Effect of Excess Counterion

Let us now consider how the presence of excess counterion due to the. addition of a strongly dissociating salt (e.g., sodium tetraphenyl borate, NaBPh4, to supply excess Na ) can affect the kinetics of a living anionic polymerization. The retarding effect of a dissociating salt forms the basis of a method by which the dissociation constant of a polymeric ion pair may be determined. 

If the polymeric ion pairs are shghtly dissociated, [X,t AM C ] can be set approximately equal to the total concentration of living ends [M ] and Eq. (8.59) 

If the added salt is strongly dissociated and a relatively large amount of salt has been added, [C ] representing the concentration of free ions in solution can be approximated by the concentration of C produced by the dissociation of the added salt, i.e., 

Equations (8.66) and (8.71) allow one to obtain k, and K from the experimental values of overall or apparent rate constant kp determined in the absence and presence of added common ion. While a plot of kp versus 1/[M ] in the absence of added common ion yields a straight line whose slope and intercept are k - kp)K and kp, respectively, a plot of kp versus 1 /[C ]sait in the presence of added conunon ion yields a straight line [cf. Eq. (8.71)] whose slope and intercept are kp-kp)K and kj, respectively, thus affording the values of k, kp, and K, individually (see Problems 8.9 and 8.10). It should be noted that the observed ion pair propagation constant k is, in fact, an apparent rate constant as it is a composite of rate constants for the contact ion pair and the solvent-separated ion pair (see Problem 8.11). 

Determine the propagation rate constants and k and the overall dissociation constant K for polystyryl sodium in THF at 25°C. (The dissociation constant of NaBPlH in THF at 25°C is 8.52x10 mol/L.) 

Problem 8.9 Polymerization of styrene with sodium naphthalene initiator was performed at 25°C in tetrahy-drofuran (THF) using a static technique (Bhattacharya et al., 1965) that is suitable for monitoring fast reactions. The conversion was determined by monitoring the residual styrene monomer during polymerization and the concentration of living ends [M ] was determined at the end of the experiment, using spectrophotometry in both cases. In independent experimental series, the overall rate constant kp was obtained [cf. Eq. (P8.8.1)] both at different concentrations of initiator (and hence [M ]) without addition of electrolyte and at different concentrations of sodium ions from externally added sodium tetraphenyl borate (NaBPlq) salt and constant concentration of initiator. The data are given below  

Problem 8.10 Calculate the concentrations of polymeric free ions and ion pairs both in the absence of electrolyte and in the presence of electrolyte NaBPh4, considering two polymerization systems of Problem 8.9 that have nearly equal concentrations of living chain ends. What percentage of the free Na ions comes from the initiator when the electrolyte is present  

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