False equilibrium

Usually fairly high concentrations of such a drug are needed for effective control of an infection because the inhibitor (the false substrate) should occupy as many active centers as possible, and also because the natural substrate will probably have a greater affinity for the enzyme. Thus the equilibrium must be influenced and, by using a high concentration of the false substrate, the false substrate-enzyme complex can be made to predominate. The bacteria, deprived of a normal metabolic process, cannot grow and multiply. Now the body s defense mechanisms can take over and destroy them. 

A state of equilibrium which does not satisfy the conditions for true equilibrium is called a state of false equilibrium. A system may remain in a given state for a long period of time, and thus appear to be in an equilibrium state. A small change... 

False equilibrium, 90, 198 Faraday s laws, 455 Findlay s rule, 307 First law of thermodynamics, 21, 31, 73... 

Determine whether each of the following statements is true or false. If a statement is false, explain why. (a) For a reaction with a very large equilibrium constant, the rate constant of the forward reaction is much larger than the rate constant of the reverse reaction, (b) At equilibrium, the rate constants of the forward and reverse reactions are equal. 

Determine which of the following statements about catalysts are true. If the statement is false, explain why. (a) In an equilibrium process, a catalyst increases the rate of the forward reaction but leaves the rate of the reverse reaction unchanged, (b) A catalyst is not consumed in the course of a reaction, (c) The pathway for a reaction is the same in the presence of a catalyst as in its absence, but the rate constants are decreased in both the forward and the reverse directions. 

False. The position of the equilibrium is unaffected by the presence of a catalyst. 

Example 4.2 used the method of false transients to solve a steady-state reactor design problem. The method can also be used to find the equilibrium concentrations resulting from a set of batch chemical reactions. To do this, formulate the ODEs for a batch reactor and integrate until the concentrations stop changing. This is illustrated in Problem 4.6(b). Section 11.1.1 shows how the method of false transients can be used to determine physical or chemical equilibria in multiphase systems. 

Equilibrium Compositions for Single Reactions. We turn now to the problem of calculating the equilibrium composition for a single, homogeneous reaction. The most direct way of estimating equilibrium compositions is by simulating the reaction. Set the desired initial conditions and simulate an isothermal, constant-pressure, batch reaction. If the simulation is accurate, a real reaction could follow the same trajectory of composition versus time to approach equilibrium, but an accurate simulation is unnecessary. The solution can use the method of false transients. The rate equation must have a functional form consistent with the functional form of K,i,ermo> e.g., Equation (7.38). The time scale is unimportant and even the functional forms for the forward and reverse reactions have some latitude, as will be illustrated in the following example. 

Example 7.12 Use the method of false transients to determine equilibrium concentrations for the reaction of Example 7.11. Specifically, determine the equilibrium mole fraction of component A at r=550K as a function of pressure, given that the reaction begins with pure A. 

FIGURE 7.6 Equilibrium concentrations calculated by the method of false transients for a non-elementary reaction. 

Solution A rigorous treatment of a reversible reaction with variable physical properties is fairly complicated. The present example involves just two ODEs one for composition and one for enthalpy. Pressure is a dependent variable. If the rate constants are accurate, the solution will give the actual reaction trajectory (temperature, pressure, and composition as a function of time). If ko and Tact are wrong, the long-time solution will still approach equilibrium. The solution is then an application of the method of false transients. 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Geochemical models can be conceptualized in terms of certain false equilibrium states (Barton et al., 1963 Helgeson, 1968). A system is in metastable equilibrium when one or more reactions proceed toward equilibrium at rates that are vanishingly small on the time scale of interest. Metastable equilibria commonly figure in geochemical models. In calculating the equilibrium state of a natural water from a reliable chemical analysis, for example, we may find that the water is supersaturated with respect to one or more minerals. The calculation predicts that the water exists in a metastable state because the reactions to precipitate these minerals have not progressed to equilibrium. 

True/False. An equilibrium must respond to the stress created by a catalyst. 

True/False. Adding calcium oxide, CaO, to the following equilibrium will have no effect. CaC03(s) 5 CaO(s) + C02(g)... 

True/False. Equilibrium constant expressions never include solids. 

True/False. Water is important in equilibrium expressions for aqueous solutions. 

The previous comparison between first and second law methods may give the false impression that the latter should always be preferred. Second law methods can be unreliable, even if a sophisticated equation is used to fit the experimental data. The problem lies in the evaluation of the equilibrium constant, which must be defined in terms of the activities of reactants and products [ 1 ]. The activity concept... 

Compare convergence times, using interval halving, Newton-Raphson, and false position, for on ideal, four-component, vapor-liquid equilibrium system. The pure component vapor pressures are ... 

The interpretation of slopes also requires meaningful rate data. When the reaction consists of a series of elementary steps (and this is always so with heterogeneous catalytic reactions), the rate coefficients obtained from a superficial treatment of a limited set of measurements may be composites of several rate and equilibrium constants for individual steps, in favorable cases constituting a product. As every step may be influenced by the substituents, the resulting effect can be easily attributed to a false elementary step. 

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