Iron rusting - a chemical reaction with a slow reaction rate. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called
Wood burning - a chemical reaction with a fast reaction rate. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called

The reaction rate or rate of reaction for a reactant or product in a particular reaction is intuitively defined as how fast a reaction takes place. A reagent or reactant is a substance or compound consumed during a Chemical reaction. A product is a substance that forms as a result of a Biological - or Chemical reaction. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called 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. Redox (shorthand for reduction-oxidation reaction describes all Chemical reactions in which atoms have their Oxidation number ( Oxidation state

Chemical kinetics is the part of physical chemistry that studies reaction rates. Chemical kinetics, also known as reaction kinetics is the study of rates of chemical processes Physical chemistry, is the application of Physics to macroscopic microscopic atomic subatomic and particulate phenomena in chemical systems It is mostly defined as a large The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering, enzymology and environmental engineering. Chemical engineering is the branch of Engineering that deals with the application of Physical science (e Enzymes are Biomolecules that catalyze ( ie increase the rates of Chemical reactions Almost all enzymes are Proteins Environmental engineering is the application of Science and Engineering principles to improve the environment (air water and/or land resources

## Formal definition of reaction rate

Consider a typical chemical reaction:

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 (P and Q). A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable A reagent or reactant is a substance or compound consumed during a Chemical reaction. A product is a substance that forms as a result of a Biological - or Chemical reaction.

According to Jerrica IUPAC's Gold Book definition[1] the reaction rate v (also r or R) for a chemical reaction occurring in a closed system under constant-volume conditions, without a build-up of reaction intermediates, is defined as:

$v = - \frac{1}{a} \frac{d[A]}{dt} = - \frac{1}{b} \frac{d[B]}{dt} = \frac{1}{p} \frac{d[P]}{dt} = \frac{1}{q} \frac{d[Q]}{dt}$

The IUPAC[1] recommends that the unit of time should always be the second. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization Compendium of Chemical Terminology (ISBN 0-86542-684-8 is a book published by IUPAC containing internationally accepted definitions for terms in Chemistry. A Closed system is a System in the state of being isolated from the environment A reaction intermediate or an intermediate is a Molecular entity that is formed from the reactants (or preceding intermediates and reacts further to give the directly 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. Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable 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 of constant volume. A Closed system is a System in the state of being isolated from the environment 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 must be taken into account: IN - OUT + GENERATION = ACCUMULATION

$F_{A0} - F_A + \int_{0}^{V} r\, dV = \frac{dN_A}{dt}$

When applied to the simple case stated previously this equation reduces to: $v= \frac{d[A]}{dt}$

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. A mass balance (also called a material balance is an application of Conservation of mass to the analysis of physical systems It is defined as the derivative of the extent of reaction with respect to time. Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable

$\dot{\xi} =\frac{d\xi}{dt} = \frac{1}{\nu_i} \frac{dn_i}{dt} = \frac{1}{\nu_i} \left(V\frac{dC_i}{dt} + C_i \frac{dV}{dt} \right)$

$\scriptstyle \nu_i$ is the stoichiometric coefficient for substance i, $\scriptstyle V$ is the volume of reaction and $\scriptstyle C_i$ is the concentration of substance i.

When side products or reaction intermediates are formed, the IUPAC[1] recommends the use of the terms rate of appearance and rate of disappearance for products and reactants, respectively.

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. Catalysis is the process in which the rate of a Chemical reaction is increased by means of a Chemical substance known as a catalyst 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

Factors that affect the rate of reaction:

• Concentration: Reaction rate increases with concentration, as described by the rate law and explained by collision theory. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance The rate law or rate equation for a Chemical reaction is an equation which links the Reaction rate with concentrations or pressures of reactants and constant The Collision theory, proposed by Max Trautz and William Lewis in 1916 and 1918 qualitatively explains how Chemical reactions occur and why Reaction As reactant concentration increases, the frequency of collision increases. Frequency is a measure of the number of occurrences of a repeating event per unit Time. A collision is an isolated event in which two or more bodies (colliding bodies exert relatively strong forces on each other for a relatively short time
• The nature of the reaction: Some reactions are naturally faster than others. The number of reacting species, their physical state (the particles that form solids move much more slowly than those of gases or those in solution), the complexity of the reaction and other factors can influence greatly the rate of a reaction. In the Physical sciences a phase is a Set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances
• Temperature: 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. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature However, the main reason why it increases the rate of reaction is that more of the colliding particles will have the necessary activation energy resulting in more successful collisions (when bonds are formed between reactants). In Chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined The influence of temperature is described by the Arrhenius equation. The Arrhenius equation is a simple but remarkably accurate formula for the temperature dependence of the Rate constant, and therefore rate of a chemical reaction As a rule of thumb, reaction rates for many reactions double or triple for every 10 degrees Celsius increase in temperature,[2] though the effect of temperature may be very much larger or smaller than this (to the extent that reaction rates can be independent of temperature or decrease with increasing temperature. A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation The Celsius Temperature scale was previously known as the centigrade scale. )

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 (also referred to as ambient temperature) is a common term to denote a certain Temperature within enclosed space at which humans are accustomed 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. In Thermodynamics, the word exothermic "outside heating" describes a process or reaction that releases Energy usually in the form of Heat, but That is valid for many other fuels, such as methane, butane, hydrogen. Methane is a Chemical compound with the molecular formula. It is the simplest Alkane, and the principal component of Natural gas. Butane, also called n -butane, is the unbranched Alkane with four Carbon Atoms CH3CH2CH2CH3 Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 . .

