Guggenheims Method

Table 2-4 gives data for the alkaline hydrolysis of phenyl cinnamate under pseudo-first-order conditions, with calculations made in order to apply the Guggenheim method. The plot according to Eq. (2-55) is shown in Fig. 2-9. From the slope the pseudo-first-order rate constant is 3.37 x 10 s . ... 

The Guggenheim method requires that data be taken at constant time increments equal to At. In the past this was often a disadvantage, particularly when the experiment was not designed to be analyzed by this method, but with modem instm-mental methods of analysis it is common to acquire a continuous record of instrument response as a function of time, so that data can be taken from this record at any desired times. 

The principal source of error in the Guggenheim method appears to lie in taking the difference A, — A,+, ). This has been circumvented in a method proposed independently by Kezdy et al. Mangelsdorf, and Swinboume. Again we write Eqs. (2-53) and (2-54), but now we divide them and rearrange to get Eq. (2-56). 

Kinetic data for the decomposition of diacetone alcohol, from Table 2-3. were obtained by dilatometry. The nonlinear least-squares fit of the data to Eq. (2-30) is shown on the left. Plots are also shown for two methods presented in Section 2.8 they are the Guggenheim method, center, and the Kezdy-Swinbourne approach, right. 

Gear s method, 118 Gibbs (free) energy of activation (see Activation parameters Free energy) Guggenheim method, 26-27... 

Cohen and Crothers also present an excellent account of their use of the Guggenheim method for extracting rate constants from incomplete segments of decay processes, in which either the starting- and/or end-points of the spectral decay are not well defined. See also Chemical Kinetics (1. Progress Curve Analysis)... 

GUGGENHEIM METHOD (FIRST-ORDER RATE CONSTANT)... 

The dipole moment of 1. l-dimethoxy-2.4.6-triphenyl-X -phosphorin 183 according to the Guggenheim method was found to have a value of ju = 1.3 D. A value of 2.7 D was found for l.l-dimethoxy-2.4.6-diphenyl-4-(4 -chlorophenyl)-X -phosphorin 184... 

Let us consider the compounds which show a small deviation from the stoichiometric composition and whose non-stoichiometry is derived from metal vacancies. The free energy of these compounds, which take the composition MX in the ideal or non-defect state, can be calculated by the method proposed by Libowitz. To readers who are well acquainted with the Fowler-Guggenheim style of statistical thermodynamics, the method here adopted may not be quite satisfactory however, the Libowitz method is understandable even to beginners who know only elementary thermodynamics and statistical mechanics. It goes without saying that the result calculated by the Libowitz method is essentially coincident with that calculated by the Fowler-Guggenheim method. 

In cases in which the endpoint cannot be determined, the Guggenheim method may be used.5 The differences between pairs of readings at t and t + At (where At is a constant time that must be at least 2 or 3 times the half-time) are plotted against t in the semilogarithmic plot, since it may be shown that... 

Absolute values of dipole moments of several dithiol-3-ones and -3-thiones have been calculated using a Guggenheim method (68ZN(B)413). An apparent discrepancy between these and other values (68ZN(B)1547) was due to the latter using another calculation, which gave relative values. When an appropriate correction factor was applied a fairly good match of values was obtained. 

Another approach is to use the Guggenheim method, which eliminates the need for either ap° or a p" value. This method requires only that one know the time dependence of some quantity that is a linear function of the reactant concentration. In the present case. 

The principal source of error in the Guggenheim method appears to lie in taking the difference (A, — This has been circumvented in a method proposed... 

Several ways have been developed to deal with a reaction for which the Aoo value is not available. The Guggenheim method, for example, uses paired... 

R. R. Odle and T. L. Guggenheim. Method for the preparation poly(ether-imide)s. US Patent6881815, assigned to General Electric Company (Pittsfield, MA), April 19, 2005. 

The differential method of Guggenheim is also applicable to reversible reactions. For example, reaction (2.21) can be treated with the Guggenheim method to obtain a Guggenheim equation for a reversible monomolecular reaction ... 

Sodium nitrate produced by the Guggenheim method from caliche is usually a crystalline product about 48 mesh in size the product contains approximately 3.5% of free moisture. Prilled product contains about 98% sodium nitrate and 0,2%-0.3% free moisture, and the size of the product is in the range of 10-20 mesh. 

Chile, production is based on the Guggenheim method, which permits ores containing under 10% nitrate to be profitably worked. Caliche is mined by open-pit operations, using draglines and power shovels, and is crushed to about 80% between 3/4 and 3/8 inches (1.9-0.95 cm). This product is leached at about 40°C wth water in a series of vats each vat has a capacity of some 10,000 tonnes of crushed ore. The underflow from each vat is heated before passing to the next since sodium nitrate has a negative heat of solution. After extraction and washing are complete, the residue is removed from the vats and transported to a waste dump. 

This shows that a plot of In (/, - / ) versus t should be linear with a slope of -fc,. It is not necessary to know the concentration of A or any values of e in order to determine the rate constant, but one does need Sometimes, it is impossible to measure / because of secondary reactions, or it is inconvenient because the reaction is slow. Such systems can be analyzed by nonlinear least-squares fitting of the data over as much of the reaction as possible, or in a more classical way by the Guggenheim method, described in more detail by Moore and Pearson (p 71), Mangelsdorf and Espenson (p 25). 

The reaction of vanadium(iv) with tris-(2,2 -bipyridyl)iron(iii), [Fe(bipy)s] + has been investigated, the Guggenheim method being used to treat the data since aquation of [Fe(bipy)8] + caused interference in the later parts of the reaction. The order is unity for both reagents and the rate law may be written -d[Fe(bipy)n/dr = (Ara + ki,[H+]-i)[Viv][Fe(bipy)i1... 

In case the value of A cannot be obtained with certainty, the classical Guggenheim method can be used to overcome this problem. But the Guggenheim method also suffers from a serious limitation, i.e., it must be certain that the reaction obeys the first-order rate law until t = °o (i.e., the reaction time at which Aobs = A J. Thus, this method may yield an erroneous value of k if it is used for the reactions of primary amines, such as methylamine, with phthalimide. However, the observed kinetic data for such reactions may be easily and relatively accurately analyzed by the iterative method (Table 7.3) rather than other conventional approaches and the Guggenheim method. 

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