Chemical kinetics

The kinetics is a category of physical chemistry. It deals with the temporal sequence of chemical reactions ( kinetics ) or physico- chemical processes (eg, diffusion, material deposition on surfaces). The kinetics is divided into two sections, the micro-kinetics and the macro-kinetics. While the microkinetics dealt only with the timing of a reaction in which macrokinetics the influence of macroscopic heat and mass transport is included. In this article I will discuss only the micro-kinetics.

• 6.1 Measurement method
• 6.2 metrics
• 6.3 mixing process 6.3.1 Determination of the reaction order
• 6.3.2 Determination of the reaction rate coefficients
• 6.3.3 Determination of the Arrhenius factor and the activation energy

• 7.1 relaxation kinetics
• 7.2 flash photolysis

The reaction rate

The basic size is carried out with the rate, the rate of reaction. It specifies how many particles are reacted per unit of time in a chemical reaction. This speed depends on many factors. Depending on the underlying model, there are different ways to look at the reaction rate.

An important factor to consider is the concentration of the present substance. The more particles containing a volume, the more collisions there will be a period of time. However, since a reaction can take place only when two particles collide with each other, the reaction rate increases with the concentration of the reactants.

If a reaction of the following type is present

Then for the forward reaction rate law

The reaction rate, the decrease in concentration of the substance A and the elapsed time. This reaction velocity is the average velocity of the reaction, as individual molecules require different long time intervals prior to entering a reaction event.

Since the decline of the reactants to the increase of the products must meet, also applies

The negative sign is required if the reaction rate is the change in concentration of the reactants, where the substance A, based. Due to the decrease in concentration of the substance A is negative (concentration of substance A at the time, concentration of substance A at the time ). In contrast, and positive.

This highly simplified model still requires some refinement in terms of:

• The activity, ie the effective concentration
• The amount of the starting materials in relation to the quantity of products
• The temperature
• The impact energy
• The presence of catalysts
• The reactions occurring gases on the partial pressure
• The orientation of large reactants (enzymes, catalyst surface ) at collision
• The Zerteilungsgrades
• The solvent influence

The reaction order

For each reaction can be a reaction equation formulated which describes the number of the reactant to react the particles with one another to form a certain number of product particles.

Would be similar to the following reaction equation ago

This would mean that two particles A with particles B, particles C and a D particles would collide to form the product E.

However, the probability that five particles and also collide simultaneously with sufficient energy extremely low.

Much more likely is that first meet two or three particles form an intermediate, this intermediate is then collides with other particles, optionally with the formation of other intermediates and finally, the product E forms, here is an example:

The decomposition of the overall reaction into individual steps in elementary reactions and their research shows how the reaction proceeds exactly.

Experimentally or on the basis of model assumptions can be determined, such as the reaction rates of the elementary reactions depend on the respective concentrations of the components A, B, C and D.

The dependence of the reaction rate of the exponent, which is received, the concentration of a specific reactant in the speed law is referred to as the reaction order with respect to these reactants.

The overall order of a reaction is the sum of the reaction orders of all reactants involved in it.

Example

Assuming that the reaction rate of the first reaction unit above is a quadratic function of the concentration of component A from this second-order reaction with respect to the component A. In the absence of other particles are involved in this reaction, the overall reaction order as well as two.

Assuming that the reaction rate of the second reaction unit above is linearly dependent on the concentration of A2 linearly on the concentration of B and not by the concentration of C from. Then the first-order reaction with respect to A2, the first order with respect to B and 0-order with respect to C. The total order is also two.

Assuming that the reaction rate of the third elementary reaction depends linearly on the concentration of A2BC, but not on the concentration of D, then there is a first order reaction with respect to A2BC and a zero-order with respect to D before. The total order is one.

The four most common, because most likely, reaction orders are:

Zero-order reactions

Such reactions are independent of the concentration of the reactants, where the reaction rate is therefore constant. This may be the case, for example, if it is light-dependent reactions ( the factor k depends on the light intensity), but only when the photon is considered as particles rather than as a shaft ( which is problematic when, the photon is absorbed in the reaction).

In which

Examples are photochemical reactions or catalytic reactions.

In pseudo- zero-order reactions, the reaction is indeed dependent on the concentration of the reactants, but make a first from a standing in a dynamic equilibrium with it other form, which is present in such large excess be formed, so that the concentration to be constant can be considered. Example is the iodination of acetone in which reacts only the enol form, the keto form is present, but they are practically 100 %.

First-order reactions

Here is catalytic or radioactive decay processes. The reaction rate is dependent only on the concentration of the disintegrating substance, namely linear.

