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A second-order reaction is second-order in only one reactant, or first-order in two reactants.
Manipulate experimentally determined second-order rate law equations to obtain rate constants
Recognize second-order reactions from experimentally determined rate laws
A second-order reaction will depend on the concentration(s) of one second-order reactant or two first-order reactants.
To determine the order of a reaction with respect to each reactant, we use the method of initial rates.
When applying the method of initial rates to a reaction involving two reactants, A and B, it is necessary to conduct two trials in which the concentration of A is held constant, and B changes, as well as two trials in which the concentration of B is held constant, and A changes.
A reaction is said to be second-order when the overall order is two. For a reaction with the general form $aA+bB\rightarrow C$, the reaction can be second order in two possible ways. It can be second-order in either A or B, or first-order in both A and B. If the reaction were second-order in either reactant, it would lead to the following rate laws:
The second scenario, in which the reaction is first-order in both A and B, would yield the following rate law:
Applying the Method of Initial Rates to Second-Order Reactions
Consider the following set of data:
Rates and initial concentrations for A and B
A table showing data for three trials measuring the various rates of reaction as the initial concentrations of A and B are changed.
If we are interested in determining the order of the reaction with respect to A and B, we apply the method of initial rates.
Determining Reaction Order in A
In order to determine the reaction order for A, we can set up our first equation as follows:
Note that on the right side of the equation, both the rate constant k and the term $(0.200)^y$ cancel. This was done intentionally, because in order to determine the reaction order in A, we need to choose two experimental trials in which the initial concentration of A changes, but the initial concentration of B is constant, so that the concentration of B cancels. Our equation simplifies to:
Therefore, the reaction is second-order in A.
Determining Reaction Order in B
Next, we need to determine the reaction order for B. We do this by picking two trials in which the concentration of B changes, but the concentration of A does not. Trials 1 and 3 will do this for us, and we set up our ratios as follows: