Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.

History

The pioneering work of chemical kinetics was done by German chemist

The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their concentrations. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will usually result in the corresponding increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. For example, combustion will occur more rapidly in pure oxygen than in air (21% oxygen).

The rate equation shows the detailed dependence of the reaction rate on the concentrations of reactants and other species present. The mathematical forms depend on the reaction mechanism. The actual rate equation for a given reaction is determined experimentally and provides information about the reaction mechanism. The mathematical expression of the rate equation is often given by

${\displaystyle v={\frac {\mathrm {d} c}{\mathrm {d} t}}=k\prod _{i}c_{i}^{m_{i}}}$

Here ${\displaystyle k}$ is the reaction rate constant, ${\displaystyle c_{i}}$ is the molar concentration of reactant i and ${\displaystyle m_{i}}$ is the partial order of reaction for this reactant. The partial order for a reactant can only be determined experimentally and is often not indicated by its stoichiometric coefficient.

Temperature

Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than activation energy: E > E_a) is significantly higher and is explained in detail by the Maxwell–Boltzmann distribution of molecular energies.

The effect of temperature on the reaction rate constant usually obeys the Arrhenius equation ${\displaystyle k=Ae^{-E_{\rm {a}}/(RT)}}$, where A is the

The 'rule of thumb' that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the α (temperature coefficient) is often between 1.5 and 2.5.

The kinetics of rapid reactions can be studied with the

A

In certain organic molecules, specific substituents can have an influence on reaction rate in neighbouring group participation.^{[citation needed]}

Pressure

Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the

In addition to this straightforward mass-action effect, the rate coefficients themselves can change due to pressure. The rate coefficients and products of many high-temperature gas-phase reactions change if an inert gas is added to the mixture; variations on this effect are called fall-off and chemical activation. These phenomena are due to exothermic or endothermic reactions occurring faster than heat transfer, causing the reacting molecules to have non-thermal energy distributions (non-Boltzmann distribution). Increasing the pressure increases the heat transfer rate between the reacting molecules and the rest of the system, reducing this effect.

Condensed-phase rate coefficients can also be affected by pressure, although rather high pressures are required for a measurable effect because ions and molecules are not very compressible. This effect is often studied using

A reaction's kinetics can also be studied with a

Absorption of light

The activation energy for a chemical reaction can be provided when one reactant molecule absorbs light of suitable wavelength and is promoted to an excited state. The study of reactions initiated by light is photochemistry, one prominent example being photosynthesis.

Experimental methods

The experimental determination of reaction rates involves measuring how the concentrations of reactants or products change over time. For example, the concentration of a reactant can be measured by spectrophotometry at a wavelength where no other reactant or product in the system absorbs light.

For reactions which take at least several minutes, it is possible to start the observations after the reactants have been mixed at the temperature of interest.

Fast reactions

For faster reactions, the time required to mix the reactants and bring them to a specified temperature may be comparable or longer than the half-life of the reaction.^[9] Special methods to start fast reactions without slow mixing step include

• Stopped flow methods, which can reduce the mixing time to the order of a millisecond^[9][10][11]
  The stopped flow methods have limitation, for example, we need to consider the time it takes to mix gases or solutions and are not suitable if the half-life is less than about a hundredth of a second.
• Chemical relaxation methods such as temperature jump and pressure jump, in which a pre-mixed system initially at equilibrium is perturbed by rapid heating or depressurization so that it is no longer at equilibrium, and the relaxation back to equilibrium is observed.^{[9][12][13][14]} For example, this method has been used to study the neutralization H₃O⁺ + OH⁻ with a half-life of 1 μs or less under ordinary conditions.^[9][14]
• Flash photolysis, in which a laser pulse produces highly excited species such as free radicals, whose reactions are then studied.^{[11][15][16][17]}

Equilibrium

While chemical kinetics is concerned with the rate of a chemical reaction,

The kinetic isotope effect is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of its isotopes.

Chemical kinetics provides information on

In some cases, equations are unsolvable analytically, but can be solved using numerical methods if data values are given. There are two different ways to do this, by either using software programmes or mathematical methods such as the Euler method. Examples of software for chemical kinetics are i) Tenua, a Java app which simulates chemical reactions numerically and allows comparison of the simulation to real data, ii) Python coding for calculations and estimates and iii) the Kintecus software compiler to model, regress, fit and optimize reactions.

-Numerical integration: for a 1st order reaction A → B

The differential equation of the reactant A is:

$${\displaystyle {\frac {d{\ce {[A]}}}{dt}}=-k{\ce {[A]}}}$$

It can also be expressed as

$${\displaystyle {\frac {d{\ce {[A]}}}{dt}}=f(t,{\ce {[A]}})}$$

${\displaystyle y'=f(x,y)}$

To solve the differential equations with Euler and Runge-Kutta methods we need to have the initial values.

See also

• Autocatalytic reactions and order creation
• Corrosion engineering
• Detonation
• Electrochemical kinetics
• Flame speed
• Heterogenous catalysis
• Intrinsic low-dimensional manifold
• MLAB chemical kinetics modeling package
• Nonthermal surface reaction
• PottersWheel Matlab toolbox to fit chemical rate constants to experimental data
• Reaction progress kinetic analysis

References