Integrated

With

Second-order reactions

In this case, reacting two reactants to one or more products. The reaction rate depends on the concentrations of the starting materials.

Or with only one substance

Integrated

In which

With different materials A and B ( which in practice is most prevalent ) and with different initial concentrations of the general solution of the integrated rate equation:

Most of bimolecular reactions in solid or liquid media follow these kinetics.

However, there is a special case where one of the reactants is present in a very large excess, so that the change in concentration over time of the reaction is negligible. This is for example the case when both water reactants and the solvent is (for example, at a hydrolysis of esters ). In this case, the reaction rate follows the laws of a first-order reaction. But since it still is a bimolecular reaction, it is called pseudo- first-order reactions (or seemingly the first order).

Another special case arises when a reaction experimentally 0th order is measured ( although a higher-order reaction occurs). Then one speaks of a reaction apparently zero order. This can in particular in catalytic processes is the case (such as enzyme catalysis, or the catalytic hydrogenation of ethene ) if the limiting factor is the number of " slots" on the catalyst and not how many times the molecules collide (since it is the direct elementary reaction as virtually no role ).

Third-order reactions

In this case, the three reactants to react one or several products. A trimolecular reaction is very rare ( statistically the probability is very low that three particles at the same time are in the same place ) and in many cases a competing ( and dominant ) bimolecular reaction is observed. An example of a truly tri-molecular reaction is the Atomrekombination. The reaction rate is dependent of three substances:

It should be noted that the factor 1/2 comes from the stoichiometric equation and not by the elementary reaction (during which, however, the exponent 3 of the elementary reaction arises ).

An example of this reaction is:

Equilibrium reactions

Many reactions are equilibrium reactions in which the product formed can react back to the starting material again.

A is the change in concentration in this case is determined by the differential equation

With the reaction parameters of the reaction and the reverse reaction.

It implies the following rate law:

Subsequent reactions

The products formed are often not stable but react by subsequent reactions. At the time law of the reactant has no effect, but the rate law for the product passes through a maximum.

Integrated rate law:

Temperature dependence of the reaction rate

RGT control ( reaction rate - temperature control ), if the temperature for a chemical reaction to 10 K increases, then the reaction rate is increased by 2 - to 4 -fold ( for reaction with an activation energy of about 50 kJ / mol).

Mathematically, and this is physically justified by the approach of Arrhenius. After that, the temperature dependence of the rate of reaction can be described by an exponential function. Already described above is the equation for a second-order reaction:

The temperature dependence is in the so-called velocity coefficient, as it applies here the Arrhenius equation. The velocity coefficient is a constant, then, as long as the temperature is not changed and can be also referred to as a speed constant. At very low temperatures, the reaction rate is extremely low and is close to the absolute zero point zero.

Kinetic studies

To study the kinetics of chemical reactions, a variety of methods.

They allow the determination of the

• Order of the reaction,
• Elementary reactions,
• Reaction rate constants,
• Temperature dependence and activation energy

The Arrhenius factor.

Measurement methods

From the variety of measurement methods should of course always the one to be selected that provides the most reliable results and is the easiest to perform. Therefore one must take into account the physical properties of the reaction components and the reaction conditions and particularly the rate / half-life of the test reaction.

General:

We distinguish:

• Continuous measurement method, in which the concentration / amount of substance of component (s) is observed throughout the reaction mixture itself, such as spectrophotometry.

• Discontinuous measuring process in which the measurement is performed at intervals, either in the reaction mixture or in the samples taken of the reaction mixture at defined times.

Discontinuous measurement methods (minutes to hours range) only recommended for slow reactions. In addition, care must be taken that the measurement is made immediately after sampling, so that the concentration / amount of substance which continue reacting substances is not distorted here.

To reduce this effect, the sample can be strongly cooling ( decrease in the reaction rate ), or one of the reactive components from the sample to remove, e.g. by precipitation.

With rapid responses (minutes to seconds ) a continuous measurement method is necessary. Often this special flow apparatuses are used.

For extremely fast reactions ( milliseconds ) Special methods are used, such as relaxation methods or flash photolysis.

Measured variables

To measure the turnover of a component a measure should be used, which can be as unique as possible and proportional associated with the concentration / amount of substance of a component. This needs to be calibrated.

It is also important conditions under which the reaction is carried out, so isobar at constant pressure, isothermal at constant temperature or isochoric at constant volume.

The most commonly used metrics are:

• Dielectric constant
• Conductivity with ionic species
• Refractive index
• Optical activity in optically active species
• Light absorption in light-absorbing species (most common methods of measurement)
• Fluorescence

All of these metrics can be either continuously or intermittently observed and are therefore suitable for fast and slow reactions.

