Definition of rate

For non-zero and the problem of defining the thennodynamic state fiinctions under non-equilibrium conditions arises (see chapter A3,2). The definition of rate of change implied by equation (A3,4,1) and equation (A3.4.2) includes changes that are not due to chemical reactions. 

Obviously dc dt = 2 dcpjtk), because for each molecule of A that reacts, two molecules of B react, so it is necessary to include the stoichiometric coefficient or at least to specify clearly what definition of rate is being used. 

Viewed in this way, the best definition of rate enhancement depends upon the relationship between enzyme and substrate concentrations and the enzyme s kinetic parameters. 

The definition of rate given in Eq. 4.2 allows us to define a rate for any given reaction. The rate calculated will be specific for that reaction, independent of which species we monitor. 

Now that we have a definition of rate, we need to develop a basic model to describe the rates of chemical reactions. The basic model takes the form of a rate law. A general rate law allows us to relate the rate of a reaction to the concentration of the reactants present. It makes sense, intuitively, that at low reactant concentrations the rate of the reaction will be quite slow. Also, at high reactant concentrations in the same reaction we would expect a faster rate. The general rate law reflects this intuition by stating that, in simple reactions, such as the one in Eq 4.1, we define the rate according to Eq. 4.4. 

Gomes, W. (1961). "Definition of Rate Constant and Activation Energy in Solid State Reactions," Nature (London) 192, 965. An article discussing the difficulties associated with interpreting activation energies for reactions in solids. 

We next ask how to define the rate of reaction in meaningful and useful ways. To answer this, let us adopt a number of definitions of rate of reaction, all... 

USEPA Definition of Rating Levels for Remediation Technologies of Groundwater... 

A simple qualitative description of how fast reaction occurs can be taken from a direct observation of how long it takes for a certain percentage reaction to occur. But in a quantitative analysis rate must be precisely defined, and once this has been done it becomes apparent how inadequate the loose definition of rate in terms of percentage reaction actually is. 

The above definition of rate refers to a chemical reaction. If we would like to use a similar term for a component, its reaction rate, or better, the... 

For those planning the use DNMR to evaluate barriers, the evaluations of sources of error covered in Section 1.1 and other published articles should be consulted. A caveat to consider the definition of rate constant carefully is in order. The author recommends the use of equation (3) and substitution into the Eyring equation as the most rehable method for obtaining an experimental value for AG. Owing to the large errors, which can arise, the use of coalescence temperatures and rate expressions at should be avoided at all costs. As primitive as it may seem, reference to Table 1 can provide a fairly accurate value for AG in most cases. 

Most of the reactions that we have considered so far happen uniformly in three-dimensional space. However, many important reactions—such as precipitations, corrosions, and many combustions—take place at surfaces. The definition of rate given earlier does not apply to surface reactions. Even so, these reactions respond to changes in concentration, pressure, and temperature in much the same way as do other reactions. 

For a stepwise reaction this definition of rate of reaction (and extent of reaction, n) will apply only if there is no accumulation of intermediate or formation of side products. It is therefore recommended that the term rate of reaction be used only in cases where it is experimentally established that these conditions apply. More generally, it is recommended that, instead, the terms rate of disappearance or rate of consumption of A (i.e., -d[A]/dt, the rate of decrease of concentration of A) or rate of appearance of P (i.e., d[P]/dt, the rate of increase of concentration of product P) be used, depending on the concentration change of the particular chemical species that is actually observed. In some cases, reference to the CHEMICAL FLUX observed may be more appropriate. 

The initially formed excited state (b state) is converted to the charge separated state (a state) by crossing over an energy barrier (E ). Definitions of rate constants are as follows kj forward rate constant of b -ja. ... 

This approach provokes strong objections. First, the basic definition of rate constant becomes blurry. Indeed, none of the coefficients in the mass action law in the whole kinetic scheme can be considered as an independent physical... 

From the definition of rate rA, we see that the rate of loss of moles of A in the reactor due to reaction is -rAV. Putting all these rates together, we find that the net rate of accumulation of moles of A in the reactor is ... 

Whal follows is a summary of key ideas relating to the definition of rate in cases in which time is Involved. Exercise 1.1 at the end of this section provides you with an opportunity to test your understanding of rate of change. 

In this section we must be careful to respect our prior concern about the definition of rate with regard to the volume of reaction mixture involved. Further, since we wish to concentrate attention on the kinetics, we shall study systems in which the conservation equation contains the reaction term alone, which is the batch reactor of equation (1-12). It is convenient to view this type of reactor in a more general sense as one in which all elements of the reaction mixture have been in the reactor for the same length of time. That is, all elements have the same age. Since the reactions we are considering here occur in a single phase, the relationships presented below pertain particularly to homogeneous batch reactions, and the systems are isothermal. 

Definition of Rate Constants, the Fundamental Differential Equation and the Law of Conservation of Mass). 275... 

Definition of rate constants in terms of kinetic constants... 

Definition of Rate Constants in Terms of Kinetic Constants Ordered Ter Bi mechanism... 

In this introductory chapter, we present the definition of rates of reaction, the general properties of the mathematical function representing the rate as well as the behavior of the ideal reactors used in the measurement of reaction rates. 

The rate equation (5.3.13) as found in the paper of Bateman et al.. Disc. Far. Soc., 10, 250 (1951) has been re-examined in the light of the correct definitions of rates given in the first chapter of the Notes. The rate of termination of R,00 should be ... 

Table 4.4. General definition of rates in different reactor operation modes.

FIG. 1—Photographic chart of sintered stainless steel transverse rupture specimens tested in 5 % aq. NaCl by immersion. Definition of ratings A—sample free from any corrosion B— up to 1 % of surface covered by stain or rust C—1-25 % of surface covered by rust D—>25 % of surface covered by rust... 

---