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==Kinetics== The speed at which reactions take place is studied by [[Chemical kinetics|reaction kinetics]]. The rate depends on various parameters, such as: * [[Reactant]] concentrations, which usually make the reaction happen at a faster rate if raised through increased collisions per unit of time. Some reactions, however, have rates that are ''independent'' of reactant concentrations, due to a limited number of catalytic sites. These are called [[Rate law#Zero-order reactions|zero order reactions]]. * [[Surface area]] available for contact between the reactants, in particular solid ones in heterogeneous systems. Larger surface areas lead to higher reaction rates. * [[Pressure]] – increasing the pressure decreases the volume between molecules and therefore increases the frequency of collisions between the molecules. * [[Activation energy]], which is defined as the amount of energy required to make the reaction start and carry on spontaneously. Higher activation energy implies that the reactants need more energy to start than a reaction with lower activation energy. * [[Temperature]], which hastens reactions if raised, since higher temperature increases the energy of the molecules, creating more collisions per unit of time, * The presence or absence of a [[catalyst]]. Catalysts are substances that make weak bonds with reactants or intermediates and change the pathway (mechanism) of a reaction which in turn increases the speed of a reaction by lowering the [[activation energy]] needed for the reaction to take place. A catalyst is not destroyed or changed during a reaction, so it can be used again. * For some reactions, the presence of [[electromagnetic radiation]], most notably [[ultraviolet light]], is needed to promote the breaking of bonds to start the reaction. This is particularly true for reactions involving [[radical (chemistry)|radicals]]. Several theories allow calculating the reaction rates at the molecular level. This field is referred to as reaction dynamics. The rate ''v'' of a [[Rate equation#First-order reactions|first-order reaction]], which could be the disintegration of a substance A, is given by: :<math chem> v= -\frac {d[\ce{A}]}{dt}= k \cdot [\ce{A}]. </math> Its integration yields: :<math chem>\ce{[A]}(t) = \ce{[A]}_{0} \cdot e^{-k\cdot t}. </math> Here ''k'' is the first-order rate constant, having dimension 1/time, [A](''t'') is the concentration at a time ''t'' and [A]<sub>0</sub> is the initial concentration. The rate of a first-order reaction depends only on the concentration and the properties of the involved substance, and the reaction itself can be described with a characteristic [[half-life]]. More than one time constant is needed when describing reactions of higher order. The temperature dependence of the rate constant usually follows the [[Arrhenius equation]]: :<math>k = k_0 e^{{-E_a}/{k_{B}T}}</math> where ''E''<sub>a</sub> is the activation energy and ''k''<sub>B</sub> is the [[Boltzmann constant]]. One of the simplest models of reaction rate is the [[collision theory]]. More realistic models are tailored to a specific problem and include the [[transition state theory]], the calculation of the [[potential energy surface]], the [[Marcus theory]] and the [[RRKM theory|Rice–Ramsperger–Kassel–Marcus (RRKM) theory]].<ref>[[#Atkins|Atkins]], p. 963</ref>
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