Equilibrium processes

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

When hydrogen is burned up in the nuclear furnace of a star, helium burning takes over, forming carbon, which in turn leads to oxygen, etc. Subsequent emission processes releasing a-particles, equilibrium processes, neutron absorption, proton capture, etc. lead to heavier elements. 

In any equilibrium process the sequence of intermediates and transition states encountered as reactants proceed to products m one direction must also be encountered and m precisely the reverse order m the opposite direction This is called the principle of microscopic reversibility Just as the reaction... 

Alcohols and carboxylic acids yield an ester and water in the presence of an acid catalyst The reaction is an equilibrium process that can be driven to com pletion by using either the alcohol or the acid in excess or by remov mg the water as it is formed... 

Esterification (Section 15 8) In the pres ence of an acid catalyst carboxylic acids and alcohols react to form esters The reac tion IS an equilibrium process but can be driven to favor the ester by removing the water that is formed... 

The Kolbe-Schmitt reaction is an equilibrium process governed by thermodynamic control The position of equilibrium favors formation of the weaker base (salicylate ion) at the expense of the stronger one (phenoxide ion) Thermodynamic control is also responsible for the pronounced bias toward ortho over para substitution Salicylate anion IS a weaker base than p hydroxybenzoate and predominates at equilibrium... 

Isopentenyl pyrophosphate undergoes an enzyme catalyzed reaction that converts It m an equilibrium process to 3 methyl 2 butenyl pyrophosphate (dimethylallyl pyrophosphate)... 

Process Description Reverse osmosis (RO) and nanofiltration (NF) processes utilize a membrane that selectively restricts flow of solutes while permitting flow of the solvent. The processes are closely related, and NF is sometimes called loose RO. They are kinetic processes, not equilibrium processes. The solvent is almost always water. 

An important characteristic of pervaporation that distinguishes it from distillation is that it is a rate process, not an equilibrium process. The more permeable component may be the less-volatile component. Perv oration has its greatest iitihty in the resolution of azeotropes, as an acqiinct to distillation. Selecting a membrane permeable to the minor corTiponent is important, since the membrane area required is roughly proportional to the mass of permeate. Thus pervaporation devices for the purification of the ethanol-water azeotrope (95 percent ethanol) are always based on a hydrophihc membrane. 

D.C. Wallace, Computer Simulation of Non-Equilibrium Processes, in Shock Waves in Condensed Matter (edited by Y.M. Gupta), Plenum, New York, 1986, pp. 37-49. 

A water molecule has amphoteric character. This means it can act as both an acid and a base. The autoionization equilibrium process in water. 

Suryanarayana, C. (ed.) (1999) Non-equilibrium Processing of Materials (Pergamon, Oxford). 

Vol. 1 CALPHAD by N. Saunders and A. P. Miodownik Vol. 2 Non-Equilibrium Processing of Materials edited by C. Suryanarayana Vol. 3 Wettability at High Temperatures by N. Eustathopoulos, M. G. Nicholas and B. Drevet... 

The same structural factors come into play in determining the position of equilibria in reversible additions to carbonyl compoimds. The best studied of such equilibrium processes is probably addition of cyanide to give cyanohydrins. 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

To use Eq. (8-57) we require an experimental measure of the transfer free energy for the reactant then Eq. (8-57) permits the transfer free energy for the transition state to be calculated. First, consider this equilibrium process ... 

The synthetic utility of the alkene metathesis reaction may in some cases be limited because of the formation of a mixture of products. The steps of the catalytic cycle are equilibrium processes, with the yields being determined by the thermodynamic equilibrium. The metathesis process generally tends to give complex mixtures of products. For example, pent-2-ene 8 disproportionates to give, at equilibrium, a statistical mixture of but-2-enes, pent-2-enes and hex-3-enes ... 

X(A1C13) = 0.5) to immobilize a ruthenium carbene complex for biphasic ADMET polymerization of an acyclic diene ester (Figure 7.4-2). The reaction is an equilibrium processes, and so removal of ethylene drives the equilibrium towards the products. The reaction proceeds readily at ambient temperatures, producing mostly polymeric materials but also 10 % dimeric material. 

Because the dissociation of a carboxylic acid is an equilibrium process, any factor that stabilizes the carboxylate anion relative to undissociated carboxylic acid will drive the equilibrium toward increased dissociation and result in increased acidity. An electron-withdrawing chlorine atom, for instance, makes chloroacetic acid (Ka = 1.4 x 10-3) approximately 80 times as strong as acetic acid introduction of two chlorines makes dichloroacetic acid 3000 times as strong as acetic acid, and introduction of three chlorines makes trichloroacetic acid more than 12,000 times as strong. 

Although compound 14 may be preferred at equilibrium, C-l in isomer 18 is particularly susceptible to nucleophilic attack because it is much less hindered than either C-2 or C-3 in 14. Once 18 is produced, it reacts selectively with hydroxide ion to give triol 19. The irreversible conversion of 18 to triol 19 drives the equilibrium process forward. 

Ketal 73 can be formed in a yield of about 60 % by refluxing a solution of tetronic acid (36), ethylene glycol, and a catalytic amount of para-toluenesulfonic acid in benzene for approximately 12 hours. With only one electrophilic site, 73 reacts smoothly with Dibal-H to give lactol 35 in 84% yield. Compound 35, a participant in a ring-chain tautomeric equilibrium process,18 should be regarded as a latent aldehyde. This substance can, in fact, serve as... 

The most straightforward preparation of A-(l-hydroxyalkyl)amides (or carbamates) involves addition of primary or secondary amides (carbamates) to aldehydes or ketones. This is an equilibrium process in which formation of the adduct is usually disfavored, except for two special cases ... 

Equation (5.47) gives the criterion for reversibility or spontaneity within subsystem A of an isolated system. The inequality applies to the spontaneous process, while the equality holds for the reversible process. Only when equilibrium is present can a change in an isolated system be conceived to occur reversibly. Therefore, the criterion for reversibility is a criterion for equilibrium, and equation (5.47) applies to the spontaneous or the equilibrium process, depending upon whether the inequality or equality is used. 

Equation (5.52) is the first of our criteria. The subscripts indicate that equation (5.52) applies to the condition of constant entropy, volume, and total moles, with the equality applying to the equilibrium process and the inequality to the spontaneous process. 

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