Other Equilibria

Other types of equilibria can be treated in much the same way as the ones discussed above. For example, there is an equilibrium constant associated with the formation of complex ions. This equilibrium constant is called the formation constant, Kf. Zn(H20)4+ reacts with ammonia to form the Zn(NH3)2+ complex ion according to the following equation  

The ofZn(NH3)2+(aq) is 7.8 x 108, indicating that the equilibrium lies to the right. 

Equilibrium experiments such as 10, 11, and 19 in Chapter 19, directly or indirectly involve filling a table like the following  

The initial amounts—concentrations or pressures—are normally zero for the products, and a measured or calculated value for the reactants. Once equilibrium has been established, the 

Measurements may include the pressure, the mass (to be converted to moles), the volume (to be used in calculations), and the pH (to be converted into either the hydrogen ion or hydroxide ion concentration). Some experiments measure the color intensity (with a spectrophotometer), which may be converted to a concentration. 

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The ladder diagram for HF/F- also can be used to evaluate the effect of pH on other equilibria that include either HF or F-. For example, the solubility of CaF2... 

There has been some interest in comparing prototropic tautomerism to other equilibria where the migrating entity is not the proton. A significant... 

Similar equations can be formulated for other equilibria, e.g. NOjVNOz", Na /Na, etc. 

If the species engage in other equilibria, the application of Rule 2 can become more complicated algebraically. The matter is in no sense intractable, however, and it will be considered in Sections 6.5, 6.6, and 6.7. 

After completing our analysis of the effects of the dominant equilibrium, we may need to consider the effects of other equilibria. The calculation of [H3 O ] in a solution of weak base illustrates circumstances where this secondary consideration is necessary. Here, the dominant equilibrium does not include the species, H3 O, whose concentration we wish to know. In such cases, we must turn to an equilibrium expression that has the species of interest as a product. The reactants should be species that are involved in the dominant equilibrium, because the concentrations of these species are determined by the dominant equilibrium. We can use these concentrations as the initial concentrations for our calculations based on secondary equilibria. Look again at Example for another application of this idea. In that example, the dominant equilibrium is the reaction between hypochlorite anions and water molecules H2 0 l) + OCr(c2 q) HOCl((2 q) + OH ((2 q) Working with this equilibrium, we can determine the concentrations of OCl, HOCl, and OH. To find the concentration of hydronium ions, however, we must invoke a second equilibrium, the water equilibrium 2 H2 0(/) H3 O (a q) + OH (a q)... 

The products generated by other equilibria have concentrations that are more than six orders of magnitude smaller than the concentrations of ions produced in the reaction corresponding to the dominant equilibrium. 

A major fluctuahon is the conformahonal behavior of molecular entities, as discussed explicitly in Chapter 9, but also in Chapters 7 and 8. Other equilibria, already menhoned above, are ionizahon and tautomerism. The former is the most... 

Equilibrium constants can be written for the ionization of weak acids and weak bases, just as for any other equilibria. For the equation... 

Note that other equilibria could be written, including the disproportionation ... 

Figure 2.17. Liquid-liquid and solid-gas equilibria in intermetallic systems. In a map based on the so-called Mendeleev number coordinates the different binary combinations are represented. Only those combinations have been coded for which the existence of liquid miscibility gaps (or of solid-gas equilibria) is known. (In the same systems, other equilibria, the formation of compounds, etc. may be present). For many systems data are lacking probably in the bottom-left comer of the figure many more boxes could be added to those representing miscibility gap. Notice that the solid-gas equilibria are relevant to systems formed by metals with a large difference between their boiling temperatures.

Non-redox equilibria are expressed in terms of equilibrium constants based on activities, whereas Eh is given in volts. To compare and combine redox equilibria with other non-redox equilibria it is often convenient to use another term, pe. pe is the negative logarithm of electron activity based on the hydrogen half cell in which the redox activity is set at unity. Because pe is expressed as mol L , this term enables redox equilibria and other equilibria to be combined and expressed in terms of a single constant. 

As discussed in part 2.3.4 choice of acyl donor in transesterifications may have significant influence. The specificity of enzymes may also be influenced by the water activity, a. There are reports showing both positive and negative reports on E. Since water is introduced in the medium other equilibria are established such as between the acyl donor and water and between the produced ester and water, both leading to the formation of acid in the system. How this influences the reaction is not clear. 

At increasing salt concentrations the conductance of all solutions investigated shows the emergence of other equilibria involving the ions and ion-pairs triple ions, quadrupoles. .. become stable species. Althought one expects from chemical relaxation theory the appearance of more relaxation processes, experimentally only one relaxation process, whatever the concentration of salt, is observed. This odd behavior is intimately related to the nature of equlllbriun perturbation and observation of the response in the field modulation method. 

The Prisoner s Dilemma equilibrium differs from all the other equilibria mentioned so far, in that it is made up of aaions each of which is the best response to anything others could do, not just to their equilibrium behavior. Equilibrium then does not require a person to have correct expectations about what others will do, since he will take the same action whatever he expects them to do. (An action of this type is called a dominant strategy. 1 If he expects wrongly, he will be surprised, perhaps unpleasantly so, but he will not regret what he did. In such cases there can be unintended consequences in equilibrium. Usually, however, surprise and regret go together. 

If there are other equilibria (intraphase) involved then the K values are replaced by the distribution ratio, D. For extractions, it makes little difference which solute appears in the numerator because the a term is usually defined in such a manner that it will have a numerical value >1. Separation factor applied to chromatographic systems is expressed as a ratio of retention data (see Section 1.4) ... 

Probably other equilibria would serve just as well. Using an equilibrium constant of 103 for this reaction and a solubility product of 1.73 X 10 3 for sodium ethoxide, the constants kx = 8 X 10 3 sec. 1 and (k2/kz) = 6 X 103 were evaluated. The value for kx is fairly firm (and agrees with NMR data which indicate that the rate constant is less than 10 sec. 1), but the value of (k2/kz) is dependent on an arbitrary choice, within limits, of the EtOHOEt equilibrium constant and the sodium ethoxide solubility product. In fact, the kinetic data are consistent with any value for... 

At the low level of TMEDA used, equilibrium (45) is not likely to be of any significance but all the other equilibria must be considered. It is clear from the results of the SEC study that several species propagate and that at —30 °C the exchange among these is quite slow. Analysis of the SEC results is complicated by the curious decision of Davidjan et al. to use different monomer and organolithium concentrations in the three experiments carried to different conversions. They concluded however that the reactivity increases in the sequence... 

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