Equilibrium and activity

Much of the work of analytical chemists involves reactions that take place at appreciable concentrations yet the equilibrium constants of fundamental importance are the thermodynamic values obtained by extrapolation to infinite dilution or to zero ionic strength. The purpose in this chapter is to examine some of the basic thermodynamic concepts that apply to solutions estimate the magnitude of the errors introduced by neglecting effects of ionic strength in aqueous solutions consider the extent to which these errors can be minimized by suitable corrections and examine the behavior of nonelectrolytes in solution. 

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The situation inside an electrolyte—the ionic aspect of electrochemistry—has been considered in the first volume of this text. The basic phenomena involve— ion—solvent interactions (Chapter 2), ion—ion interactions (Chapter 3), and the random walk of ions, which becomes a drift in a preferred direction under the influence of a concentration or a potential gradient (Chapter 4). In what way is the situation at the electrode/electrolyte interface any different from that in the bulk of the electrolyte To answer this question, one must treat quiescent (equilibrium) and active (nonequilibrium) interfaces, the structural and electrical characteristics of the interface, the rates and mechanism of changeover from ionic to electronic conduction, etc. In short, one is led into electrodics, the newest and most exciting part of electrochemistry. 

The composition of ICF can differ markedly from that of the ECF because of the separation of these compartments by the ceU membrane. The composition differences are a consequence of both the Gibbs-Donnan equilibrium and active and passive transport of ions. 

The jump-relaxation technique has also been used to study the influence of temperature on the position and on the dynamics of the tautomeric equilibrium of 6-methoxy-2(liY)-pyridone in neutral water, which was shown to be an essentially a pH-independent process. The equilibrium and activation parameters obtained indicate that the interconversion mechanism is ionic rather than concerted and involves the anionic form of the substrate in a cyclic transition state, in which at least two solvent molecules would temporarily ensure a hydrogen bond connection between the sites which undergo tautomerism (83JCS(P2)979). 

Table 5 Equilibrium and activation parameters for some A, 7V -thiobarbiturates. ...

Adamic, Howard and Ingold (2 ) have used the thermodynamic parameters for the t-Bu02 -t-BuOitBu-t equilibrium and activation parameters for irreversible radical decay to calculate activation parameters for irreversible tetroxide decomposition. Decay... 

The current frontiers for the subject of non-equilibrium thennodynamics are rich and active. Two areas dommate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Carefiil experiments [39] confinn this theory. Non-equilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. 

In addition to [A ] being qiiasi-stationary the quasi-equilibrium, approximation assumes a virtually unperturbed equilibrium between activation and deactivation (equation (A3.4.125)) ... 

The conversion of the diazoaminobenzene into aminoazobenzene is promoted by the addition of aniline hydrochloride even more readily than by that of free hydrochloric acid. The aniline hydrochloride dissociates in solution giving hydrochloric acid and aniline the former promotes the formation of the above equilibrium, and the latter by increasing the active mass of the free aniline further accelerates the condensation to aminoazobenzene,... 

Adsorption is invariably an exothermic process, so that, provided equilibrium has been established, the amount adsorbed at a given relative pressure must diminish as the temperature increases. It not infrequently happens, however, that the isotherm at a given temperature Tj actually lies above the isotherm for a lower temperature Ti. Anomalous behaviour of this kind is characteristic of a system which is not in equilibrium, and represents the combined effects of temperature on the rate of approach to equilibrium and on the position of equilibrium itself. It points to a process which is activated in the reaction-kinetic sense and which therefore occurs more rapidly as temperature is increased. 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

In a series of organic acids of similar type, not much tendency exists for one acid to be more reactive than another. For example, in the replacement of stearic acid in methyl stearate by acetic acid, the equilibrium constant is 1.0. However, acidolysis in formic acid is usually much faster than in acetic acid, due to higher acidity and better ionizing properties of the former (115). Branched-chain acids, and some aromatic acids, especially stericaHy hindered acids such as ortho-substituted benzoic acids, would be expected to be less active in replacing other acids. Mixtures of esters are obtained when acidolysis is carried out without forcing the replacement to completion by removing one of the products. The acidolysis equilibrium and mechanism are discussed in detail in Reference 115. 

