Average rate change

Similarly, with cycling temperatures, large fast cycles can cause discomfort. To avoid this, if the time to complete one cycle is less than 15 minutes and the peak-to-peak temperature variation is greater than 1.1 °C, the average rate of temperature change should be less than 2.2 °C/h (Fig. 5.9). Very slow rates of temperature change dT/dt < 0.5 °C/h) are much less difficult to adjust to and the change can go unnoticed until the temperature is beyond the comfort zone temperature. 

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. 

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... 

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

Because rates change continuously with time, accurate rate determinations must use small time intervals. At the outset of the NO2 decomposition experiment shown in Figure 15-6. the time interval between measurements is 5 seconds. For the first 5 seconds, the average rate of O2 production is as follows ... 

For the determination of rate of reaction at constant volume the concentration of a chosen reactant or product is determined at various time intervals. The change in concentration AC, for a given time interval At(t2 - q) is obtained. An average rate of reaction is then obtained by calculating AC/At. The smaller the value of At, the closer the value of the rate will be to the real rate at time (q + t2)l2 because... 

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. 

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. 

FIGURE 16.15 Isopleths of the calculated daytime average rates of net ozone production (ppb h 1) as a function of initial VOC and NOa. The model-predicted changes in VOC and NO, concentrations over an 8-h time period as the air mass is transported and reacts are shown by the arrows (adapted from Milford el al., 1994). 

In the 78-92% range of concentration of sulfuric acid, the molar absorptivity of 5-(hydroxymethyl)-2-furaldehyde increases at an average rate of 4% per 1% change in the concentration of the acid the wavelength of the absorption maximum changes from 290 to 320 nm. 

Define the average rate of change of the dependent variable... 

Figure 4.1 Defining the average rate of change of /(x) as x is incremented from xb to Xb+Ax...

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