Fraction reacted, definition

Figure 5 shows a typical mass loss in a decomposition experiment. The obvious definition would seem to be where the mass loss is steepest, which corresponds to the peak temperature T in the DTG plot. However, this is merely the point where reaction is fastest and does not represent the start of reaction, e.g. where bonds in the compound begin to break. The position of T will depend upon the sample size, packing, and heat flow properties. The point Tjis the initial temperature or onset temperature, but is not easy to identify and depends on the sensitivity of the balance and the amount of drift or noise seen. There may be traces of impurities, which decompose or promote some decomposition ahead of the main reaction. A better definition of start of reaction is the extrapolated onset temperature T. This requires drawing of tangents to the curve at the horizontal baseline and the steepest part of the curve and marking their intersection. For a reaction that starts very slowly and only speeds up later, T and Tj will be very different and a more satisfactory point would be shown as temperature where the fraction reacted a is equal to 0.05, i.e. Tq.05- Another definition of reaction temperature, important in kinetic studies, is when the reaction is half over, that is, when the fraction reacted... 

In Chap. 5, p was defined as the fraction (or probability) of functional groups that had reacted at a certain point in the polymerization. According to the current definition provided by Eq. (6.66), p is the fraction (or probability) of propagation steps among the combined total of propagation and termination steps. The quantity 1 - p is therefore the fraction (or... 

This reaction is said to be homogeneous if it occurs within a single phase. For the time being, we are concerned only with reactions that take place in the gas phase or in a single liquid phase. These reactions are said to be elementary if they result from a single interaction (i.e., a collision) between the molecules appearing on the left-hand side of Equation (1.7). The rate at which collisions occur between A and B molecules should be proportional to their concentrations, a and b. Not all collisions cause a reaction, but at constant environmental conditions (e.g., temperature) some definite fraction should react. Thus, we expect... 

Let Yrj denote the mass fractions of the K chemical species describing the reacting flow. By definition, KYa—. Assuming that the chemical species are numbered such that the major species (e.g., reactants) appear first,2 followed by the minor species (e.g., products), we can define a linear transformation by... 

The rate of decomposition of gaseous ethylene oxide (QFUO), to CH4 and CO, has been studied by Mueller and Walters (1951) by determination of the fraction (/A) of oxide (A) reacted after a definite time interval (f) in a constant-volume batch reactor. In a series of experiments, the initial pressure of the oxide (P 0) was varied. Some of the results are as follows ... 

Fractional conversion of a reactant, /A for reactant A, say, is the ratio of the amount of A reacted at some point (time or position) to the amount introduced into the system, and is a measure of consumption of the reactant. It is defined in equation 2.2-3 for a batch system, and in equation 2.3-5 for a flow system. The definition is the same whether the system is simple or complex. 

In unimolecular reactions, where complex molecules are involved, a fraction only of the activated molecules react, and this fraction is determined by specific factors. Thus a rigid parallelism between the heats of activation and the temperatures at which different reactions attain some assigned rate cannot be expected. Nevertheless in any expression containing an exponential term that term tends to play a predominant role, and a definite, if rough, parallelism still exists, showing that even in the case of more complex reactions the value of E is perhaps the most important factor in determining the rate of reaction. 

Acid consumed in the process is also in need of definition. Hydrofluoric acid is literally consumed it reacts to form heavy polymers and ultimately is pumped from the system to a combustion chamber or to a neutralization stage where the products of neutralization are hauled off to a dump or used as landfill. Sulfuric acid is consumed in a similar manner but only as a small fraction of that charged to the process, The primary effect upon sulfuric acid is that of dilution, rather than actual consumption. The fresh sulfuric acid catalyst is typically 98, 0-... 

The (cumulative) selectivity for K (fraction of reacted A that is converted to K, see definition 1.11) in a batch reactor is... 

Fig. 1. Definition of the efficiency of a separation procedure in a radioimmunoassy. In a perfect assay all the labeled antigen would distribute between the free and bound fractions. In practice, some of the free is classified as bound (assay blank, nonspecific binding), and some of the free will be nonimmunoreactive. The greater the total amount of tracer ligand that reacts in the system, the better the assay. From Chard. ...

A. Show that in the reaction jNa + jHa = NHs, assuming ideal behavior of the gases, the maximum (equilibrium) conversion of nitrogen and hydrogen into ammonia, at any definite temperature and pressure, is obtained when the reacting gases are in the proportion of 1 to 3. (Suppose the equilibrum system consists of Na and Ha molecules in the ratio of 1 to r let x be the mole fraction of NHs formed at equilibrium. Hence, set up an expression for Kp in terms of mole fractions and total pressure, and find the condition which makes dx/dr equal to zero, i.e., for maximum conversion to NHs.)... 

In the example above, the stoichiometric amount of oxygen is 2 mol, since that is the amount that would react with the 1 mol of methane. The excess amount of oxygen is 1 mol, which is a percentage excess of 50% or a fractional excess of 0.50. These definitions are employed in the solution below. 

Suppose also that, of a starting amount of 10 mol of A, 4 form the desired product B, 2 form the undesired product C, 1 forms the undesired product D, and 3 remain unreacted. While this process produces 4 mol of valuable product, it could have produced 10 if everything went the way we wanted it to, i.e., if all 10 mol of A reacted to form B. The ratio of the 4 mol of B actually produced to the 10 it potentially could have produced is called the yield (0.40 or 40%). By definition, the yield of a reaction is a measure of how much of the desired product is produced relative to how much would have been produced if only the desired reaction occurred and if that reaction went to completion. Obviously, the fractional yield must be a number between zero and unity. Another term used in conjunction with multiple reactions is selectivity. Selectivity is a measure of how predominant the desired reaction is relative to one of the side reactions. The value of the selectivity is obtained by dividing the number of moles of a desired product actually generated by the number of moles of one of the undesired products produced by a side reaction. In the example above, the selectivity of B over C is 2.0 and that of B over D is 4.0. These definitions are employed in the solution below. 

The average kinetic energy of a collection of molecules is proportional to the absolute temperature. At a particular temperature, Tj, a definite fraction of the reactant molecules have sufficient kinetic energy, KE >E, to react to form product molecules on collision. At a higher temperature, T2, a greater fraction of the molecules possess the necessary activation energy, and the reaction proceeds at a faster rate. This is depicted in Figure 16-13 a. 

Equation (1-47) is one of the few that should be committed to memory immediately. There are, of course, corresponding definitions of conversion on the basis of mass units, and in some cases fractional conversion to product (mols product made per mol reactant fed or reacted) is a useful measure. The important thing is always to be sure how the term conversion is defined. The integrated forms of simple irreversible rate laws written with conversion, x, from equation (1-47) are ... 

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