each other by using Eqn. (5) which, unlike the Eqn. (2), does not require extrapolation to concentrated solutions. This equation enables one to obtain E from the gradient and K-’ from the negative intercept of the linear plot of (Ci+ CL) vs CiCA/d. Good linear plots have been obtained for the various systems studied in the present investigation. However, for many systems the function CxCL/d
of association constant and molar extinction coefficient of some molecular complexes by graphical method Reported
Eqn. (5)
Eqn. (2) f
System
mol. 1-l
1 . mol-’ . cm-’
1,3,5-TricyanobenzeneTMPD Chloranil-indole 1,3,5-Trinitrobenzenediphenylamine Fluoranil-HMB Iodine--tetramethyl urea Iodine-methylthioacetate Iodine-methylacetate Iodinemonochloride-dioxane TCPA-naphthalene TCPA-stilbene TCPA-biphenyl TCPA-phenanthrene TCPA-anthracene TCPA-quinoline TCPA-2-methylquinoline
4.04
355
4.04
356
4.0
354
2.90
1498
2.94
1486
2.86
1510
0.5 13.56 5.98 0.73 0.55 22.80 2.27 5.98 2.73 7.78 8.75 26.84 13.70
1395 4030 701 -405 -455 813 1190 401 525 739 1161 134 219
0.50 11.76 6.33 0.75 0.52 22.2 2.27 6.76 2.69 7.52 8.47 26.32 13.2
1395 3041 685 -386 -477 819 1200 400 533 6% 1184 136 229
0.40 6: 0.72 0.52 23.86 2.8 5.5 2.9 7.3 10.3 26 15
1390 677 -410 -478 830 1000 476 500 714 1000 132 226
benzene;
TCPA-t&a-
TMPD-N, N, N’, N’--tetramethyl chlorophthalic anhydride.
K
c
E
K
K
mol * 1-l 1 . mol-’ . cm-’ mol
p-phenylenediamine;
HMB-hexamethyl
1-l 1 . mol.’ . cm-’
Equilibrium constant and molar extinction coefficient
291
d.IO'
I-
I\
F
\
I
0.9 -
I
%O
I\
I
I_ 14
40.7 20.5 I 2
0 a30
I 5
IO
I5
20
25
35
40
d/c;
Fig. 1. Plot of d vs d/C; for (A) chloranil-indole, (B) I*tetramethyl urea, (C) Kl-dioxane and (D) TCPA-phenanthrene systems.
Fig. 2. Plot of (CX+ Cfi) vs CiCg l/d for (A) chloranil-indole, ICMioxane (365 nm) and (D) TCPA-phenanthrene
(365 mm)
(B) &tetramethylurea, systems.
(C)
292
B. K. SEAL et al.
[8] P. H. EMSLIE, R. FOSTER, C. A. FYFE and I. HORMAN, Tetrahedron 21,2843 (1965). [9] S. CARTER, J. Chem. Sot.(A), 404 (1%8). [lo] S. D. Ross and M. M. LABES, I. Am. Chem. Sot. 79, 76 (1957). [l l] G. D. JOHNSONand R. E. BOWEN, I. Am. Chem. Sot. 87, 1655 (1%5). [12] S. CARTER, J. N. MURREL and E. J. ROSCH, J. Chem. Sot. 2048 (1%5). [13] D. W. TANNERand T. C. BRLJICE,J. Phys. Chem. 70, 3816 (1966). [14] J. D. CHILDS, S. D. CHRISTIANand J. GRUNDNES,J. Am. Chem. Sot. 94, 5657 (1972). [15] R. FOSTER, Organic Charge-tr&sfer Complexes, pp. 16&165 and 171-173. Academic Press, London and New York, (1%9). [16] S. D. CHRISTIANand E. E. JUCKER,J. Phys. Chem. 74, 214 (1970). [17] R. S. MULLIKEN and W. B. PERSON, Molecular Complexes, pp. 92-100. Wiley Interscience, New York (1969). [18] G. BRIEGLEB, Elektronen-LIonator-AcceptorKomplexe. Springer-Verlag, Berlin, 1961. 1191 _ _ D. A. DERANLEAU, J. Am. Chem. Sot. 91, 4044 (1964). [20] R. A. LABUDDE and M. TAMRES, J. Phys. Chem. 74, 4009 (1970). [21] M. TAMRES and J. YARWOOD, Spectroscopy and Structure of Molecular Complexes, Ch. 3, p. 221. Acknowledgement-Sincere thanks are due to Prof. R. Plenum Press, London and New York (1973). FOSTER, Dept. of Chemistry, University of Dundee, for [22] R. FOSTERand J. J. THOMPSON,Trans. Faraday Sac. supplying the raw data on the floranil-HMB system. 59, 2287 (1%3). [23] R. FOSTERand P. HANSON, Trans. Faraday Sot. 60, REFERENCES 2189 (1%4). [24] R. FOSTER,D. LL. HAMMICKand A. A. WARDLEY, J. [l] H. A. BENESIand J. H. HILDERBRAND,J. Am. Chem. Chem. Sot. 3817 (1953). Sot. 71, 2703 (1949). [25] B. DODSON, R. FOSTER, A. A. S. BRIGHT, M. I. [2] R. S. MULLIKEN, J. Am. Chem. Sot. 74, 811 (1952). FOREMAN and J. GORTON, J. Chem. Sot. B, 1283 [3] J. A. A. KETELAAR,C. VANDE STOLPE,A. GOLJDSMIT (1971). and W. DZCUBAS, Reel. Trav. Chim. Pays-Bas Belg. [26] R. L. MIDDAUGH, R. S. DRAGO and R. J. NIED71, 1104 (1952). ZIELSKI,J. Am. Chem. Sot. 86, 388 (1964). [4] R. S. Scorr, Reel. Trav. Chim. Pays-Bas [27] A. I. POPOV, C. C. Brsr and W. B. PER&N, J. Phys. Belg. 75, 787 (1956). Chem. 64, 691 (l%O). [5] R. FOSTER,J. Chem. Sot. 5098 (1957). [28] M. CHOWDHURYand S. BASU, Trans. Faraday Sot. [6] N. J. ROSE and R. S. DRAGO, J. Am. Chem. Sot. 81, 56, 355 (1960). 6138 (1959). [29] M. CHOWDHURY,J. Phys. Chem. 65, 1899 (1961). [7] W. B. PERSON,J. Am. Chem. Sot. 87, 167 (1965).
shows appreciable fluctuations which make the application of Eqn. (5) difficult for these systems. The values of K and E for various systems evaluated with the help of the Eqns. (2) and (5) agree (as seen from Table 1) in most cases among themselves and also with those evaluated by other well known procedures. The noted differences in some cases may be due to the different approach of the methods. While Eqns (2) and (5) evaluate K and e independent of each other, the other methods require the separation of K and E, through the intercept and slope of linear plots, from the product Kc, occurring in the derived equations. The system fluoranil-hexamethyl benzene has been treated by us as a 1: 1 complex while FOSTER [25] treated it as a mixture of 1: 1 and 1: 2 complexes. For this system the plot of d vs d/CD0 according to Eqn. (12) shows appreciable scatter of data points while Eqn. (5) yields a good straight line.