# Order (chemistry)

Order in the context of a chemical reaction is a concept of chemical kinetics, a subdiscipline of physical chemistry. The order of a reaction with respect to a certain reactant is defined as the power to which its concentration term in the rate equation is raised.

Example: For a chemical reaction A + 2B → C with a rate equation Rate = k[A]1[B]2 the reaction order with respect to A would be 1 and with respect to B would be 2.

The reaction order is not necessarily related to the stoichiometry of the reaction. The order of a reaction can be determined only by experiment (or deduced from a known reaction mechanism). It is not necessary that the order of a reaction is a whole number — zero and fractional values of order are possible. The knowledge of the empirically determined orders of a chemical reaction allows conclusions about the reaction mechanism.

Zeroth-order reactions are often seen for thermal chemical decompositions where the reaction rate is independent of the concentration of the reactant (changing the concentration has no effect on the speed of the reaction):

A → B
Rate = k[A]0 = k

First-order reactions with respect to all reactands are often seen for simple bi-molecular reactions where the reaction rate is directly proportional to the concentration of each reactant (doubling the concentration of one reactant speeds up the reaction by a factor of two):

A + B → C
Rate = k[A]1[B]1 = k[A][B]

Second-order reaction with respect to B (doubling the concentration of B speeds up the reaction by a factor of four):

A + 2B → C
Rate = k[A]1[B]2 = k[A][B]2

A rate law is an equation that relates concentrations of reactants to the reaction rate.

Zeroth Order First Order Second Order
Rate Law [itex]-\frac{d[a]}{dt} = k[itex] [itex]-\frac{d[a]}{dt} = k[A][itex] [itex]-\frac{d[a]}{dt} = k[A]^2[itex]
Integrated Rate Law [itex][A] = [A]_0 - kt[itex] [itex][A] = [A]_0 e^(-kt)[itex] [itex]\frac{1}{[A]} = \frac{1}{[A]_0} + kt[itex]
Units of Rate Constant {k} [itex]\frac{M}{s}[itex] [itex]\frac{1}{s}[itex] [itex]\frac{1}{Ms}[itex]
Linear Plot [itex][A] vs. t[itex] [itex]\ln ([A])[itex] vs. t [itex]\frac{1}{[A] vs. t}[itex]
Half-life [itex]t_{1/2} = \frac{[A]_0}{2k}[itex] [itex]t_{1/2} = \frac{\ln (2)}{k}[itex] [itex]t_{1/2} = \frac{1}{[A]_0 k}[itex]

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