Pairing concentration

There are two approaches to the separation of pp into the individual kp and kp values. One approach involves the experimental determination of the individual concentrations of free ions and ion pairs by a combination of conductivity with short-stop experiments or UV-visible spectroscopy. Conductivity directly yields the concentration of free ions that is, only free ions conduct. Short-stop experiments yield the total of the ion-pair and free-ion concentrations. UV-visible spectroscopy for those monomers (mostly aromatic) where it is applicable is also used to obtain the total of the free-ion and ion-pair concentrations. It is usually assumed that ion pairs show the same UV-visible absorption as free ions since the ion pairs in cationic systems are loose ion pairs (due to the large size of the negative counterions see Sec. 5-1). This approach is limited by the assumptions and/or experimental difficulties inherent in the various measurements. Conductivity measurements on systems containing low concentrations of ions are difficult to perform, and impurities can easily lead to erroneous results. The short-stop experiments do not distinguish between ion pairs and free ions, and the assumption of the equivalence of free ions and ion pairs in the spectroscopic method is not firmly established. The second approach involves determination of the... 

Consider propagation by polystyryl sodium ion pairs in a 1 M styrene solution in tetrahydrofuran. For an ion pair concentration of 2.0 x 10-3 M, calculate the relative contributions of contact and solvent-separated ion pairs to the propagation process. Use appropriate data from Table 5-12. 

An Important observation Is the concentration dependency of the ratio II/I (see equations 1 and 2). In a study of the complex formation between benzo-15-crown-5 and fluorenylsodlum In THF, 2-methyl-THF and THP the ratio of the two complexes I and II was found to depend not only on solvent but also on the total Ion pair concentration (14). The results were rationalized by assuming the formation of dimers of II on Increasing the Ion pair concentration as shown In reaction 3. Aggregation of complex I Is... 

A linear concentration dependence of the reciprocal relaxation time upon total ion-pair concentration would therefore point to a main recombination process between a simple ion and a triple ion. 

Considering these different limiting forms of the recombination term an Important tentative conclusion emerges the concentration dependence of the reciprocal relaxation time is a direct measure of the main ionic recombination process and yields therefore information on the ionic species present in solution. A linear dependence on total ion-pair concentration would therefore indicate unilateral triple ion formation or, if both kinds of triple ions are present as indicated by conductance, a sufficient difference in their stability. At this point it should be noted that the usual method of Fuoss and Draus... 

Increase of the stable Frenkel-pair concentration under irradiation of the samples is saturated (Fig.6) when the trapping of excitons at defects exceeds the exciton self-trapping in the perfect lattice. Further long-time irradiation of the samples results in an aggregation of vacancies and interstitials, which results in decrease of intensity of defect subbands (Fig.6e). 

Since equilibrium constants are defined by ion activities, which are defined by their concentrations and coefficients (see equation 4.15), they do not include ion pairing or complexation effects. In a multi-ion and multiligand solution, where ion pairing is common, it is necessary to use thermodynamic equilibrium constants to convert the ion-pair concentrations to concentrations of free ions. This equilibrium constant (Kc) is defined by concentrations, making it useful to compute ion speciation. The thermodynamic equilibrium constant (K q) used in calculating Kc is based on the following conditions I = 0 m, 25°C and 1 atm. Thus, Kc is defined by the following equation ... 

The effective local concentration determined from the longitudinal relaxation as mentioned above is roughly equal to the value of the bulk concentration where the dose-yield curve begins to deviate from the linear relationship. Assuming that the dose-yield curve starts to saturate at the bulk concentration of 8.4 mmol/dm3 or the radical-pair concentration of 4.2 mmol/dm3 due to the overlap of the spurs, the radius of the spur is estimated to be 4.5 nm. This value is in good agreement with the spur radius of 4.1 nm obtained from the relaxation measurement. This coincidence seems to support the general view that the... 

Fig. 4. Scatchard plots for the binding of tilorone hydrochloride to calf thymus DNA (a) Me. lysodeikticus DNA (b) poly (dA-dT) poly (dA-dT) (c) and poly (dG-dC) poly (dG-dC) (d). Each different symbol corresponds to a separate experiment. Thus, each figure represents a set of 4 or 5 separate experiments, r is moles of bound tilorone/base pair concentration and (u) is the concentration of unbound tilorone. Equilibrium dialysis was carried out by a procedure and an apparatus (Dianorm, supplied by Dr. Virus KG, Bonn, Germany) described by Weder et al.61 Dialysing membrane (0.02S mm thick) was sandwiched between two halves of a Teflon (round) macro-cell (dialysable volume = 1 ml). The DNA, or labelled tilorone solutions were introduced by separate micro syringes on either side of the membrane through the side valves. The valves were closed air tight and the macro-cells were fixed into a rotating machine. All equilibrium dialysis studies were carried out at 20°, and at 10 rotations/min. Under these conditions equilibrium was attained in 4-5 hr. After the equilibrium was reached 0.8 ml of the solution from either side of the membrane was withdrawn by microsyringes and the radioactivity was determined using dioxan scintillation fluid...

