THE CONCEPT OF EQUILIBRIUM

If you were to let the tube on the right sit overnight and then take another picture would the brown color look darker, lighter, 

On warming, the N2O4 becomes a gas and partially dissociates to form brown N02(g) 

Colors stop changing, equilibrium reached rate of reaction 

The equilibrium mixture results because the reaction is reversible N2O4 can form NO2, and NO2 can form N2O4. Dynamic equilibrium is represented by writing the equation for the reaction with two half arrows pointing in opposite directions I (Section 4.1)  

We can analyze this equilibrium using our knowledge of kinetics. Let s call the decomposition of N2O4 the forward reaction and the formation of N2O4 the reverse reaction. In this case, both the forward reaction and the reverse reaction are elementary reactions. As we learned in Section 14.6, the rate laws for elementary reactions can be written from their chemical equations  

Up until now, we have treated chemical equations as though they go to completion that is, we start with only reactants and end up with only products. In fact, this is not the case with most chemical reactions. Instead, if we start with only reactants, the reaction will proceed, causing reactant concentrations to decrease (as reactants are consumed) and product concentrations to increase (as products are produced). Eventually, though, the concentrations of reactants and products will stop changing. The reaction will appear to have stopped, and we will be left with a mixture of reactants and products. 

As an example, consider the decomposition of dinitrogen tetroxide (N2O4) to yield nitrogen dioxide (NO2)  

In this case, both the forward and reverse reactions are elementary reactions, so we can write their rate laws from the balanced equation  

the rate of the reverse reaction (formation of N2O4) is initially zero. The rate of the reverse reaction rises and the rate of the forward reaction falls until both rates are equal. 

It is a common error to think that equilibrium means equal concentrations of reactants and products—it does not. Equilibrium refers to the state in which forward and reverse reactions are occurring at the same rate. 

Few chemical reactions proceed in only one direction. Most are, at least to some extent, reversible. At the start of a reversible process, the reaction proceeds toward the formation of products. As soon as some product molecules are formed, the reverse process— that is, the formation of reactant molecules from product molecules—begins to take place. When the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products no longer change with time, chemical equilibrium is reached. 

Chemical equilibrium is a dynamic process. As such, it can be likened to the movement of skiers at a busy ski resort, where the number of skiers carried up the mountain on the chair lift is equal to the number coming down the slopes. Thus, although there is a constant transfer of skiers, the number of people at the top and the number at the bottom of the slope do not change. 

Note that a chemical equilibrium reaction involves different substances as reactants and products. Equilibrium between two phases of the same substance is called physical equilibrium because the changes that occur are physical processes. The vaporization of water in a closed container at a given temperature is an example of physical equilibrium. In this instance, the number of H2O molecules leaving and the number returning to the liquid phase are equal  

Liquid water in equilibrium with its vapor in a clos system at room temperature. 

Change in the concentrations of NO2 and N2O4 with time, in three situations, (a) Initially only NO2 is present, (b) Initially only N2O4 is present (c) Initially a mixture of NO 2 and N2O4 is present. In each case, equilibrium is established to the right of the vertical line. 

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The concept of equilibrium is central in thermodynamics, for associated with the condition of internal eqmlibrium is the concept of. state. A system has an identifiable, reproducible state when 1 its propei ties, such as temperature T, pressure P, and molar volume are fixed. The concepts oi state a.ndpropeity are again coupled. One can equally well say that the properties of a system are fixed by its state. Although the properties T, P, and V may be detected with measuring instruments, the existence of the primitive thermodynamic properties (see Postulates I and 3 following) is recognized much more indirectly. The number of properties for wdiich values must be specified in order to fix the state of a system depends on the nature of the system and is ultimately determined from experience. 

Why Do We Need to Know This Material In earlier chapters, we investigated the nature of the solid, liquid, and gaseous states of matter in this chapter, we extend the discussion to transformations between these states. The discussion introduces the concept of equilibrium between different phases of a substance, a concept that will prove to be of the greatest importance for chemical and biochemical transformations. We also take a deeper look at solutions in this chapter. We shall see how the presence of solutes is used by the body to control the flow of nutrients into and out of living cells and how the properties of solutions are used by oil companies to separate the components of petroleum. 

The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

The concept of equilibrium distribution of organic chemicals between medium components is widely used for the mathematical description of their degradation and migration processes in soil and other environmental compartments. This is also useful... 

Thus, in according to the concept of equilibrium distribution, the relation of an organic pollutant concentration in the soil solid and liquid phase is constant at any moment (Vasilyeva and Shatalov, 2004). The example of such an approach application for assessing exposure pathways of POPs to living biota is shown in Box 1. 

Classical thermodynamics is based on the concept of equilibrium. Time is not involved in conventional engineering thermodynamic textbooks. Heat transfer deals with rate of energy transfer, but does not cover cycles. There is a gap between thermodynamics and heat transfer. The chapter Finite-Time Thermodynamics bridges the gap between thermodynamics and heat transfer. 

Engineering thermodynamic cycle analysis is based on the concept of equilibrium and does not deal with time. Heat transfer does deal with time but not cycle analysis. Finite-time thermodynamics fills in a gap that has long existed between equilibrium thermodynamics and heat transfer. 

