P-factor

Figure 12-25 provides a rapid method of determining the pond-area requirements for a given coohng duty. Di and Do are the approaches to equilibrium for the entering and leaving water, °F V Js trie wind velocity, mFh product PQ represents the area of the pond surface, ft /(gal-min) of flowto thepond. The P factor assumes a pond with uniform flow, without turbulence, and with the water warmer than the air. 

The first peak with full asymmetry, i.e. the making current /m, will be represented by > (P x l ) (where P = factor of asymmetry as in Table 13.11). 

Because LEED theory was initially developed for close packed clean metal surfaces, these are the most reliably determined surface structures, often leading to 7 p factors below 0.1, which is of the order of the agreement between two experimental sets of 7-V curves. In these circumstances the error bars for the atomic coordinates are as small as 0.01 A, when the total energy range of 7-V curves is large enough (>1500 eV). A good overview of state-of-the-art LEED determinations of the structures of clean metal surfaces, and further references, can be found in two recent articles by Heinz et al. [2.272, 2.273]. 

Because of the minimization of the number of dangling bonds semiconductor surfaces often show large displacements of the surface atoms from their bulk lattice positions. As a consequence these surfaces are also very open and the agreement is more in the range of 7 p factor values of approximately 0.2. Determination of the structure of semiconductor surfaces is reviewed in a recent article by Kahn [2.275]. 

The introduction of the p factor yields asymmetry. Finally, the Gompertz function can be used [5] ... 

Recently, a kinetic study has been made of the substitution of diazotised sulphanilic acid in the 2 position of 4-substituted phenols under first-order conditions (phenol in excess) in aqueous buffer solutions at 0 °C131a. A rough Hammett correlation existed between reaction rates and am values, with p about -3.8 however, the point for the methoxy substituent deviated by two orders of magnitude and no explanation was available for this. The unexpectedly low p-factor was attributed to the high reactivities of the aromatic substrates, so that the transition state would be nearer to the ground state than for reaction of monosubstituted benzene derivatives. 

Finally, rates of mercuration have been measured using mercuric trifluoro-acetate in trifluoroacetic acid at 25 °C450. The kinetics were pure second-order, with no reaction of the salt with the solvent and no isomerisation of the reaction products rate coefficients (10 k2) are as follows benzene, 2.85 toluene, 28.2 ethylbenzene, 24.4 i-propylbenzene, 21.1 t-butylbenzene, 17.2 fluorobenzene, 0.818 chlorobenzene, 0.134 bromobenzene, 0.113. The results follow the pattern noted above in that the reaction rates are much higher (e.g. for benzene, 690,000 times faster than for mercuration with mercuric acetate in acetic acid) yet the p factor is larger (-5.7) if the pattern is followed fully, one could expect a larger... 

Much of the kinetic work in this category has already been described under the section relating to studies of mechanism. Additional data was obtained by Ols-son569, who measured rate coefficients (lO7 ) for dedeuteration and detritiation of thiophen by 57.02 wt. % sulphuric acid at 24.6 °C as follows [2-2H], 3,890 [2-3H], 2,000 [3-2H], 3.72 [3-3H], 2.20. The ratio of reactivities at the 2 and 3 positions (ca. 1,000) is in excellent agreement (bearing in mind the larger p-factor usually obtained with trifluoroacetic acid) with the value of ca. 1,250 which may be deduced from the data in Table 158. The ratio of dedeuteration to detritiation is 1.96 at the 2 position and 1.70 at the 3 position and thus decreases with decreasing reactivity of the reaction site. 

Analysis of substituent effects in the reaction revealed random correlations of rate with a values of substituents for the uncatalysed reaction, but for the acid-catalysed reaction, reasonable Hammett plots with p factors of —1.27 (HC104) and -1.12 (H3P04) were obtained (Table 253). 

Bromodeboronation has acquired a particular significance in recent theories of electrophilic substitution and briefly this has arisen since it was supposed to have a very high r factor relative to its p factor in a Yukawa-Tsuno analysis. (For a fuller discussion see ref. 729). It had been suggested729 that some of the rate coefficients determined for the reaction (Table 254) may be in error due to concurrent bromodeprotonation, and a reinvestigation730 of this possibility has revealed a number of points ... 

The earlier work on acidolysis of the aryl-tin bond is reviewed in reference (97). Attachment of the proton to the aryl ring is rate-determining, and the Hammett p-factor for the reaction has been shown to... 

The reaction of tributyltin hydride with ring-substituted benzyl chlorides gives a Hammett p-factor of -1-0.81, confirming the "nucleophilic character of the BusSn- radical (303). 

Log P factorization (the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original) demonstrates that lipophilicity is governed by the laws of chemistry (see Section 12.1.1) and thus provides a qualitative chemical insight into partitioning data [8]. 

As the solute descriptors (E, S, A, B and V) represent the solute influence on various solute-solvent phase interachons, the regression coefficients e, s, a, h and V correspond to the complementary effect of the solvent phases on these interactions. As an example, consider the product aA in Eq. (4). Since A is the H-bond acidity of the solute, a is the H-bond basicity of the system. In other words, the intermolecular forces discussed in Sections 12.1.1.2 and 12.1.1.3 are present in all Abraham s log P factorization equations, with the exception of those interactions involving ions. This is the reason why Abraham s equahons are valid for neutral species only. 

Poulsen T.G. and Mooldrup, P., Factors affecting water balance and percolate production for a landfill in operation, Waste Management and Research, 23 (1), 72-78, 2005. 

Rinfret, A. P. Factors affecting the erythrocyte during rapid freezing and thawing Annals of the New York Academy of Sciences, Vol. 85, Art. 2, p. 576-594, I960... 

Sayeh, E., and Uetrecht, J.P., Factors that modify penicillamine-induced autoimmunity in Brown Norway rats Failure of the Thl/Th2 paradigm. Toxicology, 163, 195, 2001. 

The presence of the h(z, P) factor makes Eq. (7.44) different from a Laplace transform of C(z). If the z dependence of h(z, P) is ignored,(34 36) then calculated concentrations of fluorophore near an interface derived from collected fluorescence are approximations. Also, the P dependence in the tf1,11 causes the integral in Eq. (7.44) to differ from the form of a Laplace transform even after the excitation term is factored out. 

Fractionations are typically very small, on the order of parts per thousand or parts per ten thousand, so it is common to see expressions like 1000 ln(a) or 1000 (a-l) that magnify the difference between a and 1. a =1.001(1000 [a-l] = 1) is equivalent to a 1 per mil (%o) fractionation. Readers of the primary theoretical literature on stable isotope fractionations will frequently encounter results tabulated in terms of P-factors or equilibrium constants. For present purposes, we can think of Pjjh as simply a theoretical fractionation calculated between some substance JiR containing the elementX, and dissociated, non-interacting atoms ofX. In the present review the synonymous term Uxr-x is used. This type of fractionation factor is a convenient way to tabulate theoretical fractionations relative to a common exchange partner (dissociated, isolated atoms), and can easily be converted into fractionation factors for any exchange reaction ... 

---