Zero-order reactions concentration-time graphs

A second-order reaction is one for which the overall reaction order is 2. If a second-order rate law depends on the concentration of only one reactant, then rate = k[A], and the time dependence of [A] is given by the integrated form of the rate law 1/[A], = 1/[A]q + kt. In this case a graph of 1/[A] t versus time yields a straight line. A zero-order reaction is one for which the overall reaction order is 0. Rate = fc if the reaction is zero order. 

Figure 6.23 shows a graph of the amount or concentration of a reactant against time. (This form of graph is obtained in most reactions, with the exception of autocatalysis or zero order reactions (Chapter 16).) You can see that the gradient of the graph continually decreases with time and, hence, the rate of reaction decreases with time. The reaction rate is zero when the reactants are all consumed and the reaction stops. 

Figure 16.1 A graph of concentration against time for a zero-order reaction... 

From the data of runs Cl to C20 and D1 to D20, calculate x, the number of moles of sucrose hydrolyzed in each time interval. If the reaction were zero order in sucrose, then we would expect that (x/0.003) = kf, where x/0.003 is the concentration of either of the product species in mol L units. Prepare a graph of the results obtained in these two series of runs, plotting x versus t, and indicate whether the data are consistent with the hypothesis that the reaction is zero order in sucrose. Note that, even if a reaction starts out being zero order in sucrose, this cannot continue indefinitely. Indeed, we expect the inversion reaction to become first order in sucrose when (S) becomes sufficiently small. 

The available data are the reactant concentration as a function of time for a single experiment, so we will need to use graphical techniques to determine the order of the reaction. There are three possibilities we can explore using the integrated rate laws we ve examined. The reaction could be zero order, first order, or second order with respect to NO2. We will need to manipulate and plot the data in various ways to determine whether there is a good fit with any of these models. (Other orders are also possible, so we should be aware that all three tests could conceivably fail.) With a spreadsheet or a graphing calculator, such manipulation of data is easy. For this example, first we will calculate all of the data needed for all three plots and then make the appropriate graphs to find the linear relationship and determine the rate law. 

Figure 22.12 The half-life of zero-, first- and second-order reactions can be determined from graphs of concentration against time.

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