Magnitudes of equilibrium constants

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 ... 

The concept of using the base 10 logarithm to express the magnitude is a widespread practice today. Equilibrium constants of chemical reactions are often noted or compared as pK values where pK = — log 10 (magnitude of equilibrium constant). For example, the extent of dissociation of acetic acid, the acid in vinegar, is quantified by an equilibrium constant of 1.8 x 10-5. Here, then, pK = — log,o (1.8 x 1(T5) = 4.74. 

Under certain conditions chromatographic retention measurements can be used to determine the magnitude of equilibrium constants for reversible associations between a sample component and a complexing agent present in the eluent. The use of migration rate data to obtain equilibrium constants for interactions between eluents of the solvent and the solute is not novel. It has been developed for paper electrophoresis (297, 292). 

The order of magnitude of equilibrium constants varies over a huge... 

The separation of metals into distinct classes was based on empirical thermodynamic data, namely, trends in the magnitude of equilibrium constants that describe the formation of metal-ion/ligand complexes. On the basis of these criteria, metal ions can be divided into three groups hard, soft, and borderline. The partition of a particular ion in each group is shown in Figure 7.1 (Nieboer and Richardson 1980 see also Morgan and Stumm 1991). 

When no complexation between M and L or when adsorption of L on the support takes place, the elution volume of L (Vl) will be V(,+V-j and the front is sharp. When the association constants increase, the advancing side of the frontalogram should become more skewed and Vl approaches Vg. Slow attainment of equilibria between M and L or slow diffusions within the gel matrix should yield similar effects on the frontalo-grams. If these effects can be excluded,the slope and breakthrough volume of L also indicate the magnitude of equilibrium constants. Similar discussion holds for the trailing side. The frontalogram is conveniently expressed as its time derivative, which shows minute differences more clearly. 

The rate of removal of surface-active contaminants from treated water using flotation depends upon many factors. In particular, it depends on the surfactant concentration in the water bulk, the magnitude of equilibrium constant of surfactant adsorption at the air-water interface, the adsorption rate of surfactants, air flow, and air bubble dimensions. The analytical equation that relates the volume and the surface concentration of the surfactant in adsorption process is the Langmuir adsorption equation (see Appendix 8.A) ... 

After elongation has proceeded for a sufficient period of time, the protomer and polymer will reach concentrations corresponding to the equilibrium constant Ko, which from our earlier discussion may be represented as k-/k+. This constant represents the critical concentration for polymer assembly, and protomer concentrations which fall below the magnitude of this constant will not spontaneously assemble. In this sec-... 

If this constant is combined with the hydrolysis constant log10 j34 = —18.4 for Th(OH)4(aq), a solubility product log]0 X 0(s) = 9.9 for Th02(s) is calculated that lies between the values for Th02(am) and Th02(cr) (see Fig. 4). This set of equilibrium constants now describes the measured solubilities at pH > 6, but fails to account for the solubility variation of more than 10 orders of magnitude at lower pH. 

It was impossible to measure the coupling constants JAx and JBx for 7 in D20 however, for 6 (see Table V) these constants were almost equal at 7.0 Hz. The magnitudes of these constants require almost equal populations for 6a and 6c and relatively low abundance of 6b. The difference in chemical shifts for HA and HB, as the chemical shifts, are temperature independent. The following conformational equilibrium is expected to approximate that which actually exists since it agrees well with the NMR and the rotational data and general expectations based on conformational analysis,... 

Equations (XV.5.8) and (XV.5.9) predict a change of rate constant with pressure which will depend logarithmically on the partial molar volume change for the transition-state reaction. An exactly similar equation, the Kelvin equation, can be written for the change of equilibrium constant with pressure. Since AY /RT is of the order of magnitude of 10 atm " for solution reactions, it is evident that the effect of these pressure changes will be of importance only at pressures in excess of 10 atm, and indeed this is verified experimentally. 

Actually, two parallel lines are obtained for hydroxo- and oxo-complexes indicating a difference by 14 orders of magnitude between equilibrium constants... 

EXAMPLE 8 Calculate the value of the equilibrium constant for a reaction with AG° equal to 255 J at 25°C. Comment on the magnitude of the constant. 

Suppose a reaction has the equilibrium constant K = 1.3 X 10 . What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached ... 

---