Chemical kinetics, also known as reaction kinetics, is the branch of
physical chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical ...
that is concerned with understanding the rates of chemical reactions. It is to be contrasted with
chemical thermodynamics
Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measureme ...
, 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
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and break ...
and yield information about the
reaction's mechanism and
transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
s, as well as the construction of
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s that also can describe the characteristics of a chemical reaction.
History
In 1864,
Peter Waage
Peter Waage (29 June 1833 – 13 January 1900) was a Norwegian chemist and professor of chemistry at the University of Kristiania. Along with his brother-in-law Cato Maximilian Guldberg, he co-discovered and developed the law of mass action ...
and
Cato Guldberg
Cato Maximilian Guldberg (11 August 1836 – 14 January 1902) was a Norwegian mathematician and chemist. Guldberg is best known as a pioneer in physical chemistry.
Background
Guldberg was born in Christiania (now Oslo), Norway. He was the el ...
pioneered the development of chemical kinetics by formulating the
law of mass action
In chemistry, the law of mass action is the proposition that the rate of the chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dy ...
, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.
[C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), 35][P. Waage, "Experiments for Determining the Affinity Law" ,''Forhandlinger i Videnskabs-Selskabet i Christiania'', (1864) 92.][C.M. Guldberg, "Concerning the Laws of Chemical Affinity", ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864) 111]
Van 't Hoff Van 't Hof and Van 't Hoff are Dutch toponymic surnames meaning "from the homestead". Other variants are ''Van Hoff'', ''Van den Hof'', ''Van der Hoff'', ''Van't Hof'' and ''Vanthof''. Notable people with these surnames include:
;Van 't Hof / Van' ...
studied chemical dynamics and in 1884 published his famous "Études de dynamique chimique". In 1901 he was awarded by the first Nobel Prize in Chemistry "in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions". After van 't Hoff, chemical kinetics deals with the experimental determination of
reaction rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per uni ...
s from which
rate law
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reac ...
s and
rate constants are derived. Relatively simple
rate law
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reac ...
s exist for
zero order reactions (for which reaction rates are independent of concentration),
first order reactions, and
second order reaction
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reactio ...
s, and can be derived for others.
Elementary reaction
An elementary reaction is a chemical reaction in which one or more chemical species react directly to form products in a single reaction step and with a single transition state. In practice, a reaction is assumed to be elementary if no reaction ...
s follow the
law of mass action
In chemistry, the law of mass action is the proposition that the rate of the chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dy ...
, but the rate law of
stepwise reaction
In chemistry, a stepwise reaction (also called an overall reaction, complex reaction, and multistep reaction, among others) is a chemical reaction with one or more reaction intermediates, which by definition involves at least two consecutive elem ...
s has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, the
rate-determining step
In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step or r/d step) or rate-limiting step. For a given reaction mechanism, the prediction of the ...
often determines the kinetics. In consecutive first order reactions, a
steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ' ...
approximation can simplify the
rate law
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reac ...
. The
activation energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
for a reaction is experimentally determined through the
Arrhenius equation
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
and the
Eyring equation
The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henr ...
. The main factors that influence the
reaction rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per uni ...
include: the
physical state of the reactants, the
concentrations of the reactants, the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on ...
at which the reaction occurs, and whether or not any
catalysts
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycl ...
are present in the reaction.
Gorban and Yablonsky have suggested that the history of chemical dynamics can be divided into three eras. The first is the van 't Hoff wave searching for the general laws of chemical reactions and relating kinetics to thermodynamics. The second may be called the
Semenov--
Hinshelwood wave with emphasis on reaction mechanisms, especially for
chain reactions. The third is associated with
Aris and the detailed mathematical description of chemical reaction networks.
Factors affecting reaction rate
Nature of the reactants
The reaction rate varies depending upon what substances are reacting. Acid/base reactions, the formation of
salts
In chemistry, a salt is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a compound with no net electric charge. A common example is table salt, with positively ...
, and
ion exchange
Ion exchange is a reversible interchange of one kind of ion present in an insoluble solid with another of like charge present in a solution surrounding the solid with the reaction being used especially for softening or making water demineralised, ...
are usually fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be slower.
