The reaction rate or rate of reaction is the speed at which reactants
are converted into products. For example, the oxidative rusting of
iron under
Earth's atmosphere
Contents 1 Formal definition 2 Influencing factors 3 Rate equation 3.1 Example of a complex reaction: Reaction of hydrogen and nitric oxide 4
Temperature
Formal definition[edit] Consider a typical chemical reaction: a A + b B → p P + q Q 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).
According to IUPAC's
Gold Book
r = − 1 a d [ A ] d t = − 1 b d [ B ] d t = 1 p d [ P ] d t = 1 q d [ Q ] d t displaystyle r=- frac 1 a frac d[mathrm A ] dt =- frac 1 b frac d[mathrm B ] dt = frac 1 p frac d[mathrm P ] dt = frac 1 q frac d[mathrm Q ] dt where [X] denotes the concentration of the substance X (= A, B, P or
Q).
Reaction rate
F A 0 − F A + ∫ 0 V v d V = d N A d t displaystyle F_ mathrm A 0 -F_ mathrm A +int _ 0 ^ V v,dV= frac dN_ mathrm A dt , where FA0 is the inflow rate of A in molecules per second, FA the outflow, and v is the instantaneous reaction rate of A (in number concentration rather than molar) in a given differential volume, integrated over the entire system volume V at a given moment. When applied to the closed system at constant volume considered previously, this equation reduces to: r = d [ A ] d t displaystyle r= frac d[A] dt , where the concentration [A] is related to the number of molecules NA by [A] = NA/N0V. Here N0 is 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. r = d ξ d t = 1 ν i d n i d t = 1 ν i d ( C i V ) d t = 1 ν i ( V d C i d t + C i d V d t ) displaystyle r= frac dxi dt = frac 1 nu _ i frac dn_ i dt = frac 1 nu _ i frac d(C_ i V) dt = frac 1 nu _ i left(V frac dC_ i dt +C_ i frac dV dt right) Here νi is the stoichiometric coefficient for substance i, equal to a, b, p, and q in the typical reaction above. Also V is the volume of reaction and Ci 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, 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 Influencing factors[edit] 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 greatly influence the rate of a reaction.
Concentration:
Reaction rate
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 (non-Arrhenius) or decrease with increasing temperature (anti-Arrhenius). Reactions without an activation barrier (e.g., some radical reactions), tend to have anti Arrhenius temperature dependence: the rate constant decreases with increasing temperature. Solvent: Many reactions take place in solution and the properties of
the solvent affect the reaction rate. The ionic strength also has an
effect on reaction rate.
Electromagnetic radiation
For example, when methane reacts with chlorine in the dark, the reaction rate is very slow. It can be sped up when the mixture 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. For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature. 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 relative mass difference between hydrogen and deuterium. Surface Area: 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: Stirring can have a strong effect on the rate of reaction for heterogeneous reactions. Diffusion limit: 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 (the coefficient in the rate equation of the reaction). Rate equation[edit] Main article: Rate equation For a chemical reaction a A + b B → p P + q Q, 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. It is often of the type: r = k ( T ) [ A ] n [ B ] m displaystyle ,r=k(T)[mathrm A ]^ n [mathrm B ]^ m For gas phase reaction the rate is often alternatively expressed by partial pressures. In these equations 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 influencing reaction rates, temperature is normally the most important one and is accounted for by the Arrhenius equation. The exponents n and m are called reaction orders and depend on the reaction mechanism. For elementary (single-step) reactions the order with respect to each reactant is equal to its stoichiometric coefficient. For complex (multistep) 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 that 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 d [ P ] d t = k ( T ) [ A ] n [ B ] m displaystyle frac d[mathrm P ] dt =k(T)[mathrm A ]^ n [mathrm B ]^ m Example of a complex reaction: Reaction of hydrogen and nitric oxide[edit] For the reaction 2 H2(g) + 2 NO(g) → N2(g) + 2 H2O(g) the observed rate equation (or rate expression) is: r = k [ H 2 ] [ NO ] 2 displaystyle r=k[ ce H2 ][ ce NO ]^ 2 , As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is third order overall: first order in H2 and second order in NO, even though the stoichiometric coefficients of both reactants are equal to 2.