Effective molarities

Consider the solution of a chain A—B where —A and —B are two reactive end groups capable of reacting reversibly with each other so as to form a new bond AB (Fig. 2). 

If the reacting groups belong to the same chain, the reaction is intramolecular and leads to the formation of a ring, whereas if the two groups belong to different chains, the reaction is intermolecular and leads to the formation of a dimeric chain. The probability that the reaction is intramolecular is proportional to whereas the probabifrty that the reaction occurs 

If Kintra and K are defmed in terms of activities rather than concentrations, the EM can be easily related to the corresponding enthalpic and entropic components  

In most of the cases, the enthalpic contribution coincides with the strain energy of the ring thus for small and medium rings with significant strain energies, EMh can be significantly lower than 1, whereas when a large 

The intercept of Eq. [4] refers to an intramolecular reaction taking place with no conformational entropy loss, that is, AS = 0 when v = 0. As a result, the negative of the intercept corresponds to the loss of entropy suffered by bimolecular reactions leading to covalent bonds, that is, AS° = —126 J mol. This value translates to EM = exp(126/J ) = 3.6 X lO molL , that is not too far from the value of 10 mol predicted by Page and Jencks. The slope of Eq. [4] impHes a drop of 16.7 J mol per added single bond, which indicates a nearly complete 

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First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu-... 

In the original equation of van Laar, the effective molar volume was assumed to be independent of composition this assumption implies zero volume-change of mixing at constant temperature and pressure. While this assumption is a good one for solutions of ordinary liquids at low pressures, it is poor for high-pressure solutions of gases in liquids which expand (dilate) sharply as the critical composition is approached. The dilated van Laar model therefore assumes that... 

Commercially available buffer solutions can be purchased for virtually any desired pH. A buffer solution commonly used to calibrate pH meters contains 0.025 m Na2HP04(aq) and 0.025 M KH2P04(aq) and has pH = 6.87 at 25°C. However, the method demonstrated in Example 11.1 would give pH = 7.2 for this solution. Because these calculations interpret activities as molarities, not effective molarities, they ignore ion—ion interactions so the values calculated are onl) approximate. 

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

Temperature control at -15° to -25°C was also required for maximum yield. The best results were obtained by maintaining a temperature of -20 to -25°C during the addition of citral anil to the acid and at -15°C for the duration of the reaction. At this temperature range, the formation of a-cyclocitral (III) is favored. Higher temperatures caused excessive polymer formation and favored formation of e-cyclocitral whereas lower temperatures caused a reduction 1n the yield of the citral mixture. At least part of the problem with the lower temperature reaction was the fact that the sulfuric acid tended to freeze around the inside of the reaction vessel causing the effective molar ratio of acid to anil to be reduced. These lower temperature reaction mixtures were also lighter in color which indicated less polymer formation but this was accompanied by a lower yield of cyclocitrals. 

Two concentrations of citrate have been routinely used as anticoagulant for tests such as PT and APTT (either 0.129 or 0.105 M). The effective molarity depends on whether the dihydrate or the anhydrous citrate salt was used in preparation of the citrate solution. A 3.2% solution of sodium citrate prepared using the dihydrate salt is 0.105 M. However, the molarity of a 3.2% solution of sodium citrate prepared with the anhydrous salt is 0.124 M. Similarly, a 3.8% solution of sodium cit-... 

The networks studied were prepared from reactions carried out at different initial dilutions. Aliquots of reaction mixtures were transferred to moulds, which were maintained at the reaction temperature under anhydrous conditions, and were allowed to proceed to complete reaction(32). Sol fractions were removed and shear moduli were determined in the dry and equilibrium-swollen states at known temperatures using uniaxial compression or a torsion pendulum at 1Hz. The procedures used have been described in detail elsewhere(26,32). The shear moduli(G) obtained were interpreted according to Gaussian theory(33 34 35) to give values of Mc, the effective molar mass between junction points, consistent with the affine behaviour expected at the small strains used(34,35). 

G. M. Whitesides, Dependence of effective molarity on linker length for an intramolecular protein-ligand system, /. Am. Chem. Soc., 129 (2007)... 

