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THEORIES OF UNIMOLECULAR REACTION RATES
1. LINDEMANN / LINDEMANN-HINSHELWOOD THEORY
This is the simplest theory of unimolecular reaction rates, and was the first to successfully explain the observed first-order kinetics of many unimolecular reactions. The proposed mechanism actually consists of a second-order bimolecular collisional activation step, followed by a rate-determining unimolecular step. k1 A + M Ë A* + M k-1 k2 A* → P Applying the steady-state approximation to the concentration of A* gives [A*] = so that the overall rate is k1 [A][M] k-1 [M] + k2
d[P] k1 k2[A][M] = k2[A*] = dT k-1 [M] + k2
This is often written as d[P] = keff[A] dT k1 k2[M] is an effective first-order rate constant. keff is, of course, a function of pressure. At k-1 [M] + k2 high pressures, collisional deactivation of A* is more likely than unimolecular reaction, keff reduces to k1 k2/k-1 and the reaction is truly first order in A. At low pressures, bimolecular excitation is the rate determining step; once formed A* is more likely to react than be collisionally deactivated. The rate constant reduces to keff=k1 [M] and the reaction is second order. where keff = Lindemann theory breaks down for two main reasons: i) The bimolecular step takes no account of the energy dependence of activation; the internal degrees of freedom of the molecule are completely neglected, and the theory consequently underestimates the rate of activation. ii) The unimolecular step fails to take into account that a unimolecular reaction specifically involves one particular form of molecular motion (e.g. rotation around a double bond for cis-trans isomerization). Subsequent theories of unimolecular reactions have attempted to address these problems. offers a solution to problem i). Hinshelwood theory
2. HINSHELWOOD THEORY
Hinshelwood modelled the internal modes of A by a hypothetical molecule having s equivalent simple harmonic oscillators of frequency ν and using statistical methods to determine the
1. LINDEMANN / LINDEMANN-HINSHELWOOD THEORY
This is the simplest theory of unimolecular reaction rates, and was the first to successfully explain the observed first-order kinetics of many unimolecular reactions. The proposed mechanism actually consists of a second-order bimolecular collisional activation step, followed by a rate-determining unimolecular step. k1 A + M Ë A* + M k-1 k2 A* → P Applying the steady-state approximation to the concentration of A* gives [A*] = so that the overall rate is k1 [A][M] k-1 [M] + k2
d[P] k1 k2[A][M] = k2[A*] = dT k-1 [M] + k2
This is often written as d[P] = keff[A] dT k1 k2[M] is an effective first-order rate constant. keff is, of course, a function of pressure. At k-1 [M] + k2 high pressures, collisional deactivation of A* is more likely than unimolecular reaction, keff reduces to k1 k2/k-1 and the reaction is truly first order in A. At low pressures, bimolecular excitation is the rate determining step; once formed A* is more likely to react than be collisionally deactivated. The rate constant reduces to keff=k1 [M] and the reaction is second order. where keff = Lindemann theory breaks down for two main reasons: i) The bimolecular step takes no account of the energy dependence of activation; the internal degrees of freedom of the molecule are completely neglected, and the theory consequently underestimates the rate of activation. ii) The unimolecular step fails to take into account that a unimolecular reaction specifically involves one particular form of molecular motion (e.g. rotation around a double bond for cis-trans isomerization). Subsequent theories of unimolecular reactions have attempted to address these problems. offers a solution to problem i). Hinshelwood theory
2. HINSHELWOOD THEORY
Hinshelwood modelled the internal modes of A by a hypothetical molecule having s equivalent simple harmonic oscillators of frequency ν and using statistical methods to determine the