The nature and strength of bonds in reactant molecules greatly influence the rate of their transformation into products.
Physical state
The
physical state (
solid
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structura ...
,
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, an ...
, or
gas) of a reactant is also an important factor of the rate of change. When reactants are in the same
phase, as in
aqueous solution
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would ...
, thermal motion brings them into contact. However, when they are in separate phases, the reaction is limited to the interface between the reactants. Reaction can occur only at their area of contact; in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant the greater its
surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of ...
per unit
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
and the more contact it with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches — one does not start with large logs right away. In organic chemistry,
on water reaction On-water reactions are a group of organic reactions that take place as an emulsion in water and have an unusual reaction rate acceleration compared with (i) the same reaction in an organic solvent, or (ii) the corresponding dry media reaction. This ...
s are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions ( are those reactions in which solute and solvent not mix properly)
Surface area of solid state
In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example,
Sherbet (powder) is a mixture of very fine powder of
malic acid
Malic acid is an organic compound with the molecular formula . It is a dicarboxylic acid that is made by all living organisms, contributes to the sour taste of fruits, and is used as a food additive. Malic acid has two stereoisomeric forms ( ...
(a weak organic acid) and
sodium hydrogen carbonate. On contact with the
saliva in the mouth, these chemicals quickly dissolve and react, releasing
carbon dioxide
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
and providing for the fizzy sensation. Also,
fireworks
Fireworks are a class of low explosive pyrotechnic devices used for aesthetic and entertainment purposes. They are most commonly used in fireworks displays (also called a fireworks show or pyrotechnics), combining a large number of devices ...
manufacturers modify the surface area of solid reactants to control the rate at which the fuels in fireworks are oxidised, using this to create diverse effects. For example, finely divided
aluminium
Aluminium (aluminum in AmE, American and CanE, Canadian English) is a chemical element with the Symbol (chemistry), symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately o ...
confined in a shell explodes violently. If larger pieces of aluminium are used, the reaction is slower and sparks are seen as pieces of burning metal are ejected.
Concentration
The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'' ...
s. 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
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combust ...
will occur more rapidly in pure oxygen than in air (21% oxygen).
The
rate equation
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial rea ...
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
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.
A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage o ...
. 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
:
Here
is the
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction.
For a reaction between reactants A and B to form product C
the reaction rate is often found to have the ...
,
is the molar concentration of reactant ''i'' and
is the partial order of reaction for this reactant. The
partial order
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary ...
for a reactant can only be determined experimentally and is often not indicated by its
stoichiometric coefficient.
Temperature
Temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on ...
usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more
thermal energy
The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, ...
. 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
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
: ''E'' > ''E''
''a'') is significantly higher and is explained in detail by the
Maxwell–Boltzmann distribution
In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
It was first defined and used ...
of molecular energies.
The effect of temperature on the reaction rate constant usually obeys the
Arrhenius equation
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
, where A is the
pre-exponential factor
In chemical kinetics, the pre-exponential factor or A factor is the pre-exponential constant in the Arrhenius equation (equation shown below), an empirical relationship between temperature and rate coefficient. It is usually designated by A w ...
or A-factor, E
a is the activation energy, R is the
molar gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment p ...
and T is the
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
.
At a given temperature, the chemical rate of a reaction depends on the value of the A-factor, the magnitude of the activation energy, and the concentrations of the reactants. Usually, rapid reactions require relatively small activation energies.
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
temperature jump
The temperature jump method is a technique used in chemical kinetics for the measurement of very rapid reaction rates. It is one of a class of chemical relaxation methods pioneered by the German physical chemist Manfred Eigen in the 1950s. In th ...
method. This involves using a sharp rise in temperature and observing the
relaxation time of the return to equilibrium. A particularly useful form of temperature jump apparatus is a
shock tube, which can rapidly increase a gas's temperature by more than 1000 degrees.
Catalysts
A
catalyst
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
is a substance that alters the rate of a chemical reaction but it remains
chemically
A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
unchanged afterwards. The catalyst increases the rate of the reaction by providing a new
reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.
