acetaldehyde, the Rice-Herzfeld mechanism is Initiation CH3CHO -> .CH3 + .CHO Propagation .CH3 + CH3CHO -> CH3CO. + CH4 CH3CO. -> .CH3 + CO Termination 2 .CH3 -> C2H6 where • denotes a free radical. To simplify the theory, the reactions of the to form a second are ignored. In the steady state, the rates of formation and destruction of methyl radicals are equal, so that so that the concentration of methyl radical satisfies [.CH3] \quad\propto \quad[CH3CHO]^{1/2}. The reaction rate equals the rate of the propagation steps which form the main reaction products and CO: in agreement with the experimental order of 3/2. Complex laws Mixed order More complex rate laws have been described as being mixed order if they approximate to the laws for more than one order at different concentrations of the chemical species involved. For example, a rate law of the form represents concurrent first order and second order reactions (or more often concurrent pseudo-first order and second order) reactions, and can be described as mixed first and second order. For sufficiently large values of [A] such a reaction will approximate second order kinetics, but for smaller [A] the kinetics will approximate first order (or pseudo-first order). As the reaction progresses, the reaction can change from second order to first order as reactant is consumed. Another type of mixed-order rate law has a denominator of two or more terms, often because the identity of the rate-determining step depends on the values of the concentrations. An example is the oxidation of an alcohol to a ketone by hexacyanoferrate (III) ion [Fe(CN)63−] with ruthenate (VI) ion (RuO42−) as catalyst. For this reaction, the rate of disappearance of hexacyanoferrate (III) is This is zero-order with respect to hexacyanoferrate (III) at the onset of the reaction (when its concentration is high and the ruthenium catalyst is quickly regenerated), but changes to first-order when its concentration decreases and the regeneration of catalyst becomes rate-determining. Notable mechanisms with mixed-order rate laws with two-term denominators include: Michaelis-Menten kinetics for enzyme-catalysis: first-order in substrate (second-order overall) at low substrate concentrations, zero order in substrate (first-order overall) at higher substrate concentrations; and the Lindemann mechanism for unimolecular reactions: second-order at low pressures, first-order at high pressures. Negative order A reaction rate can have a negative partial order with respect to a substance. For example, the conversion of ozone (O3) to oxygen follows the rate equation in