In our approach, the concept of ensemble of equilibrium subsystems introduced in our earlier chapters (see in detail Lazman and Yablonskii, 1991) was used as a very efficient tool of mathematical analysis and physico-chemical understanding. The equilibrium subsystem is such a system that corresponds to the following assumption (n—1) steps are considered to be under equilibrium conditions, one step is limiting, where n is a number of steps. In fact, the concept of "equilibrium subsystems" is a generalization of the concept of "equilibrium step", which is well known in chemical kinetics. Then, we take n of these equilibrium subsystems an ensemble of equilibrium subsystems). It was shown that solutions of these subsystems ("roots", "all roots", not just one "root") define coefficients of the kinetic polynomial. 

One problem, I think, in a detailed acceptance of simple transition state theory regarding solution systems concerns the central supposition that the transition state is in equilibrium with the reactants. If the transition state is a species which proceeds irreversibly and on one vibration period to products, it is a little difficult to demonstrate, I think, that this thermodynamic equilibrium exists. The concept of equilibrium and the concept of an irreversible process at some point must be distinct. 

In practice, the diffusion constant is modified to reflect the complex nature of the biofilm. In the development of synthetic hydrogels, the hydrophilicity of the polymer in part defines the concept of equilibrium moisture. We discussed this concept earlier when we described determination of equilibrium moisture. The first practical application is the diffusion constant. As the equilibrium moisture approaches 100%, the diffusion constant approaches that of water. 

The concept of equilibrium distribution is another area where names can cause much confusion. The equilibrium distribution of a compound between the gas and liquid phase has been expressed in various forms, i. e. Bunsen coefficientfi, solubility ratio s, Henry s Law constant expressed dimensionless Hc, or with dimensions H. These are summarized in along with equations showing the relationships between them. Another more general term to describe the equilibrium concentrations between two phases is the partition coefficient, denoted by K. It is often used to describe the partitioning of a compound between two liquid phases. 

We re already familiar with the concept of equilibrium from our study of the evaporation of liquids (Section 10.5). When a liquid evaporates in a closed container, it soon gives rise to a constant vapor pressure because of a dynamic equilibrium in which the number of molecules leaving the liquid equals the number returning from the vapor. Chemical reactions behave similarly. They can occur in both forward and reverse directions, and when the rates of the forward and reverse reactions become equal, the concentrations of reactants and products remain constant. 

To understand why the addition of thiosulfate ions (S2032 ) to silver ions (Ag+) is an extremely efficient way to remove unexposed silver ions on photographic film, it is necessary to investigate the concept of equilibrium. 

In addition, the cell reaction must also be reversible. The concept of equilibrium requires that, for a given system, the same state is obtained when equilibrium is approached from any direction. For a cell, the chemical reaction that takes place when the potential drop along the slide wire of the potentiometer is slightly greater than the emf of the cell must be the same as, but in the opposite direction to, that which takes place when the potential drop is slightly less than the emf of the cell. 

The concepts of equilibrium as the most probable state of a very large system, the size of fluctuations about that most probable state, and entropy (randomness) as a driving force in chemical reactions, are very useful and not that difficult. We develop the Boltzmann distribution and use this concept in a variety of applications. 

The above equation determines the relationship between the partial pressures of CO, C02 and 02 at equilibrium. The analysis given above is the basis of the concept of equilibrium constant discussed in the prior section. 

There are two major divisions in a discussion of solutions solution formation and solubility equilibria. The first topic deals with the mechanisms by which solutions form—different ways to describe solutions, factors that affect solution formation, and some of the physical properties of solutions. Those are the domain of this chapter. Solubility equilibria are discussed in Chapter 15, after you ve had a chance to review the concept of equilibrium. 

In this chapter, we will extend the concepts of equilibrium that have been discussed in previous chapters. In Chapter 10 we discussed the concept of equilibrium in relation to saturated solutions in which an equilibrium was established between solvated ions and undissolved solute. In Chapter 11 we discussed the solubility of different salts when we looked at the formation of precipitates. In this chapter you will see the connection between these two ideas with the introduction of the solubility product constant, Ksp, which is a quantitative means of describing solubility equilibria. This measure helps to predict and explain the precipitation of different salts from solution. You will also see how the common-ion effect, temperature, and pH affect solubility. 

The above arguments do not, however, however, detract from the utility of the concept of equilibrium constants Consider the relationships... 

Therefore, contributions to methods of data mining are included here. It is uncommon to discuss this topic in the context of reaction processes. However, as we have already discussed, data mining becomes ever more important in analyzing experiments and simulations. In conventional data analyses, the concepts of equilibrium statistical physics have been routinely applied. To the contrary, in situations in which local equilibrium breaks down, established methods do not exist to analyze experiments and simulations. Thus, data mining... 

Note that in the above discussion we used the term apparent units when referring to equilibrium constants. This term was used because the theoretical foundation for the concept of equilibrium based on thermodynamics includes a reference state for each substance, which always causes the units of concentration or pressure to cancel. We will explore this situation thoroughly in Chapter 10, but we will introduce this concept in Section 6.4. 

The Concept of Equilibrium Constants. If the solution is not ideal and Raoult s Law and Dalton s Law are not applicable it is necessary to make an empirical correction. For an ideal solution the relationship between the mole fractions of a given component in the liquid and vapor phases is given by... 

The above also illustrates the arbitrariness in the specification of Kp. The numerical value of the equilibrium constant would have been different if another pressure unit had been used or if some other method of expressing concentrations had been employed. Nevertheless, once the equilibrium constant has been determined for a particular set of physical parameters, this same value can be used to determine x for any other set of conditions at the same temperature. The above value of Kp holds so long as P is expressed in bars. It is this feature that renders the concept of equilibrium constants very useful. 

Develop a model that shows the concept of equilibrium. Be sure that your model includes the impact of Le Chatelier s principle on equilibrium. 

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