In the case of 7-AI2O3, the (100) face calculations of concentration of oxygen site-pairs for various coverages of surface hydroxy-groups revealed that there were about twice as many syn- as an/z-elimination sites. Under reaction conditions, the surface hydroxyl concentration and therefore oxygen site-pair concentration favours alk-2-ene orientation (Saytzev) and anti-ehmination occurs due to the lower energy of activation. It was also shown that cw-alk-2-ene formation is sterically less demanding than frans-alk-2-ene... 

The free ions and ion pairs play a distinct role in the dielectric properties of electrolyte solutions. Due to the saturation of the dipole orientation near free ions, the dielectric constant of the system decreases with the increase of free ion concentration. Ion pairs possess the dipole moments and produce an additional contribution to the dielectric properties. Due to the new polarization effect, the dielectric constant of the entire system increases with the increase of the ion pair concentration. It is generally accepted to distinguish the solvent dielectric constant, es, and the solution dielectric constant, e [3], The dielectric constant of the solvent describes the polarization effect of the solvent molecules in the presence of ions es decreases with the increase of ion concentration. The dielectric constant of the solution also includes the polarization effect from the ion pairs that can increase or decrease with the increase of ion concentration. Due to this, e > es, and only for a completely dissociated electrolyte, (a = 1) e = es. 

The measured Eh of natural waters (particularly of surface-waters) often represents a mixed potential and thus has little or no thermodynamic meaning. For this reason many researchers have chosen to chemically analyze natural waters for their concentrations of individual redox pairs, rather than computing questionable redox pair concentrations from the measured Eh via the Nernst equation. The analysis of leachate from Well 201 in Table A12.4 includes measured Eh and pH values and concentrations of Fe(III)(aq), Fe(l )(aq), As(III)(aq), and As(V)(aq). Separately compute the Eh that corresponds to the directly measured concentrations of each redox pair and compare these values to the measured Eh. Solve the problem using MINTEQA2 and comment on the results. 

Problem 8.13 Consider propagation by polystyryl sodium ion pairs in a IM styrene solution in tetrahydrofuran at 20° C. For an ion pair concentration of 2.0x 10 M, calculate the relative contributions of contact and solvent-separated ion pairs to the propagation process. [Data At 20°C, rate constant for contact ion pair, k = 24 L/mol-s rate constant for solvent-separated ion pair, k, = 5.5x10 L/mol-s equilibrium constant for interconversion between contact ion pair and solvent separated ion pair, Kcs — 2.57x10 . ]... 

Lee et al. (67) reported in 1993 that at high pH, complexes termed M-DNA form between the nucleobase pairs within calf thymus (CT), bacterial or synthetic DNA, and the divalent metal ions, Zn, Ni, or Co " ". The chemical nature of M-DNA has been investigated using methods that probe changes in DNA properties, but do not directly probe the coordination of the metal ions. Titration of a d(T-G)i5 d(C-A)i5 duplex with Zn " " at pH 8.5 monitored by NMR spectroscopy showed a decrease in the intensity of the imino peaks with the increasing concentration of Zn " " and the complete disappearance of these peaks when the Zn " " concentration became almost equal to that of the DNA base pairs (67). The transformation induced by Ni " " of B- to M-DNA for CT DNA in solutions with 1.1 mM base pair concentrations led to the release of 1.1 equiv of protons per base pair (68). Based on these results, Lee and co-workers... 

A conformation change in the B-DNA to M-DNA transformation was inferred based on surface plasmon resonance studies (70). For the B- to M-DNA transformation to take place, it was necessary that a threshold concentration of metal ions be present in solution. For example, the transformation of B- to M-DNA in a solution with a DNA base pair concentration of 1.1 mM took place after the concentration of Ni " " reached a threshold concentration of... 

Cation and ion-pair concentrations are calculated in the next step based on the above anion concentrations and activities. Taking Ca as an example, the mass balance on total dissolved Ca is ... 

The formation of ion pairs such as CaHCOj and the others considered in equation (19.36) reduces the concentration of free (unassociated) anions such as HCOJ , Cl, and SO4 . The concentrations of all free anions are therefore reduced at this stage by the amount of each tied up in ion pairs and complexes. This changes the ionic strength as well, so new estimates of the activity coefficients must also be made at this point. The calculation of free cation and ion pair concentrations is then repeated with these new estimates of anion molalities and activity coefficients. The iteration is continued until the mass balances for all cations and acid anions (such as equations (19.32) and (19.36) agree satisfactorily vk ith measured quantities. 

An ideal system of liiKar chain molecule is certainly only fictitious. In reality, the intermolecular foicra exert an important influence on tte defect concentration and energetics. Since chain molecules with j and k defect units may assume entirely different conformations (cf Fig. 2.3), the pair concentrations x would haw to be split up into a sum, viz. 

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