Reversible Reactions—Chemical Equilibrium

When some CaCOs first reacts with H30", the rate of the forward reaction is large. The rate of the reverse reaction is zero until some products form. As the reaction proceeds, the forward reaction rate slows as the reactant concentrations decrease. At the same time, the reverse rate increases as more products of the forward reaction form. When the two rates become equal, the reaction reaches chemical equilibrium. Because reaction rates depend on concentrations, there is a mathematical relationship between product and reactant concentrations at equilibrium. For the reaction of limestone and acidified water, the relationship is... 

Many chemical reactions do not completely convert reactants to products. A mixture of products and reactants exists, and its composition will remain constant until the experimental conditions are changed. This mixture is in a state of chemical equilibrium. The reaction continues indefinitely (dynamic), but the concentrations of products and reactants are fixed (equilibrium) because the rates of the forward and reverse reactions are equal. This is a dynamic equilibrium. 

The synthesis of methyl formate is a typical esterification reaction with a conversion limitation due to chemical equilibrium. Such reactions are suitably carried out in an RD column [1, 13, 62], Methanol (MeOH) and formic acid (FA) are converted to methyl formate (MF) and water (W) according to the reversible reaction... 

Most processes are catalyzed where catalysts for the reaction are known. The choice of catalyst is crucially important. Catalysts increase the rate of reaction but are unchanged in quantity and chemical composition at the end of the reaction. If the catalyst is used to accelerate a reversible reaction, it does not by itself alter the position of the equilibrium. When systems of multiple reactions are involved, the catalyst may have different effects on the rates of the different reactions. This allows catalysts to be developed which increase the rate of the desired reactions relative to the undesired reactions. Hence the choice of catalyst can have a major influence on selectivity. 

Figure 2,9 Various measures can be taken to increase equilibrium conversion in reversible reactions. (From Smith and Petela, The Chemical Engineer, Dec. 17, 1991 reproduced by permission of the Institution of Chemical Engineers.)...

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

Both the principles of chemical reaction kinetics and thermodynamic equilibrium are considered in choosing process conditions. Any complete rate equation for a reversible reaction involves the equilibrium constant, but quite often, complete rate equations are not readily available to the engineer. Thus, the engineer first must determine the temperature range in which the chemical reaction will proceed at a... 

Every chemical reaction can go in either forward or reverse direction. Reactants can go forward to products, and products can revert to reactants. As you may remember from your general chemistry course, the position of the resulting chemical equilibrium is expressed by an equation in which /Cec], the equilibrium constant, is equal to the product concentrations multiplied together, divided by the reactant concentrations multiplied together, with each concentration raised to the power of its coefficient in the balanced equation. Eor the generalized reaction... 

Chemical reactions involving gases carried out in closed containers resemble in many ways the H20(/)-H20(g) system. The reactions are reversible reactants are not completely consumed. Instead, an equilibrium mixture containing both products and reactants is obtained. At equilibrium, forward and reverse reactions take place at the same rate. As a result, the amounts of all species at equilibrium remain constant with time. 

Expressions (27) and (29) show how the rates of reaction (26) and its reverse, reaction (28), depend upon the concentrations. Now we can apply our microscopic view of the equilibrium state. Chemical changes will cease (on the macroscopic scale) when the rate of reaction (26) is exactly equal to that of reaction (28). When this is so, we can equate expressions (27) and (29) ... 

It is found that after the elapse of a sufficient time interval, all reversible reactions reach a state of chemical equilibrium. In this state the composition of the equilibrium mixture remains constant, provided that the temperature (and for some gaseous reactions, the pressure also) remains constant. Furthermore, provided that the conditions (temperature and pressure) are maintained constant, the same state of equilibrium may be obtained from either direction of a given reversible reaction. In the equilibrium state, the two opposing reactions are taking place at the same rate so that the system is in a state of dynamic equilibrium. 

Guldberg and Waage (1867) clearly stated the Law of Mass Action (sometimes termed the Law of Chemical Equilibrium) in the form The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances . Active mass was interpreted as concentration and expressed in moles per litre. By applying the law to homogeneous systems, that is to systems in which all the reactants are present in one phase, for example in solution, we can arrive at a mathematical expression for the condition of equilibrium in a reversible reaction. 

Like physical equilibria, all chemical equilibria are dynamic equilibria, with the forward and reverse reactions occurring at the same rate. In Chapter 8, we considered several physical processes, including vaporizing and dissolving, that reach dynamic equilibrium. This chapter shows how to apply the same ideas to chemical changes. It also shows how to use thermodynamics to describe equilibria quantitatively, which puts enormous power into our hands—the power to control the And, we might add, to change the direction of a reaction and the yield of products,... 

Like phase changes, chemical reactions tend toward a dynamic equilibrium in which, although there is no net change, the forward and reverse reactions are still taking place, but at matching rates. What actually happens when the formation of ammonia appears to stop is that the rate of the reverse reaction,... 

