+ NaBr + HO\mathit{t}-Bu Pseudo-first order If the concentration of a reactant remains constant (because it is a catalyst, or because it is in great excess with respect to the other reactants), its concentration can be included in the rate constant, leading to a pseudo–first-order (or occasionally pseudo–second-order) rate equation. For a typical second-order reaction with rate equation if the concentration of reactant B is constant then where the pseudo–first-order rate constant The second-order rate equation has been reduced to a pseudo–first-order rate equation, which makes the treatment to obtain an integrated rate equation much easier. One way to obtain a pseudo-first order reaction is to use a large excess of one reactant (say, [B]≫[A]) so that, as the reaction progresses, only a small fraction of the reactant in excess (B) is consumed, and its concentration can be considered to stay constant. For example, the hydrolysis of esters by dilute mineral acids follows pseudo-first order kinetics, where the concentration of water is constant because it is present in large excess: CH3COOCH3 + H2O -> CH3COOH + CH3OH The hydrolysis of sucrose () in acid solution is often cited as a first-order reaction with rate The true rate equation is third-order, however, the concentrations of both the catalyst and the solvent are normally constant, so that the reaction is pseudo–first-order. Summary for reaction orders 0, 1, 2, and n Elementary reaction steps with order 3 (called ternary reactions) are rare and unlikely to occur. However, overall reactions composed of several elementary steps can, of course, be of any (including non-integer) order. Here stands for concentration in molarity (mol · L−1), for time, and for the reaction rate constant. The half-life of a first-order reaction is often expressed as t1/2 = 0.693/k (as ln(2)≈0.693). A typical first-order reaction has a lifetime τ = 1/k. Fractional order In fractional order reactions, the order is a non-integer, which often indicates a chemical chain reaction or other complex reaction mechanism. For example, the pyrolysis of acetaldehyde () into methane and carbon monoxide proceeds with an order of 1.5 with respect to acetaldehyde: The decomposition of phosgene () to carbon monoxide and chlorine has order 1 with respect to phosgene itself and order 0.5 with respect to chlorine: The order of a chain reaction can be rationalized using the steady state approximation for the concentration of reactive intermediates such as free radicals. For the pyrolysis of