A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage o ...
to occur with in a lower
activation energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
. In
autocatalysis
A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction.Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 199 ...
a reaction product is itself a catalyst for that reaction leading to
positive feedback
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...
. Proteins that act as catalysts in biochemical reactions are called
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different molecule ...
s.
Michaelis–Menten kinetics
In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the ra ...
describe the
rate of enzyme mediated reactions. A catalyst does not affect the position of the equilibrium, as the catalyst speeds up the backward and forward reactions equally.
In certain organic molecules, specific substituents can have an influence on reaction rate in
neighbouring group participation.
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
activity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution.
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
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability ...
). 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
diamond anvils.
A reaction's kinetics can also be studied with a
pressure jump approach. This involves making fast changes in pressure and observing the
relaxation time of the return to equilibrium.
Absorption of light
The activation energy for a chemical reaction can be provided when one reactant molecule absorbs light of suitable
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
and is promoted to an
excited state
In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers t ...
. The study of reactions initiated by light is
photochemistry
Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible light (400– ...
, one prominent example being
photosynthesis
Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored i ...
.
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
Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as sp ...
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
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
of the reaction.
[ Laidler, K. J. ''Chemical Kinetics'' (3rd ed., Harper and Row 1987) p.33-39 ] 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
[Atkins P. and de Paula J., ''Physical Chemistry'' (8th ed., W.H. Freeman 2006) p.793 ] 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
The temperature jump method is a technique used in chemical kinetics for the measurement of very rapid reaction rates. It is one of a class of chemical relaxation methods pioneered by the German physical chemist Manfred Eigen in the 1950s. In th ...
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.[Atkins P. and de Paula J., ''Physical Chemistry'' (8th ed., W.H. Freeman 2006) pp.805-7 ] 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.[
* ]Flash photolysis
Flash photolysis is a pump-probe laboratory technique, in which a sample is first excited by a strong pulse of light from a pulsed laser of nanosecond, picosecond, or femtosecond pulse width or by another short-pulse light source such as a fla ...
, in which a laser pulse produces highly excited species such as free radicals
In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron.
With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spon ...
, whose reactions are then studied.[Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) p.94-97 ]
Equilibrium
While chemical kinetics is concerned with the rate of a chemical reaction, thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
determines the extent to which reactions occur. In a reversible reaction
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.
: \mathit aA + \mathit bB \mathit cC + \mathit dD
A and B can react to form C and D or, in the ...
, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal (the principle of dynamic equilibrium
In chemistry, a dynamic equilibrium exists once a reversible reaction occurs. Substances transition between the reactants and products at equal rates, meaning there is no net change. Reactants and products are formed at such a rate that the ...
) and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, the Haber–Bosch process for combining nitrogen and hydrogen to produce ammonia. Chemical clock
A chemical clock (or clock reaction) is a complex mixture of reacting chemical compounds in which the onset of an observable property (discoloration or coloration) occurs after a predictable induction time due to the presence of clock species at a ...
reactions such as the Belousov–Zhabotinsky reaction
A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element in ...
demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium.
Free energy
In general terms, the free energy change (ΔG) of a reaction determines whether a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be very exothermic
In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity ...
and have a very positive entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
change but will not happen in practice if the reaction is too slow. If a reactant can produce two products, the thermodynamically most stable one will form in general, except in special circumstances when the reaction is said to be under kinetic reaction control. The Curtin–Hammett principle applies when determining the product ratio for two reactants interconverting rapidly, each going to a distinct product. It is possible to make predictions about reaction rate constants for a reaction from free-energy relationships.
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 isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass number ...
s.
Chemical kinetics provides information on residence time
The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distrib ...
and heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction ...
in a chemical reactor
A chemical reactor is an enclosed volume in which a chemical reaction takes place. In chemical engineering, it is generally understood to be a process vessel used to carry out a chemical reaction, which is one of the classic unit operations in che ...
in chemical engineering
Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials in ...
and the molar mass distribution The molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely hav ...
in polymer chemistry
Polymer chemistry is a sub-discipline of chemistry that focuses on the structures of chemicals, chemical synthesis, and chemical and physical properties of polymers and macromolecules. The principles and methods used within polymer chemistry are ...
. It is also provides information in corrosion engineering
Corrosion engineering is an engineering specialty that applies scientific, technical, engineering skills, and knowledge of natural laws and physical resources to design and implement materials, structures, devices, systems, and procedures to mana ...
.
Applications and models
The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performing catalytic cracking
Fluid Catalytic Cracking (FCC) is the conversion process used in petroleum refineries to convert the high-boiling point, high-molecular weight hydrocarbon fractions of petroleum (crude oils) into gasoline, olefinic gases, and other petroleum prod ...
of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur.
Chemical Kinetics is frequently validated and explored through modeling in specialized packages as a function of ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contras ...
-solving (ODE-solving) and curve-fitting.
Numerical methods
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
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
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:
:
It can also be expressed as:
: which is the same as
To solve the differential equations with Euler and Runge-Kutta methods we need to have the initial values.
* Euler method → simple but inaccurate.
At any point is the same as;
:
We can approximate the differentials as discrete increases:
: ≃ ∆y/∆x = (x+∆x)-y(x)∆x
The unknown part of the equation is y(x+Δx), which can be found if we have the data for the initial values.
* Runge-Kutta methods → it is more accurate than the Euler method.
In this method, an initial condition is required: y=y0 at x=x0. The problem is to find the value of y when x=x0 + h, where h is a given constant.
It can be shown analytically that the ordinate at that moment to the curve through (x0, y0) is given by the third-order Runge-Kutta formula.
In first-order ordinary equations, the Runge-Kutta method uses a mathematical model that represents the relationship between the temperature and the rate of reaction. It is worth it to calculate the rate of reaction at different temperatures for different concentrations. The equation obtained is:
* Stochastic methods
In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined is a time interval (''time series'') or a region of space (''random field'').
Familiar examples ...
→ probabilities of the differential rate laws and the kinetic constants.
In an equilibrioum reaction with direct and inverse rate constants, it is easier to transform from A to B rather than B to A.
As for probability computations, at each time it choose a random number to be compared with a threshold to know if the reaction runs from A to B or the other way around.
See also
* Autocatalytic reactions and order creation
*Detonation
Detonation () is a type of combustion involving a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations propagate supersonically through shock waves with ...
*Electrochemical kinetics
Electrochemical kinetics is the field of electrochemistry that studies the rate of electrochemical processes. This includes the study of how process conditions, such as concentration and electric potential, influence the rate of oxidation and redu ...
* Eurokin
*Flame speed The flame speed is the measured rate of expansion of the flame front in a combustion reaction. Whereas ''flame velocity'' is generally used for a fuel, a related term is explosive velocity, which is the same relationship measured for an explosive. ...
*Heterogenous catalysis
In chemistry, heterogeneous catalysis is catalysis where the phase of catalysts differs from that of the reactants or products. The process contrasts with homogeneous catalysis where the reactants, products and catalyst exist in the same phase. Ph ...
*Intrinsic low-dimensional manifold In chemical kinetics, an intrinsic low-dimensional manifold is a technique to simplify the study of reaction mechanisms using dynamical systems, first proposed in 1992.
The ILDM approach fixes a low dimensional surface which describes well the slow ...
* MLAB chemical kinetics modeling package
* Nonthermal surface reaction
* PottersWheel Matlab toolbox to fit chemical rate constants to experimental data
*Reaction progress kinetic analysis
In chemistry, reaction progress kinetic analysis (RPKA) is a subset of a broad range of kinetic techniques utilized to determine the rate laws of chemical reactions and to aid in elucidation of reaction mechanisms. While the concepts guiding rea ...
*Corrosion engineering
Corrosion engineering is an engineering specialty that applies scientific, technical, engineering skills, and knowledge of natural laws and physical resources to design and implement materials, structures, devices, systems, and procedures to mana ...
References
External links
Chemistry applets
Chemical Kinetics of Gas Phase Reactions
Kinpy: Python code generator for solving kinetic equations
Reaction rate law and reaction profile - a question of temperature, concentration, solvent and catalyst - how fast will a reaction proceed
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Jacobus Henricus van 't Hoff