Reaction progress graphs

Figure 2.1 Reaction progress graph exergonic reaction...

Figure 2.2 Reaction progress graph endergonic reaction...

If we let and t2 represent the times corresponding to reaction progress variables and <5J, respectively, the time ratio t2/tl for fixed values of <5 and <5 will depend only on the ratio of rate constants k. One may readily prepare a table or graph of <5 versus k t for fixed k and then cross-plot or cross-tabulate the data to obtain the relation between k and ktt at a fixed value of <5. Table 5.1 is of this type. At specified values of <5 and S one may compute the difference log(fe1t)2 — log f) which is identical with log t2 — log tj. One then enters the table using experimental values of t2 and tx and reads off the value of k = k2/kv One application of this time-ratio method is given in Illustration 5.5. 

The presence of a lag period in many coupled assays and difficulties in determining the linear portion of a curve present the main problems in the calculation of enzyme activity using reaction rate analysers. In the simplest instruments the slope of the curve in the first few seconds of the reaction is extrapolated into a straight line or, if the reaction is known to show a lag period, the rate of reaction after a defined period of time can be measured. The more sophisticated instruments use microcomputers to determine the linear portion of the curve and calculate the enzyme activity directly from the slope. The second derivative of the reaction progress curve (rate of change of the slope) can be monitored by the computer and when a value of zero is held for a period of time (10—15 seconds) this indicates a linear section of the graph. From the value for the slope, the enzyme activity can be calculated. 

Now examine the graph in Figure 6.2. The blue line on the graph shows the concentration of product C as the reaction progresses, based on the data in Table 6.1. 

Consider the following graph of the total free energy of reactants and products versus reaction progress for a general reaction, Reactants — Products ... 

Where does the activated complex appear in a graph of how potential energy changes with reaction progress ... 

The reaction rate depends on the concentrations oj reactants, and as a result, the graph [referring to the concentration of reactant-time graph] shows that the gradient at any point along with the line will decrease. As the gradient is equal to reaction rate, as rate=d[C]/dt, this shows that reaction rate decreases as the reaction progresses. [UF-I-05]... 

The graphs show that rate of a reaction is not constant but varies with time due to changes in the concentrations of reactants (Figure 6.25). As the reaction progresses the reactants are continually being used up. Since the rate of a reaction varies with time, it is usually necessary to express the rate at a particular time instead of averaging... 

Now if we plot these quantities of ammonia nitrogen as ordinates against time intervals as abscissae, we shall obtain the graph shown in Fig. 31. From the graph we can obtain the reaction velocity in moles/I./sec. It is the initial reaction velocity which is of interest, since as the reaction progresses the conditions change as a result of the disappearance of the substrate and the accumulation of the reaction products, etc. 

Fig, 6,3 The rate of a chemical reaction is the slope (without the sign) of the tangent to the curve showing the variation of concentration of a species with time. This graph is a plot of the concentration of a reactant, which is consumed as the reaction progresses. The rate of consumption decreases in the course of the reaction as the concentration of reactant decreases. 

Chemical and pharmaceutical research organizations generate, analyze and distill large volumes of scientific data. Laboratory notebooks track daily research progress, accumulating data in the form of structures, equations, reactions, tables, graphs and text. Tables are commonly used to contain information relating to... 

Consider the following graph representing the progression of a reaction with time. 

Figure 14 displays the product formation of H20, N2, C02, and CO. The concentration C(t) is represented by the actual number of product molecules formed at time t. Each point on the graphs (open circles) represents an average over a 250-fs interval. The number molecules in the simulation were sufficient to capture clear trends in the chemical composition of the species involved. It is not surprising to find that the rate of H20 formation is much faster than that of N2. Fewer reaction steps are required to produce a triatomic species like water, whereas the formation of N2 involves a much more complicated mechanism.108 Furthermore, the formation of water starts around 0.5 ps and seems to have reached a steady state at 10 ps, with oscillatory behavior of decomposition and formation clearly visible. The formation of N2, on the other hand, starts around 1.5 ps and is still progressing (as the slope of the graph is slightly positive) after 55 ps of simulation time, albeit slowly. 

A typical graph of the progress of protein hydrolysis by the pH-stat technique is shown in Figure B2.2.5. The pH-stat technique offers reliability, reproducibility, and simplicity. In addition, the technique has the advantage that no secondary reaction is needed. However, if the equipment needed to perform a pH-stat experiment is not available, the ninhydrin and TNBS techniques are good alternatives. 

If the initial flow velocity is 400 cm s 1, calculate the time to reach an observation point 1 cm along the reaction tube. If the acceleration is such that the velocity increases progressively to 800, 1200 and 1600 cm s-1, calculate the reaction times corresponding to these flow rates. If the absorbances corresponding to these times are 0.124, 0.437, 0.655 and 0.812, draw a graph showing the progress of reaction. 

To interpret new experimental chemical kinetic data characterized by complex dynamic behaviour (hysteresis, self-oscillations) proved to be vitally important for the adoption of new general scientific ideas. The methods of the qualitative theory of differential equations and of graph theory permitted us to perform the analysis for the effect of mechanism structures on the kinetic peculiarities of catalytic reactions [6,10,11]. This tendency will be deepened. To our mind, fast progress is to be expected in studying distributed systems. Despite the complexity of the processes observed (wave and autowave), their interpretation is ensured by a new apparatus that is both effective and simple. 

This data is quite often placed on a graph to illustrate the progression of the reaction. Figures 16.1 and 16.2 show typical curves for the appearance and disappearance of a substance. 

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