The Rate-Limiting Step

When heterogeneous reactions are carried out at steady state, the rates of each of the three reaction steps in series (adsorption, surface reaction, and desorption) are equal to one another  

The concept of a Since we observe only the total resistance, it is our task to find which 

An example of an adsorption-limited reaction is the synthesis of ammonia the reaction of carbon monoxide and nitric oxide is an example of a sm-face-limited reaction. The synthesis of ammonia from hydrogen and nitrogen, 

Since we obscrv c only the total resistance. A,o, it is our task to lind which resistance is much larger (say. 1(H) fl) than the other two resistances (say, 0.1 Q). Thus, if we could lower the largest resistance, the current / (i.e.,, would 

An example of an adsorption-limited reaction is the synthesis of ammonia from hydrogen and nitrogen, 

The rate-limiting step is believed to be the adsorption of the Nj molecule as an N atom. 

An example of a surface-limited reaction is the reaction of two noxious automobile exhaust products, CO and NO. 

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Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

The rate-limiting step typically occurs at the air—Hquid interface and, for biological species without diffusion limitations, the overall relationship can be simply written at steady state as... 

The neurotransmitter must be present in presynaptic nerve terminals and the precursors and enzymes necessary for its synthesis must be present in the neuron. For example, ACh is stored in vesicles specifically in cholinergic nerve terminals. It is synthesized from choline and acetyl-coenzyme A (acetyl-CoA) by the enzyme, choline acetyltransferase. Choline is taken up by a high affinity transporter specific to cholinergic nerve terminals. Choline uptake appears to be the rate-limiting step in ACh synthesis, and is regulated to keep pace with demands for the neurotransmitter. Dopamine [51 -61-6] (2) is synthesized from tyrosine by tyrosine hydroxylase, which converts tyrosine to L-dopa (3,4-dihydroxy-L-phenylalanine) (3), and dopa decarboxylase, which converts L-dopa to dopamine. 

The dopamine is then concentrated in storage vesicles via an ATP-dependent process. Here the rate-limiting step appears not to be precursor uptake, under normal conditions, but tyrosine hydroxylase activity. This is regulated by protein phosphorylation and by de novo enzyme synthesis. The enzyme requites oxygen, ferrous iron, and tetrahydrobiopterin (BH. The enzymatic conversion of the precursor to the active agent and its subsequent storage in a vesicle are energy-dependent processes. 

Electrode kinetics lend themselves to treatment usiag the absolute reaction rate theory or the transition state theory (36,37). In these treatments, the path followed by the reaction proceeds by a route involving an activated complex where the element determining the reaction rate, ie, the rate limiting step, is the dissociation of the activated complex. The general electrode reaction may be described as ... 

Catecholamine biosynthesis begins with the uptake of the amino acid tyrosine into the sympathetic neuronal cytoplasm, and conversion to DOPA by tyrosine hydroxylase. This enzyme is highly localized to the adrenal medulla, sympathetic nerves, and central adrenergic and dopaminergic nerves. Tyrosine hydroxylase activity is subject to feedback inhibition by its products DOPA, NE, and DA, and is the rate-limiting step in catecholamine synthesis the enzyme can be blocked by the competitive inhibitor a-methyl-/)-tyrosine (31). 

In reaction engineering, laboratory catal54ic reactors are tools or instruments to study how catalysts behave in some desired reaction. Quantitatively, the investigator wants to know how much of the desired product can be made per unit weight of catalyst, how much raw material will be used, and what byproducts will be made. This is the basic information needed to estimate the costs and profitability of the process. The economic consequence of our estimates also forces us to clarify what the rate limiting steps are, and how much transfer processes influence the rates, i.e., everything that is needed for a secure scale-up. Making the... 

If a sequence of reaction steps consists only of irreversible steps, then all forward rates must be equal. When this occurs, the intermediates or active centers concentrations will adjust themselves to achieve this. The reaction that consumes the active center or intermediate of the highest concentration is the rate limiting step. Even in this case all rates must be equal. One should be cautious when speaking about the slowest rate perhaps the smallest rate constant would be somewhat better. 

For a sequenee of reaetion steps two more eoneepts will be used in kinetics, besides the previous rules for single reaetions. One is the steady-state approximation and the seeond is the rate limiting step eoneept. These two are in strict sense incompatible, yet assumption of both causes little error. Both were explained on Figure 6.1.1 Boudart (1968) credits Kenzi Tamaru with the graphical representation of reaction sequences. Here this will be used quantitatively on a logarithmic scale. 

Remarks The aim here was not the description of the mechanism of the real methanol synthesis, where CO2 may have a significant role. Here we created the simplest mechanistic scheme requiring only that it should represent the known laws of thermodynamics, kinetics in general, and mathematics in exact form without approximations. This was done for the purpose of testing our own skills in kinetic modeling and reactor design on an exact mathematical description of a reaction rate that does not even invoke the rate-limiting step assumption. 

In the native protein these less stable ds-proline peptides are stabilized by the tertiary structure but in the unfolded state these constraints are relaxed and there is an equilibrium between ds- and trans-isomers at each peptide bond. When the protein is refolded a substantial fraction of the molecules have one or more proline-peptide bonds in the incorrect form and the greater the number of proline residues the greater the fraction of such molecules. Cis-trans isomerization of proline peptides is intrinsically a slow process and in vitro it is frequently the rate-limiting step in folding for those molecules that have been trapped in a folding intermediate with the wrong isomer. 

As with simple imines, the identity of the rate-limiting step changes with solution pH.. s the pH decreases, the rate of the addition decreases because protonation of the amino compound reduces the concentration of the nucleophilic unprotonated form. Thus, whereas the dehydration step is normalfy rate-determining in neutral and basic solution, addition becomes rate-determining in acidic solutions. 

A postulated meehanism for a reaetion in the forward direetion must also hold true for the reverse reaetion. Three eorollaries of this guideline should be borne in mind when postulating a reaetion meehanism. First, the rate-limiting step for the reverse... 

Tubular reactors often offer the greatest potential for inventory reduction. They are usually simple, have no moving parts, and a minimum number of joints and connections that can leak. Mass transfer is often the rate-limiting step in gas-liquid reactions. Novel reactor designs that increase mass transfer can reduce reactor size and may also improve process yields. 

Since NFI3 is highly water-soluble and neutralization within the droplet occurs rapidly, " the rate-limiting step in acid neutralization is normally NH 3 transport to the air/droplet interface, which is dependent on [NH3]4 and particle surface area. At high [NH3J4, the rate of NH, uptake across the air/droplet interface is given by... 

These experiments verified that cleavage of the C—H bond is occurring in the rate-limiting step, but proof of the necessity of a trans relationship of the C—H to the nitrogen-mereury complex was lacking. Indications that such a relation was necessary are found in studies of the mercuric acetate oxidation of alkaloids, which will be discussed subsequently. 

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