Hirschfelder rule

Activation energies for bimolecular reactions have been correlated with bond energy data by the use of the Hirschfelder rules (19). 

This reaction is 19.2 kcal./mole exothermic. However, as pointed out by Friel and Krieger (31), according to the Hirschfelder rules (43) this reaction should have an activation energy of about 28% of the sum of the energies of the two bonds being broken or about 57 kcal./mole. Friel and Krieger point out that the reaction... 

An impression of the reliability of such correlations is given in Figure 2.19, which presents the data used for the correlation of Semenov. There is quite a bit of scatter apparent, such that the rather generous limits indicated in the figure should be kept in mind. Benson reports also that neither of the two Hirschfelder rules is better than about 5 kcal/mol, which is enormous when one is concerned with activation energies, and that occasionally much larger discrepancies are encountered. Hence we take these as qualitative norms to provide guidance rather than quantitative numbers to provide definition, [see also Z.G. Szabo, Chem. Soc. (London) Spec. Publ., 16, 113 (1962)]. 

Since polarizabilities of groups or atoms are also manifested in bond strengths, some form of Hirschfelder s rule can also be developed to treat these types of reactions (Laidler, 1987). For example, the activation energies for many molecular elimination reactions seem to be correlated with one-third of the sum of the dissociation energies of the bonds that are being broken. This empirical relationship seem to hold well for a large variety of HX elimination reactions (see Table XI). 

Hirschfelder s rules represent another useful tool that can be used to estimate the activation energies of exothermic metathesis reactions (Laidler, 1987). According to these rules, the activation energy of an atom metathesis reaction is given by... 

The glory results. For the NO-results two choices of eRm lead to two different fits at this moment it is uncertain which choice should be preferred. For the H2-results the eRm- lues of Helbing (1968) and Butz (1971) are given in parentheses to be compared with the f Rm-values used for the q2 12/42 s fit- The H2-He results are obtained from the IIP and AIP of Riehl (1973), and from the IIP of Gengenbach (1972) and the AIP of Shafer (1973). The Rm,JRm values were calculated from (23). The Rm values for NO were derived from Tully (1973) and from the values of Hirschfelder (1965) using combination rules for H2 from Helbing (1968) and Butz (1971). 

Ar and Oz-Kr the other one based on combination rules and the potential parameters found in Hirschfelder (1965). Although the first choice is the only one based upon experiments on related systems one has to keep in mind that differential cross section measurements explore a different region of the IP than do the total collision cross section measurements. In other cases (Butz, 1971 and Kupperman, 1973) differences of about 30% were... 

The purpose of this section is to present only those aspects of molecular dynamics which are useful in providing a theoretical rationalization for the semiempirical Redlich-Kwong equation of state and for the algebraic form of the combining rules for mixtures. No attempt is made to derive the relations presented in this section. For a rigorous treatment the reader should consult the published works on the siibject, such as Prausnitz (1969) or Hirschfelder et al. (1964), which have supplied most of the information summarized in this section. 

The dilBEerence between (2.7.9) and (2.7.11) is generally rather small. However the arithmetic mean corresponds to a stronger mutual interaction. We shall briefly call dispersion forces the cases in which the combining rule (2.7.8), (2.7.9) is valid. Indeed the combining rule may be partly justified by the London theory of dispersion forces (cf. Hirschfelder et al. [1954]). 

The usual procedure is then to use for non-polar molecules the combining rules (2.7,8), (2.7.15) and to compare the calculated results with the experimental ones. This procedure is used systematically in the textbook of Hirschfelder, Curtiss and Bird [1954]. The agreement is generally as good as may be expected. 

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