Reaction equilibrium criteria

The decrease in Gibbs free energy as a signpost of spontaneous change and AG = 0 as a criterion of equilibrium are applicable to any kind of process, provided that it is occurring at constant temperature and pressure. Because chemical reactions are our principal interest in chemistry, we now concentrate on them and look for a way to calculate AG for a reaction. 

The basic criterion for the establishment of chemical reaction equilibrium is that... 

The basic criterion for equilibrium with respect to a given chemical reaction is that the Gibbs free energy change associated with the progress of the reaction be zero. 

The equilibrium constant expresses the point of minimum free energy for a chemical reaction, as set forth in Equation 3.3, in terms of the chemical potential functions above. The criterion for equilibrium becomes,... 

We can apply the criterion of equilibrium expressed in Equation (9.17) to chemically reacting systems. Consider the reaction... 

Structural and molecular biologists often study the temperature dependence of the equilibrium position of a reaction or process. The Gibbs free energy undoubtedly provides the correct thermodynamic criterion of equilibrium. An understanding of this parameter can be achieved from either a macroscopic level (classical thermodynamics) or a molecular level (statistical thermodynamics). Ultimately, one seeks to understand the factors influencing AG° for a specific reaction. 

It can be seen that the entropy will vanish, that is the process will be isentropic if d fc = 0 or if AFB =0. Since dSB contains the specific reaction rate as a factor, this term will be zero if the composition is frozen through the nozzle, since it implies that the reaction rate itself is zero. On the other hand the term A FB will vanish if the flow through the nozzle is in equilibrium at all points since the general criterion for equilibrium is that the free energy change for infinitesimal variation of the system shall vanish. It should be noted that the entropy considered here is the total entropy and includes the entropy of formation. 

This criterion of equilibrium provides a general method for determination of equilibrium states. One writes an expression for G as a function of the numbers of moles (mole numbers) of the species in the several phases, and then finds the set of values for the mole numbers that minimizes G subject to the constraints of mass conservation. This procedure can be applied to problems of phase, chemical-reaction, or combined phase and chemical-reaction equilibrium it is most useful for complex equilibrium problems, and is illustrated for chemical-reaction equilibrium in Sec. 15.9. 

To apply this criterion, one develops an expression for dG as a function of the mole numbers of the species in the various phases, and sets it equal to zero. The resulting equation along with those representing the conservation of mass provide working equations for the solution of equilibrium problems. Equation (13.53) leads directly to Eq. (10.3) for phase equilibrium and it is applied to chemical-reaction equilibrium in Chap. 15. 

Thus the quantity Vtfi, represents, in general, the rate of change of the total Gibbs energy of the system with the reaction coordinate at constant T and P. Figure 15.1 shows that this quantity is zero at the equilibrium state. Therefore a criterion of chemical-reaction equilibrium is... 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

The concept of the chemical potential is introduced here because this property plays an important role in reacting systems. In this context one may consider that a reaction moves in the direction of decreasing chemical potential, reaching equilibrium only when the potential of the reactants equals that of the products [3], Thus, from Eq. (16) the criterion for equilibrium for combustion products of a chemical system at constant T and P is... 

The basic criterion for equilibrium with a single reaction is ... 

Carnot s equations, 146-147 Carnot s theorem, 142-143 Chemical potential, 298, 302, 303 as equilibrium criterion, 298-299, 503 for ideal gas, 302 for ideal solution, 303 Chemical reaction equilibrium constant for, 504-516 equilibrium conversion of, 518-528, 533-542 heat effects of, 116-133 reaction coordinate for, 497-501 reversible, 41-42, 505-507 standard property changes for, 125, 505 stoichiometry, 497-501... 

In order to ensure that dS = 0, the coefficient of the term must equal zero. Consequently, the criterion for chemical reaction equilibrium is... 

The criterion for chemical reaction equilibrium is thus that the energy difference between reactants and products is zero, AfiR = 0. Hence, we can define the equilibrium constant for the model reaction by ... 

