Reaction rate
Overview
 
The reaction rate or speed of reaction for a reactant or product
Product (chemistry)
Product are formed during chemical reactions as reagents are consumed. Products have lower energy than the reagents and are produced during the reaction according to the second law of thermodynamics. The released energy comes from changes in chemical bonds between atoms in reagent molecules and...

 in a particular reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

 is intuitively defined as how fast or slow a reaction takes place. For example, the oxidation of iron under the atmosphere is a slow reaction which can take many years, but the combustion of butane in a fire is a reaction that takes place in fractions of a second.

Chemical kinetics
Chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...

 is the part of physical chemistry
Physical chemistry
Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

 that studies reaction rates.
Encyclopedia
The reaction rate or speed of reaction for a reactant or product
Product (chemistry)
Product are formed during chemical reactions as reagents are consumed. Products have lower energy than the reagents and are produced during the reaction according to the second law of thermodynamics. The released energy comes from changes in chemical bonds between atoms in reagent molecules and...

 in a particular reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

 is intuitively defined as how fast or slow a reaction takes place. For example, the oxidation of iron under the atmosphere is a slow reaction which can take many years, but the combustion of butane in a fire is a reaction that takes place in fractions of a second.

Chemical kinetics
Chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...

 is the part of physical chemistry
Physical chemistry
Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

 that studies reaction rates. The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...

, enzymology and environmental engineering
Environmental engineering
Environmental engineering is the application of science and engineering principles to improve the natural environment , to provide healthy water, air, and land for human habitation and for other organisms, and to remediate polluted sites...

.

Formal definition of reaction rate

Consider a typical chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

:
aA + bB → pP + qQ


The lowercase letters (a, b, p, and q) represent stoichiometric coefficients, while the capital letters represent the reactants (A and B) and the products
Product (chemistry)
Product are formed during chemical reactions as reagents are consumed. Products have lower energy than the reagents and are produced during the reaction according to the second law of thermodynamics. The released energy comes from changes in chemical bonds between atoms in reagent molecules and...

 (P and Q).

According to IUPAC's Gold Book
Gold Book
The Compendium of Chemical Terminology is a book published by the International Union of Pure and Applied Chemistry containing internationally accepted definitions for terms in chemistry...

 definition
the reaction rate r for a chemical reaction occurring in a closed system
Closed system
-In physics:In thermodynamics, a closed system can exchange energy , but not matter, with its surroundings.In contrast, an isolated system cannot exchange any of heat, work, or matter with the surroundings, while an open system can exchange all of heat, work and matter.For a simple system, with...

 under constant-volume conditions, without a build-up of reaction intermediate
Reaction intermediate
A reaction intermediate or an intermediate is a molecular entity that is formed from the reactants and reacts further to give the directly observed products of a chemical reaction. Most chemical reactions are stepwise, that is they take more than one elementary step to complete...

s, is defined as:
,

where [X] denotes the concentration of the substance X. (NOTE: Rate of a reaction is always positive. '-' sign is present in the reactant involving terms because the reactant concentration is decreasing.) The IUPAC recommends that the unit of time should always be the second. In such a case the rate of reaction differs from the rate of increase of concentration of a product P by a constant factor (the reciprocal of its stoichiometric number) and for a reactant A by minus the reciprocal of the stoichiometric number. Reaction rate usually has the units of mol dm−3 s−1.
It is important to bear in mind that the previous definition is only valid for a single reaction, in a closed system
Closed system
-In physics:In thermodynamics, a closed system can exchange energy , but not matter, with its surroundings.In contrast, an isolated system cannot exchange any of heat, work, or matter with the surroundings, while an open system can exchange all of heat, work and matter.For a simple system, with...

of constant volume. This most usually implicit assumption must be stated explicitly, otherwise the definition is incorrect: If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.

For any system in general the full mass balance
Mass balance
A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...

 must be taken into account: IN - OUT + GENERATION = ACCUMULATION


When applied to the severe case stated previously this equation reduces to:

For a single reaction in a closed system of varying volume the so called rate of conversion can be is used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time.



is the stoichiometric coefficient for substance , is the volume of reaction and is the concentration of substance .

When side products or reaction intermediates are formed, the IUPAC recommends the use of the terms rate of appearance and rate of disappearance for products and reactants, properly.

Reaction rates may also be defined on a basis that is not the volume of the reactor. When a catalyst is used the reaction rate may be stated on a catalyst weight (mol g−1 s−1) or surface area (mol m−2 s−1) basis. If the basis is a specific catalyst site that may be rigorously counted by a specified method, the rate is given in units of s−1 and is called a turnover frequency.

Factors influencing rate of reaction

  • The nature of the reaction: Some reactions are naturally faster than others. The number of reacting species, their physical state
    Phase (matter)
    In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

     (the particles that form solids move much more slowly than those of gases or those in solution
    Solution
    In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...

