Integral method

The integral method of determining the rate of a reaction makes use of the integral form of a rate law.

Just like the half-life method and the differential method, the integral method is useful for reactions involving a single reactant, e.g.

N_2O_5(g)\rightleftharpoons 2NO_2(g)+\frac{1}{2}O_2(g)

If the order of the reaction is known, we can determine the value of the rate constant by plotting the appropriate integral rate equations below using experiment data and finding the vertical intercept of the respective linear functions.


Rate law

Integral rate equation

0 rate=k [A]=-kt+[A]_0
1 rate=k[A] ln[A]=-kt+[A]_0
2 rate=k[A]^2 \frac{1}{[A]}=kt+\frac{1}{[A]_0}

If the order of the reaction is not known, the integral rate equation that gives a straight line with the experiment data is the one that describes the order of the reaction. The integral method can also be used together with the initial rate method and the isolation method in determining the unknowns of a rate equation with multiple reactants.


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