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SecondOrder Reactions
A secondorder reaction is secondorder in only one reactant, or firstorder in two reactants.
Learning Objectives

Manipulate experimentally determined secondorder rate law equations to obtain rate constants

Recognize secondorder reactions from experimentally determined rate laws
Key Points
 A secondorder reaction will depend on the concentration(s) of one secondorder reactant or two firstorder 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.
Terms

reaction mechanism
The stepbystep sequence of elementary transformations by which overall chemical change occurs.

secondorder reaction
A reaction that depends on the concentration(s) of one secondorder reactant or two firstorder reactants.
Full Text
A reaction is said to be secondorder when the overall order is two. For a reaction with the general form
or
The second scenario, in which the reaction is firstorder in both A and B, would yield the following rate law:
Applying the Method of Initial Rates to SecondOrder 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
Therefore, the reaction is secondorder 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:
Note that both k and the concentrations of A cancel. Also,
Therefore, the reaction is zeroorder in B.
Overall Reaction Order
We have determined that the reaction is secondorder in A, and zeroorder in B. Therefore, the overall order for the reaction is secondorder
Initial rate method of kinetics
Using the method of initial rates to determine reaction order.
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Key Term Reference
 Rate law
 Appears in these related concepts: ZeroOrder Reactions, The Equilibrium Constant, and The Rate Law
 concentration
 Appears in these related concepts: Calculating Equilibrium Concentrations , Factors that Affect Reaction Rate, and Molarity
 ratio
 Appears in these related concepts: Classification, Interpreting Ratios and Other Sources of Company Information, and Benchmarking
 reactant
 Appears in these related concepts: The Law of Conservation of Mass, Writing Chemical Equations, and Chemical Reactions and Molecules
Sources
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Cite This Source
Source: Boundless. “SecondOrder Reactions.” Boundless Chemistry. Boundless, 21 Jul. 2015. Retrieved 22 Jul. 2015 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/chemicalkinetics13/theratelawconcentrationandtime99/secondorderreactions4185661/