Equilibrium constant for association

D. Measurement of Equilibrium Constants for Association Processes In Solution... 

In hydrocarbon solvents it is known that most of the growing chains are associated and it is necessary to enquire what effect this has on the copolymerization mechanism. The reactivity ratios measured from copolymer composition are unaffected because they refer to a common ion-pair. The equilibrium constants for association cancel and the reactivity ratios measured give a true measure of the relative propagation constants of the two monomers. No assessment can be made of the real reactivity of two types of active chain with the same monomer, however. In this case the observed rates are a function of the relative reactivities of the free ion-pairs and also of the relative extents of association. For example in hydrocarbon solvents polystyryllithium reacts with butadiene much more rapidly than does polybutadienyllithium. Until we know the two equilibrium constants for self-association we cannot find out if the increased rate is due to greater intrinsic reactivity or to a higher concentration of free polystyryllithium. In polar solvents or in hydrocarbon solvents in the presence of small amounts of ethers, these difficulties do not arise as self-association is no longer important. 

The concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

If a titratable group on a protein molecule can combine with substances, other than hydrogen ions, which may be present in a protein solution, then its titration properties will be altered. If the combining substance is present at a thermodynamic activity an, and if it combines with the basic form of the titratable group only, the equilibrium constant for association being ku, then the apparent hydrogen ion dissociation constant Xapp of the group becomes... 

Huggins, Pimentel, and Shoolery measured NMR shifts of chloroform in acetone and in triethylamine (982). This study furnishes corroborative evidence that the chloroform-base interaction can be classified as a H bond. More important, however, it serves as a prototype of the use of NMR chemical shifts in the study of complex formation. Huggins et al, based their analysis on an expression analogous to equation (7). They show that two data—the experimental values of 5 in pure chloroform and at infinite dilution, combined with the equilibrium constant for association—permit csdculation of the entire concentration dependence of 5. This implies that the measurement of 5 over the range from pure liquid to infinite dilution gives an estimate of the equilibrium constant. Of course the temperature dependence of the constant gives the heat of association. The appropriate equations are given in reference 982 where they are used to obtain K and A// for the association of chloroform with the bases acetone and triethylamine. 

Cis (NH3)2PtCl2 and other Pt(II) complexes react only slowly with the nucleic bases. The slowness may be essential to their efficacy as tumor Inhibitors, for It provides Integrity and neutrality during circulation and passage Into cells. Equilibrium constants for association of els (NH3)2Pt(II) complexes with nucleic bases remain unknown. It has been argued that published constants fall to reflect systems at equilibrium (. The aqueous chemistry of Pt(II) relevant to biological molecules has received review (2),... 

Xrx Conditional equilibrium constant for association of RX with surface (L mol )... 

For more highly charged ions appreciable ion pairing does occur in aqueous solutions at concentrations of the order of 1 M for 1 2 or 2 1 type salts and even at concentrations of 0.1 M for 2 2 or salts with more highly charged ions. The equilibrium constants for association of the latter (e.g., MgS04) are of the order of 100-200 M- . 

Non-polar ligands bond much more weakly than H2O or SO2. The equilibrium constant for association of 803" with CO2, which has only a weak quadrupole moment, is 1.7 bar" at 296 K, four orders of magnitude lower than that determined for the addition of the first water molecule 120]. The dissociation energy of the S04 (CO2) complex is correspondingly low at 27.2 kJ mol" (A5d" = 86.6 J mol" K" ). 

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