Equilibrium in closed systems

In open systems, we must modify the expression describing dG at equilibrium in closed systems, namely... 

Flow processes inevitably result from pressure gradients witliin tire fluid. Moreover, temperature, velocity, and even concentration gradients may exist witliin the flowing fluid. This contrasts witlr tire uniform conditions tlrat prevail at equilibrium in closed systems. The distribution of conditions in flow systems requires tlrat properties be attributed to point masses of fluid. Thus we assume tlrat intensive properties, such as density, specific enthalpy, specific entropy, etc., at a point are determined solely by the temperature, pressure, and composition at tire point, uirinfluenced by gradients tlrat may exist at tire point. Moreover, we assume that the fluid exlribits tire same set of intensive properties at the point as tlrough it existed at equilibrium at tire same temperature, pressure, and composition. The implication is tlrat an equation of state applies locally and instantaneously at any point in a fluid system, and tlrat one may invoke a concept of local state, independent of tire concept of equilibrium. Experience shows tlrat tlris leads for practical purposes to results in accord with observation. 

San] Study of flic carbon solubility in Fe-Cr melts under conditions of Bouduard s equilibrium in closed system wifli a slowest flow rate of CO 1460, 1545, and 1560°C 0 - 24.5 at.% Cr, 0 - 6.46 at.% C, liquid phase... 

Let us first consider mixtures of pure CO and C02, all points of which lie on the X axis. The equilibrium in this system is fully described by Equation 3. As the temperature increases, the equilibrium constant decreases, and CO becomes stable. It is apparent (Figure 4) that, as the temperature increases, the intersections of the curves for different temperatures move close to pure CO, thus increasing the region of no graphite deposition. 

Lincoff, A. H., Gossett, J. M. (1984) The determination of Henry s law constants for volatile organics by equilibrium partitioning in closed systems. In Gas Transfer at Water Surfaces. Brutsaert, W., Jirka, G. H., Eds., pp. 17-26, D. Reidel Publishing Co., Dordrecht, The Netherlands. 

This treatment was used to determine the high-temperature equilibrium in the system and combined with a standard four sub-lattice treatment of the ordered phase, equivalent to the BWG treatment for a binary f.c.c. lattice. The Cu-Au diagram generated by this means (Fig. 7.11) is quite close to that obtained by an early MC calculation (Binder 1980), but the latter result is not now universally accepted (Ducastelle 1991). Sundman and Mohri (1990) suggested that their hybrid... 

TABLE 2-5 Effect of Equilibrium Constant on Extent of Reaction and Degree of Polymerization in Closed System... 

One particular pattern of behaviour which can be shown by systems far from equilibrium and with which we will be much concerned is that of oscillations. Some preliminary comments about the thermodynamics of oscillatory processes can be made and are particularly important. In closed systems, the only concentrations which vary in an oscillatory way are those of the intermediates there is generally a monotonic decrease in reactant concentrations and a monotonic, but not necessarily smooth, increase in those of the products. The free energy even of oscillatory systems decreases continuously during the course of the reaction AG does not oscillate. Nor are there specific individual reactions which proceed forwards at some stages and backwards at others in fact our simplest models will comprise reactions in which the reverse reactions are neglected completely. 

How does this apply in chemical reactions In closed systems, chemical reactions proceed spontaneously until equilibrium is reached. When a system is at equilibrium, the rate of product formation exactly equals the... 

The final possibility, a uniformly interesting movie, would have to depict a process with thousands or millions of critical steps occuring in a definite order, each step necessary to understand the next, as in an industrial process, the functioning of a digital computer, or the development of an embryo. Enzymes, having been optimized by natural selection, may be expected to have somewhat complex mechanisms of action, perhaps with several equally important critical steps, but not with thousands of them. There is reason to believe that processes with thousands of reproducible non-trivial steps usually occur only in systems that are held away from thermal equilibrium by an external driving force. They thus belong to the realm of complex behavior in continuously dissipative open systems, rather than to the realm of relaxation processes in closed systems. 

Gray, B. F., 1970, Oscillatory approach to equilibrium in closed chemical systems. Trans. Faraday Soc. 66,363-371. 

Detailed equilibrium must occur in closed systems, whereas in open systems, particularly in those that are far from being in equilibrium due to their exchange with the environment, the situation is much more complicated. Primarily, steady-state solutions can be multiple, i.e. the rates of substance formation and consumption can be balanced on many points. 

Consider a closed system consisting of two phases in equilibrium. Within closed system, each of the individual phases is an open system, free to tr mass to the other. Equation (10.2) may therefore be written for each phase ... 

Attaining and measuring an equilibrium weight of sorbed water vapor. Gravimetric measurement of moisture uptake can occur continuously or discontinuously. Continuous measurement usually involves placing a sample on a balance in a temperature- and relative humidity-controlled environment. Microbalances in closed systems have been used successfully for this purpose, " and commercial systems are now available that can accurately and precisely control relative humidity and simultaneously monitor sample weight. 

For each of these idealized models there is a stationary state. For a continuous open system, this is the steady state. Rate laws and steady material flows arc required to define the steady state. For a closed system, equilibrium is the stationary state. Equilibrium may be viewed as simply the limiting case of the stationary state when the flows from the surroundings approach zero. The simplicity of closed-system models at equilibrium is in the rather small body of information required to describe the time-invariant composition. We now turn our attention to the principles of chemical thermodynamics and the development of tools for the description of equilibrium states and energetics of chemical change in closed systems. 

Equilibrium Displacements in Closed Systems the Theorems of van t Hoff and Le Chatelier. 

The term d jdt is of course the reaction velocity v. The reaction velocity is zero if A = 0, since the system is then in equilibrium. In close proximity to equilibrium we may assume that the velocity is proportional to the affinity... 

Given sufficient time, chemical substances in contact with each other tend to come to chemical equilibrium. Chemical equilibrium is the time-invariant, most stable state of a closed system (the. state of minimum Gibbs free energy). We study chemical equilibrium concepts so as to learn the direction of spontaneous change of chemical reactions in any system, especially for conditions of constant temperature and pressure. We want to be able to compute the hypothetical equilibrium stale of a system. We would like to predict the conditions for equilibrium in different systems and at different temperatures and pressures without having to measure them. 

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