Frequency factor Arrhenius equation

A Pre-exponential factor in Arrhenius equation (frequency factor)... 

Estimate this value for polystyrene with a monomer concentration of 1.2 mole/ L. The heat of polymerization is 68.65 kJ/g mole. Use a value of 10 s" for (Arrhenius equation frequency factor). 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

In comparison to the constant of propagation of the a-helix formation (kp — 1010s 1) and the double-helix formation (kp — 107s-1), a comparatively small parameter concerning the formation of triple helix has been found (fcp = 8 x 10 3s1). A higher entropy of activation is assumed as the main cause of this occurrence which means a lower frequence factor in the Arrhenius equation. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

Increases in reaction rate with temperature are often found to obey the Arrhenius equation, from which the apparent values of the reaction frequency factor, A, and the activation energy, E, are calculated. The possibility that the kinetic obedience changes with temperature must also be considered. 

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... 

Arrhenius parameters The pre-exponential factor A (also called the frequency factor) and the activation energy Ea. See also Arrhenius equation. aryl group An aromatic group. Example —C6H5, phenyl. 

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

Activation energy and frequency factor (pre-exponential coefficient). The Arrhenius equation can be rewritten in logarithmic form ... 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

According to the Arrhenius equation for the reaction rate constant, k = Ae Ea/rt, where A is the frequency factor and the exponential factor contains the activation energy, EA, we can write for the respective rate constants... 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

Pre-exponential (acton the constant A in the Arrhenius equation (also called the frequency factor) this pre-exponential factor is associated with the frequency of collosions between molecules, and with the probability that these conditions result in a reaction (see also Activation Energy and Arrhenius Equation). 

A change in the reaction temperature affects the rate constant k. As the temperature increases, the value of the rate constant increases and the reaction is faster. The Swedish scientist, Arrhenius, derived a relationship that related the rate constant and temperature. The Arrhenius equation has the form k = Ae-E /RT. In this equation, k is the rate constant and A is a term called the frequency factor that accounts for molecular orientation. The symbol e is the natural logarithm base and R is universal gas constant. Finally, T is the Kelvin temperature and Ea is the activation energy, the minimum amount of energy needed to initiate or start a chemical reaction. 

Another method for determining the activation energy involves using a modification of the Arrhenius equation. If we try to use the Arrhenius equation directly, we have one equation with two unknowns (the frequency factor and the activation energy). The rate constant and the temperature are experimental values, while R is a constant. One way to prevent this difficulty is to perform the experiment twice. We determine experimental values of the rate constant at two different temperatures. We then assume that the frequency factor is the same at these two temperatures. We now have a new equation derived from the Arrhenius equation that allows us to calculate the activation energy. This equation is ... 

Comparing equation (4.22) with Arrhenius equation, i.e. k = Ae act/sr, the Arrhenius factor (or frequency factor) is given as... 

Arrhenius equation jPHYS CHEMj The relationship that the specific reaction rate constant k equals the frequency factor constant s times exp (-AHact/RT), where AHact is the heat of activation, R the gas constant, and T the absolute temperature. ar ra-ne-3s i kwa-zhon ... 

This is the well-known Arrhenius equation in which A is referred to as the frequency factor or pre-exponential factor. 

A plot of In k against the reciprocal of the absolute temperature (an Arrhenius plot) will produce a straight line having a slope of —EJR. The frequency factor can be obtained from the vertical intercept. In A. The Arrhenius relationship has been demonstrated to be valid in a large number of cases (for example, colchicine-induced GTPase activity of tubulin or the binding of A-acetyl-phenylalanyl-tRNA to ribosomes ). In practice, the Arrhenius equation is only a good approximation of the temperature dependence of the rate constant, a point which will be addressed below. 

For an estimation of the order of magnitude of the preexponential factor in the Arrhenius equation for a surface reaction between simple molecules, the terms f and f7A may be taken as equal to 1 since they include only vibrational modes that are degenerate if hv > A B7 v being the vibration frequency) (21). The values of fK for molecules in the gas phase are calculated in the usual manner. 

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