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 unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time.
Chemical kinetics is the part of physical chemistry that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used to deduce probable reaction mechanisms. The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering, enzymology and environmental engineering.

Formal definition

Consider a typical balanced chemical reaction:

\mathit\, A + \mathit\, B -> \mathit\, P + \mathit\, Q

The lowercase letters represent stoichiometric coefficients, while the capital letters represent the reactants and the products.
According to IUPAC's Gold Book definition
the reaction rate for a chemical reaction occurring in a closed system at constant volume, without a build-up of reaction intermediates, is defined as
where denotes the concentration of the substance. The reaction rate thus defined has the units of mol/.
The rate of a reaction is always positive. A negative sign is present to indicate that the reactant concentration is decreasing. The IUPAC recommends that the unit of time should always be the second. The rate of reaction differs from the rate of increase of concentration of a product by a constant factor and for a reactant by minus the reciprocal of the stoichiometric number. The stoichiometric numbers are included so that the defined rate is independent of which reactant or product species is chosen for measurement. For example, if and, then is consumed three times more rapidly than, but is uniquely defined. An additional advantage of this definition is that for an elementary and irreversible reaction, is equal to the product of the probability of overcoming the transition state activation energy and the number of times per second the transition state is approached by reactant molecules. When so defined, for an elementary and irreversible reaction, is the rate of successful chemical reaction events leading to the product.
The above definition is only valid for a single reaction, in a closed system of constant volume. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
For an open system, the full mass balance must be taken into account:
where
When applied to the closed system at constant volume considered previously, this equation reduces to
where the concentration is related to the number of molecules by with denoting the Avogadro constant.
For a single reaction in a closed system of varying volume, the so-called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time:
where 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 the rate of increase of concentration and rate of the decrease of concentration 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 mass or surface area 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".

Influencing factors

Factors that influence the reaction rate are the nature of the reaction, concentration, pressure, reaction order, temperature, solvent, electromagnetic radiation, catalyst, isotopes, surface area, stirring, and diffusion limit. Some reactions are naturally faster than others. The number of reacting species, their physical state, the complexity of the reaction and other factors can greatly influence the rate of a reaction.
Reaction rate increases with concentration, as described by the rate law and explained by collision theory. As reactant concentration increases, the frequency of collision increases. The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in the concentration of the gas. The reaction rate increases in the direction where there are fewer moles of gas and decreases in the reverse direction. For condensed-phase reactions, the pressure dependence is weak.
The order of the reaction controls how the reactant concentration affects the reaction rate.
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 resulting in more successful collisions. The influence of temperature is described by the Arrhenius equation. For example, coal burns in a fireplace in the presence of oxygen, but it does not when it is stored at room temperature. 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. That is valid for many other fuels, such as methane, butane, and hydrogen.
Reaction rates can be independent of temperature or decrease with increasing temperature. Reactions without an activation barrier, tend to have anti-Arrhenius temperature dependence: the rate constant decreases with increasing temperature.
Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength also has an effect on the reaction rate.
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 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 reacts with chlorine in the dark, the reaction rate is slow. It can be sped up when the mixture is put under diffused light. In bright sunlight, the reaction is explosive.
The presence of a catalyst increases the reaction rate by providing an alternative pathway with a lower activation energy. For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature.
The kinetic isotope effect consists of a different reaction rate for the same molecule if it has different isotopes, usually hydrogen isotopes, because of the relative mass difference between hydrogen and deuterium.
In reactions on surfaces, which take place, for example, during heterogeneous catalysis, 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 can have a strong effect on the rate of reaction for heterogeneous reactions.
Some reactions are limited by diffusion. All the factors that affect a reaction rate, except for concentration and reaction order, are taken into account in the reaction rate coefficient.

Rate equation

For a chemical reaction, 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. For a closed system at constant volume, this is often of the form
For reactions that go to completion, or if only the initial rate is analyzed, this simplifies to the commonly quoted form
For gas phase reaction the rate equation is often alternatively expressed in terms of partial pressures.
In these equations 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 time and concentration. Of all the parameters influencing reaction rates, temperature is normally the most important one and is accounted for by the Arrhenius equation.
The exponents and are called reaction orders and depend on the reaction mechanism. For an elementary reaction, the order with respect to each reactant is equal to its stoichiometric coefficient. For complex reactions, however, this is often not true and the rate equation is determined by the detailed mechanism, as illustrated below for the reaction of H₂ and NO.
For elementary reactions or reaction steps, the order and stoichiometric coefficient are both equal to the molecularity or number of molecules participating. For a unimolecular reaction or step, the rate is proportional to the concentration of molecules of reactant, so the rate law is first order. For a bimolecular reaction or step, the number of collisions is proportional to the product of the two reactant concentrations, or second order. A termolecular step is predicted to be third order, but also very slow as simultaneous collisions of three molecules are rare.
By using the mass balance 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