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Introduction
The Arrhenius equation is the foundation of all predictive expressions used to calculate reaction-rate constants because it represents the effect of the temperature on the speed of a chemical reaction. k represents the reaction-rate constant, A symbolizes the frequency about which atoms and molecules collide in a way that causes a reaction, E represents the activation energy for the reaction, R represents the ideal gas constant (8.314 joules per kelvin per mole), and T represents the absolute temperature in the Arrhenius equation.
The equation, which is often expressed as an exponential function, predicts that a minor increase in reaction temperature will result in a significant rise in the size of the reaction-rate constant.
Formula of Arrhenius Equation
The Arrhenius equation can be written in two different ways. Whether you have an activation energy in terms of the energy per mole (just like in chemistry) or energy per molecule determines which one you utilize (more common in physics). The equations are nearly the same, however the units are not.
In chemistry, the Arrhenius equation is commonly expressed as follows:
where k is the rate constant.
A is an exponential factor that is a constant for a specific chemical reaction and is used to calculate the frequency of particle collisions.
E is the reaction’s activation energy (typically expressed in Joules per mole or J/mol).
The universal gas constant is R.
The absolute temperature is denoted by T. (in Kelvins)
The exponential part in the Arrhenius equation means that as the activation energy diminishes, the rate constant of a reaction rises exponentially. The rate of a reaction increases exponentially because it is directly proportional to the rate constant of the reaction. Because a reaction with a low activation energy does not require as much energy to achieve the transition state as a reaction with a higher activation energy, it should occur faster.
Standard Form of Arrhenius equation
The more typical form of the equation in physics is:
T are the same as previously
E is the activation energy of the chemical reaction in Joules.
KB denotes the Boltzmann constant.
The units of A in both variants of the equation are like those of the rate constant. The units change depending on the reaction’s order. Because A has units of per second (s-1), it is also known as the frequency factor in a first-order reaction. The constant k denotes the number of particle collisions per second that result in a reaction, whereas A denotes the number of collisions per second that are proper (which may or may not result in a reaction).
The temperature change is minimal enough in most computations that the activation energy is not affected by it. To put it another way, knowing the activation energy is usually not required to compare the effect of the temperature on reaction rate. This makes the arithmetic a lot easier.
The rate of a chemical reaction can be increased by either increasing the temperature of the reaction or decreasing its activation energy, as shown in the equation. Catalysts accelerate reactions for this reason.
Difference between Eyring and Arrhenius equation
The main distinction between the Arrhenius and Eyring equations is that the former is an empirical equation, whilst the latter is based on statistical mechanical explanation.
In physical chemistry, the Arrhenius equation and the Eyring equation are two key equations. The Eyring equation is comparable to the empirical Arrhenius equation when we assume a constant enthalpy of activation and a constant entropy of activation.
The main distinction between the Arrhenius and Eyring equations is that the former is an empirical equation, whilst the latter is based on statistical mechanical explanation. Furthermore, the Arrhenius equation is utilized to represent temperature fluctuation of diffusion coefficients, population of crystal vacancies, creep rates, and a variety of other thermally induced phenomena, whereas the Eyring equation is used in transition state theory and elsewhere, better known as activated complex theory.
Conclusion
Chemical reactions occur more quickly at greater temperatures, as is well known. When milk is stored at room temperature rather than in the refrigerator, it spoils significantly faster; butter spoils much faster in the summer than in the winter; and eggs hard boil much faster at sea level than in the highlands. Chilly-blooded animals, such as reptiles and insects, are also more sedentary on cold days for the same reason.
The reason behind this is simple to comprehend. At the molecular level, thermal energy connects motion to direction. Molecules travel quicker and collide more violently as the temperature rises, dramatically increasing the possibility of bond cleavages and rearrangements. Whether it’s through collision theory, transition state theory, or just common sense, there’s always a way.
The Arrhenius equation is a straightforward yet amazingly precise formula for determining the temperature dependence of the reaction rate constant, and thus the rate of a chemical process. One of the most important relationships in physical chemistry is the activation energy-Boltzmann distribution law equation, which combines the notions of activation energy with the Boltzmann distribution law.