• Solvent: Many reactions take place in solution and the properties of the solvent affect the reaction rate. A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. The ionic strength as well has an effect on reaction rate. The ionic strength, I, of a solution is a function of the Concentration of all Ions present in a Solution.
• Pressure: The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in concentration of the gas. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface For condensed-phase reactions, the pressure dependendence is weak.
• Electromagnetic Radiation: Electromagnetic radiation is a form of energy so it may speed up the rate or even make a reaction spontaneous, as it provides the particles of the reactants with more energy. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. 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.

For example when methane reacts with chlorine in the dark, the reaction rate is very slow. Methane is a Chemical compound with the molecular formula. It is the simplest Alkane, and the principal component of Natural gas. Chlorine (ˈklɔriːn from the Greek word 'χλωρóς' ( khlôros, meaning 'pale green' is the Chemical element with Atomic number 17 and It can be sped up when the mixture is put under diffused light. In Chemistry, a mixture is a substance made by combining two or more different materials without a chemical reaction occurring (the objects do not bond together 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. Catalysis is the process in which the rate of a Chemical reaction is increased by means of a Chemical substance known as a catalyst In Chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined

For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature. Platinum (ˈplætɪnəm is a Chemical element with the Atomic symbol Pt and an Atomic number of 78

• Isotopes: The kinetic isotope effect consists in a different reaction rate for the same molecule if it has different isotopes, usually hydrogen isotopes, because of the mass difference between hydrogen and deuterium. Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides The kinetic isotope effect ( KIE) is a variation in the Reaction rate of a Chemical reaction when an Atom in one of the reactants is replaced Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1
• Surface Area: In reactions on surfaces, which take place for example during heterogeneous catalysis, the rate of reaction increases as the surface area does. 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 Heterogeneous catalysis is a Chemistry term which describes Catalysis where the Catalyst is in a different phase (ie That is due to the fact that more particles of the solid are exposed and can be hit by reactant molecules.
• Order: The order of the reaction controls how the reactant concentration affects reaction rate. See also Rate equation The Order of reaction, in Chemical kinetics, with respect to a certain Reactant is defined as the power
• Stirring: Stirring can have a strong effect on the rate of reaction for heterogeneous reactions. Homogeneous reactions are Chemical reactions in which the reactants are in the same phase, while heterogeneous reactions have Reactants in two

All the factors that affect a reaction rate are taken into account in the rate equation of the reaction.

## Rate Equation

Main article: Rate equation

For a chemical reaction 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 of each reactant. The rate law or rate equation for a Chemical reaction is an equation which links the Reaction rate with concentrations or pressures of reactants and constant A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called In mathematics the word expression is a term for any well-formed combination of mathematical symbols In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance It is of the kind:

$\,r = k(T)[A]^{n'}[B]^{m'}$

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. See also Rate equation The Order of reaction, in Chemical kinetics, with respect to a certain Reactant is defined as the power Chemistry, a reaction mechanism is the step by step Sequence of Elementary reactions by which overall Chemical change occurs.

Stoichiometry, molecularity (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. Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable Molecularity in Chemistry is the number of colliding molecular entities that are involved in a single Reaction step. See also Rate equation The Order of reaction, in Chemical kinetics, with respect to a certain Reactant is defined as the power 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. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834

By combining the rate law with a mass balance for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. A mass balance (also called a material balance is an application of Conservation of mass to the analysis of physical systems For a closed system with constant volume such an expression can look like

$\frac{d[C]}{dt} = k(T)[A]^{n'}[B]^{m'}$

## Temperature dependence

Main article: Arrhenius equation

Each reaction rate coefficient k has a temperature dependency, which is usually given by the Arrhenius equation:

$k = A e^{ - \frac{E_a}{RT} }$

Ea is the activation energy and R is the gas constant. The Arrhenius equation is a simple but remarkably accurate formula for the temperature dependence of the Rate constant, and therefore rate of a chemical reaction The Arrhenius equation is a simple but remarkably accurate formula for the temperature dependence of the Rate constant, and therefore rate of a chemical reaction In Chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working Since at temperature T the molecules have energies given by a Boltzmann distribution, one can expect the number of collisions with energy greater than Ea to be proportional to $e^{\frac{-E_a}{RT}}$. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature WikipediaWikiProject Probability#Standards for a discussion of standards used for probability distribution articles such as this one A is the pre-exponential factor or frequency factor. See also Arrhenius equation In Chemical kinetics, the preexponential factor or A factor is the pre-exponential constant in the Arrhenius equation

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-phase reactions (i. Condensed matter physics is the field of Physics that deals with the macroscopic physical properties of Matter. e. , when reactants and products are solids or liquid) is usually suffficiently 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:

$A + B \rightleftharpoons |A \cdots B|^{\ddagger} \rightarrow P$

the activation volume, $\Delta V^{\ddagger}$, is:

$\Delta V^{\ddagger} = \bar{V}_{\ddagger} - \bar{V}_A - \bar{V}_B$

where $\bar{V}$ denote the partial molar volumes of the reactants and products and $\ddagger$ 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 molal-concentration) with pressure at constant temperature to be:

$-RT \left(\frac{\partial ln k_x}{\partial P} \right)_T = \Delta V^{\ddagger}$

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, depeding on the value of $\Delta V^{\ddagger}$. 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 atomospheric (0. 1 MPa) to 50 MPa (which gives $\Delta V^{\ddagger}$=-0. 025 L/mol)[3].

## Examples

For the reaction

$2H_2 (g) + 2 NO(g) \rarr N_2 (g) + 2 H_2O (g)$

The rate equation is:

$r = k [H_2]^1[NO]^2 \,$

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 reation rate. For example, in:

1. $2 NO \ \overrightarrow\longleftarrow \ N_2O_2$ (fast equilibrium)
2. $N_2O_2 + H_2 \rarr N_2O + H_2O$ (slow)
3. $N_2O + H_2 \rarr N_2 + H_2O$ (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.