Chemical equilibrium volume effect

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

In the preceding chapter, the choice of reactor type was made on the basis of the most appropriate concentration profile as the reaction progressed, in order to minimize reactor volume for single reactions or maximize selectivity (or yield) for multiple reactions for a given conversion. However, there are still important effects regarding reaction conditions to be considered. Before considering reaction conditions, some basic principles of chemical equilibrium need to be reviewed. 

Table 2.3 summarizes the essential relationships for pressure effects on chemical equilibrium for the variable-pressure standard-state convention. Note, that these relationships can apply to any consistent choice of standard part ial molar volumes, for example, one for which an ionic medium such as seawater is adopted as the solute reference state. For detailed discussion of applications to seawater see, for example, Millero (1969) and Whitfield (1975). A compie-... 

The effect of pressure on a chemical equilibrium follows the principle of le Chatelier an increase in temperature shifts the equilibrium in the direction of highest enthalpy for an endothermic reaction, an increase in pressure in that of smallest volume. The relation giving the temperature effect is obtained by differentiating Eq. (7.3) at constant pressure, resulting in... 

Chemical equilibrium represents a balance between forward and reverse reactions. In most cases, this balance is quite delicate. Changes in experimental conditions may disturb the balance and shift the equilibrium position so that more or less of the desired product is formed. When we say that an equilibrium position shifts to the right, for example, we mean that the net reaction is now from left to right. Variables that can be controlled experimentally are concentration, pressure, volume, and temperature. Here we will examine how each of these variables affects a reacting system at equilibrium. In addition, we will examine the effect of a catalyst on equilibrium. 

Only a brief outline of the effects of pressure on rates and equilibria is given here since the subject is amply documented elsewhere. " It has long been appreciated that the position of a chemical equilibrium may be shifted by the application of external pressure in reactions in both the liquid and the gaseous phase. This shift in equilibrium favours the direction of the reaction which results in the smaller volume this is an application of the Le Chatelier s principle. In gas-phase reactions the term volume denotes the total volume of the system in dilute solutions the term volume denotes the algebraic sum of the partial molar volumes of the individual reagents and products. The thermodynamic relationship which summarizes this effect is... 

Pressure can have a large influence on the position of chemical equilibrium for reactions occurring in the gaseous phase. An increase in pressure favors a shift in the direction that results in a reduction in the volume of the system. But for reactions occurring in solutions, normal pressure changes have a negligible effect on the equilibrium because liquids caimot be compressed the way gases can. 

Chemical equilibrium responds to a "stress" by moving to the side that relieves the effect of "stress" and returns the system to equilibrium, according to Le Chatlier s Principle. If we add heat to an exothermic reaction it will shift toward the reactants on the left. If we add mass, concentration, or pressure on the reactant side of the equilibrium, the system responds by shifting toward the products. If we can remove products from the reaction zone (the system or control volume), then we also shift the reaction equilibrium to the right. In fact, even if we remove just one of the products from a set of products, the system will shift to the right. 

In (5.49), kf represents the effective reaction rate constant including internal transport resistances of the catalyst packing. stands for the catalyst volume installed in the column. For Da 3> 1 the chemical reaction approaches chemical equilibrium, for Da 1 the reaction is far from its equilibrium. 

The partial molar volume is a thermodynamic quantity that plays an essential role in the analysis of pressure effects on chemical reactions, reaction rate as well as chemical equilibrium in solution. In the field of biophysics, the pressure-induced denaturation of protein molecules has continuously been investigated since an egg white gel was observed under the pressure of 7000 atmospheres [60]. The partial molar volume is a key quantity in analyzing such pressure effects on protein conformations When the pressure in increased, a change of the protein conformation is promoted in the direction that the partial molar volume reduces. A considerable amount of experimental work has been devoted to measuring the partial molar volume of a variety of solutes in many different solvents. However, analysis and interpretation of the experimental data are in many cases based on drastically simplified models of solution or on speculations without physical ground, even for the simplest solutes such as alkali-halide ions in aqueous solution. Matters become more serious when protein molecules featuring complicated conformations are considered. 

Halide ions are poor nucleophiles and do not give an acyl addition product. Other weak nucleophiles give a low yield of an acyl addition product because the reaction is reversible. If this equilibrium can be controlled, there is a chance the product may be isolated or it may undergo another reaction. An equilibrium is effectively controlled by apphcation oiLe Chatelier s principle, which states that changes in concentration, temperature, volume, or partial pressure in a chemical system at equilibrium will shift the equilibrium to counteract that change. This principle is named after Henry Louis Le Chatelier (France/ Italy 1850-1936). In acyl addition reactions, changing the concentration and temperature is the most common action. 

Factors That Affect Chemical Equilibrium Changes in concentration can affect the position of an equilibrium state—that is, the relative amounts of reactants and products. Changes in pressure and volume may have the same effect for gaseous systems at equilibrium. Only a change in temperature can alter the value of equilibrium constant. A catalyst can establish the equilibrium state faster by speeding the forward and reverse reactions, but it can change neither the equilibrium position nor the equilibrium constant. 

Pressure is a fundamental physical property that affects various thermodynamic and kinetic parameters. Pressure dependence studies of a process reveal information about the volume profile of a process in much the same way as temperature dependence studies illuminate the energetics of the process (83). Since chemical transformations in SCF media require relatively high operating pressures, pressure effects on chemical equilibria and rates of reactions must be considered in evaluating SCF reaction processes (83-85). The most pronounced effect of pressure on reactions in the SCF region has been attributed to the thermodynamic pressure effect on the reaction rate constant (86), and control of this pressure dependency has been cited as one means of selecting between parallel reaction pathways (87). This pressure effect can be conveniently evaluated within the thermodynamic framework provided by transition state theory, which has often been applied to reactions in solutions (31,84,88-90). This theory assumes a true chemical equilibrium between the reactants and an activated transition... 

In this expression, JCis the equilibrium constant for a given chemical equilibrium and the reaction volume A V is the difference between the volumes of the final and initial states in any particular process, for example, due to a change in molecule packing, electrostatic action of charges, solvation, and hydration effects. From Eq. (9.1), it is clear that the sign of the reaction volume A V imposes the direction of equilibrium shifts induced by pressure. If A V is negative, the equilibrium shifts... 

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