Equilibrium constant magnitude

The Equilibrium Constant Calculating Equilibrium Constants Magnitude of the Equilibrium Constant... 

Finally, a consideration of equilibrium chemistry can only help us decide what reactions are favorable. Knowing that a reaction is favorable does not guarantee that the reaction will occur. How fast a reaction approaches its equilibrium position does not depend on the magnitude of the equilibrium constant. The rate of a chemical reaction is a kinetic, not a thermodynamic, phenomenon. Kinetic effects and their application in analytical chemistry are discussed in Chapter 13. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

Thermodynamically, the formation of methane is favored at low temperatures. The equilibrium constant is 10 at 300 K and is 10 ° at 1000 K (113). High temperatures and catalysts ate needed to achieve appreciable rates of carbon gasification, however. This reaction was studied in the range 820—1020 K, and it was found that nickel catalysts speed the reaction by three to four orders of magnitude (114). The Hterature for the carbon-hydrogen reaction has been surveyed (115). 

Chelation is an equilibrium system involving the chelant, the metal, and the chelate. Equilibrium constants of chelation are usually orders of magnitude greater than are those involving the complexation of metal atoms by molecules having only one donor atom. 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

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. 

It is seen that the three values for the equilibrium constant (k) range from 0.00443 to 0.00565 with an average value of 0.00504. The two values for the densities of the methanol/water associate are in reasonable agreement and have a magnitude that would be expected for the hydrogen bonded associate. 

The system is initially at equilibrium with concentrations Ca and c. Now we rapidly perturb the system so as to alter the magnitude of the equilibrium constant. Let the new equilibrium concentrations, toward which the actual concentrations will relax, be Ca and c. (Clearly one of these will be greater than and one will be less than the initial concentrations.) The concentrations at any time t are Ca and c. ... 

Sometimes, knowing only the magnitude of the equilibrium constant, it is possible to decide on the feasibility of a reaction. Consider, for example, a possible method for fixing atmospheric nitrogen—converting it to a compound—by reaction with oxygen ... 

This is an extremely small pressure, as you might have guessed from the small magnitude of the equilibrium constant. 

Because equilibrium constants must be raised to a power when a chemical equation is multiplied by a factor, and therefore change in magnitude, these rules are only general guidelines. 

It is of interest that, as a consequence of the peculiar state of reactants in such systems, reactions rates and equilibrium constants are very often altered by several orders of magnitude as compared with those in homogeneous solution [114,115],... 

The magnitudes of equilibrium constants vaiy over a tremendous range and depend on the nature of the reaction as well as on the temperature of the system. Many reactions have veiy large equilibrium constants. For example, the reaction between H2 and Br2 to form HBrhas a huge equilibrium constant ... 

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. 

Because the magnitude of the equilibrium constant is veiy large, almost all of the starting materials will be converted to products. Because of this, the problem is easier to solve by taking the reaction to completion and then returning to equilibrium. 

Because the two equilibrium constant expressions have similar magnitudes, a solution of the silver-ammonia complex generally has a significant concentration of each of the species that participate in the equilibria. The details of such calculations are beyond the scope of general chemistry. When the solution contains a large excess of ligand, however, each step in the complexation process proceeds nearly to completion. Under these conditions we can apply the standard seven-step approach to a single expression that describes the formation reaction of the complete complex. 

The magnitude of this equilibrium constant indicates that the redox reaction goes essentially to completion. This reflects the fact that bromine is a potent oxidizing agent and copper is relatively easy to oxidize. 

As explained by Franks (1972), this again shows that the component balance equations, for the different components of the mixture, will thus have different time constants, which depend on the relative magnitudes of the equilibrium constants K and which again can lead to possible problems of numerical stiffness. 

The magnitude of the equilibrium constant is defined by the free energy of polymerization. The larger the negative value of the change in the free energy due to polymerization, the more products will form before equilibrium is established. This observation has been summarized (and greatly simplified) in Eq. 3.7. 

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