Energy profile and rate law

Energy Profile and Rate Law for SN2 Reactions Reaction Order... 

Energy Profile and Rate Law of SN1 Reactions Steady State Approximation... 

We are not very interested in reactions in the gas phase, but fortunately reactions in solution follow more or less the same laws so the reaction of a proton source like HCl and a water molecule in an inert solvent would have the rate expression rate = kx [HCl] x IH2OJ. Expressing the same idea graphically requires an energy profile diagram like those we used for equilibria but concentrating rather more on AG than on AG0. 

Each pathway corresponds to a different mechanism, a different rate law, and a different activation energy. Figure 12 shows the potential energy profiles for the uncatalyzed reaction and for catalysis by three different catalysts. Because the catalyzed pathways have lower activation energy barriers, the catalysts speed up the rate of the reaction. 

Hence, conversion and temperature profiles in a plug-flow tubular reactor with constant outer wall temperature are simulated by solving two coupled first-order ODEs that represent mass and thermal energy balances at high Peclet numbers. They are summarized here for completeness in terms of a generic rate law 3R when only one chemical reaction occurs ... 

Answer Two. The thermal energy balance is not required when the enthalpy change for each chemical reaction is negligible, which causes the thermal energy generation parameters to tend toward zero. Hence, one calculates the molar density profile for reactant A within the catalyst via the mass transfer equation, which includes one-dimensional diffnsion and multiple chemical reactions. Stoichiometry is not required because the kinetic rate law for each reaction depends only on Ca. Since the microscopic mass balance is a second-order ordinary differential eqnation, it can be rewritten as two coupled first-order ODEs with split boundary conditions for Ca and its radial gradient. 

In Chapter 5 the conservation-of-energy equations (2.7-2) and (4.1-3) will be used again when the rate of accumulation is not zero and unsteady-state heat transfer occurs. The mechanistic expression for Fourier s law in the form of a partial differential equation will be used where temperature at various points and the rate of heat transfer change with time. In Section 5.6 a general differential equation of energy change will be derived and integrated for various specific cases to determine the temperature profile and heat flux. 

Figure 9.8 summarizes the general ideas presented in Sections 9.2 and 9.3. At least four types of energy profiles have been recognized for individual electrophilic aromatic substitution reactions. Case A is the case of rate-determining generation of the electrophile. It is most readily identified by kinetics. A rate law independent of... 

The species HI is a reaction intermediate it does not appear in the experimental rate law. In this case, the intermediate species is a well-known stable molecule. Often, when postulating mechanisms, we have to invoke less well-known and less stable species and in these instances, we have to rely on the chemical reasonableness of the basic assumptions. The presence of a reaction intermediate leads to a slightly more complicated reaction profile. The reaction profile for the two steps in the proposed mechanism is shown in Figure 20-14. We see that there are two transition states and one reaction intermediate. Since the transition state for the first step is the highest point on the reaction profile, the first step is the rate-determining step. It is important to understand the difference between a transition state (activated complex) and a reaction intermediate. The transition state represents the highest energy structure involved in a reaction (or step in a mechanism). Transition states exist only momentarily and can never be isolated, whereas reaction intermediates can sometimes be isolated. Transition states have partially formed bonds, whereas reaction intermediates have fully formed bonds. 

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