Equilibrium for dissociation

Other workers have added THF or H2O to the carrier gas stream in efforts to affect the requisite vapor pressure increase in Ba(/3-diketonate)2 compounds. " The objective of all these experiments was to coordinatively saturate the barium atom in the vapor phase by incorporation of the lone pair electrons on the oxygen atoms of the neutral ligands into the bonding sphere of the metal. At the temperatures demanded for vapor transport, the equilibrium for dissociation of these ligands is rather unfavorable therefore, any anticipated gain will be minimal. 

Phosphines and related P(III) compounds typically serve as ancillary ligands, but the dissociation of these ligands is crucial to the reactivity described in later chapters. Tolman correlated the ligand cone angle with the equilibrium for dissociation from NiL compounds.The extent of ligand dissociation in these nickel complexes and in related palladium complexes increases in the order PMej < PMe Ph < PMePlq < PEtj < PPhj < PPr j < PCyj < PPhBu, . 

Also, from the reaction equilibrium for dissociation of H2O (2H2O H3O+ -f OH-), one can write... 

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

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. 

In a recent paper [11] this approach has been generalized to deal with reactions at surfaces, notably dissociation of molecules. A lattice gas model is employed for homonuclear molecules with both atoms and molecules present on the surface, also accounting for lateral interactions between all species. In a series of model calculations equilibrium properties, such as heats of adsorption, are discussed, and the role of dissociation disequilibrium on the time evolution of an adsorbate during temperature-programmed desorption is examined. This approach is adaptable to more complicated systems, provided the individual species remain in local equilibrium, allowing of course for dissociation and reaction disequilibria. 

In the above scheme, F-ADP-P represents the transition state energetically identical to the F-ADP BeFj state. The transition from F-ADP-P to F-ADP-Pj would be slow and rate limiting for P release. In this scheme, which resembles the one proposed for ATP hydrolysis on myosin (e.g., Hibberd and Trentham, 1986), Pj binds to F-ADP in rapid equilibrium, while dissociation of Pi following cleavage of ATP is slow. 

We will list the elementary steps and decide which is rate-limiting and which are in quasi-equilibrium. For ammonia synthesis a consensus exists that the dissociation of N2 is the rate-limiting step, and we shall make this assumption here. With quasi-equilibrium steps the differential equation, together with equilibrium condition, leads to an expression for the coverage of species involved in terms of the partial pressures of reactants, equilibrium constants and the coverage of other intermediates. 

For dissociation at 226 and 230 nm, the determined j3 values for the fast and slow oxygen atoms are 1.3/1.5 and 0.7/0.8, respectively. The former value corresponds to a bond angle of 120°, close to the ozone ground state equilibrium bond angle of 117°. The reduced anisotropy parameter of 0.8 implies a more strongly bent geometry with a bond angle of 100°. 

Scheme 7 P-Cl Dissociation equilibrium for P-chloro-NHPs. (Data from [20])...

In contrast to the reactions of the cycloamyloses with esters of carboxylic acids and organophosphorus compounds, the rate of an organic reaction may, in some cases, be modified simply by inclusion of the reactant within the cycloamylose cavity. Noncovalent catalysis may be attributed to either (1) a microsolvent effect derived from the relatively apolar properties of the microscopic cycloamylose cavity or (2) a conformational effect derived from the geometrical requirements of the inclusion process. Kinetically, noncovalent catalysis may be characterized in the same way as covalent catalysis that is, /c2 once again represents the rate of all productive processes that occur within the inclusion complex, and Kd represents the equilibrium constant for dissociation of the complex. 

Such internal thermodynamic equilibria where A is a protein are found for non-metal components, including free coenzymes and substrates where B is a small molecule, or where free M is an ion of either a non-metal, e.g. Cl" or HCOj, or a metal, e.g. K+ or Mg2+, or is H+, and they are involved in, even necessary for, catalysis, pumping and cooperative controls of many metabolic paths. All such combinations reach equilibrium, as long as exchange is fast, where a fast rate can be taken as, say, 10-3 s for dissociation in cells. Note that equilibria with defined binding constants for AB or AM formation in any system reduce the number of variables and hence AB and AM concentrations are defined by those of free A, B and M, leaving two independent variables for each equilibrium. In some cases, the... 

The equilibrium constant of hexaphenylethane dissociation, in striking contrast to the rate constant for dissociation, varies considerably with solvent. The radical with its unpaired electron and nearly planar structure probably complexes with solvents to a considerable extent while the ethane does not. Since the transition state is like the ethane and its solvation is hindered, the dissociation rate constants change very little with solvent.12 13 From an empirical relationship that happens to exist in this case between the rate and equilibrium constants in a series of solvents, it has been calculated that the transition state resembles the ethane at least four times as much as it resembles the radical. These are the proportions that must be used if the free energy of the transition state in a given solvent is to be expressed as a linear combination of the free energies of the ethane and radical states.14... 

Complex cyanides are compounds in which the cyanide anion is incorporated into a complex or complexes. These compounds are different in chemical and toxicologic properties from simple cyanides. In solution, the stability of the cyanide complex varies with the type of cation and the complex that it forms. Some of these are dissociable in weak acids to give free cyanide and a cation, while other complexes require much stronger acidic conditions for dissociation. The least-stable complex metallocyanides include Zn(CN)42 , Cd(CN)3 , and Cd(CN)42 moderately stable complexes include Cu(CN)2, Cu(CN)32, Ni(CN)42, and Ag(CN)2 and the most stable complexes include Fe(CN)64, and Co(CN)6. The toxicity of complex cyanides is usually related to their ability to release cyanide ions in solution, which then enter into an equilibrium with HCN relatively small fluctuations in pH significantly affect their biocidal properties. 

The dependence of rate constants for approach to equilibrium for reaction of the mixed oxide-sulfide complex [Mo3((i3-S)((i-0)3(H20)9] 1+ with thiocyanate has been analyzed into formation and aquation contributions. These reactions involve positions trans to p-oxo groups, mechanisms are dissociative (391). Kinetic and thermodynamic studies on reaction of [Mo3MS4(H20)io]4+ (M = Ni, Pd) with CO have yielded rate constants for reaction with CO. These were put into context with substitution by halide and thiocyanate for the nickel-containing cluster (392). A review of the chemistry of [Mo3S4(H20)9]4+ and related clusters contains some information on substitution in mixed metal derivatives [Mo3MS4(H20)re]4+ (M = Cr, Fe, Ni, Cu, Pd) (393). There are a few asides of mechanistic relevance in a review of synthetic Mo-Fe-S clusters and their relevance to nitrogenase (394). 

The paired cation Pn+A The relative concentrations of the paired and unpaired cations are governed by an Ostwald-type equilibrium with dissociation constant KD. The magnitude of this is governed by the size and shape of the ions and the dielectric constant of the solvent. In contrast to anionic polymerisations, there is no definite evidence for distinguishing between tight and solvent-separated ion-pairs. 

The equilibrium for a weak acid is described by K, the acid dissociation constant. 

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