    ), the complexity of the reaction and other factors can influence greatly the rate of a reaction.
  • Concentration
    Concentration
    In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

    : Reaction rate increases with concentration, as described by the rate law and explained by collision theory
    Collision theory
    Collision theory is a theory proposed by Max Trautz and William Lewis in 1916 and 1918, that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. For a reaction to occur the reactant particles must collide. Only a certain fraction of the total...

    . As reactant concentration increases, the frequency
    Frequency
    Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

     of collision
    Collision
    A collision is an isolated event which two or more moving bodies exert forces on each other for a relatively short time.Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies...

     increases.
  • Pressure
    Pressure
    Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

    : The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in concentration of the gas. For condensed-phase reactions, the pressure dependence is weak.
  • Order: The order of the reaction controls how the reactant concentration (or pressure) affects reaction rate.
  • Temperature
    Temperature
    Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

    : Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles, as explained by collision theory. However, the main reason that temperature increases the rate of reaction is that more of the colliding particles will have the necessary activation energy
    Activation energy
    In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...

     resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the Arrhenius equation
    Arrhenius equation
    The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish...

    . As a rule of thumb
    Rule of thumb
    A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...

    , reaction rates for many reactions double for every 10 degrees Celsius
    Celsius
    Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

     increase in temperature, though the effect of temperature may be very much larger or smaller than this.

For example, coal burns in a fireplace in the presence of oxygen but it doesn't when it is stored at room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...

. The reaction is spontaneous at low and high temperatures but at room temperature its rate is so slow that it is negligible. The increase in temperature, as created by a match, allows the reaction to start and then it heats itself, because it is exothermic
Exothermic
In thermodynamics, the term exothermic describes a process or reaction that releases energy from the system, usually in the form of heat, but also in the form of light , electricity , or sound...

. That is valid for many other fuels, such as methane
Methane
Methane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel...

, butane
Butane
Butane is a gas with the formula C4H10 that is an alkane with four carbon atoms. The term may refer to any of two structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, butane refers only to the unbranched n-butane isomer; the other one being called "methylpropane" or...

, and hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

.

Reaction rates can be independent of temperature (non-Arrhenius) or decrease with increasing temperature (anti-Arrhenius). Reactions without an activation barrier (e.g. some radical
Radical (chemistry)
Radicals are atoms, molecules, or ions with unpaired electrons on an open shell configuration. Free radicals may have positive, negative, or zero charge...

 reactions), tend to have anti Arrhenius temperature dependence: the rate constant decreases with increasing temperature.
  • Solvent
    Solvent
    A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...

    : Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength
    Ionic strength
    The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts...

     also has an effect on reaction rate.
  • Electromagnetic radiation
    Electromagnetic radiation
    Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

    and intensity of light
    Irradiance
    Irradiance is the power of electromagnetic radiation per unit area incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter , while the cgs units are ergs per square centimeter...

    : Electromagnetic radiation is a form of energy. As such, it may speed up the rate or even make a reaction spontaneous as it provides the particles of the reactants with more energy. This energy is in one way or another stored in the reacting particles (it may break bonds, promote molecules to electronically or vibrationally excited states...) creating intermediate species that react easily. As the intensity of light increases, the particles absorb more energy and hence the rate of reaction increases.

For example when methane
Methane
Methane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel...

 reacts with chlorine
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

 in the dark, the reaction rate is very slow. It can be sped up when the mixture
Mixture
In chemistry, a mixture is a material system made up by two or more different substances which are mixed together but are not combined chemically...

 is put under diffused light. In bright sunlight, the reaction is explosive.
  • A catalyst: The presence of a catalyst increases the reaction rate (in both the forward and reverse reactions) by providing an alternative pathway with a lower activation energy
    Activation energy
    In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...

    .

For example, platinum
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

 catalyzes the combustion of hydrogen with oxygen at room temperature.
  • Isotopes: The kinetic isotope effect
    Kinetic isotope effect
    The kinetic isotope effect is the ratio of reaction rates of two different isotopically labeled molecules in a chemical reaction. It is also called "isotope fractionation," although this term is somewhat broader in meaning...

     consists in a different reaction rate for the same molecule if it has different isotopes, usually hydrogen
    Hydrogen
    Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

     isotopes, because of the mass difference between hydrogen and deuterium
    Deuterium
    Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

    .
  • Surface Area: In reactions on surfaces
    Reactions on surfaces
    By reactions on surfaces it is understood reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants...

    , which take place for example during heterogeneous catalysis
    Heterogeneous catalysis
    In chemistry, heterogeneous catalysis refers to the form of catalysis where the phase of the catalyst differs from that of the reactants. Phase here refers not only to solid, liquid, vs gas, but also immiscible liquids, e.g. oil and water. The great majority of practical heterogeneous catalysts...

