Temperature, rate constant independent

With = 1 and mP = 2, the low-temperature rate constant is then determined mainly by for a given value of E. The low-temperature and temperature independent kinetic isotope effect k /k is, therefore, determined by which is obtained experimentally at high temperatures. In other words, kg /kg and the high-temperature kinetic isotope effects cannot be varied independently of each other, which is not in agreement with experimental data. This effect can be associated with heavy atom tunneling during the H-transfer. The tunneling mass is increased and the low-temperature H/D isotope effect decreased. 

The data of Smith and Zellner (107) were obtained at total pressures of either 10 to 20 torr of helium (with 0.1-0.5 torr H2O) or 20 torr (10 torr H2 + 10 torr N2O), and were reported to be independent of the diluent gas used. Their Arrhenius activation energy is In good agreement with that determined by Perry, Atkinson, and Pitts (89) (Table 6), but their room-temperature rate constant Is a factor of 2 to 3 higher than that obtained at 25 torr total pressure of argon by Perry, Atkinson, and Pitts (89). Obviously at least one other study, preferably using a different technique. Is necessary to resolve these differences. 

For 5=1, the normal transition state theory rate constant is independent of temperature at high temperatures and varies exponentially with temperature in the limit of low temperatures kT small compared with the barrier height U ) as... 

The origin of the isotope effect is the dependence of coq and co on the reacting particle mass. Classically, this dependence comes about only via the prefactor coq [see (2.14)], and the ratio of the rate constants of transfer of isotopes with masses mj and m2 m2 > mj) is temperature-independent and equal to... 

The proportionality constant k is called the rate constant (or rate coefficient or specific rate). The rate constant is independent of the concentrations of A, B,. .., but may depend upon environmental factors such as the temperature and solvent, and of course its magnitude depends on the particular reaction being studied. 

Collision theory leads to this equation for the rate constant k = A exp (-EIRT) = A T exp (,—EIRT). Show how the energy E is related to the Arrhenius activation energy E (presuming the Arrhenius preexponential factor is temperature independent). 

Usually the Arrhenius plot of In k vs. IIT is linear, or at any rate there is usually no sound basis for coneluding that it is not linear. This behavior is consistent with the conclusion that the activation parameters are constants, independent of temperature, over the experimental temperature range. For some reactions, however, definite curvature is detectable in Arrhenius plots. There seem to be three possible reasons for this curvature. 

If a data set containing k T) pairs is fitted to this equation, the values of these two parameters are obtained. They are A, the pre-exponential factor (less desirably called the frequency factor), and Ea, the Arrhenius activation energy or sometimes simply the activation energy. Both A and Ea are usually assumed to be temperature-independent in most instances, this approximation proves to be a very good one, at least over a modest temperature range. The second equation used to express the temperature dependence of a rate constant results from transition state theory (TST). Its form is... 

In addition to the chemical inferences that can be drawn from the values of AS and AH, considered in Section 7.6, the activation parameters provide a reliable means of storing and retrieving the kinetic data. With them one can easily interpolate a rate constant at any intermediate temperature. And, with some risk, rate constants outside the experimental range can be calculated as well, although the assumption of temperature-independent activation parameters must be kept in mind. For archival purposes, values of AS and AH should be given to more places than might seem warranted so as to avoid roundoff error when the exponential functions are used to reconstruct the rate constants. 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

Every reaction has its own characteristic rate constant that depends on the intrinsic speed of that particular reaction. For example, the value of k in the rate law for NO2 decomposition is different from the value of k for the reaction of O3 with NO. Rate constants are independent of concentration and time, but as we discuss in Section 15-1. rate constants are sensitive to temperature. 

The assessment of k is of some importance since it relates to the question as to how much if any of the free energy of activation barrier is due to the spin-forbidden character of the transition. From the experimental point of view, Eq. (49) shows that the transmission coefficient k and the activation entropy AS appear in the temperature-independent part of the rate constant and thus cannot be separated without additional assumptions. Possible approaches to the partition of — TAS have been discussed in Sect. 4 for spin transition complexes of iron(II) and iron(III). If the assumption is made that the entropy of activation is completely due to k, minimum values between 10 and 10 are obtained for iron(II) and values between 10 and 10 for iron(III). There is an increase of entropy for the transition LS -+ HS and thus the above assumption implies that the transition state resembles the HS state. On the other hand, volumes of activation indicate that the transition state should be about midway between the LS and HS state. This appears indeed more reasonable and has the... 

In this equation it is the reaction rate constant, k, which is independent of concentration, that is affected by the temperature the concentration-dependent terms, J[c), usually remain unchanged at different temperatures. The relationship between the rate constant of a reaction and the absolute temperature can be described essentially by three equations. These are the Arrhenius equation, the collision theory equation, and the absolute reaction rate theory equation. This presentation will concern itself only with the first. 

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