For slow reactions can also measure it:

• Volume at isobaric conditions in reactions with gas generation / consumption
• Pressure at isochoric conditions in gases
• Heat of reaction (rare)

Since all measurements are dependent on temperature, should be used isothermally, that is, the calibration should be carried out at a defined temperature which must be maintained for the measurement.

Mixing process

At slow to fast reactions mixing methods are mainly used. This defined quantities of the reactants are mixed together immediately as possible using simple stirrer, flow tubes or high-precision mixing chambers.

The concentrations of the substances are continuously or intermittently observed. For this purpose, for example, drawn at regular time intervals, samples and analyzed by gas chromatography or HPLC.

Are known then:

• The initial concentration (s)
• Different concentrations at times
• The reaction temperature

The following are the principles of kinetic studies should be represented in simplified with the help of the mixing process.

Determining the reaction order

When the initial concentrations varied method, the initial concentrations of the various reactants in several reaction mixtures can be varied at otherwise constant reaction conditions.

Per approach, the initial concentration should ideally be only one reactant is varied so that the effect can be clearly assigned. Furthermore, the mixing volumes must be calculated accurately.

In all the tests after a defined reaction time, the conversion of a reactant or product is determined and used to calculate the reaction rate:

Now there are various options:

• Doubled when the initial concentration of a reactant is doubled: first-order dependence on the concentration of this reactant.
• Quadrupled when the initial concentration of a reactant is doubled: second-order dependence on the concentration of this reactant.
• Remains the same regardless of the initial concentration of a reactant: zero-order dependence of the concentration of said reactants.

Etc.

The total order is derived from the sum of the individual orders.

Determination of the reaction rate coefficients

It is defined a starting concentration of the reactant A is selected and the concentration thereof is repeatedly or continuously monitored during the reaction. The reaction order with respect to A must be known.

At different times, and so one obtains different concentrations etc.

These pairs of values ​​and the initial concentration can be employed in the worked time law of the respective reaction order and graphically apply ( Arrhenius plot ):

• 0 order:

• 2nd order:

In all cases are obtained from the slope of the resulting graph. The more data points you have, the more accurate the result.

At 0-order reactions, there is a linear relationship between [A] and the time t, at the first -order reactions between ln [ A] and the time t, wherein the second -order reactions is between 1 / [A] and the time t. By determining experimentally which function linearly with time running ( it is the concentration values ​​obtained in the various equations of linear relations a ), one can determine the order of a reaction.

Determining the Arrhenius factor and the activation energy

After the above process is determined, etc. at several temperatures, etc.

By forming the Arrhenius equation is obtained:

At the onset of the paired values ​​and graphical plotting against one obtains a straight line. The pitch corresponds to the negative of the activation energy of the y-intercept of the logarithm of the Arrhenius factor.

History of the kinetics

First qualitative investigations have been made ​​for 1777 by CF Wenzel in his Doctrine of the relationship of the body, Dresden 1777. Later also CL Berthollet and William Higgins busy with kinetic problems.

The first truly fundamental work on the kinetics of the hydrolysis of cane sugar under acid influence, was presented by L. Wilhemy in 1850.

Jacobus Henricus van't Hoff examined in 1896, the saponification of ethyl acetate and hydrolysis of chloroacetic acid. Mathematically, he formulated the rate equations of the reactions. He also developed the basic laws to temperature dependence of the reaction rate.

Svante Arrhenius improved the derivation and gave as a rule of thumb for the change in reaction rate with increasing temperature by 1 K, an increase in the reaction rate by approximately 12% (see RGT rule). E. Scheffer and W. Brandsma introduced in 1926 a the standard Gibbs energy of activation for the rate constant.

Relaxation kinetics

Reactions with half-lives in the millisecond range or less can be observed only with difficulty; on mixing process is therefore completely omitted here. Instead, relaxation processes can be used. In these, the reagents are mixed together; the reaction is allowed to proceed until a reaction equilibrium has been established. Then the equilibrium is abruptly disturbed and observing how quickly the equilibrium is again the relaxation. According to the new equilibrium, the concentrations are determined again and the new equilibrium constant is calculated.

Depending on the number of reactants and reaction order, and with knowledge of the equilibrium constants of the newly hired equilibrium can be calculated from the relaxation time of the rate coefficients of the forward and reverse reactions of extremely fast processes.

Proven relaxation techniques are the temperature jump method, the pressure jump method and the field hopping (→ Main article: relaxation method ).

Flash photolysis

Here, a strong light flash is produced by a first flash apparatus, which leads to the photolysis of a chemical compound. A short time later carried out a second, weaker flash, which is used for spectrophotometric measurement of a reactant.

This method is particularly suitable for free-radical processes.