Unique instantaneous reaction

In the remainder of the chapter, the term reaction rate is used specifically to mean the unique instantaneous reaction rate written here. The two conditions relating to unique average rates described in Section 13.1 of the Study Guide also apply here. 

In the remainder of the chapter, the term reaction rate is used specifically to mean the unique instantaneous reaction rate written above. 

The differential coefficients d[R]/df and d P]/df are the mathematical expressions for the slope of the tangent drawn to a curve at the time of interest. Similarly, the unique instantaneous rate of a reaction is defined as in Eq. 2, but with differential coefficients ... 

When the stoichiometric coefficients, va, vy, etc., are included in the rate law, as in Equation 3.5, the reaction has a unique rate constant (k) under specified conditions regardless of whether the rate is measured by monitoring the changing concentration of A, B or C. It also follows from Equation 3.5 that (except for zero-order reactions) the instantaneous rate of a reaction changes as the reaction proceeds, as will be illustrated later in Fig. 3.1. Thus, k is the parameter which measures whether the reaction (imprecisely expressed) is fast or slow . In any case, it follows that any property of a reacting system which relates (preferably directly) to the concentration of any component in the chemical reaction maybe monitored to measure the rate and, hence, to investigate the rate law and quantify the rate constant. 

In this technique, an rf encodable microchip is coupled with a capsule of derivatized polystyrene resin such that each unique synthesis site can be tagged with a unique identifier code. The inert nature of the rf transponder construction renders this tagging strategy compatible with virtually all synthetic methods. Additionally, the noninvasive transmission or retrieval of information from any capsule is unambiguous and instantaneous, avoiding the possibility of long reaction and/or analysis times associated with chemical tags. 

The tremendous release of energy from nuclear reactions makes possible a unique family of applications for long-lived radioisotopes that are important to health, science, and industry. Whereas fission and fusion occur almost instantaneously, other radioactive decay processes occur in times ranging from a few minutes to thousands of years. The general areas of application may be grouped into irradiation, thermal energy generation, and tracer applications.57... 

In our illustrative calculated results, chain transfer reactions are neglected in order to highlight unique characteristics of emulsion polymerization. However, the radical entry rate into a polymer particle is often much smaller than the chain transfer frequency in emulsion polymerization usually. In such cases, dead polymer chain formation is dominated by chain transfer reactions, and the instantaneous weight fraction distribution is given by the following most probable distribution ... 

Pipeline Mixers used as Reactors for Fast C/C Reactions. Taylor (1996) and colleagues (1998) conducted a study to determine scale-up procedures for fast C/C reactions in pipeline mixers. They used the fourth Bourne reaction, which is the acid catalyzed hydrolysis of dimethoxypropane (DMP) to acetone and methanol. This is an extremely rapid reaction when catalyzed by HCl. The competitive reaction scheme, which is a unique one, is one in which NaOH reacts practically instantaneously with the HCl to remove the catalyst for the hydrolysis reaction. A water/ethanol solution of NaOH and DMP was fed as a main stream to a Kenics helical element mixer and an aqueous side stream containing slightly greater (abour 5% greater) than equimolar amount of NaOH was fed as the side stream. The product was analyzed by GC for methanol and acetone. For extremely rapid mixing, essentially no hydrolysis occurred however, for slow mixing, essentially all the DMP is hydrolyzed because acidic conditions cause very rapid hydrolysis of the DMP. 

WebReactions (http //www.WebReactions.net) is a new, unique reaction search system offering direct retrieval of reaction precedents through the Internet. For a limited time the 400000-reaction archive from InfoChem GmbH, Munich, is available for searching without cost. The Web-Reactions system is easy to learn and use, though it works only with Netscape Navigator, not Internet Explorer 5.0. It is virtually instantaneous in displaying matches, not just for... 

Microwave heating, being specific and instantaneous, is unique and has found a place in chemical synthesis. Specifically, the solvent-free reactions are convenient to perform and have dear advantages over conventional heating procedures, as... 

Instead of specifying only the nuclear coordinates It (r) as a function of time during a reaction, we will also monitor the nuclear momenta p(r) to gain a complete picture of the molecular dynamics in what we call phase space. One advantage of working in phase space is that, unlike configuration space, it is unique. Although trajectories may cross in coordinate space, they never cross in phase space if two trajectories have the same instantaneous values of (p, x) then they necessarily must have arisen from the same initial condition. The... 

The nc-Li4Ti50i2 negative electrode was developed to have a unique nanostructure that can operate at unusually high current densities. Nanocrystalline s attached onto carbon nanofibers were prepared by a unique technique (UC method) of a mechanochemical sol-gel reaction under ultracentrifugal force field [22], followed by an instantaneous heat treatment under vacuum for very short duration... 

Instantaneous growth of coke was assumed, that is, the rate-determining step is the rate of site coverage by coke precursor. The molecular mass of coke, Me, is unique and determined by the reaction conditions. It is independent of time. 

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