Equilibrium constant, dissociation

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

The strength of a weak acid is measured by its acid dissociation constant, which IS the equilibrium constant for its ionization m aqueous solution... 

The acid dissociation constant has the same form m Brpnsted-Lowry as m the Arrhenius approach but is expressed m the concentration of H30" rather than The concentration terms [H30" ] and [H" ] are considered equivalent quantities m equilibrium constant expressions... 

Equilibrium constants for the dissociation of cyanohydnns according to the equation... 

All these facts—the observation of second order kinetics nucleophilic attack at the carbonyl group and the involvement of a tetrahedral intermediate—are accommodated by the reaction mechanism shown m Figure 20 5 Like the acid catalyzed mechanism it has two distinct stages namely formation of the tetrahedral intermediate and its subsequent dissociation All the steps are reversible except the last one The equilibrium constant for proton abstraction from the carboxylic acid by hydroxide is so large that step 4 is for all intents and purposes irreversible and this makes the overall reaction irreversible... 

Acid dissociation constant (Section 1 12) Equilibrium constant for dissociation of an acid... 

The equilibrium constant for a reaction in which a solid dissociates into its ions... 

The equilibrium constant for this reaction is called an acid dissociation constant, K-, and is written as... 

A species that can serve as both a proton donor and a proton acceptor is called amphiprotic. Whether an amphiprotic species behaves as an acid or as a base depends on the equilibrium constants for the two competing reactions. For bicarbonate, the acid dissociation constant for reaction 6.8... 

The equilibrium position for any reaction is defined by a fixed equilibrium constant, not by a fixed combination of concentrations for the reactants and products. This is easily appreciated by examining the equilibrium constant expression for the dissociation of acetic acid. 

Substituting equations 6.39 and 6.40 into the equilibrium constant expression for the dissociation of HE (equation 6.35) and solving for the concentration of H3O4 gives us... 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

Equilibrium Constants Another application of acid-base titrimetry is the determination of equilibrium constants. Consider, for example, the titration of a weak acid, HA, with a strong base. The dissociation constant for the weak 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... 

Ionic polymers may exist as undissociated, unsolvated ion pairs undissociated ion pairs solvated to some extent solvated ions dissociated to some extent or some combination of these. The propagation rate constant kp and the dissociation equilibrium constant K of the lithium salt of anionic... 

The basic thermodynamic data for the design of such reactions can be used to assess the dissociation energies for various degrees of dissociation, and to calculate, approximately, tire relevant equilibrium constants. One important source of dissociation is by heating molecules to elevated temperamres. The data below show the general trend in the thermal dissociation energies of a number of important gaseous molecules. 

In these examples tire entropy change does not vaty widely, and the value of the equilibrium constant is mainly determined by the heat of dissociation. It can be concluded, tlrerefore, that niuogen is one of the most stable diatomic molecules, and tlrat chlorine is tire most stable diatomic halogen molecule. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

In the case of hydrogen, for example, at a teiuperamre of 2500 K, the equilibrium constant for dissociation has the value, calculated from the tlrermo-dynamic relation between the Gibbs energy of formation and the equilibrium constant of 6.356 x 10 " and hence at a total pressure of 10 atmos, the degree of dissociation is 0.126 at 2500 K, which drops to 8.32 x 10 at 2000 K. 

When substances ionise their neutral species produce positive and negative species. The ionisation constants are those constant values (equilibrium constants) for the equilibria between the charged species and the neutral species, or species with a larger number of charges (e.g. between mono and dications), l ese ionisation constants are given as pK values where pK = -log K and K is the dissociation constant for the equilibrium between the species [Albert and Serjeant The Determination of Ionisation Constants, A Laboratory Manual, 3rd Edition, Chapman Hall, New York, London, 1984, ISBN 0412242907]. 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

When a Br nsted plot includes acids or bases with different numbers of acidic or basic sites, statistical corrections are sometimes applied in effect, the rate and equilibrium constants are corrected to a per functional group basis. If an acid has p equivalent dissociable protons and its conjugate base has q equivalent sites for proton addition, the statistically corrected forms of the Br insted relationships are... 

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... 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

An expression for the ionization of H2CO3 under such conditions (that is, in the presence of dissolved CO2) can be obtained from Kh, the equilibrium constant for the hydration of CO2, and from the first acid dissociation constant for H2CO3 ... 

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