The criterion of equilibrium being reached in such a reaction, 1 e in one in which the temperature and volume are maintained constant, is simply that at the equilibrium point the Free Energy is a minimum, and therefore if we consider the system when equilibrium is reached and imagine the reaction to go to a small extent, namely, the transformation of hi molecules from one side of the equilibrium to the other, then the work done or free energy change is zero This is wntten algebraically (S/)tv = o 1... 

Further, the criterion that equilibrium is reached when (8A)XV = o, applies to reactions in solutions Take the simplest case of diffusion of a solute from a region of high concentration to one of low Equilibrium is reached when the work entailed by a small virtual change m the system can be equated to zero Suppose we have a solute at concentrations Cy and and osmotic pressures Px and P2 in the same vessel By means of osmotic membranes (the whole vessel being supposed to be surrounded by solvent of infinite extent) we can imagine 8 moles transferred from Px to P2 the work being < j WP, which will be zero... 

By considering the reaction system at constant T and p, and equilibrium criterion V, dG = 0, one arrives at the same conclusion that Equation (4.119) is the condition of chemical reaction equilibrium. 

In Section 4.1.6, the fnndamental criterion of chemical reaction equilibrium was derived, yielding a corelationship between the chemical potentials of all the components participating in a given chemical reaction. Given that the chemical potentials of the reactants and products are not all independent, the criterion of chemical reaction equilibrinm can be used to determine the equilibrium compositions of the reacting species. The development and nse of the chemical equilibrium relations are the focns of this section. 

When a chemical reaction proceeds, we have established (by reference to experiment) that energy will be conserved. But we have not found a way of predicting in which direction the reaction will go. In other words we have not found a suitable definition of the position of equilibrium. We have discovered that for molecular systems (which may approach equilibrium by endothermic processes) the energy, unlike the potential energy in mechanical systems, does not provide a sufficient criterion for equilibrium. A new factor must be introduced which will enable us to understand why heat always flows from hot to cold bodies and why a perfect gas will expand to fill its container, even though no loss of energy (by the system) accompanies these processes. 

Certain equilibrium states of thermodynamic systems are stable to small fluctuations others are not. For example, the equilibrium state of a simple gas is stable to all fluctuations, as are most of the equilibrium states we will be concerned with. It is possible, however, to carefully prepare a subcooled liquid, that is, a liquid below its normal solidiflcation temperature, that satisfies the equilibrium criteria. This is an tin-.stable equilibrium. state because the slightest disturbance, such as tapping on the. side of the containing ve.s.sel, will cause the liquid to freeze. One sometimes encounters mixtures that, by the chemical reaction equilibrium criterion (see Chapter 13). should react however, the chemical reaction rate is so small as to be immeasurable at the temperature of interest. Such a mixture can achieve a state of thermal equilibrium that is stable with respect to small fluctuations of temperature and pressure. If, however, there is a sufficiently large, but temporary, increase in temperature. so that die rate of the chemical reaction is appreciable for some period of time) and then the system... 

In this section we shall generalize the equations obtained in Sec. 6-1 to include positive or negative changes in the mass of the system due to a transfer of mass between the system and its surroundings. A criterion for equilibrium for a homogeneous open system in which there are no chemical reactions is immediately obtainable from Eq. (6-6) in the form... 

Equation (8-10) is the criterion for equilibrium in the system containing r chemically reacting substances. If no products of the reaction are present, SX 0 only and the criterion for equilibrium becomes... 

Can the criteria (7.6.3) for reaction equilibrium, which require all affinities to be zero, be reconciled with the general criterion for isothermal-isobaric equilibrium, namely dG = 0 (7.1.40) ... 

The objective here is to show that the reaction equilibrium criteria (7.6.3) are a consequence of the more general equilibrium criterion (7.1.40) that applies to any NPT system, including reacting systems. Consider a system of C species confined to a closed vessel and maintained at constant T and P by contact with an external heat and work reservoir. The species may undergo 51 independent chemical reactions. Since T and P are fixed for the entire system, the NPT criterion for equilibrium (7.1.40) applies that is, when all reactions are complete and equilibrium is reached, the system s total Gibbs energy will be a minimum,... 

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