Kinetics vs. Equilibrium

A reaction that is limited by equilibrium is finished. Waiting longer will make no difference. An example of this is the absorption of H S from refinery fuel gas into an amine solution. Depending on the concentration of the HjS in the fuel gas, the amine solution will become saturated with H S. Mixing the fuel gas and the amine solution for a longer period of time will not push more of the H S into the amine solution. The reaction is complete, and we say the absorption of H S by amine is limited by equilibrium. 

A similar problem occurs in the amine solution regenerator or stripper (see Fig. 33.1). The H S strips out easily. Residual CO, which is more tightly boimd to the amine molecule, requires lots of trays and lots of steam to strip out. 

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Bordwell, F. G. Matthews, W. S. Vanier, N. R. Acidities of carbon acids. IV. Kinetic vs equilibrium acidities as measures of carbanion stabilities. The relative effects of phenylthio, diphe-nylphosphino, and phenyl groups./. Am. Chem. Soc. 1975, 97, 442-443. 

Equilibrium control vs. kinetic, 395 Equilibrium reactions, controlling, 65-66 Equilibrium reactors, simulating, 436 Equipment... 

FIGURE 2 Illustration of cooperative vs. noncooperative unfolding transitions. If the native state of a protein (A/) is denatured into the unfolded state (I/) in a single transition (pathway 1), then it is a two-state or cooperative unfolding transition. Alternatively, the native state may be converted into one or more intermediate states (pathway 2). For example, if a protein is comprised of multiple domains, one of the domains may be unfolded first. It is also possible to form a completely different intermediate before unfolding completely. The presence of intermediate species may be observed using kinetic or equilibrium techniques. However, intermediates detectable by kinetic methods may or may not be observable by equilibrium methods. 

So far, we have examined specific cases to illustrate the effect of kinetics vs. thermodynamics upon reacting systems (butadiene) and how the thermodynamic property Gibbs energy allows us to calculate equilibrium compositions by quantifying the trade-off between energy and entropy (HCl). We now wish to develop a general approach so that we can analyze the chemical reaction equilibria for any system of interest. 

The interfacial transfer kinetics were then investigated by perturbing the equilibrium, through the depletion of Cu + in the aqueous phase, by reduction to Cu at an UME located in close proximity to the aqueous-organic interface. This process promoted the transfer of Cu into the aqueous phase, via the transport and decomplexation of the cupric ion-oxime complex, resulting in an enhanced steady-state current at the UME. Approach curve measurements of i/i oo) vs. d allowed the kinetics of the transfer process to be determined unambiguously [9,18]. 

The dynamics of interstrand hole transport have also been investigated for several hairpins possessing GACC hole transport sequences in which a GG secondary donor is located in the complementary strand [41]. Kinetic data for 4GACC are reported in Fig. 9 and the resulting equilibrium data in Table 1. Comparison of the values of kt for 4GACC and 4GAGG shows that there is a kinetic penalty of 1/6 for inter- vs intrastrand hole transport. A... 

Franke [47] undertook a comprehensive electroanalytical study of K2S207 mixtures with K2S04, which is formed by Eqs. (47) and (48) and V2Os, a widely-used oxidation catalyst for S02. Pure pyrosulfate under N2 or air (Fig. 38a,b) shows only the reduction to S02 and sulfate, Eq. (48) (all potentials are vs. Ag/Ag+). When S02 is added, a new reduction and oxidation peak appear (Fig. 38c,d). When the electrolyte was pre-saturated with K2S04 (ca. 4 wt.%) (Fig. 39) the gas composition had no direct effect on the voltammetry. Although the equilibrium for Eq. (49) lies well to the right at this temperature, 400 °C, the kinetics are quite slow in the absence of a catalyst. The equilibrium between pyrosulfate and sulfate, Eq. (47), lies well to the left (K = 2 x 10-6), but will proceed to the right in the absence of S03. Thus, the new peaks are sulfate oxidation, Eq. (43), and S03 reduction to sulfite ... 

The equilibrium constant for ATRP, XATRp= k/kd, provides critical information about the position of dynamic equilibrium between dormant and active species during polymerization (Scheme 4). The relative magnitude of KATRp can be easily accessed from the polymerization kinetics using ln([M]0/[M]t) vs.t plots, which provide values... 

A point which emerges very clearly from the above discussion of structural effects on SN2 ring-closure reactions, is that there is a special effect, namely, a substantial reduction of non-bonded interactions in the transition states for closing of the smallest rings. This effect is held responsible for remarkably high kinetic EM s for the 3- and 4-membered rings in spite of their extremely low equilibrium EM s, and unusually high rate ratios of 5- vs 6-membered... 

Measurements of terrestrial Mg isotope ratios on a plot of A Mg vs. 5 Mg are all within the region bounded by the equilibrium and kinetic mass fractionation laws given expected uncertainties (Fig. 5). Apparently, all of the terrestrial reservoirs represented by the data thus far are related to the primitive chondrite/mantle reservoir by relatively simple fractionation histories. Adherence of the data to the regions accessible by simple mass fractionation processes in Figure 5 (the shaded regions in Fig. 3) is testimony to the veracity of the fractionation laws since there is no reason to suspect that Mg could be affected by any processes other than purely mass-dependent fractionation on Earth. 

Figure 5. A plot of A Mg vs. 5 Mg for terrestrial Mg materials. Within best estimates of uncertainties (cross) all of the data lie in the region bounded by equilibrium and kinetic mass fractionation laws. Waters, carbonates, and organic Mg (chlorophyll) have higher A Mg values than mantle and crustal Mg reservoirs represented by mantle pyroxene, loess, and continental basalts. The difference in A Mg values is attributable to episodes of kinetic mass fractionation.

Figure 7. A Mg vs. 5 Mg plot of calcite speleothems and their drip waters from the Soreq cave site, Israel (data from Galy et al. 2002) compared with seawater. The horizontal trend of the data suggests that Mg in carbonates is related to aqueous Mg by equilibrium fractionation processes. Results of a three-isotope regression, shown on the figure and in Table 3, confirm that the (3 value defined by the data is similar to the predicted equilibrium value of 0.521 and distinct from kinetic values. The positive A Mg characteristic of the speleothem carbonates is apparently inherited from the waters. The positive A Mg values of the waters appear to be produced by kinetic fractionation relative to primitive terrestrial Mg reservoirs (the origin).

Figure 8. A Mg vs. 5 Mg plot of limestone, dolostone, and marble samples (data from Galy et al. 2002) compared with a sample of foraminifera of various species (Chang et al. 2003) and seawater (Chang et al. 2003, this study). The broadly horizontal trend of the carbonates at elevated A Mg suggests a component of equilibrium fractionation relative to seawater. The P value derived by regression of these 5 Mg and 5 Mg data is within the range for equilibrium fractionation and statistically distinguishable from purely kinetic fractionation.

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