Enthalpy of aggregation

The above process, Eq. (25), is in conflict with the currently available theoretical results (Table 5) regarding the dissociation enthalpies of aggregated organolithiums. A similar conclusion was reached by Brown in 1966 70>. This assessment is fortified by the fact that the measured 941 energy of activation for the reaction of styrene with n-butyllithium, 18 kcal/mole, is a value far lower than that required if the calculated dissociation enthalpy of the n-butyllithium aggregates is included in the overall energetics of the initiation event. Thus, it would seem that any mechanism which involves only unassociated organolithiums as reactive entities is invalid. 

Standard-State Enthalpy Changes (AH°). To expedite calculations, thermochemical data are ordinarily presented in the form of standard-state enthalpy changes of the system AH°(T,P), with the requirement that materials start and end at the same temperature (T) and pressure (P) and in their standard states of aggregation, i.e.,... 

Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

When the free enthalpy of reaction AG for the transformation of the structure of a compound to any other structure is positive, then this structure is thermodynamically stable. Since AG depends on the transition enthalpy AH and the transition entropy AS, and AH and AS in turn depend on pressure and temperature, a structure can be stable only within a certain range of pressures and temperatures. By variation of the pressure and/or the temperature, AG will eventually become negative relative to some other structure and a phase transition will occur. This may be a phase transition from a solid to another solid modification, or it may be a transition to another aggregate state. 

When an element enters into a reaction, its standard Gibbs free energy and standard enthalpy of formation are taken as zero if its state of aggregation is that selected as the basis for... 

In general, the standard enthalpy of micellization is large and negative, and an increase in temperature results in an increase in the c.m.c. the positive entropy of micellization relates to the increased mobility of hydrocarbon side chains deep within the micelle as well as the hydrophobic effect. Hoffmann and Ulbricht have provided a detailed account of the thermodynamics of micellization, and the interested reader will find that their tabulated thermodynamic values and treatment of models for micellar aggregation processes are especially worthwhile. 

If the enthalpy of formation of 4-lithiobutyl methyl ether is interpolated between the values for the lithiopropyl and the lithiopentyl ethers to be —285 kJ moP, then the enthalpy of isomerization to the less stable 3-lithiobutyl methyl ether is - -10 klmoP, which is about half that of isomerization of n-butyl lithium to 5ec-butyl lithium (-1-21.3 kJmol ). However, a linear interpolation assumes the same strain energy for the 6-membered 4-lithiobutyl ether as for the above 5- and 7-membered cu-lithioalkyl methyl ethers. If it is less strained, then the isomerization enthalpy would be larger. How much of the isomerization enthalpy difference is due to other differences, such as intramolecular complexation and/or aggregation among the various species, is not known. Unfortunately, there is no enthalpy of formation measurement for the delithiated 7-methoxynorbornane. 

If all of these polymeric organolithiums are converted into unassociated, TMEDA -coordinated species at an R value of ca. 1.0, then the data in Fig. 7 can be used to estimate the difference in enthalpies of association for these aggregates. At an R value of 1.0, the cumulative heat in calories can be associated with the process shown in Eq. (21), where... 

The values of the CMC or CMT collected as a function of temperature or concentration can be used to extract the enthalpic and entropic contributions to the association process. For a closed association mechanism with relatively large aggregation number and a narrow distribution, the standard free energy and standard enthalpy of micelle formaMi nd AH°, per mole of the solute in the micelle) are related to the CMC and its temperature dependence in the form (Lindman and V fennerstrom, 1980 Zhou and Chu, 1994). 

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