5. Collection and Analysis of Rate Data

Learning Resources

Solved Problem Example 5-2

	Use the integral method to determine the reaction order for the di-tert-butyl peroxide decomposition described in Example 5-1. Solution Recalling Example 5-1, the combined mole balance and rate law for a constant-volume batch reactor can be expressed in the form
		(E5-1.5)
	As a first guess we might try zero order,= 0, for which equation (ES-1.5) becomes
		(CDE5-1.1)
	Integrating gives us
Assuming a zero-order reaction	If this is the correct order, a plot of PTversus t should be linear. After using the data in Table CDE5-1.1 to obtain Figure CDE5-1.1, we see that PT is not a linear function of t. Consequently, we conclude that the reaction is not zero-order.
	Figure CDE5-1-1
	Next we try second order,= 2:
	Integrating yields
Assuming a second-order reaction	If the reaction is second order, a plot ofversus t should be linear:
	After forming Table CDE5-1.1, a plot ofversus t was constructed and is shown in Figure CDE5-1.2. From the curvature of the plot, we conclude that the reaction is not second order.
	Figure CDE5-1-2
	Finally, we try first order (i.e.= 1). If zero, first, or second order do not seems to describe the reaction rate equation, it is usually best to try some other method of determining the reaction order. for= 1,
	Integrating with limits,when t = 0 yields
	If the reaction is first order, a plot ofversus t should be linear. After completing Table CDE5-1.2 using the raw data, a plot ofas a function of time is made using semilog paper as shown in Figure CDE5-1.3. From the plot we see thatis indeed linear with time, and we therefore conclude that the decomposition of di-tert-butyl peroxide follows first-order kinetics. From the slope of the plot in Figure CDE5-1.3, we can determine the specific reaction rate, k = 0.08 min -1
	Figure CDE5-1.3