Reaction profile

Activation parameters are often composite. Consider the value of AFf in the exchange of Cr(III) with HjO (Sect. 2.3.3), The values of k and AFf are related to the intrinsic rate and 

It is very important therefore to have information on the thermodynamic parameters, in this instance AF. These can be measured directly by diiatometry or from the relationship d nK/dP)T= - V/RTf Since AF = -3.8 cm mol-, AF5 = -0.9 + 3.8 = 2.9 cm moF, Ref. 102. We can represent the progress of this and any other reaction pic-torially by a reaction profile, using the concept of the activated complex. The reaction profile shows, often in a qualitative but useful fashion, the change of any activation parameter (AG , A//T AS Ref. 110 or AF Ref. Ill) as a function of the extent of the reaction (termed the reaction coordinate). Since each step in a reaction will have an associated transition state, and thus a separate reaction profile, we may have a continuous series of such profiles joining the reactants to the ultimate product. 

The form of the reaction profile will depend on the relative values of the rate constants. Fig. 2.5. Several interesting points may be made. 

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Mineva T, Russo N and Sicilia E 1998 Solvation effects on reaction profiles by the polarizable continuum model coupled with Gaussian density functional method J. Oomp. Ohem. 19 290-9... 

Fig. 13.9. Schematic reaction profile for the EZ isomerization of stilbene. The reaction coordinate 6 is the torsion angle about the double bond. [From FI. Meier, Angew. Chem. Int. Ed. Engl. 31 1399 (1992)]. Reproduced by permission of Wiley-VCH.

Using the same values of the kinetic parameters as in Type 1, and given C o = 0-1 mo 1/1, it is possible to solve Equation 6-155 with Equations 6-127 and 6-128 simultaneously to determine the fractional conversion X. A computer program was developed to determine the fractional conversion for different values of (-iz) and a temperature range of 260-500 K. Eigure 6-30 shows the reaction profile from the computer results. 

FIGURE 14.1 Reaction profile showing large AG for glucose oxidation, free energy change of —2,870 kj/mol catalysts lower AG, thereby accelerating rate. 

What we can display is the free energy of reactants, transition states, intermediates, and products. They are shown separated on a horizontal scale for convenience the abscissa is not defined. This display will be called a reaction profile diagram. 

Two examples of reaction profile diagrams are shown in Fig. 4-5 for the A = I <=s P sequence. The rate constants chosen give values of kss of 0.99 s-1 in case (1) and 0.0099 s l in (2). In the first diagram, step 1 is almost rate-controlling, and in the other, step 2. In Fig. 4-5 note the depth of the well in which the intermediate resides... 

Reaction profile diagrams for two sets of rate constants in the system A-—> I—h... 

Other authors identify the RCS as the one with the highest-lying transition state in a reaction profile diagram. But this, too, fails in the general sense it does not allow for irreversible reactions where an intermediate may be more stable than the reactants. 

We shall now derive a result first obtained24 by more complicated mathematics than the alternative25 given here. The 1992 Nobel Prize in Chemistry was awarded to R. A. Marcus for developing this work. We construct a family of reaction profiles (see Fig. 10-8) for different members of the series. The horizontal axis is now used to show the relative locations of the transition states. The larger AG is, the closer to product the transition states lies, and the larger AG is. By assuming that the sensitivity coefficient... 

Wilkinson s method for, 32-33 with respect to a species, 6 with respect to concentration, 16 with respect to time. 16 Reaction profile diagram. 84—85 Reaction rates, effect on of concentrations, 9 of ionic strength, 206-214 of light, 9... 

The FEP and PDLD approaches developed in the previous chapters can be used conveniently to calculate the effect of genetic mutations. For example, one can calculate the reaction profile for the native and mutant... 

FIGURE 13.30 A reaction profile for an exothermic reaction. In the activated complex theory of reaction rates, it is supposed that the potential energy (the energy due to position) increases as the reactant molecules approach each other and reaches a maximum as they form an activated complex. It then decreases as the atoms rearrange into the bonding pattern characteristic of the products and these products separate. Only molecules with enough energy can cross the activation barrier and react to form products. 

FIGURE 13.35 (a) If the rate-determining step (RDS) is the second step, the rate law for that step determines the rate law for the overall reaction. The orange curve shows the "reaction profile" for such a mechanism, with a lot of energy required for the slow step. The rate law derived from such a mechanism takes into account steps that precede the RDS. (b) If the rate-determining step is the first step, the rate law for that step must match the rate law for the overall reaction. Later steps do not affect the rate or the rate law. (c) If two routes to the product are possible, the faster one (in this case, the lower one) determines the rate of the reaction in the mechanism forming the upper route, the slow step (thinner line) is not an RDS. 

Describe the action of catalysts in terms of a reaction profile (Section 13.14). 

The mechanism of the reaction A - B consists of two steps, with the formation of a reaction intermediate. Overall, the reaction is exothermic, (a) Sketch the reaction profile, labeling the activation energies for each step and the overall enthalpy of reaction, (h) Indicate on the same diagram the effect of a catalyst on the first step of the reaction. 

Step 2 N202 + H2 — N,0 + H,0 Step 3 N20 + H2 — N, + H,0 (a) Which step in the mechanism is likely to be rate determining Explain your answer, (b) Sketch a reaction profile for the overall reaction, which is known to be exothermic. Label the activation energies of each step and the overall reaction enthalpy. 

The following schematic reaction profile is for the reaction A - D. (a) Is the overall reaction exothermic or endothermic Explain your answer, (b) How many intermediates are there Identify them, (c) Identify each activated complex and reaction intermediate, (d) Which step is rate determining Explain your answer, (e) Which step is the fastest Explain your answer. 

Figure 8.2 Reaction profile of batch and CSTR reactors...

The effects of reaction temperature, pressure and catalyst amount on the catalytic activity were also studied with TBAC. The results are summarized in Table 2. The conversion of EC increased with the increase of reaction temperature and the amount of catalyst. The conversion of EC and the selectivity of DMC increased as the pressure increased finm 250 psig to 350 psig. But, at the pressure over 350 psig, the EC conversion decreased. Although CO2 is not required for this reaction, its presence alters the reaction profile. It is reported that high pressure of CO2 can inhibit the decomposition of EC to ethylene oxide and C02[12]. 

As already pointed out above, the following chapter will concentrate on the most recent advances in catalysis using complex ferrates. It is divided by the type of ferrate employed in order to demonstrate common reaction profiles. 

A. Lipski, S. Klatte, B. Bendinger, and K. Altendorf, Differentiation of gram-negative, non-fermentative bacteria isolated from biofilters on the basis of fatty acid composition, quinone system, and physiological reaction profile, Appl. Environ. Microbiol. 58 2060 (1992). 

Figure 9.2. Reaction profiles involving a conical intersection (a) a photochemical reaction (b) an upwards excursion via a conical intersection in a nonadiabatic reaction (c) a chemiluminescent reaction.

Figure 9.17. Adiabatic and nonadiabatic reaction profiles for the TICT process.

We are now in a position to discuss the reaction profile outlined in Figure 9.17 in the full space of coordinates corresponding to the branching space Xj X2 of a conical intersection and the torsional coordinate X3. This discussion will be focused on four related concepts ... 

Figure 8.2. Reaction profile for 2-nitroacetophenone hydrogenation at 323 K and 5 barg hydrogen pressure.

Figure 31.1 - Reaction profile and product distribution obtained in the hydrogenation reaction carried out by using Cu/Si02...

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