# How to solve an Arrhenius equation

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### introduction

In classical thermodynamics, changes in the internal energy, enthalpy, free energy and free enthalpy of the equilibrium constants are assigned to a reaction. This description in the imagination of thermodynamics considers an initial and final state of a reaction and provides information,

• whether a reaction
• and in what direction they

can expire. However, thermodynamics does not provide any information about the path and the speed with which different paths are traversed.

Fundamentally, the terms reaction coordinate, elementary reaction, reaction order, molecularity and reaction run number are introduced in a chapter on the reaction mechanism.

### Reaction speed

Changes in the concentration of the reactants over time are always observed experimentally. While the position of equilibrium in a reaction, i. H. the concentrations of educts and products in thermodynamic equilibrium, which depends on the energy difference between the partners, the height of the energy barrier between educts and products on the reaction coordinate plays a role in the reaction rate. The speed of a chemical reaction can be defined in different ways. This reaction rate is a central concept of kinetics and results from the time change in the concentration of a reactant per formula conversion. By definition, however, the reaction speed must always assume a positive value. The following applies to a simple reaction:

Reaction speed
a = Concentration of an eductb = Concentration of a product

The solution to this differential equation is called the velocity equation. It is often approximately of the form:

Rate equation

is the temperature-dependent rate constant of the reaction. The sum of the exponents of the rate equation is called the reaction order.

### Temperature dependence of the reaction rate constants

Rate constants are temperature dependent. The Arrhenius equation reflects this temperature dependence.

### Laws of Time

There are essentially two different approaches to determining the time law of a reaction. In the differential methods, the partial orders of the reaction with respect to the individual reaction partners are determined, while in the integration methods, a differential rate equation is set up with the help of experimental data and this is then integrated. The analytical integration of differential rate equations is only easily possible in simple cases (e.g. with a first order reaction). Instead of solving such a differential equation (DGL) analytically, one can also numerically integrate the experimentally determined data with the help of a computer. This process is also called formal integration. In order to be able to set up the rate equation for a reaction, one must follow the concentration of a reactant during the reaction. The extinction of the sample is often used as the measurement signal, as this is proportional to the concentration according to Lambert-Beer's law. The evaluation method according to Swinbourne or linearization according to Guggenheim is often used to determine the rate constants.

### Special reactions

The conversion of the starting materials of a chemical reaction into their products does not usually take place directly. Reactions that do not take place in a single elementary step are called complex reactions. The basic types of complex reactions are equilibrium reactions, subsequent reactions and parallel reactions.