Scott equation

Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.

The LFER correlation according to the Swain-Scott equation for nucleophilic attack on /3-propiolactone. Data are from Ref. 13. 

Spin trap, 102 Statistical kinetics, 76 Steady-state approximation, 77-82 Stiff differential equations, 114 Stoichiometric equations, 12 Stopped-flow method, 253-255 Substrate titration, 140 Success fraction approach, 79 Swain-Scott equation, 230-231... 

The following overall nucleophilicity order for Sn2 mechanisms (in protic solvents) was given by Edwards and Pearson RS > ArS >1 >CN > OH > Nj > Br > ArO > Cl > pyridine > AcO > H2O. A quantitative relationship (the Swain-Scott equation) has been worked out similar to the linear free energy equations considered in Chapter 9 ... 

ISO 37 gives a relation to calculate the distance between the pulley centres which corresponds to the elongation percentage for which the stress is required. This relation is equivalent to the simplification of Scotts equation ... 

The Hammett and Taft equations are not the only linear free-energy relationships known. We shall encounter others—for example, the Bronsted relations, and the Grunwald-Winstein and Swain-Scott equations later in this book. 

To get a better understanding of what the Swain-Scott equation means, we have rewritten it in Equation 4.22 in the form that makes the linear free-energy relationship more apparent. 

A point of key importance in study of solvolysis is the nucleophilicity of the solvent. Whereas the Y and other scales have been available for measuring ionizing power for some years, there has been no satisfactory scale for nucleophilicity. Swain, Mosely, and Bown attempted to set up an equation for correlation of solvolysis rates that included both nucleophilicity and ionizing power 112 their system did not prove particularly helpful for understanding mechanism.113 The Swain-Scott equation, discussed in Chapter 4 (p. 185), was not evaluated for solvents. 

Second-order rate constants for the reactions of phenacyl bromide with a number of anionic or neutral nucleophiles in 3 2 (v/v) acetone-water have been measured at several temperatures.141 Correlation analysis with the Bronsted equation or Swain-Scott equation is not satisfactory. Better results were obtained with the two-parameter Edwards equation. 

Solvolysis of the R,R and R,S isomers of 2-bromo-9-(l-X-ethyl)fluorenes, X = Cl, Br, I, or OBs, in 25% (v/v) acetonitrile in water has been studied with respect to rates of formation of elimination products and of substitution products (X = OH or NHCOMe).142 The parent 9-(l-X-ethyl)fluorenes and the 2,2/-dibromo-9-(l-X-ethyl)-fluorenes were also studied. Various effects of leaving group and of the presence of nucleophiles on the competition between the reactions were observed and the Bronsted equation was applied to the results for the elimination reactions. A related study of solvolysis of 9-(X-methyl)fluorenes, X = I, Br, or Bs, was also carried out, in which the Swain-Scott equation was applied to nucleophilic selectivities in the S 2 reactions.143... 

Note again that 5 here differs from s in the Swain-Scott equation which refers to the slope of a plot of log k versus the nucleophilicity parameter n (or N) rather than electrophilicity parameter (E). 

According to the Scott equation, plotting ln(ti/2) versus ln(l/FN) should give a straight line. This is what Leider (50) observed with a series of fluids in the Scott equation range. However, Leider and Bird (49) extended the analysis to include stress overshoot phenomena by using a semiempirical expression for the shear stress ... 

Their experimental results are shown in Fig. E6.14b, which plots dimensionless halftime versus dimensionless reciprocal force. Clearly, the Scott equations describe the experimental results given earlier as ti /nX = 1. They recommend that the choice of the parameter X be made on the basis of the Power Law parameters m and n and a similar Power Law relationship of the primary normal stress difference function 4 1 (y) = n 1 as... 

The relative reactivities of Table 9 differ from those towards saturated carbon atom, as measured by the w-values of the Swain-Scott equation,... 

The original Hildebrand and Scott equation was obtained on the premise that nonpolar liquids possessed a spherical symmetry. For liquids without symmetry, the molecules tend to orient. The result of orientation could contribute to the departure of the surface properties from the bulk properties of polar and hydrogen-bonded liquids. This departure should be enhanced in the case of a long-chain polymer. 

Under a separate study (17), we found that oxygenated liquids generally do not follow the Hildebrand and Scott equation. For the simplest oxygenated liquids—e.g., ethers and esters—the proper equation should be ... 

McCauley and King [204] have carried out a careful quantitative study of kinetic salt effects of halides and product ratios in the acid catalyzed hydrolysis of diazoacetone in water which confirms the validity of rate eqn. (47). The fraction of halogenoacetone formed completely corresponds to the relative magnitude of the second term (dependent on [X-]) in the rate equation. The results obtained for fcHCI, hbt and ftm obey the Swain—Scott equation (54) with s = 0.35 [203]. The experimental fcH... 

Table 1.6 shows nucleophiles ranked by one measure of nucleophilicity. These nucleophilicities are based on the relative reactivities of the nucleophile and water with methyl bromide at 25°C. The nucleophilicity n is calculated according to the Swain-Scott equation ... 

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