Hildebrand method

Careful observations of the course of iodo-de-diazoniation demonstrate that the detailed pathway of such reactions is still relatively complex. For instance, after adding a solution of KI to a solution of an arenediazonium salt, normally molecular iodine appears to be formed first, followed by a precipitate and evolution of N2. Carey and Millar (1960) isolated the salt ArNJIj- on adding iodide to the diazo-nium salt. Ion pairs (ArNjHlg-), suggested as primary products by Meyer et al. (1979), were identified for diazonium halides (Cl- and Br-) by Israel et al. (1983) as 1 1 complexes on the basis of JOB analyses of visible spectra (Benesi-Hildebrand method). Iodides were, however, not included in that investigation. 

In addition, the stability constants of amine complexes were determined with the dyed-host 40 using the Benesi-Hildebrand method in acetonitrile and chloroform at 25 °C [23], The data show the following order of complex stability ... 

The stoichiometry and association constants of the inclusion complexes formed between BPHTs and CDs were classically calculated by means of the Scatchard and Benesi-Hildebrand methods [101,102]. Assuming a 1 1 stoichiometry ratio, the following equilibrium 1 is established ... 

EXPERIMENT 3.7 DETERMINATION OF THE FORMATION CONSTANT FOR PYRIDINE BINDING TO A/,A/ -DISALICYLALDEHYDE-1,3-PROPANEDI IMINENICKEL(II), [Ni(salpd)], USING THE DOUBLE RECIPROCAL (BENESI-HILDEBRAND) METHOD... 

Q7.12 What is the significance of plants and organisms synthesizing PCs with n > 2 Q7.13 Read Pre-lab 3.7.b. Why can you not treat the data by the Benesi-Hildebrand method ... 

F. B. Hildebrand, Methods of Applied Mathematics (Dover, New York, 1992). 

The complex equilibrium constant was also determined by the Benesi--Hildebrand method which, at 298 K, amounts to K = 0.109 0.042 dm / mol and is of the same order as the constant determined on the basis of the spectroscopic data in the near infrared. It follows from... 

Determination of the interassociation equilibrium constant for the A—T interaction using the Benesi and Hildebrand method. (Reprinted with permission from Kuo, S. W., and Cheng, R. S. 2009. DNA-like interactions enhance the miscibility of supramolecular polymer blends. 

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and methods for its prediction have been developed in maiiy forms and by many workers. For binary systems the Van Laar (Eq. (1.4-18)], Wilson [Eq. (1.4-23)], NRTL (Eq. (1.4-27)], and UmQUAC [Eq. (t.4-3ti)] relationships are useful for predicting liqnid-iffiase nonidealities, but they require some experimental data. When no dim are available, and an approximate nonideality correction will suffice, the UNIFAC approach (Eq. (1.4-31)], which utilizes functional group contributions, may be used. For special cases involving regular solutions (no excess entropy of mixing), the Scatchard-Hildebrand method provides liquid-phase activity coefficients based on easily obtained pure-component properties. 

Despite its limitations [48], the Benesi-Hildebrand method can be considered for rapidly determining the stoichiometry and binding constants of a host-pyrene system by fluorescence spectroscopy this method, still commonly employed for such determination, is based on Eq. (13.11) [55-59] ... 

Heptakis-(5-amino)-(6-deoxy)- p-CD Fluorescence 1 2 Job s plot Nonlinearized version for Benesi-Hildebrand method 2002 [1 00)... 

Diphenyl disulfide cyclophane Fluorescence 1 1 Job plot Benesi-Hildebrand method 2013 [108]... 

After substituting the binding isotherm ([H G] = I[G]oK,IH] / (1 + K.,[H])]) for [H G] and assuming that [H] = [H]e we get the first equation below. The assumption is only valid when [H]o >> [G] . A double reciprocal plot of 1 / A A as a function of 1 / [H] gives a line from which Ac can be calculated from the intercept, and fC, can be calculated from the slope. This is called the Benesi-Hildebrand method, and it has seen extensive use in both artificial and biological molecular recognition. 

Show all the mathematics that leads to the double reciprocal plot used in the Benesi-Hildebrand method. How much does the host need to be kept in excess over the guest so we can safely assume that [H] = [H]o ... 

Furthermore, m-cresol and m-halogenated phenols have been polymerized in aqueous buffer solution only in the presence of 2,6-di-0-methyl-[)-cyclodextrin [90]. In the absence of cyclodextrin, only insoluble materials in very low yields were obtained under aqueous conditions from these phenols [81]. The structure of the host-guest complexes between cyclodextrin and the phenols was characterized by 2D NMR [48,90] and the association constants of the cyclodextrin complexes were determined by the Benesi-Hildebrand method. Firrthermore, 3-fluorophenol, 3-chlorophenol, and 3-bromophenol were successfully polymerized in various aqueous organic solvents such as methanol, acetone, or isopropanol [115]. 

Methods have been developed to determine the equilibrium constants for these complexes in solution by measuring the intensity of their absorption bands as a function of the donor and acceptor concentrations in solution. This procedure is called the Benesi-Hildebrand method... 

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). 

Exner, O. (1997) Calculating equilibrium constants from spectral data reliability of the Benesi-Hildebrand method and its modifications. Chemom. Intell. Lab. Syst., 39, 85-93. 

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