Hydroxyl exponent

If the hydroxyl exponent is defined in the same manner as the hydrogen exponent, and the negative logarithm of Kw is designated by pKw, then equation (5) becomes ... 

For many purposes, especially when dealing with small concentrations, it is cumbersome to express concentrations of hydrogen and hydroxyl ions in terms of moles per litre. A very convenient method was proposed by S. P. L. Sorensen (1909). He introduced the hydrogen ion exponent pH defined by the relationships ... 

Hydrodynamic radii of poly(benzyl ether) dendrimers are shown in Fig. 5. Data for monodendrons with a hydroxyl focal group and tridendrons fall on the same curve. The value of the exponent v in Eq. (4) is 0.46 of low MW. At high MW it is 0.26 [48]. Data on low MW linear polystyrene in benzene [74] have been included in Fig. 5 for comparison. They highlight the little difference in the actual values of the hydrodynamic radii of linear polystyrene and low MW poly(benzyl ether) dendrimers. Deviations are observed only when MW>5xl03. Furthermore, the MW dependence of the radii of polystyrene and poly(benzyl ether) dendrimers are the same at low MW. This indicates that it remains impossible to draw major conclusions about the conformation of the low MW dendrimers from their global properties. The low values of the hydrodynamic radii of the high MW dendrimers, on the other hand, attest to their compact conformation. A similar transition to more compact dendrimers has recently been shown in a direct comparison of linear and dendritic poly(benzyl ethers) [75]. 

Fig. 1. Autocatalytic replication system examined by von Kiedrowski [G. von Kie-drowski, Angew. Chem., ltd. Ed. Engl. 98, 932 (1986)]. The trinucleotide substrates can be aligned on a hexamer template for ligation. The 3 -phosphate of one trinucleotide is activated by treatment with 1 -(3-dimethylaminopropyl )-3-ethylcarbodiimide and is attacked by the 5 -hydroxyl of the adjacent trinucleotide. The 3 and 5 ends of the template, and the termini of the trinucleotides that are not adjacent following annealing, are chemically protected to avoid possible side reactions. After ligation, the individual strands of the double-stranded molecule can separate and template new ligation reactions (however, because the hexamer duplex is more stable than the free hexamer, the rate of template accumulation will be proportional to the square root of the template concentration, rather than a higher order exponent).

The term pOH is sometimes used in an analogous way for the hydroxyl-ion exponent, that is... 

The exponents P and a of Eqs. 9-90 and 9-91 measure the sensitivity of a reaction toward the basicity or acidity of the catalyst. It is easy to show that as P and a approach 1.0 general base or general acid catalysis is lost and that the rate becomes exactly that of specific hydroxyl ion or specific hydrogen ion catalysis. 

Conversely, in a solution of a salt of a strong base and weak acid, the hydroxyl ion exponent at 100° is likewise lowered to the same extent. 

This treatment is easily generalized and leads to the conclusion that in water or similar solvents general acid catalysis will be observable only for intermediate values of the exponent a. If a is too small, the catalytic effect of acids will be swamped by that of the solvent, while if a approaches unity, the effect of all other acids will be masked by that of the hydrogen ion. Similar conclusions apply to basic catalysis. It is possible, therefore, that those reactions in aqueous solution which appear to show specific catalysis by hydrogen or hydroxyl ions (cf. preceding sub-section) do not constitute a special class of reaction, but are actually... 

It can be seen that the derivative with respect to the hydroxyl groups removes just one hydroxyl group from the compound and takes care that every possibility to remove just one hydroxyl group in the molecule is taken into account, cf. Fig. 17.4. Thus, because trimethylolpropane contains three hydroxyl groups on forming the derivative, the exponent 3 will come down. In other words, the derivative generates the reactive species in the correct portion. 

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