Changes in Equilibrium Constants

Because for dilute aqueous concentrations the molality is approximately equal to the molarity, it is not uncommon to write equilibrium concentrations in units of molarity. (In fact, this is how it is usually done in introductory courses.) However, this adds an additional approximation in our expression of reaction quotients and equilibrium constants. 

What is the proper expression for the equilibrium constant, in terms of pressures, for the following chemical equilibrium Assume that conditions are near standard pressures. 

The other species in the equilibrium are condensed phases and, if we are close to standard pressures, do not affect the numerical value of K. 

The amounts of the dissolved ions are expressed as a molality, while the amounts of the gases are expressed as pressures. 

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To estimate the effects of changing from methyl to /t-nitrophenyl ester on the addition reaction, we use the change in equilibrium constant for addition of hydroxide to acetate esters, which was estimated as AAG° = 4.3kcal/mol. We assnme the same change applies to snlfates and phosphates. Then, from the free energy change for addition of hydroxide to dimethyl sulfate, we get AG° = Mkcal/ mol for the reaction given below. 

The relationship between the standard free energy change in equilibrium constant at various temperatures... 

Figure 8-1 Student data showing that the equilibrium quotient of concentrations for the reaction Fe3 + SCN Fe(SCN)21 decreases as potassium nitrate is added to the solution. Color Plate 3 shows the fading of the red color of Fe(SCN)2 after KN03 has been added. Problem 13-11 gives more information on this chemical system. [From R. J. Stolzberg, "Discovering a Change in Equilibrium Constant with Change in Ionic Strength," J. Chem. Ed. 1999, 76.640.]...

There is little or no indication of curvature in Fig. 10 and in this respect the plot is again similar to those of Figs. 1 and 3. The behavior may be interpreted in terms of compensation between changes in thermodynamic driving force for the reaction and variations in intrinsic activation barrier, both depending on changes in equilibrium constant for the reaction, as discussed already (pp. 77-90). 

Expected Range of pH Values. Changes in solution pH in rock-water systems may result from two primary causes. The first cause is due to changes in equilibrium constants with variation in temperature and pressure. For example, the neutral pH of pure water changes from 7.00 at 20°C to approximately 5.6 at 200°C and 300 bars pressure due to changes in the value of the dissociation constant for water. Precipitation, dissolution, oxidation, or reduction of phases with consumption or generation of hydrogen ion is the second primary cause of pH variation. 

The relationship suggested above between the frequency shift accompanying protonation (or any other chemical reaction) and the change in equilibrium constant upon excitation is formalized in the Forster cycle (Forster, 1950), illustrated in Fig. 2. Proceeding from... 

In the same way as changes in reactivity reflect the nature of the transition state, a change in equilibrium constant corresponds to a change in the thermodynamic stability of the carbocation intermediate. For example, substituent effects on the basicities of arylcarbonyl derivatives ArCOR provide a reference for the formation of a-hydroxycarbocations (17). 

The thermodynamic data presented in Table 4-6 reveal that the change in equilibrium constant is in the direction anticipated, with more ionization occurring as the... 

This problem becomes particularly acute for trace elements where apparently small changes in equilibrium constants or pH or redox potential or temperature may produce very large changes in trace element speciation. 

The size of the change in equilibrium constant with temperature is a function of AH°, as described by the van t Hoff equation, Eq. 24 ... 

The equilibrium constant for (31) at 100 C decreases by a fraction of ca. 10 on transfer from DMAC to 88 % MeOH-HgO. This is because the Sif2 anion-cation reaction is much more strongly influenced by solvent transfer than the back reaction between polar molecules. The large change in equilibrium constant for a process of this charge type with solvent transfer warns us that acid-base indicator systems of this charge... 

Further Thermodynamic Considerations. The change in equilibrium constant of the water-gas shift reaction with temperature is shown in Figure 7. At equilibrium carbon monoxide conversion decreases with temperature. From the data in Table II and from the prediction equation... 

Figure 7. Change in equilibrium constant of the water-gas shift reaction with...

Changing temperature always causes a shift in equilibrium systems—sometimes toward more products and sometimes toward more reactants. For example, some industrial reactions that yield an equilibrium mixture with less than 1% products at room temperature will yield more than 99% products at higher temperature. This shift in equilibrium systems is reflected in changes in equilibrium constants that accompany changes in temperature. 

If the two states have different associated water volumes Vz and V, then there is a part of AG that is nosm(Vz — Vy) and a change in equilibrium constant K that is... 

Qualitatively we may use jS as an index of the transition state along the reaction path. If the transition state is reactant-like m 0 (Fig. 3) and 13 is thus close to zero when the transition state is product-like Wj = 0 (Fig. 3) and j8 is thus unity. The usually linear Bronsted relationships occurring in nature presumably result from a relatively small change in equilibrium constant as the reaction changes from endothermic to exothermic there should be a smooth change from y8 = 1 to P = 0. 

Solvent oscillators are localised but their induced dipole moments increase with molecular size. On this basis we expect dispersion forces to be greater between picrate and methanol than between picrate and water. This accounts for the change in equilibrium constant of the reaction... 

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