Chemical reactions irreversible, entropy change

For a closed system, if the change of mole numbers dNk is due to irreversible chemical reactions, the entropy production is... 

Transport effects together with nonequilibrium effects, such as finite-rate chemical reactions and phase changes, have their roots in the molecular behavior of the fluid and are dissipative. Dissipative phenomena are associated with thermodynamic irreversibility and an increase in global entropy. 

Irreversible processes correspond to the time evolution in which the past and the future play different roles. In processes such as heat conduction, diffusion, and chemical reaction there is an arrow of time. As we have seen, the second law postulates the existence of entropy 5, whose time change can be written as a sum of two parts One is the flow of entropy deS and the other is the entropy production dtS, what Clausius called uncompensated heat, ... 

The concept of affinity introduced in the foregoing chapter (section 3.5) can apply to all the physicochemical changes that occur irreversibly. Let us now discuss the physical meaning of the affinity of chemical reactions. As mentioned in the foregoing, we have in Eq. 3.27 the fundamental inequality in entropy balance of irreversible processes as shown in Eq. 4.1 ... 

A chemical reaction is an irreversible process that produces entropy. The general criterion of irreversibility is d S > 0. Criteria applicable under particular conditions are readily obtained from the Gibbs equation. The changes in thermodynamic potentials for chemical reactions yield the affinity A. All four potentials U, H, A, and G decrease as a chemical reaction proceeds. The rate of reaction, which is the change of the extent of the reaction with time, has the same sign as the affinity. The reaction system is in equilibrium state when the affinity is zero. 

Irreversible processes of phase transfer and chemical reaction within a closed system, whether homogeneous (a single phase) or heterogeneous (more than one phase), lead to T djS > 0. At equilibrium, T djS = 0. For fixed S and V constraints, dE = —T djS. A reversible process corresponds to zero internal entropy change and a minimum in dE. 

The method developed here is in many ways analogous to that employed by Schottky, Ulich and Wagner. Both methods emphasize the criterion for establishing the irreversibility of a chemical reaction and for deciding whether the reaction will proceed spontaneously in a particular direction. In De Bonder s method this criterion appears immediately the production of entropy must be positive. On the other hand Schottky, Ulich and Wagner employ as the criterion of irreversibility the loss of useful work associated with the real process when compared with a hypothetical reversible process. As is shown in chap. V, these criteria are equivalent for isothermal changes. For non-isothermal changes, however, the concept of loss of useful work... 

This is known as the Clausius inequality and has important applications in irreversible processes. For example, dS > (dQ/T) for an irreversible chemical reaction or material exchange in a closed heterogeneous system, because of the extra disorder created in the system. In summary, when we consider a closed system and its surroundings together, if the process is reversible and if any entropy decrease takes place in either the system or in its surroundings, this decrease in entropy should be compensated by an entropy increase in the other part, and the total entropy change is thus zero. However, if the process is irreversible and thus spontaneous, we should apply Clausius inequality and can state that there is a net increase in total entropy. Total entropy change approaches zero when the process approaches reversibility. 

The thermodynamics of irreversible processes begins with three basic microscopic transport equations for overall mass (i.e., the equation of continuity), species mass, and linear momentum, and develops a microscopic equation of change for specific entropy. The most important aspects of this development are the terms that represent the rate of generation of entropy and the linear transport laws that result from the fact that entropy generation conforms to a positive-definite quadratic form. The multicomponent mixture contains N components that participate in R independent chemical reactions. Without invoking any approximations, the three basic transport equations are summarized below. 

The change of total entropy is dS = dgS + diS. The term deS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term diS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is diS/dt = JkXk. A near-equilibrium system is stable to fluctuations if the change of entropy production is negative, i.e. Ai5 < 0. For isolated systems, dS/dt > 0 shows the tendency toward disorder as d S/dt = 0 and dS = diS > 0. For nonisolated systems, diS/dt > 0 shows irreversible processes, such as chemical reactions, heat conduction, diffusion, or viscous dissipation. For states near global equilibrium, d S is a bilinear form of flows and forces that are related in linear form. 

