Unimolecular rates

The unimolecular rate law can be justified by a probabilistic argument. The number (A Vdc x dc) of particles which react in a time dt is proportional both to this same time interval dt and to the number of particles present (A Vc x c). However, this probabilistic argument need not always be valid, as illustrated in figure A3.4.2 for a sunple model [20] ... 

A specific unimolecular rate constant for the decay of a highly excited molecule at energy E and angular momentum J takes the fomr... 

This yields die qiiasi-stationaty reaction rate with an effective unimolecular rate constant... 

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemaim-FIinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

If Other fall-off broadening factors arising m unimolecular rate theory can be neglected, the overall dependence of the rate coefficient on pressure or, equivalently, solvent density may be represented by the expression [1, 2]... 

Borkovec M, Straub J E and Berne B J The influence of intramolecular vibrational relaxation on the pressure dependence of unimolecular rate constants J. Chem. Phys. 85 146... 

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

In deriving the RRKM rate constant in section A3.12.3.1. it is assumed that the rate at which reactant molecules cross the transition state, in the direction of products, is the same rate at which the reactants fonn products. Thus, if any of the trajectories which cross the transition state in the product direction return to the reactant phase space, i.e. recross the transition state, the actual unimolecular rate constant will be smaller than that predicted by RRKM theory. This one-way crossing of the transition state, witii no recrossmg, is a fiindamental assumption of transition state theory [21]. Because it is incorporated in RRKM theory, this theory is also known as microcanonical transition state theory. 

In particular, the probability of finding the unimolecular reactant within its potential energy well decreases according to this law. Thus F detemrines tire lifetune of the state and the state specific unimolecular rate constant is... 

The theory of isolated resonances is well understood and is discussed below. Mies and Krauss [79, ] and Rice [ ] were pioneers m treating unimolecular rate theory in temis of the decomposition of isolated Feshbach resonances. 

Hase W L 1983 Variational unimolecular rate theory Acc. Chem. Res. 16 258-64... 

Pesiherbe G H and Hase W L 1996 Statistical anharmonic unimolecular rate constants for the... 

Miller W H 1979 Tunneling corrections to unimolecular rate constants, with applications to formaldehyde J. Am. Chem. See. 101 6810-14... 

Song K and Hase W L 1999 Fitting classical microcanonical unimolecular rate constants to a modified RRK expression anharmonic and variational effects J. Chem. Phys. 110 6198-207... 

Mies F H and Krauss M 1966 Time-dependent behavior of activated molecules. High-pressure unimolecular rate constant and mass spectra J. Cham. Phys. 45 4455-68... 

Hase W L, Cho S-W, Lu D-H and Swamy K N 1989 The role of state specificity in unimolecular rate theory Chem. Phys. 139 1-13... 

Lu D-H and Hase W L 1989 Monoenergetic unimolecular rate constants and their dependence on pressure and fluctuations in state-specific unimolecular rate constants J. Phys. Chem. 93 1681-3... 

Song K and Hase W L 1998 Role of state specificity in the temperature- and pressure-dependent unimolecular rate constants for H02->H+02 dissociation J. Phys. Chem. A 102 1292-6... 

Note that in the low pressure limit of iinimolecular reactions (chapter A3,4). the unimolecular rate constant /fu is entirely dominated by energy transfer processes, even though the relaxation and incubation rates... 

Line No. Naphthalene substituents Nucleophile (solvent) Unimolecular rate constant (temp. °C) 10 A ,sec i Activation energy kcal mole-1 Frequency factor logioA Ref. 

Pseudo-unimolecular rate constants measured at various temperatures, one of which is tabulated. 

Pseudo-unimolecular rate constant in sec. f Water was added to absolute ethanol to make 99.8% ethanol. 

Collisions at low ion energies (where Equation 1 can be applied) lead to a short-lived complex between the ion and the molecule—i.e., both collision partners move with the same linear velocity in the direction of the incident ion. The decay of the complex may be described by the theory of unimolecular rate processes if its excess energy can fluctuate between the various internal degrees of freedom. For example, the isotope effect in the reaction of Ar+ with HD may be explained by the properties of... 

The effects of ring substituents on the rate are consistent with a unimolecular rate-determining cleavage. " ... 

This rate can also be fit quantitatively by the LH unimolecular rate expression (solid curves) with... 

Figure 4 summarizes rates for NO, N2O, N02 and NH3 decomposition on Pt and Rh. Curves shown are calculated LH unimolecular rate expressions, Equation 11. Although data points are omitted for clarity, all measured rates agree with these curves to at least 20%. 

Plots of the concentration of carboxylate formed vs. time were drawn for each copolymer, and the initial rates of hydrolysis were determined by measurement of the slope of the tangent to the curve at zero time. The pseudo-unimolecular rate constant (K) is given by ... 

The calculated pseudo-unimolecular rate constants (k) for the hydrolysis reaction [Fig. 3], clearly show the inhibiting effect of AMPS, relative to sodium acrylate at all three temperatures. 

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