Average rate of a reaction

To avoid the ambiguity associated with several ways of reporting a reaction rate, we can report a single unique average rate of a reaction without specifying the species. The unique average rate of the reaction a A + b > r C + d D is any of the following four equal quantities ... 

The average rate of a reaction is the change in concentration of a species divided by the time over which the change takes place the unique average rate is the average rate divided by the stoichiometric coefficient of the species monitored. Spectroscopic techniques are widely used to study reaction rates, particularly for fast reactions. 

The average rate of a reaction can be expressed as the change in concentration (A c) over some time interval... 

The average rate of a reaction is the average change in the concentration of a reactant or product per unit time over a given time interval. For example, using the data in Table 6.1, you can determine the average rate of the reaction from t = 0.0 s to t = 5.0 s. 

You can see this calculation in Figure 6.2. On a concentration-time graph, the average rate of a reaction is represented by the slope of a line that is drawn between two points on the curve. This line is called a secant. 

The slope of a tangent drawn to a concentration-time curve represents the instantaneous rate of the reaction. The slope of a secant is used to determine the average rate of a reaction. 

For most reactions that you will study the average rate of a reaction (near the start of the reaction) at a particular time t seconds can be taken to be... 

The average rate of a reaction is analogous to the average speed of a car. If the average position of a car is recorded at two different times, then... 

Table 12.2 illustrates how the average rate of a reaction decreases with time. Why does the average rate decrease with time How does the instantaneous rate of a reaction depend on time Why are initial rates used by convention ... 

Explain why the average rate of a reaction depends on the length of the time interval over which the rate is measured. 

Explain what is meant by the average rate of a reaction. 

Alternatively, the average rate of a reaction may be defined as the rate at which the product concentration rises over a period of time ... 

The concepts introduced here for the description of reaction rates are used whenever we expiore such bioiogicai processes as enzymatic transformations, eiectron transfer reactions in metaboiism, and the transport of moiecuies and ions across membranes. The average rate of a reaction is defined in terms of the rate of change of the concentration of a designated species ... 

To set up expressions for the instantaneous rate of a reaction, we consider At to be very small so that t and t + At are close together we determine the concentration of a reactant or product at those times and find the average rate from Eq. 1. Then we decrease the interval and repeat the calculation. We can imagine continuing the process until the interval At has become infinitely small (denoted d/) and the change in molar concentration of a reactant R has become infinitesimal (denoted d R]). Then we define the instantaneous rate as... 

Write the mathematical equation used to determine the average rate of a chemical reaction. What factor is held constant What are the variables ... 

As an excellent, simple example of how fluctuating parameters can affect a reacting system, one can examine how the mean rate of a reaction would differ from the rate evaluated at the mean properties when there are no correlations among these properties. In flow reactors, time-averaged concentrations and temperatures are usually measured, and then rates are determined from these quantities. Only by optical techniques or very fast response thermocouples could the proper instantaneous rate values be measured, and these would fluctuate with time. 

In the following ThoughtLab, you will use experimental data to draw a graph that shows the change in concentration of the product of a reaction. Then you will use the graph to help you determine the instantaneous rate and average rate of the reaction. 

As quantitatively as possible, state a relationship between [CH3COOH] and the average rate of the reaction. 

In this section, you learned how to express reaction rates and how to analyze reaction rate graphs. You also learned how to determine the average rate and instantaneous rate of a reaction, given appropriate data. Then you examined different techniques for monitoring the rate of a reaction. Finally, you carried out an investigation to review some of the factors that affect reaction rate. In the next section, you will learn how to use a rate law equation to show the quantitative relationships between reaction rate and concentration. 

In transition-state theory, the absolute rate of a reaction is directly proportional to the concentration of the activated complex at a given temperature and pressure. The rate of the reaction is equal to the concentration of the activated complex times the average frequency with which a complex moves across the potential energy surface to the product side. If one assumes that the activated complex is in equilibrium with the unactivated reactants, the calculation of the concentration of this complex is greatly simplified. Except in the cases of extremely fast reactions, this equilibrium can be treated with standard thermodynamics or statistical mechanics . The case of... 