    , the rate of reaction increases as the surface area does. That is because more particles of the solid are exposed and can be hit by reactant molecules.
  • Stirring
    Mixing (process engineering)
    In industrial process engineering, mixing is a unit operation that involves manipulating a heterogeneous physical system, with the intent to make it more homogeneous...

    : Stirring can have a strong effect on the rate of reaction for heterogeneous reactions
    Homogeneous and heterogeneous reactions
    Homogeneity and heterogeneity are concepts relating to the uniformity or lack thereof in a substance. A material that is homogeneous is uniform in composition or character; one that is heterogeneous lacks uniformity in one of these qualities....

    .


All the factors that affect a reaction rate, except for concentration and reaction order, are taken into account in the rate equation of the reaction.

Rate equation

For a chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

 n A + m B → C + D, the rate equation or rate law is a mathematical expression used in chemical kinetics to link the rate of a reaction to the concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

 of each reactant. It is of the kind:

In this equation k(T) is the reaction rate coefficient or rate constant, although it is not really a constant, because it includes all the parameters that affect reaction rate, except for concentration, which is explicitly taken into account. Of all the parameters described before, temperature is normally the most important one.

The exponents n and m are called reaction orders and depend on the reaction mechanism
Reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.Although only the net chemical change is directly observable for most chemical reactions, experiments can often be designed that suggest the possible sequence of steps in...

.

Stoichiometry
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...

, molecularity
Molecularity
Molecularity in chemistry is the number of colliding molecular entities that are involved in a single reaction step. While the order of a reaction is derived experimentally, the molecularity is a theoretical concept and can only be applied to elementary reactions...

 (the actual number of molecules colliding) and reaction order only coincide necessarily in elementary reactions, that is, those reactions that take place in just one step. The reaction equation for elementary reactions coincides with the process taking place at the atomic level, i.e. n molecules of type A are colliding with m molecules of type B (n plus m is the molecularity).

For gases the rate law can also be expressed in pressure units using e.g. the ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

.

By combining the rate law with a mass balance
Mass balance
A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...

 for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. For a closed system with constant volume such an expression can look like

Temperature dependence

Each reaction rate coefficient k has a temperature dependency, which is usually given by the Arrhenius equation
Arrhenius equation
The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish...

:


Ea is the activation energy
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...

 and R is the gas constant
Gas constant
The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...

. Since at temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 T the molecules have energies given by a Boltzmann distribution
Boltzmann distribution
In chemistry, physics, and mathematics, the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution...

, one can expect the number of collisions with energy greater than Ea to be proportional to . A is the pre-exponential factor or frequency factor.

The values for A and Ea are dependent on the reaction. There are also more complex equations possible, which describe temperature dependence of other rate constants which do not follow this pattern.

Pressure dependence

The pressure dependence of the rate constant for condensed
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

-phase reactions (i.e., when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice.

The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex:


the activation volume, , is:


where denote the partial molar volumes of the reactants and products and indicates the activation-state complex.

For the above reaction, one can expect the change of the reaction rate constant (based either on mole-fraction or molar-concentration) with pressure at constant temperature to be:


In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure.

Reactions can increase or decrease their rates with pressure, depending on the value of . As an example of the possible magnitude of the pressure effect, some organic reactions were shown to double the reaction rate when the pressure was increased from atmospheric (0.1 MPa) to 50 MPa (which gives =-0.025 L/mol).

Examples

For the reaction
The rate equation (or rate expression) is:

The rate equation does not simply reflect the reactants stoichiometric coefficients in the overall reaction: it is first order in H2, although the stoichiometric coefficient is 2 and it is second order in NO.

In chemical kinetics the overall reaction is usually proposed to occur through a number of elementary steps. Not all of these steps affect the rate of reaction; normally it is only the slowest elementary step that affect the reaction rate. For example, in:
  1. (fast equilibrium)
  2. (slow)
  3. (fast)


Reactions 1 and 3 are very rapid compared to the second, so it is the slowest reaction that is reflected in the rate equation. The slow step is considered the rate determining step. The orders of the rate equation are those from the rate determining step.

See also

  • Reaction rate constant
  • Rate equation
    Rate equation
    The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with concentrations or pressures of reactants and constant parameters . To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system...

  • Dilution (equation)
    Dilution (equation)
    Dilution is a reduction in the concentration of a chemical . It is the process of reducing the concentration of a solute in solution, usually simply by mixing with more solvent. To dilute a solution means to add more solvent without the addition of more solute...

  • Diffusion-controlled reaction
  • Steady state approximation
  • Collision theory
    Collision theory
    Collision theory is a theory proposed by Max Trautz and William Lewis in 1916 and 1918, that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. For a reaction to occur the reactant particles must collide. Only a certain fraction of the total...

     and transition state
    Transition state
    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 energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always...

    are chemical theories that attempt to predict and explain reaction rates.

External links

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