Chemical/physical equilibrium

Another important area of analytical chemistry, which receives some attention in this text, is the development of new methods for characterizing physical and chemical properties. Determinations of chemical structure, equilibrium constants, particle size, and surface structure are examples of a characterization analysis. 

By the components of the system we are to understand the least number of independently variable constituents, in terms of which the composition of every phase in the system can be completely specified. The number of components will therefore contribute to the total number of independent variables defining the state of chemical and physical equilibrium of the system. It is not necessary that the components shall be actual constituents of the system all that is required is that they shall be independently variable, Le.y the least number has been chosen. Thus, in systems composed of solid fuming sulphuric acid in presence... 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

Gorin, MA, An Equilibrium Theory of Ionic Conductance, Journal of Chemical Physics 7, 405, 1939. 

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sample temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/aT is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 K after cross-linking is feQ. (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.)...

Boynton, F. P., 1960, Chemical equilibrium in multicomponent polyphase systems. Journal of Chemical Physics 32, 1880-1881. 

Brinkley, S. R., Jr., 1947, Calculation of the equilibrium composition of systems of many components. Journal of Chemical Physics 15, 107-110. 

White, W. B., 1967, Numerical determination of chemical equilibrium and the partitioning of free energy. Journal of Chemical Physics 46,4171-4175. 

RONALD W. MISSEN is Professor Emeritus (Chemical Engineering) at the University of Toronto. He received his B.Sc, and M.Sc. in chemical engineering from Queen s University, Kingston, Ontario, and his Ph.D. in physical chemistry from the University of Cambridge, England. He is the co-author of CHEMICAL REACTION EQUILIBRIUM ANALYSIS, and has authored or co-authored about f 50 research articles. He is a fellow of the Chemical Institute of Canada and the... 

Physical equilibrium. When two phases are in equilibrium, the chemical potentials / -. for each component i must be equal in each phase. The K-factorsT. = y-j/x- can be obtained from this condition, using the relationship ... 

King, E. J. "Acid-Base Equilibria in "The International Encyclopedia of Physical Chemistry and Chemical Physics Topic 15, Equilibrium Properties of Electrolyte Solutions" Vol. 4, Robinson, R. A., Ed., Pergamon Press, 1965 (distributed by The MacMillan Co., New York). ... 

In this case a vapour-liquid system, where high concentrations occur and ail components are volatile, will be considered. The liquid and vapour bulk are not in physical equilibrium. In the liquid phase the following reversible chemical reaction occurs ... 

The liquid bulk is assumed to be at chemical equilibrium. Contrary to gas-liquid systems, for vapour-liquid systems it is not possible to derive explicit analytical expressions for the mass fluxes which is due to the fact that two or more physical equilibrium constants m, have to be dealt with. This will lead to coupling of all the mass fluxes at the vapour - liquid interface since eqs (15c) and (19) have to be satisfied. For the system described above several simulations have been performed in which the chemical equilibrium constant K = koiAo2 and the reaction rate constant koi have been varied. Parameter values used in the simulations are given in Table 5. The results are presented in Figs 9 and 10. 

FIA is a fixed-time analytical methodology, since neither physical equilibrium (homogenization of a portion of the flow) nor chemical equilibrium (reaction completeness) has been attained by the time the signal is detected. The operational timing must be highly reproducible, because the measurements are made under non-steady-state conditions, so that small changes may give rise to serious errors in the results obtained. 

The arguments treated in the two preceding sections were developed in terms of simple equilibrium thermodynamics. The weathering of rocks at the earth s surface by the chemical action of aqueous solutions, and the complex water-rock interaction phenomena taking place in the upper crust, are irreversible processes that must be investigated from a kinetic viewpoint. As already outlined in section 2.12, the kinetic and equilibrium approaches are mutually compatible, both being based on firm chemical-physical principles, and have a common boundary represented by the steady state condition (cf eq. 2.111). 

Any observable effect of isotopic substitution on the rate or extent of a chemical/physical process. Equilibrium isotopic perturbation measurements can provide valuable information about kinetic isotope effects on enzymic catalysis. NMR shift difference measurements are also useful in detecting the effects of isotopic substitution on a fast (degenerate) equilibrium between two species differing only in their specific isotopic substitution . The... 

Any experimental technique that discloses the time-re-solved behavior of a chemical/physical process. These approaches allow one to surmount the inherent limitations of steady-state and/or equilibrium kinetic measurements in the detection and quantification of species that comprise the internal equilibria of enzymic catalysis. 

Ilya Prigogine, the founding editor of Advances in Chemical Physics, died May 25, 2003. He was born in Moscow, fled Russia with his family in 1921, and, after brief periods in Lithuania and Germany, settled in Belgium, which was his home for 80 years. His many profound contributions to the theory of irreversible processes included extensions of both macroscopic thermodynamic analysis and statistical mechanical analysis of time-dependent processes and the approach to equilibrium. While sometimes controversial, these contributions were uniformly of outstanding intellectual merit and always addressed to the most fundamental issues they earned him international repute and the Nobel Prize in Chemistry in 1977. Arguably equally important was his creation of a school of theoretical chemical physics centered at the University of Brussels, as well as the mentoring of numerous creative and productive scientists. 

Weakliem, P. C. and Carter, E. A. Constant temperature molecular dynamics simulations of Si(100) and Ge(100) equilibrium structure and short-time behavior. Journal of Chemical Physics 96, 3240 (1992). 

The overall absolute hydroxyl concentration n is calculated by the Boltzmann statistical distribution formula. This method for determining absolute hydroxyl concentrations was applied in investigations8 6 8-13 on the importance of hydroxyl for various flames, as carried out at the Institute of Chemical Physics, It was shown that hydroxyl was formed under flame conditions. In other words, hydroxyl was of a chemical, and not of an equilibrium, nature, and played an important part in combustion processes. 

Before process options can be selected, site characterization and feasibility studies must determine key chemical, physical, and microbiological properties of the site. The objectives of these initial studies are to identify rate-limiting factors for later field applications and to obtain kinetic and equilibrium data for process design. 

This is a short but critically important section. When a system is at equilibrium, it has no tendency to change in either direction (forward or reverse) and will remain in its state until it is disturbed from outside the system. For example, when a block of metal is at the same temperature as its surroundings, it is in thermal equilibrium with them, and energy has no tendency to flow into or out of the block as heat. When a gas confined to a cylinder by a piston has the same pressure as the surroundings, the system is in mechanical equilibrium with the surroundings, and the gas has no tendency to expand or contract (Fig. 7.21). When a solid, such as ice, is in contact with its liquid form, such as water, at certain conditions of temperature and pressure (at 0°C and 1 atm for water), the two states of matter are in physical equilibrium with each other, and there is no tendency for one form of matter to change into the other form. Physical equilibria, which include vaporization as well as melting, are dealt with in detail in Chapter 8. When a chemical reaction mixture reaches a certain composition, it seems to come to a halt. A mixture of substances at chemical equilibrium has no tendency either to produce... 

Equilibrium—both physical and chemical, and including the equilibrium between a liquid and its vapor—is of enormous importance in chemistry, and it is important to acquire an understanding of the processes involved. Chemical equilibrium, which is examined in Chapter 9, deals with the equilibrium among the reactants and products of a chemical reaction. In this chapter, we deal with physical equilibrium, the state in which two or more phases of a substance coexist without a tendency to change. 

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