Concentration jump

FIG. 23-16 Concentration jump at the inlet of a closed ends vessel with dispersion. Second-order reaction with kCat = 5. 

Concentration-jump methods, such as the pH-jump technique cited earlier, can be used in relaxation kinetics, but this approach is described later (Section 4.4). 

Stopped flow is sometimes described as concentration jump kinetics. Variations... 

Time/s Hypothetical experiment with [Ph3C ]o = 0 Concentration-jump experiment ... 

The entries were reconstructed for Eq. (3-30) from the rate constant values of kI = 0.406 s l and k 1 = 383 L mol"1 1 from Ref. 2. One calculation is for the reaction starting with A alone, and the other for a concentration-jump experiment with a two-fold dilution of a solution made up to have an original concentration of A of 2.84 X... 

Returning yet again to the concentration-jump data for the triphenyl methyl system, we find in Fig. 3-4 plots of 8, versus time and of In[8,/(a - 4A 1<5,)] versus time. The values of 8, follow from the values of [A], given in Table 3-2. Least-squares fitting gives fci = 0.401 0.001 s-1. 

The lines show data for the triphenyl methyl system, Eq. (3-30). The data represent the results of a relaxation experiment consisting of a concentration jump (i.e., a dilution) on a pre-equilibrated solution. The solid line shows the least-squares fit of the second data set in Table 3-2 according to Eq. (3-36). Panel A shows 5, itself, and panel B the quantity ln[S,/(a - 4K-- 5,)], as in Eq. (3-35). 

We shall now consider a simplifying approximation for the system A 2P. The reaction proceeds at a rate expressed in terms of S by Eq. (3-33). If the shift resulting from the concentration jump is small, the term AK l82 is negligible in comparison to (1 + 4 l [P](,)S. In that case, the solution is... 

Opposing reactions. Use the data on the right side of Table 3-2, concerning the triphenyl methyl radical, to calculate ki. This experiment refers to the concentration-jump method in which the parent solution was diluted with solvent to twice its initial volume. 

Opposing reactions. Derive a kinetic equation for the system A P + Q that expresses the time dependence of 8, the shift in a concentration-jump experiment. Could 8 also be regarded as the difference between the timed value of [A] and the equilibrium value of [A] If so, what are the limitations on the ways in which A, P, and Q might be mixed ... 

Concentration-jump method. The following disproportionation equilibrium has been studied by the concentration-jump technique 13... 

Competition reactions ad eosdem, 106 ad eundem, 105 (See also Reactions, trapping) Competitive inhibitor, 92 Complexation equilibria, 145-148 Composite rate constants, 161-164 Concentration-jump method, 52-55 Concurrent reactions, 58-64 Consecutive reactions, 70, 130 Continuous-flow method, 254—255 Control factor, 85 Crossover experiment, 112... 

Reaction scheme, defined, 9 Reactions back, 26 branching, 189 chain, 181-182, 187-189 competition, 105. 106 concurrent, 58-64 consecutive, 70, 130 diffusion-controlled, 199-202 elementary, 2, 4, 5, 12, 55 exchange, kinetics of, 55-58, 176 induced, 102 opposing, 49-55 oscillating, 190-192 parallel, 58-64, 129 product-catalyzed, 36-37 reversible, 46-55 termination, 182 trapping, 2, 102, 126 Reactivity, 112 Reactivity pattern, 106 Reactivity-selectivity principle, 238 Relaxation kinetics, 52, 257 -260 Relaxation time, 257 Reorganization energy, 241 Reversible reactions, 46-55 concentration-jump technique for, 52-55... 

T Higuchi, S Dayal, I Pitman. Effects of solute-solvent complexation reactions on dissolution kinetics Testing of a model by using a concentration jump technique. J Pharm Sci 61 695, 1972. 

Let Xj->s and x2->s+. The two integrals tend to zero while the other terms remain finite because of the concentration jump. The velocity ds/dt of the discontinuity is therefore... 

