Bjerrum parameter

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

The concentration c that appears in the Debye-Hiickel-Onsager equation pertains only to the free ions. This concentration becomes equal to the analytical concentration (which is designated here as only if every ion from the ionic lattice from which the electrolyte was produced is stabilized in solution as an independent mobile charge carrier i.e., c if there is ion-pair formation. Whether ion-pair formation occurs depends on the relative values of a, the distance of closest approach of oppositely charged ions, and the Bjerrum parameter g = (z z Co/2 T) 1/e. When the condition for ion-pair formation is satisfied and when a > the ions remain free. 

The expression for vr shows that it is the product of the ionic concentration c and e lz T, which is called the Bjerrum parameter. The virial series is an expansion in the total ionic concentration c at a fixed value of... 

Bjerrum parameter, see Eq. (19b) distance parameter, see Figs. 2 and 3 also gas constant distance variable entropy... 

Bardeen potential, 340, 341 Bjerrum parameter, 112 Born-Green-Yvon equation, 22-24, 122... 

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