Effective charge and transition-state structure in solution, 27, 1 Effective molarities of intramolecular reactions, 17,183 Electrical conduction in organic solids, 16,159 Electrochemical methods, study of reactive intermediates by, 19, 131 Electrochemical recognition of charged and neutral guest species by redox-active receptor molecules, 31, 1... 

Intramolecular reactions, effective molarities for, 17,183 Intramolecular reactions, of chain molecules, 22,1... 

Exocyclic reactions for aromatic carboxylic esters 174 Exocyclic reactions for aliphatic carboxylic esters 187 Endocyclic reactions for carboxylic esters 191 Carbon acid participation for carboxylic esters 195 Effective molarities 198 Ring size 199 Initiating nucleophile 200 Phosphate and sulphonate esters 200... 

To investigate this dendritic effect, a dimeric model compound was synthesized which mimics the tethered relationship of two catalytic units within one branch of the PAMAM dendrimer. All dendritic catalysts were more active in the HKR than the parent complex. Furthermore, the dendritic catalysts also displayed significantly higher activity than the dimeric model compound. The authors proposed that this positive dendritic effect arises from restricted conformation imposed by the dendrimer structure, thereby creating a bigger effective molarity of [Co(salen)] units. Alternatively, the multimeric nature of the dendrimer, may lead to higher order in productive cooperative interactions between the catalytic units. 

Kinetics of cyclisation. The cyclisation constant C 4 The effective concentration eff and the effective molarity EM 6... 

In the last two decades, there has been a large accumulation of experimental evidence as well as of theoretical interpretations of intramolecular reactions. One notes, however, that attention has been focused on the phenomena of immediate interest to the various specialists. As a consequence of the fact that specialisation implies intensification of knowledge on the one hand but limitation on the other, there has still been insufficient communication and cross-fertilisation between the different schools. This situation is well exemplified by the two most extensive reviews on intramolecular phenomena, namely, that of Kirby (1980), entitled Effective Molarities for Intramolecular Reactions , and that of Winnik (1981a), entitled Cyclisation and the Conformation of Hydrocarbon Chains , which present different approaches and apparently unrelated facts and theories. 

Hypothetical gas-phase cyclisation reactions. Effective molarities and thermodynamic parameters ... 

The values of 0(ASD) /2.3O3 R listed in Table 5 are the entropic components of log EM. These are the log EM- alues for ideal strainless cyclisation reactions, i.e. reactions where 0AH° = 0. It is of interest to note that, as far as the entropic component is concerned, symmetry corrected effective molarities on the order of 102 106M are found. This observation leads to the important conclusion that cyclisation reactions of chains up to about 7 skeletal bonds are entropically favoured over reactions between non-connected 1 M end-groups. The intercept of 33 e.u. corresponds to an effective molarity of exp(33/R) or 107 2M, which may be taken as a representative value for the maximum advantage due to proximity of end-groups in intramolecular equilibrium reactions. It compares well with the maximum EM of about 108M estimated by Page and Jencks (1971). 

Interface, the air-water, chirality and molecular recognition in monolayers at, 28, 45 Intermediates, reactive, study of, by electrochemical methods, 19, 131 Intermediates, tetrahedral, derived from carboxylic acids, spectroscopic detection and investigation of their properties, 21, 37 Intramolecular reactions, effective molarities for, 17, 183 Intramolecular reactions, of chain molecules, 22, 1... 

Obviously, in such cases the CD is acting as a true catalyst in esterolysis. The basic cleavage of trifluoroethyl p-nitrobenzoate by a-CD occurs by both pathways approximately 20% by nucleophilic attack and approximately 80% by general base catalysis (GBC) (Komiyama and Inoue, 1980c). The two processes are discernible because only the former leads to the observable p-nitrobenzoyl-CD. For the ester, Ks = 3.4 mM and kjka = 4.4 for the GBC route (1.25 for the nucleophilic route), and so KTS = 0.77 mM. For reaction within the ester CD complex [28], it was estimated that the effective molarity of the CD hydroxyl anion was 21-210 m (for Br0nsted /3 = 0.4 to 0.6 for GBC). Such values are quite reasonable for intramolecular general base catalysis (Kirby, 1980). 

I EFFECTIVE MOLARITIES FOR CYCUZATION REACTIONS 225 A Reactions of the carboxylic acid group 225... 

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