Concentrations, equilibrium constant for

Specifically the concentration equilibrium constant for the hydration is about 180 in water-dioxane mixtures at 25°. The main reaction for the interconversion, starting from the enol, is therefore ... 

According to equation (1.100), concentration equilibrium constant is equal to the thermodynamical divided by the product of activities coefficients (y., p., ). Therefore, concentration equilibrium constants for... 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

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... 

Since the equilibrium constant for this reaction is large, we may treat the reaction as if it went to completion. The new concentrations of NH4+ and NH3 are therefore... 

The equilibrium constant for reaction 9.1 is Ky,y, or 1.00 X 10. Since this is such a large value we can treat reaction 9.1 as though it goes to completion. After adding 10.0 mb of NaOH, therefore, the concentration of excess HCl is... 

The equilibrium constant for reaction 9.2 is large K = KJK = 1.75 X 10 ), so we can treat the reaction as one that goes to completion. Before the equivalence point, the concentration of unreacted acetic acid is... 

This method provides a reasonable estimate of the piQ, provided that the weak acid is neither too strong nor too weak. These limitations are easily appreciated by considering two limiting cases. For the first case let s assume that the acid is strong enough that it is more than 50% dissociated before the titration begins. As a result the concentration of HA before the equivalence point is always less than the concentration of A , and there is no point along the titration curve where [HA] = [A ]. At the other extreme, if the acid is too weak, the equilibrium constant for the titration reaction... 

At the equivalence point, the moles of Fe + initially present and the moles of Ce + added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe and Ce + are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, E q, using just the Nernst equation for the analyte s half-reaction or the titrant s half-reaction. We can, however, calculate... 

Aqueous solutions buffered to a pH of 5.2 and containing known total concentrations of Zn + are prepared. A solution containing ammonium pyrrolidinecarbodithioate (APCD) is added along with methyl isobutyl ketone (MIBK). The mixture is shaken briefly and then placed on a rotary shaker table for 30 min. At the end of the extraction period the aqueous and organic phases are separated and the concentration of zinc in the aqueous layer determined by atomic absorption. The concentration of zinc in the organic phase is determined by difference and the equilibrium constant for the extraction calculated. 

The equilibrium constant for an acid-base indicator is determined by preparing three solutions, each of which has a total indicator concentration of 1.35 X lQ-5 M. The pH of the first solution is adjusted until it is acidic enough to ensure that only the acid form of the indicator is present, yielding an absorbance of 0.673. The absorbance of the second solution, whose pH was adjusted to give only the base form of the indicator, was measured at 0.118. The pH of the third solution was adjusted to 4.17 and had an absorbance of 0.439. What is the acidity constant for the acid-base indicator ... 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

The general formula for the initiator species can be written H B, where the degree of separation or ion pairing depends on the polarity of the medium and the possibility of specific solvation interactions. If we represent the equilibrium constant for the reactions in (6.DD) and (6.EE) by K, the initiator concentration can be written as... 

The acidity of a lydrocarbon can be determined in an analogous way. If the electronic spectra of the neutral and anionic forms are sufficiently different, the concentrations of each can be determined directly, and the equilibrium constant for... 

For cases when the concentration of water remains almost constant with respect to the other species, one can define the following reaction equilibrium constants for Eqs. (8.15) and (8.16), respectively ... 

Evidently the perturbation is small enough if r <<< 1, so the extent of the acceptable perturbation is governed by the concentrations and the equilibrium constant. For Scheme I it is seen that r = 0, so the perturbation in this case is not limited to small values. Brouillard and co-workers have analyzed many systems from this point of view. 

The overall direction of the reaction will be determined by the relative concentrations of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction. The enzyme can be considered to have two sites for substrate (or product) binding an adenine nucleotide site, where ATP or ADP binds, and a creatine site, where Cr or CrP is bound. In such a mechanism, ATP and ADP compete for binding at their unique site, while Cr and CrP compete at the specific Cr-, CrP-binding site. Note that no modified enzyme form (E ), such as an E-PO4 intermediate, appears here. The reaction is characterized by rapid and reversible binary ES complex formation, followed by addition of the remaining substrate, and the rate-determining reaction taking place within the ternary complex. 

It should be noted that whereas a completely soluble hydroxide (e.g. NaOH) will give a solution of high pH in which the pH will increase with concentration of the hydroxide, the pH of a solution of a sparingly soluble hydroxide will depend upon the equilibrium constant for hydrolysis and the activity of metal ions. 

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. 

The general approach illustrated by Example 18.7 is widely used to determine equilibrium constants for solution reactions. The pH meter in particular can be used to determine acid or base equilibrium constants by measuring the pH of solutions containing known concentrations of weak acids or bases. Specific ion electrodes are readily adapted to the determination of solubility product constants. For example, a chloride ion electrode can be used to find [Cl-] in equilibrium with AgCl(s) and a known [Ag+]. From that information, Ksp of AgCl can be calculated. 

Write an equationforthe reaction of chloroacetic acid (Ka = 1.5 X 103) with trimethylamine (Kj, = 5.9 X 10 5). Calculate die equilibrium constant for die reaction. If 0.10 M solutions of these two species are mixed, what will be their concentrations at equilibrium ... 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

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