Dilute solution equilibrium constant

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

However, in dilute solution [H O] is virtually conslant ([H,0] = 55.5 since 1 litre of water contains 1000/18 mol of H O) and taking this into the above expression for the equilibrium constant we obtain a second constant... 

Auto-association of A-4-thiazoline-2-thione and 4-alkyl derivatives has been deduced from infrared spectra of diluted solutions in carbon tetrachloride (58. 77). Results are interpretated (77) in terms of an equilibrium between monomer and cyclic dimer. The association constants are strongly dependent on the electronic and steric effects of the alkyl substituents in the 4- and 5-positions, respectively. This behavior is well shown if one compares the results for the unsubstituted compound (K - 1200 M" ,). 4-methyl-A-4-thiazoline-2-thione K = 2200 M ). and 5-methyl-4-r-butyl-A-4-thiazoline-2-thione K=120 M ) (58). 

Most reactions involve reactants and products that are dispersed in a solvent. If the amount of solvent is changed, either by diluting or concentrating the solution, the concentrations of ah reactants and products either decrease or increase. The effect of these changes in concentration is not as intuitively obvious as when the concentration of a single reactant or product is changed. As an example, let s consider how dilution affects the equilibrium position for the formation of the aqueous silver-amine complex (reaction 6.28). The equilibrium constant for this reaction is... 

Customarily, because the term [HgO] is essentially constant in dilute aqueous solutions, it is incorporated into the equilibrium constant Alto give a new term, K, the acid dissociation constant (where K = [HgO]). Also, the term [HjO ] is often replaced by H, such that... 

In the dilute aqueous solution normally used for measuring acidity, the concentration of water, H20], remains nearly constant at approximately 55.4 M at 25 °C. We can therefore rewrite the equilibrium expression using a new quantity called the acidity constant, Ka. The acidity constant for any acid HA is simply the equilibrium constant for the acid dissociation multiplied by the molar concentration of pure water. 

Solid Bi2S3 does not appear in the expression for K,p, because it is a pure solid and its activity is 1 (Section 9.2). A solubility product is used in the same way as any other equilibrium constant. However, because ion-ion interactions in even dilute electrolyte solutions can complicate its interpretation, a solubility product is generally meaningful only for sparingly soluble salts. Another complication that arises when dealing with nearly insoluble compounds is that dissociation of the ions is rarely complete, and a saturated solution of Pbl2, for instance, contains substantial... 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

As thermodynamic stability indexes for the hydrocarbon ions, pA R+ and pA a values [(4) and (5)] have been widely applied for the carbocation and carbanion, respectively, in solution. Here K + stands for the equilibrium constant for the reaction (6) of a carbocation and a water molecule stands for the equilibrium constant for the reaction (7) of a hydrocarbon with a water molecule to give the conjugate carbanion. The equilibrium constants are given by (8) and (9) for dilute aqueous solutions. Obviously, the reference system for the pKn+ scale is the corresponding alcohol, and... 

All in aqueous solution at 25°C standard states are 1 M ideal solution with an infinitely dilute reference state, and the pure liquid for water equilibrium constants from reference 100, except as noted. 

Since H20 is in large excess as the solution is dilute, its concentration is taken as constant. It is amalgamated with the equilibrium constant K to give a new constant fCh, called the hydrolysis constant, which is given by... 

The equilibrium constant of this reaction in a dilute solution is... 

However, in dilute aqueous solution, the concentration of H20 is practically constant, and its concentration is conventionally built into the value of the equilibrium constant. The new constant, variously called Ku or K, for acids (Kh or Kt for bases), docs not have the water concentration term in the denominator ... 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

The activities a, of dilute solutions are simply the concentrations of the solutes and the equilibrium constant can be used to determine the pH of a solution when a known amount of acid is dissolved in water. The proton concentration and hence pH is given by the solution of the general quadratic ... 

Upon addition of a solution of sulfuric acid in D20 the reaction of A-acetoxy-A-alkoxyamides obeys pseudo-unimolecular kinetics consistent with a rapid reversible protonation of the substrate followed by a slow decomposition to acetic acid and products according to Scheme 5. Here k is the unimolecular or pseudo unimolecular rate constant and K the pre-equilibrium constant for protonation of 25c. Since under these conditions water (D20) was in a relatively small excess compared with dilute aqueous solutions, the rate expression could be represented by the following equation ... 

Equation (4.1) expresses that the ratio of the concentrations of A in the gas phase and the water phase, respectively, is a constant at equilibrium. This constant is temperature dependent but is independent of the quantity of A as long as dilute solutions are dealt with. 

Mercury-chloride complexes in dilute solutions. This slightly more difficult example will be useful in showing how to handle poorly conditioned systems of equations. It is assumed that mercury chloride HgCl2 is dissolved in pure water with a molality m = 10 5 mol kg-1. Given the equilibrium constants for chloride complex formation... 

K is equilibrium constant. If we consider the reference standard state to be gaseous, K = K because the activity and fugacity coefficients are unity in very dilute solution and ideal gas, respectively. Then ( g)0 and (ks)o will be the same. 

However, the equilibrium constant must still be considered as pure and dimensionless numbers (according to the classical relation —AG° = RT In Ks). All molar concentrations in the expression of Ks should thus be interpreted as molar concentrations relative to a standard state of 1 mol dm-3 i.e. they are the numerical values of the molar concentrations5 . If the solution is not dilute enough, the equilibrium constants can still be written with concentrations but they must be considered as apparent stability constants. 

The techniques used in the critical evaluation and correlation of thermodynamic properties of aqueous polyvalent electrolytes are described. The Electrolyte Data Center is engaged in the correlation of activity and osmotic coefficients, enthalpies of dilution and solution, heat capacities, and ionic equilibrium constants for aqueous salt solutions. 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

In dilute solutions, the concentration of water is almost constant. Multiplying both sides of the equilibrium expression by [H2O] gives the product of two constants on the left side. This new constant is called the acid dissociation constant, K. (Some chemists refer to the acid dissociation constant as the acid ionization constant. With either name, the symbol is Xg.)... 

In Equation 1.15, q represents the adsorbed amount of solute, ns and qs are the saturation capacities (number of accessible binding sites) for site 1 (nonstereoselect-ive, subscript ns) and site 2 (stereoselective, subscript s), and fens and bs are the equilibrium constants for adsorption at the respective sites [54]. It is obvious that only the second term in this equation is supposed to be different for two enantiomers. Expressed in terms of linear chromatography conditions (under infinite dilution where the retention factor is independent of the loaded amount of solute) it follows that the retention factor k is composed of at least two distinct major binding increments corresponding to nonstereoselective and stereoselective sites according to the following... 

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