The value found above is the average rate of the reaction in a given time interval. It may be required to find the instantaneous rate. 

Often, chemists want to know the rate of a reaction at a specific time f rather than the rate averaged over a time interval At. For example, what is the rate of formation of N02 at time f = 350 s If we make our measurements at shorter and shorter time intervals, the triangle defined by A[N02] and At will shrink to a point, and the slope of the hypotenuse of the triangle will approach the slope of the tangent to the curve, as shown in Figure 12.2. The slope of the tangent to a con-centration-versus-time curve at a time f is called the instantaneous rate at that particular time. The instantaneous rate at the beginning of a reaction (f = 0) is called the initial rate. 

The rate of a reaction relating to a surface as a whole is obtained by the averaging expression (13) over all the local configurations differing in the number of particles of A in the c.s. around particle i ... 

According to transition state theory, the rate of a reaction is the number of activated complexes passing per second over the top of potential energy barrier. This rate is equal to the concentration of activated complex times the average velocity with which a complex moves across to the product side. The activated complex is not in a state of stable equilibrium, since it lies at a maximum potential energy. 

Instantaneous Rate of a Reaction It is the rate of a reaction when the average rate is taken over a very small interval of time. 

Since the concentrations of reactants always decrease with time, any rate expression involving a reactant will include a negative sign. The average rate of this reaction from 0 to 50 seconds is then... 

The relation shown here suggests that a measure of the intrinsic rate of a reaction, corrected for its driving force, is given by AF = AF — 0.5 AF°. This amounts to taking the average AF for the reaction in the forward and reverse directions. Under conditions where Marcus relation ki2 = ( 11 12 12/) (42) is applicable, AF = (AF ii-f AF 22 — RT In /). Values for these intrinsic activation free energies are given in Table III. This table shows some patterns of relative reactivity as well as some apparent anomalies. For example, the relative intrinsic... 

In an early paper on the subject Szepe and Levenspiel [refe 10) introduced the notion of separability. The equations (1), (2) and (3), In which the deactivation function is a variable factor multiplying the initial rate of a reaction, correspond to their definition of separability. It may be useful to remind here that any kinetic treatment assuming ideal surfaces or accepting an average activity for the catalytic sites is bound to lead to such a form, provided, of course, there is no shift in rate determining steps. The question whether the deactivation is separable or not reduces to the question generally encountered in kinetic studies is it necessary to account explicitly for non uniform activity of the catalytic sites ... 

In Section 17.1, you learned how to calculate the average rate of a chemical reaction given the initial and final times and concentrations. The word average is important because most chemical reactions slow down as the reactants are consumed. To understand why most reaction rates slow over time, recall that the collision theory states that chemical reactions can occur only when the reacting particles collide and that reaction rate depends upon reactant concentration. As reactants are consumed, fewer particles collide and the reaction slows. Chemists use the concept of rate laws to quantify the results of the collision theory in terms of a mathematical relationship between the rate of a chemical reaction and the reactant concentration. 

The average rate of a chemical reaction is the change in concentration of one of the reactants or products over a finite interval of time. The instantaneous rate is the slope of a plot of concentration versus time at a particular point in time. The rate of the reaction is given by the rate for a particular species divided by its stoichiometric coefficient. 

There is one important practical difference between chemical kinetics and nuclear kinetics. In chemical kinetics the concentration of a reactant or product is monitored over time, and the rate of a reaction is then found from the rate of change of that concentration. In nuclear kinetics the rate of occurrence of decay events, —dN/dt, is measured directly with a Geiger counter or other radiation detector. This decay rate—the average disintegration rate in numbers of nuclei per unit time—is called the activity A. 

---