As a technique for selective surface illumination at liquid/solid interfaces, TIRF was first introduced by Hirschfeld(1) in 1965. Other important early applications were pioneered by Harrick and Loeb(2) in 1973 for detecting fluorescence from a surface coated with dansyl-labeled bovine serum allbumin, by Kronick and Little(3) in 1975 for measuring the equilibrium constant between soluble fluorescent-labeled antibodies and surface-immobilized antigens, and by Watkins and Robertson(4) in 1977 for measuring kinetics of protein adsorption following a concentration jump. Previous rcvicws(5 7) contain additional references to some important early work. Section 7.5 presents a literature review of recent work. 

Using a concentration jump as the perturbation, Sutherland et a/.(113) measured the kinetics of binding of fluorescein-labeled human IgG (present as an antigen in solution) to surface-immobilized sheep anti-human IgG. Two TIRF surfaces were used a planar slide and a fiber-optic cylinder. Also using a TIRF recovery after a concentration jump, Kalb et a/,(114) measured the slow ( 10 4 s 1) unbinding kinetics of anti-trinitrophenol (TNP) antibodies in solution and a TNP-derivatized lipid in a planar bilayer. 

Phase separation through NG generates the second phase with the equilibrium composition on the phase diagram that corresponds to the moment of phase separation through concentration jump as described in Figure 3.18a. The Tg difference in each phase, therefore,... 

We now discuss two additional solutions of Fick s second law (Eq. 18-14) for particular boundary conditions. The first one deals with diffusion from a surface with fixed boundary concentration, C0, into the semi-infinite space. The second one involves the disappearance ( erosion ) of a concentration jump. Both cases will be important when dealing with the transport through boundaries (Chapter 19). No derivations will be given below. The interested reader is referred to Crank (1975) and Carslaw and Jaeger (1959) or to mathematical textbooks dealing with particular techniques for solving Eq. 18-14. 

Figure 18.5 Diffusion at a concentration jump between area A and B. By redefining the concentrations in A and...

The dashed line in Fig. 19.7 gives the concentration in zone B expressed as the corresponding A-phase equilibrium concentration. This modified representation is like an extrapolation of the A-phase concentration scheme into system B. In fact, it is the same as considering the variability of activity or fugacity of the chemical, rather than its concentration, through the adjacent media. Consequently, the concentration jump at the phase boundary disappears the concentration profile (or more accurately the chemical activity profile) across the boundary looks like that shown in Fig. 19.6. 

Though in principle the steady-state solution of Eq. 20-50 together with the mentioned boundary conditions can be derived by well-known techniques (see Chapter 22), we will spare the reader the derivation. Instead, we prefer to discuss the qualitative aspects of the concentration of species A and D across the stagnant film. In order to make it easier to read Fig. 20.12, we draw the concentrations of A and D as if the equilibrium constant Kr of Eq. 12-17 and the Henry s law constant of compound A were 1. Thus, [A] and [D] at equilibrium are equal, and [A] does not show a concentration jump at the air-water interface. Note that the following... 

There are two inconveniences connected with model (a) How to explain in such a kinetic scheme that the transported P-mer does not belong to the gel itself, although it evidently causes the concentration jump c, - c, + 5c, on the sharp boundary surface between sol and gel This dicrepancy only vanishes in the reversible-thermodynamic equilibrium where 5c, - 0 and 5Q/K - 0 for any P however, A - 0 (and not A -+ 1, as should be expected) is obtained from Eq. (27c) in this case, because ks must stay finite and positive in the reversible polymer transport. 

Concentration jump 10H—102 (conventional) 103-10 3 (stopped flow) Spectrophotometric Fluorimetric and many others... 

The stopped-flow method is more often used than any other technique for observing fast reactions with half-lives of a few milliseconds. Another attribute of this method is that small amounts of reactants are used. One must realize, however, that flow techniques are relaxation procedures that involve concentration jumps after mixing. Thus, the mixing or perturbation time determines the fastest possible rate that can be measured. Stopped-flow methods have been widely used to study organic and inorganic chemical reactions and to elucidate enzymatic processes in biochemistry (Robinson, 1975 1986). The application of stopped-flow methods to study reactions on soil constituents is very limited to date (Ikeda et ai, 1984a). 

Negishi, H., Sasaki, M., Iwaki, T, Hayes, K. F., and Yasunaga, T. (1984). Kinetic study of adsorption-desorption of methanol on H-ZSM-5 using a new gas-concentration jump technique. J. Phys. Chem. 88, 5564-5569. 

---