Determining the order of a reaction

Since the rate of a reaction may be proportional to different powers of the concentrations of the several reactants, we need to determine the dependence of the rate on each of these concentrations. If, for example, the rate is kc c then if B and C are present in great excess (while the concentration of A is very small), the concentrations of B and C will remain effectively constant throughout the reaction. The rate will then be proportional only to c%. By altering the initial concentration of A, we can determine the order a. The procedure is repeated by having A and C present in excess to determine /, and so on. This is the isolation method for determining the order of a reaction. We used this idea in deriving Eqs. (32.45) and (32.46). 

Suppose that a reaction is ath order with respect to the reactant A and that all the other reactants are present in great excess. Then the rate law is 

Taking the logarithm of both sides of this equation, we obtain 

Equation (32.47) can be used in another way. The initial slope of the curve of Ca versus t is measured f or several different initial concentrations. Then the logarithm of the negative of the initial slope is plotted against the logarithm of the initial concentration. The slope of this plot, according to Eq. (32.47), is the order of the reaction. 

It should be mentioned that considering the uncertainties in the data it is sometimes quite difficult to decide whether a reaction is first or second order. 

---

Determine the order of a reaction, its rate law, and its rate constant from experimental data (Examples 13.1 and L3.2 and Self-Tests 13.2 and 13.3). 

The order of the above reaction is, therefore, 1.5 + 0.5 = 2. This is typical of situations where the order of reaction and the molecularity of the reaction are the same. It may, however, be noted that the form of rate law, which determines the order of a reaction, can only be derived by actual experiment, and that may or may not be equal to the molecularity of the reaction as provided by the equation representing that reaction. Thus, a general reaction... 

Therefore, if In C is plotted against t, as shown in Fig. 2, the plot will be a straight line with an intercept (at t = 0) of In Co, and the slope of the line (m) will be — k. Such plots are commonly used to determine the order of a reaction that is, if a plot of In C versus time is a straight line, the reaction is assumed to be a first-order or pseudo-first-order process. 

The rate of loss of reactant is negative because the concentration decreases with time The gradient at the start of the reaction is called the initial rate. Analysing the initial rates method is an extremely powerful way of determining the order of a reaction. 

How the graphical method is most useful in determining the order of a reaction ... 

Response-surface methodology has also been used to gain theoretical insight into a reacting system (B19) and to determine the order of a reaction (P3). 

Morris, "A New Twist on the Iodine Clock Reaction Determining the Order of a Reaction," J. Chem. Educ., Vol. 76,1999,530-531. 

The difference between the molecularity and the order of a reaction is important. The molecularity of a reaction, or a step within a reaction, describes what happens on the molecular level. The order of a reaction describes what happens on the macroscopic scale. We determine the order of a reaction by watching the products of a reaction appear or the reactants disappear. The molecularity of the reaction is something we deduce to explain these experimental results. 

The most obvious method of determining the order of a reaction is to determine the amount of dmg decomposed after various intervals and to substitute the data into the integrated equations for zero-, first- and second-order... 

Limitations of Methods. All the plots discussed above for determining the order of a reaction are valid either for nonreversible reactions or at low values of conversion. 

Determine the order of a reaction, and suggest a possible mechanism based on its rate equation. 

---