Logarithms of association

Estimated and measured common logarithms of association constants for some trace metal-inorganic ligand ion pairs... 

Table 6. Logarithm of Association Constants (M" ) of 16 and 17 with (Z)-Amino Acids and (Z)-Peptides ...

FIGURE 11.2 Affinity spectra (represented as fraction of sites against the logarithm of association constant) for (a) phosphoric acid (b) an equimolar mixture of acetic and dipico-linic acids. 

Table 1 Logarithms of association constants of peptides and some low-affinity substrates with glycopeptide antibiotics.

Table 4 Logarithms of association constants of nucleotides and nucleosides with differently protonated forms of kanamycin A (Kan) and tetrandrine derivatives at 25 °C.

Table 6 Logarithms of association constants and thermodynamic parameters (kJ mol selectors 7, 8, quinine, and quinidine in methanol at 25 °C. ) for binding of (T )-5, (5)-5, and 6 to the chiral ...

The group contribution method allows the approximate calculation of solubility by summing up fragmental values associated with substmctural units of the compounds (see Section 7.1). In a group contribution model, the aqueous solubility values are computed by Eq. (12), where log S is the logarithm of solubility, C is the number of occurrences of a substmctural group, i, in a molecule, and is the relative contribution of the fragment i. 

Figure 29. Graph of the Logarithm of the Water/Methanol Association Equilibrium Constant against the Reciprocal of the Absolute Temperature...

The structure of this equation suggests that we associate //+ with the chemical potential of cations and [a++p+(F) + a+ p (F)] with the logarithm of the activity coefficient relative to cations in the MFA. In addition to their thermodynamic significance, these coefficients characterize the symmetry of... 

The conductivity of a solution containing such molecular ions may be small compared with the value that would result from complete dissociation into atomic ions. In this way, in the absence of neutral molecules, we can have a weak electrolyte. The association constant for (29) has a value that is, of course, the reciprocal of the dissociation constant for the molecular ion (PbCl)+ the logarithms of the two equilibrium constants have the same numerical value, but opposite sign. 

We will now derive expressions for Zm that can then be substituted into the above equations to calculate the thermodynamic properties. In doing so, we note that, in all instances, these properties are related to the logarithm of Zm. Since the Z s associated with different degrees of freedom are multiplied,... 

Thus, when the associated (protonated) and dissociated (conjugate base) species are present at equal concentrations, the prevailing hydrogen ion concentration [H+] is numerically equal to the dissociation constant, A. If the logarithms of both sides of the above equation are... 

In contrast to the weights formalism, the partition function approach directly employs the ideal flat-histogram expression in (3.36). Its goal is not to determine q but Q(N. V, T) directly, or more precisely in this case, the N dependence of Q. Due to numerical reasons, we usually work instead with the associated thermodynamic potential which is the logarithm of the partition function of interest in this case it is In Q = — 7/1 =. A, where we have used script i as an abbreviation. Thus our sampling scheme becomes... 

Fig. 9. Logarithm of the cation activity coefficient versus the square root of the concentration for the system of manganese ions and cation vacancies in sodium chloride at 500°C. Filled-in circles represent the association theory with Rq = 2a, and open circles the association theory with R = 6/2. Crosses represent the present theory with cycle diagrams plus diagrams of two vertices, and triangles represent the same but with triangle diagram contributions added.

Fig. 3. Plot of the logarithm of the association constants for the exchange reaction AaX2 + BaXa 5=5 2 ABXa versus the function of the size parameters predicted by theory.

The residuals discussed thus far have been associated with some dependent variable, such as the reaction rate r. It is particularly advantageous in pinpointing the type of defect present in an inadequate model to expand this definition to include parametric residuals. The parametric residual, then, is simply the difference between a value of a given parameter estimated from the data and that predicted from a model. For example, the dots in Fig. 17 represent the logarithm of the alcohol adsorption constants measured in alcohol dehydrogenation experiments from isothermal data at each of several temperature levels (FI). The solid line represents the expectation that these... 

The equilibrium constant (commonly symbolized describing the dissociation of a compound into two or more compounds, ions, or atoms. For the reaction A -t B = A-B, the dissociation constant is [A][B]/[A-B]. The dissociation constant is the reciprocal of the association constant and the negative logarithm of the is the pT d ... 

Symbol for dissociation constant, equal to the reciprocal of the association constant. The negative logarithm of this constant is the pXd. See Dissociation Constant ... 

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