The physical data index summarizes the quantitative data given for specific compounds in the text, tables and figures in Volumes 1-7. It does not give any actual data but includes references both to the appropriate text page and to the original literature. The structural and spectroscopic methods covered include UV, IR, Raman, microwave, MS, PES, NMR, ORD, CD, X-ray, neutron and electron diffraction, together with such quantities as dipole moment, pX a, rate constant and activation energy, and equilibrium constant. 

The basic kinetic properties of this allosteric enzyme are clearly explained by combining Monod s theory and these structural results. The tetrameric enzyme exists in equilibrium between a catalytically active R state and an inactive T state. There is a difference in the tertiary structure of the subunits in these two states, which is closely linked to a difference in the quaternary structure of the molecule. The substrate F6P binds preferentially to the R state, thereby shifting the equilibrium to that state. Since the mechanism is concerted, binding of one F6P to the first subunit provides an additional three subunits in the R state, hence the cooperativity of F6P binding and catalysis. ATP binds to both states, so there is no shift in the equilibrium and hence there is no cooperativity of ATP binding. The inhibitor PEP preferentially binds to the effector binding site of molecules in the T state and as a result the equilibrium is shifted to the inactive state. By contrast the activator ADP preferentially binds to the effector site of molecules in the R state and as a result shifts the equilibrium to the R state with its four available, catalytically competent, active sites per molecule. 

Equilibrium constants and activation parameters have been determined [76ACS(B)101] [for a review see 82AHC(30)127]. Ionization potentials for tautomeric 2-hydroxyselenophenes have been analyzed by comparison with IP data for compounds derived from either tautomeric form. The enol form could not be detected [75ACS(B)647]. 

A low-pressure process has been developed by ICl operating at about 50 atm (700 psi) using a new active copper-based catalyst at 240°C. The synthesis reaction occurs over a bed of heterogeneous catalyst arranged in either sequential adiabatic beds or placed within heat transfer tubes. The reaction is limited by equilibrium, and methanol concentration at the converter s exit rarely exceeds 7%. The converter effluent is cooled to 40°C to condense product methanol, and the unreacted gases are recycled. Crude methanol from the separator contains water and low levels of by-products, which are removed using a two-column distillation system. Figure 5-5 shows the ICl methanol synthesis process. 

Pourbaix has evaluated all possible equilibria between a metal M and HjO (see Table 1.7) and has consolidated the data into a single potential-pH diagram, which provides a pictorial summary of the anions and cations (nature and activity) and solid oxides (hydroxides, hydrated oxides and oxides) that are at equilibrium at any given pH and potential a similar approach has been adopted for certain M-H2O-X systems where A" is a non-metal, e.g. Cr, CN , CO, SOj , POj", etc. at a defined concentration. These diagrams give the activities of the metal cations and anions at any specified E and pH, and in order to define corrosion in terms of an equilibrium activity, Pourbaix has selected the arbitrary value of 10 ° g ion/1, i.e. corrosion of a metal is defined in terms of the pH and potential that give an equilibrium activity of metal cations or anions > 10 g ion/1 conversely, passivity and immunity are defined in terms of an equilibrium activity of < 10 g ion/1. (Note that g ion/1 is used here because this is the unit used by Pourbaix in the S.I, the relative activity is dimensionless.)... 

It should be noted that Fig. 1.15 (top) is based entirely on thermodynamic data and is therefore correctly described as an equilibrium diagram, since it shows the phases (nature and activity) that exist at equilibrium. However, the concepts implicit in the terms corrosion, immunity and passivity lie outside the realm of thermodynamics, and, for example, passivity involves both thermodynamic and kinetic concepts it follows that Fig. 1.15 (bottom) cannot be regarded as a true equilibrium diagram, although it is based on one that has been constructed entirely from thermodynamic data. 

Previous Considerations have been confined to the effect of pressure and concentration upon coverage, but in an electrochemical equilibrium the activity and chemical potentials of the species adsorbing at the interface will also be a function of the potential difference A4>. For a solution containing unit activity of the species the effective pressure of the species at the interface is given by... 

Electrodes such as Cu VCu which are reversible with respect to the ions of the metal phase, are referred to as electrodes of the first kind, whereas electrodes such as Ag/AgCl, Cl" that are based on a sparingly soluble salt in equilibrium with its saturated solution are referred to as electrodes of the second kind. All reference electrodes must have reproducible potentials that are defined by the activity of the species involved in the equilibrium and the potential must remain constant during, and subsequent to, the passage of small quantities of charge during the measurement of another potential. 

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