All chemical equilibria are dynamic equilibria. Although there is no further net change at equilibrium, the forward and reverse reactions are still taking place. 

Chemical reactions reach a state of dynamic equilibrium in which the rates of forward and reverse reactions are equal and there is no net change in composition. 

A catalyst speeds up both the forward and the reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard Gibbs free energy of reaction depends only on the identities of the reactants and products and is independent of the rate of the reaction or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

In principle, Equation (7.28) is determined by equating the rates of the forward and reverse reactions. In practice, the usual method for determining Kkinetic is to run batch reactions to completion. If different starting concentrations give the same value for Kkinetic, the functional form for Equation (7.28) is justified. Values for chemical equilibrium constants are routinely reported in the literature for specific reactions but are seldom compiled because they are hard to generalize. 

Look again at Figure 16-1 If two NO2 molecules can form a bond when they collide, then that bond also can break apart when an N2 O4 molecule distorts. The concept of reversibility is a general principle that applies to all molecular processes. Every elementary reaction that goes in the forward direction can also go In the reverse direction. As a consequence of reversibility, we can write each step in a chemical mechanism using a double arrow to describe what happens at chemical equilibrium. 

It is possible to carry out this type of kinetic analysis whether a mechanism is simple or elaborate. That is, we can always derive the equilibrium expression for a reaction by applying reversibility and setting forward and reverse rates equal to one another at equilibrium. It is unnecessary to go through this procedure for every chemical equilibrium. As our two examples suggest, inspection of the overall stoichiometry always gives the correct expression for the equilibrium constant. That is, a reaction of the form tjA + iBf ofD + eE has an... 

Later we shall see how fundamental quantities such as /i can be estimated from first principles (via a basic knowledge of the molecule such as its molecular weight, rotational constants etc.) and how the equilibrium constant is derived by requiring the chemical potentials of the interacting species to add up to zero as in Eq. (20). The above equations relate kinetics to thermodynamics and enable one to predict the rate constant for a reaction in the forward direction if the rate constant for the reverse reaction as well as thermodynamic data is known. 

Chemical equilibrium The state reached in a reversible reaction when the forward reaction is proceeding at the same rate as the reverse reaction. 

A chemical reaction in which the products react to re-form the original reactants is called a reversible reaction. For example, club soda is a mixture of carbon dioxide gas and water. The water and carbon dioxide react forming carbonic acid (H2C03). Carbonic acid decomposes to again form water and carbon dioxide. A state of equilibrium is reached in which the amounts of carbonic acid, water, and carbon dioxide remain constant. The overall reaction can be written as follows. 

Customarily chemical equilibrium has very instructively been introduced by describing the underlying meaning of reversible and irreversible reactions. 

Here, the sign of equality (=) has been replaced by the double oppositely directed arrows (s=) called a sign of reversibility. Such a reaction is called a reversible reaction. The reversibility of reactions can be detected when both the forward and the reverse reactions occur to a noticeable extent. Generally, such reactions are described as reversible reactions. The most important criterion of a reaction of this type is that none of the reactants will become exhausted. When the reaction is allowed to take place in a closed system from where none of the substances involved in the reaction can escape, one obtains a mixture of the reactants and the products in the reaction vessel. Every reversible reaction, depending on its nature, will after some time reach a stage when the reactants and the products coexist in a state of balance, and their amounts will remain unaltered for unlimited time. Such a state of a chemical reaction is called chemical equilibrium, and the point of such an equilibrium varies only with temperature. 

Incompleteness of the reaction this is the chief criterion of chemical equilibria. A reversible reaction is never complete in any direction provided none of the products is allowed to escape from the system. Stated differently, in the equilibrium condition, the reactants and the products are all present simultaneously in the reaction vessel. If any of the substances were to vanish, its concentration would become zero and the value of the equilib-... 

Such esterifications and acetal formations are achieved through enzyme catalyses. However, such reactions are relatively rare in aqueous conditions chemically. This is because the reversed reactions, hydrolysis, are much more favorable entropically. Kobayashi and co-workers found that the same surfactant (DBSA) that can catalyze the ether formation in water (5.2 above) can also catalyze the esterification and acetal formations reactions in water.52 Thus, various alkanecarboxylic acids can be converted to the esters with alcohols under the DBSA-catalyzed conditions in water (Eq. 5.6). Carboxylic acid with a longer alkyl chain afforded the corresponding ester better than one with a shorter chain at equilibrium. Selective esterification between two carboxylic acids with different alkyl chain lengths is therefore possible. 

When setting the conditions in chemical reactors, equilibrium conversion will be a major consideration for reversible reactions. The equilibrium constant Ka is only a function of temperature, and Equation 6.19 provides the quantitative relationship. However, pressure change and change in concentration can be used to shift the equilibrium by changing the activities in the equilibrium constant, as will be seen later. 

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