The Rose-Drago Method

For a 1 1 complex (C) formed between a Lewis acid (A = I2) and a Lewis base (B = CeHiiI) according to the reaction A - - B C, the expression of the equilibrium constant in molar concentration units is 

The concentration of the complex is obtained from the visible band of diiodine as follows. A highly diluted cyclohexane solution (So) of diiodine at concentration C obeys Beer s law at any wavelength A.  

A solution (Si) containing diiodine at initial concentration C and the base at initial concentration C, hence the complex at concentration Cc, shows the absorptions of h, B and C. The total absorbance (A), at wavelength A, is 

Substituting jC l into Equation 7.26 and rearranging allows the concentfation of 

Substituting this expression for Cc into Equation (7.23) yields 

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When the assumption [G]o = [G] can not be applied, other approximation or regression methods have to be employed. Here, the regression method is shown. Typical examples of the regression methods are the Rose-Drago [17], Nakano [18], and Greswell-Allred [19] methods. Because of its wide applicability, a practical guide based on the Rose-Drago method is presented here for an example from UV/vis spectroscopy. 

The Rose-Drago method is described here using a 1 1 host-guest complexation stoichiometry detected by UV/vis spectroscopy. The observed property is the absorbance which is followed in a titration experiment to collect the necessary absorbance data. For the data treatment with the Rose-Drago method, a spreadsheet program is attached as Appendix 2.2 [20]. 

Estimation of the error of the Rose-Drago method for NMR spectroscopic data is essentially same as that for UV/vis spectroscopy, which is described in corresponding sections. 

The fact that the determination of diiodine complexation constants is dependent on a second unknown makes values more uncertain than the hydrogen-bond formation constants. A revision of the statistical evaluation of diiodine complexation constants obtained by the popular Benesi-Hildebrand method [53] shows [57] that the confidence interval is always much larger than previously reported. Examples of revised 95% confidence limits are (in 1 mol ) 0.32-0.40, 0.53-1.86 and 1.10-1.32 for the complexation constants of diiodine with 1-bromobutane, benzene and dioxane, respectively. However, better 95% confidence intervals can be obtained. A careful application of the Rose-Drago method to the complexation of diiodine with carbonyl bases gives [62], for example 0.53 0.04 (benzaldehyde), 1.12 0.06 (acetone), 8.1 0.7 (AA -dimethylbenzamide) and 15 0.4 (A,A-dimethylacetamide) (in 1 mol , in heptane at 25 °C). 

The equiUbrium constant is determined by the Rose-Drago method, as described in experiment 7.7, at five temperatures from -5 to +55 °C. At each temperature, the initial diiodine concentration is 0.0015 mol and five initial DMSO concentrations are studied... 

The equilibrium constant values calculated by the Rose-Drago method, as explained in experiment 7.7, are summarized in Table 7.13. 

In this section, the way to apply the original Rose-Drago method for UV/vis spectroscopy to NMR titration data is described, especially for host-guest systems on fast exchange. 

Figure Graphical expression to appreciate the determined K according to Rose-Drago method...

A wide variety of methods has been devised for the treatment of experimental data. The simple and rigorous method of Rose-Drago is used here. 

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