no effect on the rate. The rate law for a first order reaction is Although not affecting the above math, the majority of first order reactions proceed via intermolecular collisions. Such collisions, which contribute the energy to the reactant, are necessarily second order. The rate of these collisions is, however, masked by the fact that the rate determining step remains the unimolecular breakdown of the energized reactant. The half-life is independent of the starting concentration and is given by . Examples of such reactions are: 2N2O5 -> 4NO2 + O2 [CoCl(NH3)5]^2+ + H2O -> [Co(H2O)(NH3)5]^3+ + Cl- H2O2 -> H2O + 1/2O2 In organic chemistry, the class of SN1 (nucleophilic substitution unimolecular) reactions consists of first-order reactions. For example, in the reaction of aryldiazonium ions with nucleophiles in aqueous solution, , the rate equation is where Ar indicates an aryl group. Second order A reaction is said to be second order when the overall order is two. The rate of a second-order reaction may be proportional to one concentration squared, or (more commonly) to the product of two concentrations, As an example of the first type, the reaction is second-order in the reactant and zero order in the reactant CO. The observed rate is given by and is independent of the concentration of CO. For the rate proportional to a single concentration squared, the time dependence of the concentration is given by The time dependence for a rate proportional to two unequal concentrations is if the concentrations are equal, they satisfy the previous equation. The second type includes nucleophilic addition-elimination reactions, such as the alkaline hydrolysis of ethyl acetate: CH3COOC2H5 + OH- -> CH3COO- + C2H5OH This reaction is first-order in each reactant and second-order overall: If the same hydrolysis reaction is catalyzed by imidazole, the rate equation becomes The rate is first-order in one reactant (ethyl acetate), and also first-order in imidazole, which as a catalyst does not appear in the overall chemical equation. Another well-known class of second-order reactions are the SN2 (bimolecular nucleophilic substitution) reactions, such as the reaction of n-butyl bromide with sodium iodide in acetone: CH3CH2CH2CH2Br + NaI -> CH3CH2CH2CH2I + NaBr(v) This same compound can be made to undergo a bimolecular (E2) elimination reaction, another common type of second-order reaction, if the sodium iodide and acetone are replaced with sodium tert-butoxide as the salt and tert-butanol as the solvent: CH3CH2CH2CH2Br + NaO\mathit{t}-Bu -> CH3CH2CH=CH2