Reaction rate temperature dependent

The rate of a reaction is temperature-dependent. To avoid a determinate error resulting from a systematic change in temperature or to minimize indeterminate errors due to fluctuations in temperature, the reaction cell must have a thermostat to maintain a constant temperature. 

The oxidation of nitric oxide, NO, is a reaction involved in smog production. It is moderately rapid at normal temperatures. The oxidation of methane, CHt (household gas), however, occurs so slowly at room temperature that we may say that, for all practical purposes it doesn t react at all. Again, the difference in the reaction rates must depend upon specific characteristics of the reactants, NO and CH,. 

For an elementary reaction the temperature dependence of the rate constant is given by the Arrhenius equation... 

The reaction rate, rj, depends on temperatures and concentrations rj f, c,=i.J- All reactions mentioned in this table are operated adiabatically if y = 0. Note that... 

The donor-acceptor complexes [Ir(/r-dmpz)(CO)(PPh2 0(CH2)2R )]2 exhibit photo-induced electron-transfer rate constants of 1012s—1 and charge recombination rates slower than 2 x 10los-1 when R = pyridine and 4-phenylpyridine.534 Further studies on these complexes revealed that recombination reactions were temperature dependent and slower for the deuterated acceptors.535... 

In this case the reaction rate will depend not only on the system temperature and pressure but also on the properties of the catalyst. It should be noted that the reaction rate term must include the effects of external and intraparticle heat and mass transfer limitations on the rate. Chapter 12 treats these subjects and indicates how equation 8.2.12 can be used in the analysis of packed bed reactors. 

The second key process design parameter is the reaction rate, which depends on temperature, pressure, and concentrations. Rates of reaction... 

Temperature Correction Factor The rate of the above reaction is temperature dependent. Hence, if the temperature (experimental) is higher or lower than that used to define a unit of activity, a definite correction factor should be applied as per Table 2.10. 

A representation of all of the elementary reactions that lead to the overall chemical change being investigated. This representation would include a detailed analysis of the kinetics, thermodynamics, stereochemistry, solvent and electrostatic effects, and, when possible, the quantum mechanical considerations of the system under study. Among many items, this representation should be consistent with the reaction rate s dependence on concentration, the overall stoichiometry, the stereochemical course, presence and structure of intermediate, the structure of the transition state, effect of temperature and other variables, etc. See Chemical Kinetics... 

For such reactions the temperature-dependent term, the reaction rate constant, has been found in practically all cases to be well represented by Arrhenius law ... 

Experimental data show that the reaction rate constant depends on temperature, and often in the following form ... 

Except for radioactive decays, other reaction rate coefficients depend on temperature. Hence, for nonisothermal reaction with temperature history of T(t), the reaction rate coefficient is a function of time k(T(t)) = k(t). The concentration evolution as a function of time would differ from that of isothermal reactions. For unidirectional elementary reactions, it is not difficult to find how the concentration would evolve with time as long as the temperature history and hence the function of k(t) is known. To illustrate the method of treatment, use Reaction 2A C as an example. The reaction rate law is (Equation 1-51)... 

The reaction rate coefficients in the above equations may be related to reaction rates per pair of particles 2/, in nuclear physics (e.g., Fowler et al., 1975 Harris et al., 1983) by k = Xj/(1 + 5/ ), where 8 = 0 except for i= , for which 5/ = 1. That is, for Reactions 2-145 and 2-147 in which two identical particles collide to react, the definition of k is half of defined by nuclear physicists and for reactions in which different particles collide, the definition of k is the same as Xij. The reaction rate coefficients depend on temperature in a complicated way (Table 2-3) and may be calculated as the average value of the product of relative velocity times cross section. The concentrations of the intermediate species can be derived as follows. From Equation 2-155, 145 [ H] = ki4e[ H]pH]. That is. 

In specifying rate constants in a reaction mechanism, it is common to give the forward rate constants parameterized as in Eq. 9.83 for every reaction, and temperature-dependent fits to the thermochemical properties of each species in the mechanism. Reverse rate constants are not given explicitly but are calculated from the equilibrium constant, as outlined above. This approach has at least two advantages. First, if the forward and reverse rate constants for reaction i were both explicitly specified, their ratio (via the expressions above) would implicitly imply the net thermochemistry of the reaction. Care would need to be taken to ensure that the net thermochemistry implied by all reactions in a complicated mechanism were internally self-consistent, which is necessary but by no means ensured. Second, for large reaction sets it is more concise to specify the rate coefficients for only the forward reactions and the temperature-dependent thermodynamic properties of each species, rather than listing rate coefficients for both the forward and reverse reactions. Nonetheless, both approaches to describing the reverse-reaction kinetics are used by practitioners. 

For each reaction in a surface chemistry mechanism, one must provide a temperature dependent reaction probability or a rate constant for the reaction in both the forward and reverse directions. (The user may specify that a reaction is irreversible or has no temperature dependence, which are special cases of the general statement above.) To simulate the heat consumption or release at a surface due to heterogeneous reactions, the (temperature-dependent) endothermicity or exothermicity of each reaction must also be provided. In developing a surface reaction mechanism, one may choose to specify independently the forward and reverse rate constants for each reaction. An alternative would be to specify the change in free energy (as a function of temperature) for each reaction, and compute the reverse rate constant via the reaction equilibrium constant. 

The identity relation between the concentration of the catalyzing product or the temperature and the concentration of the initial substance or product allows us to express the chemical reaction rate, which depends on several variables (c, A or T), as a function of only the concentration of the initial substance for a given initial concentration. 

Here we treat the more realistic case that the right-hand side of equation (5.53) is nonlinear. Such a nonlinearity is generally introduced by a nonconstant reaction rate that depends upon the temperature as exemplified by the Arrhenius dependence (2.1). 

In principle, the reaction rates might depend on temperature and on all concentrations, i.e. ... 

In computations of very fine spatial and temporal resolution, local chemical equilibrium cannot be assumed and the chemical reactions are described as finite-rate reactions. The temperature dependence of the reaction rate is presented as an Arrhenius reaction ... 

We now enquire how it is that a catalyst is able to accelerate the rate of a reaction. We may start with the concept proposed by Svante Arrhenius to describe the effect of temperature on a homogeneous (i.e. non-catalysed) gas-phase reaction he stated that reaction rate r depended on the fraction of colliding molecules that between them had more than a critical amount of energy, which he called the activation energy E. This fraction increased exponentially with temperature in line with the Boltzmann distribution fraction, so that... 

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