[3] In chemical kinetics, the overall reaction rate is often explained using a mechanism consisting of a number of elementary steps. Not all of these steps affect the rate of reaction; normally the slowest elementary step controls the reaction rate. For this example, a possible mechanism is: 2 NO(g) ⇌ N2O2(g) (fast equilibrium) N2O2 + H2 → N2O + H2O (slow) N2O + H2 → N2 + H2O (fast) Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate determining step. This is a bimolecular elementary reaction whose rate is given by the second order equation: r = k 2 [ H 2 ] [ N 2 O 2 ] displaystyle r=k_ 2 [ ce H2 ][ ce N2O2 ], , where k2 is the rate constant for the second step. However N2O2 is an unstable intermediate whose concentration is determined by the fact that the first step is in equilibrium, so that [N2O2] = K1[NO]2, where K1 is the equilibrium constant of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants r = k 2 K 1 [ H 2 ] [ NO ] 2 displaystyle r=k_ 2 K_ 1 [ ce H2 ][ ce NO ]^ 2 , This agrees with the form of the observed rate equation if it is
assumed that k = k2K1. In practice the rate equation is used to
suggest possible mechanisms which predict a rate equation in agreement
with experiment.
The second molecule of H2 does not appear in the rate equation because
it reacts in the third step, which is a rapid step after the
rate-determining step, so that it does not affect the overall reaction
rate.
Temperature
k = A e − E a R T displaystyle k=Ae^ - frac E_ mathrm a RT Ea is the activation energy and R is the gas constant. 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−Ea⁄RT. 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 that do not follow this pattern.
A chemical reaction takes place only when the reacting particles
collide. However, not all collisions are effective in causing the
reaction. Products are formed only when the colliding particles
possess a certain minimum energy called threshold energy. As a rule of
thumb, reaction rates for many reactions double for every 10 degrees
Celsius
A + B ⇌ A⋯B‡ → P the activation volume, ΔV‡, is: Δ V ‡ = V ¯ ‡ − V ¯ A − V ¯ B displaystyle Delta V^ ddagger = bar V _ ddagger - bar V _ mathrm A - bar V _ mathrm B where V̄ denotes the partial molar volume of a species 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 on molar-concentration) with pressure at constant temperature to be:[2]:390 ( ∂ ln k x ∂ P ) T = − Δ V ‡ R T displaystyle left( frac partial ln k_ x partial P right)_ T =- frac Delta V^ ddagger RT 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 ΔV‡. 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 ΔV‡ = −0.025 L/mol).[5] See also[edit] Rate of solution
Dilution (equation)
Diffusion-controlled reaction
Steady state approximation
Collision theory
Notes[edit] ^ a b c IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Rate of reaction". ^ a b Laidler, K. J.; Meiser, J.H. (1982). Physical Chemistry. Benjamin/Cummings. ISBN 0-8053-5682-7. ^ Laidler, K. J. (1987). Chemical Kinetics (3rd ed.). Harper & Row. p. 277. ISBN 0060438622. ^ Connors, Kenneth (1990). Chemical Kinetics:The Study of Reaction Rates in Solution. VCH Publishers. p. 14. ISBN 978-0-471-72020-1. ^ Isaacs, Neil S. (1995). "Section 2.8.3". Physical Organic Chemistry (2nd ed.). Harlow: Addison Wesley Longman. ISBN 9780582218635. External links[edit] Chemical kinetics, reaction rate, and order (needs flash player) Reaction kinetics, examples of important rate laws (lecture with audio). Rates of reaction Overview of Bimolecular Reactions (Reactions involving tw |