Ionization constant, water temperature dependence

Corresponding dependencies in van t Hoff coordinates, although almost linear, show different directions in their slope, which is dependent on the particular pH chosen for this particular model (Figure 2-f8). Note that in this model the effect of temperature on the change of the dissociation constants of the buffer species and model basic analyte species were taken into account on the basis of standard relationship of the equilibrium constant with the temperature (Ki = exp[AG/i r]). It has been shown that the dissociation constants of particular acidic species and basic species show some specific variations of their ionization constants with temperature in methanoFwater and acetoni-trUe/water mobile phases [40,41],... 

The ionization of water is so important in the study of aqueous equilibria that the equilibrium constant is given the special symbol, Kw. It can be seen that, Kw, like all equilibrium constants, depends on temperature. Since Kw is larger (the forward reaction is encouraged) at higher temperatures, the forward reaction must consume heat, so the ionization of water must be endothermic. 

The activity of the solvent molecule HS in a single-component solvent is constant and is included in Kus. The concentration of ions is mostly quite low. For example, self-ionization occurs in water according to the equation 2H20— H30+ + OH". The conductivity of pure water at 18°C is only 3.8 X 10"8 Q"1 cm-1, yielding a degree of self-ionization of 1.4xl0"19. Thus, one H30+ or OH" ion is present for every 7.2 x 108 molecules of water. Some values of Kus are listed in Table 1.5 and the temperature dependence of the ion product of water Kw is given in Table 1.6. 

CD reactions sometimes proceed via a metal hydroxide intermediate the concentration of OH ions in the solution is particularly important in such cases. Since almost all CD reactions are carried out in aqueous solutions, the pH of the deposition solution will give this concentration. In translating pH into OH concentration, the very temperature-dependent ioiuzation constant of water should be kept in mind, as mentioned previously. The reason for this can be seen from Table 1.2, which gives the OH concentration in water at a pH of 10 (a typical pH value for many CD reactions), calculated from the ionization constant of water, from the relation... 

This equation is essentially an equilibrium constant relationship between the electron and hole concentrations in the semiconductor. It is much like the ionization constant expression for the dissociation of water, which can be related to the concentrations of H+(aq) and OH (aq) through the relationship [H+][OH ] = /fw = 1 x 10 " M. The only difference between these two expressions is that the temperature dependence of the water dissociation equilibrium constant is contained implicitly in the value of K, but is explicit in the relationship expressed by equations (5) and (6). The most important point to remember is that increases in the sample temperature will produce exponential increases in the electron and hole concentrations for an intrinsic semiconductor. Thus, the conductivity of intrinsic semiconductors increases exponentially with temperature. In contrast, the conductivity of metals decreases with increasing temperature. ... 

An application of continuum solvation calculations that has not been extensively studied is the effect of temperature. A straightforward way to determine the solvation free energy at different temperatures is to use the known temperature dependence of the solvent properties (dielectric constant, ionization potential, refractive index, and density of the solvent) and do an ab initio solvation calculation at each temperature. Elcock and McCammon (1997) studied the solvation of amino acids in water from 5 to 100°C and found that the scale factor a should increase with temperature to describe correctly the temperature dependence of the solvation free energy. Tawa and Pratt (1995) examined the equilibrium ionization of liquid water and drew similar conclusions. An alternative way to study temperature effect is through the enthalpy of solvation. The temperature dependence of is related to the partial molar excess enthalpy at infinite dilution,... 

Equation 9 has been successfully used to reproduce experimental values of the ionization constants of water and several aqueous complexes at higher temperatures and pressures . Eugster and Baumgartner (1 have used a relationship similar to Equation 9 for estimating the pressure dependence of aqueous complexes in supercritical fluids. 

As well as the inherent effects of temperature on the ionization of weakly acidic and basic functional groups, precise calculation of pK values from potenti-ometric titration requires the autoprotolysis constant for water, pKw- This quantity has been shown by careful measurements [90, 91] to be very temperature dependent, with values ranging from 14.943s at 0 °C to 13.017i at 60 °C and 12.264 at 100 °C [92-94]. 

The HX rates are also dependent on temperature. An increase in temperature affects HX rates primarily hy altering the water ionization constant, K, and thus increasing the concentration of OH . Further, some evidence suggests that temperature may also affect the collisional rate constant, k, in Equation 1.2 hy altering buffer viscosity and thus the diffusional collisional rate constant [24, 25]. A more recent study, however, has indicated that the effect of bulk viscosity on HX is negligible [30]. Theoretical HX rates can be determined as a function of temperature by a modified form of the Arrhenius equation (Eq. 1.4) and reference HX rate constants determined experimentally at 20°C ... 

Fig. 20.1. Comparison of the ionization constants of HjSO and H3PO4 (left scale), with those of several polymers measured in water at room temperature without added salt (right scale). For the polymers, the a dependence, when available, is determined by potentiometric titration using the p/f = pH + log a/1 — a empirical equation. For PEO, pK is not precisely known and a possible range of values deduced from those of ethers is indicated. The black circles are p/f values for PjVP and P4VP ( 5) according to M. Satoh ef uE Macromolecules 22 (1989) 1808-12 and for BPEI according to C. J. Bloys Van Treslong ef al., Reel. Trav. Chim. Pays-Bos 93 (1974) 171-8. The letters P, S and T refer to the pK values of the primary, secondary and tertiary amino groups in BPEI respectively, estimated by C. J. Bloys Van Treslong, Reel. Trav. Chim. Pays-Bas 97 (1978) 9-21.

The symbol k0 is an intercept term that is equal to k for the parent (unsubstituted) compound. The reaction constant p depends on reaction conditions such as solvent and temperature, representing the susceptibility of the reaction to environmental effects. In contrast, the substituent constant up is a measure of the electronic effect of replacing hydrogen by a given substituent, and is assumed to be independent of the reaction conditions. By defining p = 1 for the room temperature ionization of substituted benzoic acids in water, Hammett calculated op values directly for 13 substituents, and predicted those for a further 17 substituents by applying the primary rrP values to other reactions. Later work increased the number of aP values to 44 and the number of reaction series to 51 [35]. 

The role of the metal ion in ester hydrolysis catalysed by CPA has been examined with both Zn +- and Co +-substituted enzymes. When the terminal carboxyl of the substrate is electrostatically linked to argenine-145 and the aromatic side-chain lies in a hydrophobic pocket, the only residues close enough to the substrate to enter catalysis are glutamate-270, tyrosine-248, the metal ion, and its associated water. Low-temperature studies aid the elucidation of the mechanism. Between - 25 and - 45 °C in ethylene glycol-water mixtures two kinetically discrete processes are detected, the slower of which corresponds to the catalytic rate constant. The faster reaction is interpreted as deacylation of a mixed anhydride acyl-enzyme intermediate formed by nucleophilic attack by glutamate-270 on the substrate (Scheme 6). Differences in the acidity dependences of the catalytic rate constant with the metal ions Zn + (p STa 6.1) and Co +-(pATa 4.9) suggest that ionization of the metal-bound water molecule occurs and is involved in the decay of the anhydride. The catalytic rate constant shows an isotope effect in DgO. 

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