The p factor

Equation (4.11) can be compared with the experimental Arrhenius equation (4.1), care being taken with the units of k and R in the exponential term. 

For some reactions ZAb and A have similar values, but there are also many reactions for which they differ by many powers of ten. This requires postulating another factor, p which limits the theoretical rate of reaction, and whose magnitude can be found by comparison with experiment. 

Watching units of k and R, and equating e0 with a molecular EA, makes kca c = /cohs if 

As the complexity of the reactants increases the p factor decreases, and the discrepancy with collision theory increases. This reflects the inadequacy of simple collision theory, especially the neglect of the internal structures of the reactants, and intermolecular interactions. 

This p factor has also been interpreted as a preference for a certain direction, or angle of approach, of the reacting molecules. Molecular beam experiments show some reactions to have a quite decided preference for a specific direction and/or angle of approach. 

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

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... 

As in the case of the SjN ratio, the relative precision of relaxation rate/ time estimates is linearly proportional to both the p-factor as well as to the v-factor. 

A linear relationship between the standard enthalpies and entropies of a series of structurally related molecular entities undergoing the same reaction thus, AH° -I3AS° = constant or AAH° = (3AS°. When P > 0, this relationship is referred to as an isoequilibrium relationship. When the absolute temperature equals the factor P (often referred to as the isoequilibrium temperature), then all substituent effects on the reaction disappear (i e., AAG° = 0). In other words, a reaction studied at T = p will exhibit no substituent effects. This would suggest that, when one studies substituent effects on a reaction rate, the reaction should be studied at more than one temperature. Note also that the p factor in the Hammett equation changes sign at the isoequilibrium temperature. See Isokinetic Relationship... 

Table 8.1 shows the P factors for some acidic components capable of hydrogen bonding, which as might be expected, increase from CH3OH to (CF3)2COH. It should be noted that this order of acidity was used by us intuitively in earlier... 

Note, that the p factor will not appear if a unique ordering of the indices of the operators is imposed. 

The p factor could also be a consequence of the physically naive hard sphere model used. This model requires that there be no intermolecular interactions either at close distances or at a distance. This has been shown not to be the case, with evidence coming from many aspects of physical chemistry. Also, vibrations and rotations do affect reaction, as is shown by experiments with molecular beams. 

Hence for this reaction using the rough and ready magnitudes quoted, AS = —220 J mol 1 K Since AS /R correlates with the p factor the large negative value for AS corresponds to a low p factor. 

If the p factor is taken to be unity, then the predicted A factor for collision theory =... 

The p factor is the density of the fluid in pounds per cubic foot (lb/ft3). It may represent a gas or liquid. If gas, the pressure loss should not be greater than 10% of the pipe run inlet pressure. 

Termination of RNA synthesis occurs at specific sites along the DNA template. There are two modes of termination events those that require a termination protein, the p factor, and those that depend only on the transcription of regions of DNA containing stop signals. 

The second type of terminator lacks the U region and requires the p termination factor for RNA chain release. The p factor is a hexamer of 45 kD subunits that binds a stretch of 72 nucleotides of single-stranded RNA. The p factor hydrolyzes ribonucleoside triphosphates to nucleoside diphosphates in the presence of single-stranded RNA and moves unidirectionally along nascent mRNA toward the transcription bubble and breaks the RNA-DNA hybrid, pulling away the RNA. 

Between the reactions, there are differential demands for resonance. This may, in particular, account for the low values in reaction 2, which should have the lowest demand for resonance. [The p factor for reaction I is smaller, but refers to a high temperature and is equivalent to... 

The p factor of - 5.7 claimed for mercuriation of substi-tuled selenophenes was based on a few results for electron-withdrawing subslituents and did not include selenophene itself (66CHE686). 

Finally, for 5-exchange of I-aryltetrazoles, electron-supplying substituents in the aryl ring decreased, and electron-withdrawing substituents in the aryl ring increased the reaction rate, as expected. The p factor at 30°C is 1.4 for reaction of the 4-ethyltetrazolium ion via the ylide mechanism (in 9 M CF,C02D) and 1.3 for reaction of the free base (in piperidine-MeOD-DMF) (69TL3377). 

The reaction of aryldiazonium ions with l-(4 -sulfophenyl)-3-methyl-pyrazolium-5-one (7.70) takes place at the 4-position, and the p factor for the effects of substituents in the aryl ring of the diazo ion is 3.29, similar to that for coupling at the 1-position of 2-hydroxynaphthalene-6-sulfuric acid (69CCC3895). For coupling at the 4-position of l-phenyl-2,3-dimeth-ylpyrazolium-5-one (7.71) the corresponding p factor was 3.60 (69CC3905). 

This gas-phase reaction provides the only method currently available for determining hydrogen-bonded pyridine free base. The method requires neither assumptions, extrapolations, nor approximations the p factor of the reaction is sufficiently small that the reactivities of the pyridine and benzene derivatives can be compared directly. The method was first introducted for determining the electrophilic reactivity of pyridine [62JCS4881 71JCS(B)2382] using 1-arylethyl acetates (9.109). Subsequent determinations used I-aryl-l-methylethyl acetates. (9.110) and i-arylethyl methyl carbonates (9.111) [79JCS(P2)228],... 

An extensive set of data has been obtained by Noyce and Virgilio (73JOC2660) for solvolysis of 1-aryl-l-methylethyl chlorides (9.115-9.119) in 80% aqueous ethanol at 70°C, for which the p factor for benze-noid compounds is -4.0. The log k/kQ values are given in Table 9.14, along with 8 log k/k0 values, the differences between the observed values and those calculated from the standard cr values and the p factor of -4.0. Thus a positive value means that the compound is more reactive... 

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