Formulation of a theory of entropy along these lines continued during the twentieth century, and for a large class of systems we now have a theory in which the entropy change can be calculated in terms of the variables that characterize the irreversible processes. For example, the modem theory relates the rate of change of entropy to the rate of heat conduction or the rates of chemical reaction. To obtain the change in entropy, it is not necessary to use infinitely slow reversible processes. 

Though Gibbs did not consider irreversible chemical reactions, equation (4.1.1) that he introduced included all that was needed for the consideration of irreversibility and entropy production in chemical processes. By making the important distinction between the entropy change S due to exchange of matter and energy with the exterior, and the irreversible increase of entropy djS due to chemical reactions [2, 3], De Bonder formulated the thermodynamics of irreversible chemical transformations. And we can now show he took the uncompensated heat of Clausius and gave it a clear expression for chemical reactions. 

Let us look at equation (4.1.2) from the viewpoint of entropy flow d S and entropy production diS, that was introduced in the previous chapter. To make a distinction between irreversible chemical reactions and reversible exchange with the exterior, we express the change in the mole numbers dN as a sum of two parts ... 

Figure 4.2 The changes in entropy d S due to irreversible chemical reactions are formulated using the concept of affinity. The illustrated reaction has affinity A = (px + I y 2pz), in which p are chemical potentials...

The concepts of chemical potential and affinity not only describe chemical reactions but also the flow of matter from one region of spaee to another. With the concept of chemical potential, we are now in a position to obtain an expression for the entropy change due to diffusion, an example of an irreversible process we saw in the previous chapter (Fig. 3.8). The idea of chemical potential... 

An example of the minimization of F is a reaction, such as 2H2(g)+ 02(g) 2H20(g), that takes place at a fixed value of T and V (Fig. 5.2(a)X To keep T constant, the heat generated by the reaction has to be removed. In this case, following De Bonder s identification of the entropy production in an irreversible chemical reaction (4.1.6), we have Td S = —Y i. i d Nk = —dF. Another example is the natural evolution in the shape of a liquid drop (Fig. 5.2(b)). In the absence of gravity (or if the liquid drop is small enough that the change... 

The Helmholtz free energy is a state function. We can show that F is a function of T, Vmd Nk and obtain its derivatives with respect to these quantities. From (5.1.2) it follows that dF = dU — TdS — SdT. For the change of entropy due to exchange of energy and matter, we have Td S = dU-FpdV— For the change of entropy due to irreversible chemical reaction, we have Td S =—Y i ii d Nk.. For the total change in entropy we have T dS = T deS + Td S. Substituting these expressions for dU and dS into the... 

Within the past 50 years our view of Nature has changed drastically. Classical science emphasized equilibrium and stability. Now we see fluctuations, instability, evolutionary processes on all levels from chemistry and biology to cosmology. Everywhere we observe irreversible processes in which time symmetry is broken. The distinction between reversible and irreversible processes was first introduced in thermodynamics through the concept of entropy , the arrow of time as Arthur Eddington called it. Therefore our new view of Nature leads to an increased interest in thermodynamics. Unfortunately, most introductory texts are limited to the study of equilibrium states, restricting thermodynamics to idealized, infinitely slow reversible processes. The student does not see the relationship between irreversible processes that naturally occur, such as chemical reactions and heat conduction, and the rate of increase of entropy. In this text, we present a modem formulation of thermodynamics in which the relation between rate of increase of entropy and irreversible processes is made clear from the very outset. Equilibrium remains an interesting field of inquiry but in the present state of science, it appears essential to include irreversible processes as well. 

A chemical reaction with a Gibbs free energy change less than zero (negative) can proceed spontaneously, irreversibly, and can produce work. If the reaction is run reversibly, then the maximum work, other than pV work, is AG, for the reaction as written. If the reaction is run irreversibly then there is some entropy production and some work may be done, but less than AG. If no work is done then the rate of entropy production is... 

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