Rate Equation - Second-order Reactions

Second-order Reactions

A second-order reaction depends on the concentrations of one second-order reactant, or two first-order reactants.

For a second order reaction, its reaction rate is given by:

or or

In several popular kinetics books, the definition of the rate law for second-order reactions is written instead as. This effectively conflates the 2 inside the constant, k, whose numerical meaning then becomes different. This simplifying convention is followed in the integrated rate laws provided below. It should be noted however that this simplification leads to potentially problematic inconsistencies, i.e. if the reaction rate is described in terms of product formation vs reactant disappearance. Instead, the option of keeping the 2 in the rate law (rather than absorbing it into a rate constant with an altered meaning) maintains a consistent meaning for k and is considered more correct technically. This more technically consistent convention is almost always used in peer-reviewed literature, tables of rate constants, and simulation software.

The integrated second-order rate laws are respectively

or

₀ and ₀ must be different to obtain that integrated equation.

The half-life equation for a second-order reaction dependent on one second-order reactant is . For such a reaction, the half-life progressively doubles as the concentration of the reactant falls to half its initial value.

Another way to present the above rate laws is to take the log of both sides:

Examples of a Second-order reaction