Average, Instantaneous, and Initial Reaction Rates

Examining the rate of a real reaction reveals an important point not only the concentration, but the rate itself varies with time as the reaction proceeds. Consider the reversible gas-phase reaction between ethylene and ozone, one of many reactions that can be involved in the formation of photochemical smog  

For now, we consider only reactant concentrations. You can see from the equation coefficients that for every molecule of C2H4 that reacts, a molecule of O3 reacts with it. In other words, the concentrations of both reactants decrease at the same rate in this particular reaction  

By measuring the concentration of either reactant, we can follow the reaction rate. 

Suppose we have a known concentration of O3 in a closed reaction vessel kept at 30°C (303 K). Table 16.1 shows the concentration of O3 at various times during the first minute after we introduce C2H4 gas. The rate over the entire 60.0 s is the total change in concentration divided by the change in time  

CHAPTER 16 Kinetics Rales and Mechanisms of Chemical Reactions 

Concentration of O3 at Various Times in hs Reaction with C2H4 at 303 K 

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Average, Instantaneous, and Initial Reaction Rates Rate and Concentration... 

Understand ho w reaction rate is expressed in terms of changing reactant and product concentrations over time, and distinguish among average, instantaneous, and initial rates ( 16.2) (SP 16.1) (EPs 16.7-16.19)... 

Expressing the Reaction Rate Average Instantaneous, and Initial... 

The average reaction rate is the change in reactant (or product) concentration over a change in time, Af. The rate slows as reactants are used up. The instantaneous rate at time t is obtained from the slope of the tangent to a concentration vs. time curve at time t. The initial rate, the instantaneous rate at f = 0, occurs when reactants are just mixed and before any product accumulates. The expression for a reaction rate and its numerical value depend on which reaction component is being monitored. 

Define reaction rate. Distinguish between the initial rate, average rate, and instantaneous rate of a chemical reaction. Which of these rates is usually fastest The initial rate is the rate used by convention. Give a possible explanation as to why. 

Define reaction rate. Distinguish between the initial rate, average rate, and instantaneous rate of a chemical reac-... 

FIGURE 13.2 The scaling fit factors (Equation 13.15). s=0.5 in the limit of diffusion controlled initiation, and s=0 in the limit of decomposition controlled initiation. The sohd points are from fits to separate reactions under specific Am and initiator concentrations, whereas the crosses show intrareactional crossover from decomposition control to diffusion control averaged over many reactions where the crossover is prominent due to starting Am and initiator concentrations. Instantaneous molar fraction of VB, inst.vB versus conversion for batch and two feed rates during VB/ AM free radical copolymerization reactions. Adapted with permission from Kreft T, Reed WF. Direct monitoring of the crossover from diffusion-controlled to decomposition-controlled initiation in free radical polymerization. Macromol Chem Phys 2008 209 2463-2474. 

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. 

In discussions that follow, the term rate means instantaneous rate unless indicated otherwise. The instantaneous rate at t = 0 is called the initial rate of the reaction. To understand the difference between average and instantaneous rates, imagine you have just driven 98 mi in 2.0 hr. Your average speed for the trip is 49 mi/hr, but your instantaneous speed at any moment during the trip is the speedometer reading at that moment. 

The rate changes as the reaction proceeds fastest at the beginning, when reactant concentration is highest, and slowest at the end. Average rate is the concentration change over a period of time, and instantaneous rate is the change at any instant. Kinetic studies typically measure the initial rate, the rate at the moment the reactants are mixed, so product is absent. (Section 16.2)... 

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