Schofield Plots

Although the theoretical values for the slopes are often obtained from kinetic data at room temperature, this is not the case (and the recalculation of the free-base rate coefficients also fails) for data obtained at higher temperature. This discrepancy may be attributed to the variation of acidity function with temperature. In a redetermination of the variation of HR 

For benzene, the slope of the Moodie-Schofield plot is 1.0 in the (narrow) range 63-68 wt% H2S04, but the slope increases to 1.2 at higher acidity [68JCS(B)800]. This may diminish the utility of a comparison of 

Thus plots of log k 2 versus -H0 for reaction of conjugate acids should yield a line of zero slope, whereas compounds reacting via the free base should give straight lines with a unit negative slope (Fig. 3.4). Other slopes may be obtained, and this reflects the proportionality between the acidity function followed and -H0. The method was first applied to the kinetic data for 4-pyridone, which was thereby shown to react as the free base at lower acidities and as the conjugate acid at higher ones (Fig. 3.5). 

The method can be applied only at or near room temperature because although the values of H0 up to 90°C are well known, the variation of the pAa of nitric acid with temperature, and indeed the precise acidity function followed by nitric acid, are not known attempts to determine these factors have failed [75JCS(P2)1600]. 

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Figure 6.20 Plot of log k vs. cr + for the Beckmann rearrangement of acetophenone oximes in 98.2 percent sulfuric acid at 80°C. From B. J. Gregory, R. B. Moodie, and K. Schofield, J. Chem. Soc., 13, 338 (1970). Reprinted by permission of K. Schofield and The Chemical Society.

The distinction between vapour- and liquid-expanded films may be difficult to make in practice. The most sensitive tests are to plot the FA-F curves as suggested by Schofield and Rideal (.Proc. Boy. Soc. A, 110, 170 (1926) cf. h, p. 370) and see whether, when produced, these pass through the origin or to measure the surface pressure as accurately as possible between areas ranging from about 100 to 1,000 sq. A. For the distinction to be made with certainty the measurements must be made down to the second place of decimals. 

Schofield and Bideal1 have mapped the relation between F and A for the longer chain, yet still appreciably soluble, fatty acids from 6 to 12 carbons long, using Frumkin s measurements of the surface tension of their solutions.8 Their results are shown in the upper six curves of Fig. 29, the product FA being plotted as ordinates and the surface pressure F as abscissae. For comparison, the results for the acids from 12-15 carbon atoms, determined by spreading the acid and measuring the surface... 

Analyses of the variation of transition temperatures with composition (Fig. 24) reveal an unambiguous departure from linearity (Schofield and Redfern 1993). For example, the plateau region is more extensive than in other oxide systems, ranging from 0 spontaneous strain is plotted as a function of composition (Fig. 25), the data depart slightly from ideal second-order behavior. Schofield et al. (1997) attribute this deviation and the broad plateau to the short-range interaction length of the strain fields associated with the Zn cations. 

Tn his classic book (I) N. K. Adam discussed the behavior of very dilute - monolayers at the air/water (A/W) interface and using measurements published ear her by Jessop and himself (2, 3, 4), he showed that surface pressure (n)-area (A) isotherms for insoluble uncharged species, when plotted on a nA vs. n basis, suggested a limit of IkT at zero II. The same limit was also suggested by Schofield and Rideal s plot (5) of Frumkin s surface tension data (6) using the Gibbs adsorption isotherm to calculate A. Adam (I) stressed that n should be measured to the second decimal place to establish this limit unequivocally Adam and Jessop (4) provide one of the few sound extrapolations to this limit with their data on the esters of some dicarboxylic acids. 

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