Arrhenius equationis a simple but remarkably accurate formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrheniusin 1889, based on the work of Dutch chemist Jacobus Henricus van t Hoffwho had noted in 1884 that Van t Hoffs equationfor the temperature dependence of equilibrium constantssuggests such a formula for the rates of both forward and reverse reactions. Arrhenius provided a physical justification and interpretation for the formula. [ 1 ]Currently, it is best seen as an empiricalrelationship. [ 2 ]It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy. A historically useful generalization supported by Arrhenius equation is that, for many common chemical reactions at room temperature, the reaction rate doubles for every 10 degree Celsius increase in temperature. Equation Arrhenius equation gives the dependence of the rate constantof a chemical reactionon the absolute temperature(in kelvin), whereis the pre-exponential factor(or simply theprefactor),is the activation energy, andis the Universal gas constant. Alternatively, the equation may be expressed as The only difference is the energy units of: the former form uses energy per mole, which is common in chemistry, while the latter form uses energy per moleculedirectly, which is common in physics. The different units are accounted for in using either= Gas constantor the Boltzmann constantas the multiplier of temperature. The units of the pre-exponential factorare identical to those of the rate constant and will vary depending on the order of the reaction. If the reaction is first order it has the units s−1, and for that reason it is often called the frequencyfactororattempt frequencyof the reaction. Most simply,is the number of collisions that result in a reaction per second,is the total number of collisions (leading to a reaction or not) per second and is the probability that any given collision will result in a reaction. It can be seen that either increasing the temperature or decreasing the activation energy (for example through the use of catalysts) will result in an increase in rate of reaction. Given the small temperature range kinetic studies occur in, it is reasonable to approximate the activation energy as being independent of the temperature. Similarly, under a wide range of practical conditions, the weak temperature dependence of the pre-exponential factor is negligible compared to the temperature dependence of thefactor; except in the case of barrierless diffusion-limited reactions, in which case the pre-exponential factor is dominant and is directly observable. Arrhenius plot Main article: Arrhenius plot Taking the natural logarithmof Arrhenius equation yields: This has the same form as an equation for a straight line: So, when a reaction has a rate constant that obeys Arrhenius equation, a plot of ln(k) versusT−1gives a straight line, whose gradient and intercept can be used to determineEaandA. This procedure has become so common in experimental chemical kinetics that practitioners have taken to using it todefinethe activation energy for a reaction. That is the activation energy is defined to be (-R) times the slope of a plot of ln(k) vs. (1/T) Modified Arrhenius equation The modified Arrhenius equation [ 3 ]makes explicit the temperature dependence of the pre-exponential factor. If one allowsarbitrarytemperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverse problem (i.e., determining the prefactor and activation energy from experimental data) becomes singular. The modified equation is usually of the form whereT0is a reference temperature and allowsnto be a unitless power. Clearly the original Arrhenius expression above corresponds ton= 0. Fitted rate constants typically lie in the range -1
Posted on: Sat, 15 Mar 2014 10:00:20 +0000
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