The Magnitude of an Equilibrium Constant

As discussed above, when we express pressures in bar and concentrations in mol/L, the units of and are, respectively, (bar) and (mol/L) . Because Ar gas = -1 for this reaction, we have = 3.4 bar and K = 2.8 X 10 (mol/L) = 2.8 X 10 LmoH. For convenience, we often omit the units when specifying the value of Kp or and when substituting pressures or concentrations into the corresponding equilibrium constant expressions, as we did in this example. 

PRACTICE EXAMPLE A For the reaction 2 NHsfg) value of K for this reaction  

as we established in Chapter 13, the value of K provides a measure of the thermodynamic stability of products relative to that of reactants. The large value of K for the water synthesis reaction signifies that, from a thermodynamic perspective, 2 mol of H20(l) is much more stable than 2 mol and 1 mol 02(g)- small value of K for the decomposition of CaC03(s) indicates that 1 mol CaO(s) and 1 mol CO i are much less stable than 1 mol CaC03(s). 

A very large value of K signifies that the reaction, as written, exhibits a strong tendency to go to completion. An equilibrium mixture contains about as much product as can be formed from the given initial amounts of reactants. 

TABLE 15.3 Equilibrium Constants of Some Common Reactions 

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The magnitude of an equilibrium constant tells us nothing about how fast the system will reach equilibrium. Equilibrium constants are thermodynamic quantities, whereas the speed of a reaction is a kinetic quantity. The two are not related. Rather, an equilibrium constant is a measure of the extent to which a reaction occurs. 

Kinetic-isotope effects are frequently complicated by the effects of isotope substitutions on equilibrium constants. We have seen in Chapter 9 that reactions frequently occur in more than a single step, and that the overall rate may depend upon the magnitude of an equilibrium constant. A simple case is when there is a rapidly established preequilibriura, as in the mechanism... 

We learn to interpret the magnitude of an equilibrium constant and how its value depends on the way the corresponding chemical equation is expressed. 

Before doing calculations with equilibrium constants, it is valuable to understand what the magnitude of an equilibrium constant can tell us about the relative concentrations of reactants and products in an equilibrium mixture. It is also useful to consider how the magnitude of any equilibrium constant depends on how the chemical equation is expressed. 

Relate the magnitude of an equilibrium constant to the relative amounts of reactants and products present in an equilibrium mixture (Section 15.3). 

Think About it The magnitude of an equilibrium constant reveals whether products or reactants are favored, so the reciprocal relationship between values of forward and reverse reactions should make sense. A very large Kc value means that products are favored. In the reaction of hydrogen ion and hydroxide ion to form water, the value of K,. is very large, indicating that the product, water, is favored. 

The statement that a catalyst cannot change the magnitude of an equilibrium constant is correct only if (1) the forward and backward reactions of an equilibrium process follow strictly the same mechanism, i.e., forward and backward reactions must involve the same transition states (if there is one or more than... 

The Magnitude of an Equilibrium Constant—The magnitude of the equilibrium constant can be used to determine the outcome of a reaction. For large values of K the reaction goes to completion, with all reactants converted to products. A very small equilibrium constant, for example, a large negative power of ten, indicates that practically none of the reactants have been converted to products. Finally, equilibrium constants of an intermediate value, for example, between 10 ° and 10 °, indicate that some of the reactants have been converted to products. 

While the consistency between the reported experimental E° values for the Br/Br" couple is encouraging, it should be noted that all values rely upon the reported equilibrium constant for reaction (18). As noted in Fornier de Violet s review (127), the magnitude of this formation constant is contentious, with reported results ranging from 3.3 x 103 to 2.2 x 105 M l. The most recent value is 1.1 x 10s M-1, and it is the value accepted, albeit reluctantly, in this review. An estimate of E° can be made that is relatively insensitive to this equilibrium constant by using some recently available data. Klaning and Wolff reported that for... 

Equilibrium constants can be very large or very small. The magnitude of the constant provides us with important information about the composition of an equilibrium mixture. For example, consider tire reaction of carbon monoxide and chlorine gases at 100°C to form phosgene (COCI2), a toxic gas that is used in Ihe manufacture of certain polymers and insecticides. 

An important theorem of statistical mechanics relates a property of kinetics to a property of equilibrium. At equilibrium, a system undergoes thermal fluctuations. Remarkably, the magnitudes of these equilibrium fluctuations are related to how fast the system approaches equilibrium. This theorem is quite general, and applies to many different physical and chemical processes. It allows you to determine the diffusion constant, viscosity, and other transport properties from knowledge of the equilibrium fluctuations. 

Matty of the equilibiiiun problems we encounter involve equilibrium constants, such as K, and Ksp, that are very small. Often, this enables us to neglect the unknown x in the denominator of the equilibrium expression, which simplifies the math necessary to solve the problem [ Section 16.5], The solution of an equilibrium problem involving complex ion formation is complicated both by the magnitude of and by the stoichiometry of the reaction. Consider the combination of aqueous copper(II) ions and ammonia to form the complex ion Cu(NH3)4 ... 

In principle, the shifts of the individual species in rapid equilibrium may be extracted by the application of known equilibrium constants to the results from solutions covering a range of compositions. This has been done for zinc and cadmium halide systems. Such treatments assume that the shift of an individual species is independent of the concentrations of the other species present. However, results for the nonlabile complexes of group VIII metals suggest that there will be some dependency but it is difficult to estimate the possible magnitude for metals such as cadmium. The accuracy of a determined chemical shift is poor if the species does not have a large concentration in at least one solution measured. Finally, considerable errors may be involved if the NMR measurements are made under different conditions (e.g., higher concentration) from those for which the equilibrium constants were evaluated. 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

Whenever we make an approximation, we must verify that it is valid by comparing the value calculated using the approximation with the approximation itself Most equilibrium constants are uncertain by about 5%, so x can be neglected whenever its value is two or more orders of magnitude smaller than the value from which it is subtracted or added. 

Although the transport properties, conductivity, and viscosity can be obtained quantitatively from fluctuations in a system at equilibrium in the absence of any driving forces, it is most common to determine the values from experiments in which a flux is induced by an external stress. In the case of viscous flow, the shear viscosity r is the proportionality constant connecting the magnitude of shear stress S to the flux of matter relative to a stationary surface. If the flux is measured as a velocity gradient, then... 

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