Chemical kinetics, also known asreaction kinetics, is the branch ofphysical chemistry that is concerned with understanding the rates of chemical reactions. It is different fromchemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of achemical reaction and yield information about thereaction's mechanism andtransition states, as well as the construction ofmathematical models that also can describe the characteristics of a chemical reaction.
History
The pioneering work of chemical kinetics was done by German chemistLudwig Wilhelmy in 1850.[1] He experimentally studied the rate ofinversion of sucrose and he usedintegrated rate law for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later byWilhelm Ostwald. In 1864,Peter Waage andCato Guldberg published thelaw of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.[2][3][4]
Van 't Hoff studied chemical dynamics and in 1884 published his famous "Études de dynamique chimique".[5] In 1901 he was awarded the first Nobel Prize in Chemistry "in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions".[6] After van 't Hoff, chemical kinetics dealt with the experimental determination ofreaction rates from whichrate laws andrate constants are derived. Relatively simplerate laws exist forzero order reactions (for which reaction rates are independent of concentration),first order reactions, andsecond order reactions, and can be derived for others.Elementary reactions follow thelaw of mass action, but the rate law ofstepwise reactions has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, therate-determining step often determines the kinetics. In consecutive first order reactions, asteady state approximation can simplify therate law. Theactivation energy for a reaction is experimentally determined through theArrhenius equation and theEyring equation. The main factors that influence thereaction rate include: thephysical state of the reactants, theconcentrations of the reactants, thetemperature at which the reaction occurs, and whether or not anycatalysts are present in the reaction.
Gorban and Yablonsky have suggested that the history of chemical dynamics can be divided into three eras.[7] The first is the van 't Hoff wave searching for the general laws of chemical reactions and relating kinetics to thermodynamics. The second may be called theSemenov-Hinshelwood wave with emphasis on reaction mechanisms, especially forchain reactions. The third is associated withAris and the detailed mathematical description of chemical reaction networks.
Factors affecting reaction rate
Nature of the reactants
The reaction rate varies depending upon what substances are reacting. Acid/base reactions, the formation ofsalts, andion exchange are usually fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be slower.
The nature and strength of bonds in reactant molecules greatly influence the rate of their transformation into products.
Physical state
Thephysical state (solid,liquid, orgas) of a reactant is also an important factor of the rate of change. When reactants are in the samephase, as inaqueous solution, thermal motion brings them into contact. However, when they are in separate phases, the reaction is limited to the interface between the reactants. Reaction can occur only at their area of contact; in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant the greater itssurface area per unitvolume and the more contact it with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches — one does not start with large logs right away. In organic chemistry,on water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions (those in which solute and solvent are not mixed properly).
Surface area of solid state
In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example,Sherbet (powder) is a mixture of very fine powder ofmalic acid (a weak organic acid) andsodium hydrogen carbonate. On contact with thesaliva in the mouth, these chemicals quickly dissolve and react, releasingcarbon dioxide and providing for the fizzy sensation. Also,fireworks manufacturers modify the surface area of solid reactants to control the rate at which the fuels in fireworks are oxidised, using this to create diverse effects. For example, finely dividedaluminium confined in a shell explodes violently. If larger pieces of aluminium are used, the reaction is slower and sparks are seen as pieces of burning metal are ejected.
The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon theirconcentrations. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will usually result in the corresponding increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. For example,combustion will occur more rapidly in pure oxygen than in air (21% oxygen).
Therate equation shows the detailed dependence of the reaction rate on the concentrations of reactants and other species present. The mathematical forms depend on thereaction mechanism. The actual rate equation for a given reaction is determined experimentally and provides information about the reaction mechanism. The mathematical expression of the rate equation is often given by
Here is thereaction rate constant, is the molar concentration of reactanti and is the partial order of reaction for this reactant. Thepartial order for a reactant can only be determined experimentally and is often not indicated by itsstoichiometric coefficient.
Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have morethermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater thanactivation energy:E > Ea) is significantly higher and is explained in detail by theMaxwell–Boltzmann distribution of molecular energies.
At a given temperature, the chemical rate of a reaction depends on the value of the A-factor, the magnitude of the activation energy, and the concentrations of the reactants. Usually, rapid reactions require relatively small activation energies.
The 'rule of thumb' that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where theα (temperature coefficient) is often between 1.5 and 2.5.
The kinetics of rapid reactions can be studied with thetemperature jump method. This involves using a sharp rise in temperature and observing therelaxation time of the return to equilibrium. A particularly useful form of temperature jump apparatus is ashock tube, which can rapidly increase a gas's temperature by more than 1000 degrees.
Generic potential energy diagram showing the effect of a catalyst in a hypothetical endothermic chemical reaction. The presence of the catalyst opens a new reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.
Acatalyst is a substance that alters the rate of a chemical reaction but it remainschemically unchanged afterwards. The catalyst increases the rate of the reaction by providing a newreaction mechanism to occur with in a loweractivation energy. Inautocatalysis a reaction product is itself a catalyst for that reaction leading topositive feedback. Proteins that act as catalysts in biochemical reactions are calledenzymes.Michaelis–Menten kinetics describe therate of enzyme mediated reactions. A catalyst does not affect the position of the equilibrium, as the catalyst speeds up the backward and forward reactions equally.
Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because theactivity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution.
In addition to this straightforward mass-action effect, the rate coefficients themselves can change due to pressure. The rate coefficients and products of many high-temperature gas-phase reactions change if an inert gas is added to the mixture; variations on this effect are calledfall-off andchemical activation. These phenomena are due to exothermic or endothermic reactions occurring faster than heat transfer, causing the reacting molecules to have non-thermal energy distributions (non-Boltzmann distribution). Increasing the pressure increases the heat transfer rate between the reacting molecules and the rest of the system, reducing this effect.
Condensed-phase rate coefficients can also be affected by pressure, although rather high pressures are required for a measurable effect because ions and molecules are not very compressible. This effect is often studied usingdiamond anvils.
A reaction's kinetics can also be studied with apressure jump approach. This involves making fast changes in pressure and observing therelaxation time of the return to equilibrium.
Absorption of light
The activation energy for a chemical reaction can be provided when one reactant molecule absorbs light of suitablewavelength and is promoted to anexcited state. The study of reactions initiated by light isphotochemistry, one prominent example beingphotosynthesis.
Experimental methods
The Spinco Division Model 260 Reaction Kinetics System measured the precise rate constants of molecular reactions.
The experimental determination of reaction rates involves measuring how the concentrations of reactants or products change over time. For example, the concentration of a reactant can be measured byspectrophotometry at a wavelength where no other reactant or product in the system absorbs light.
For reactions which take at least several minutes, it is possible to start the observations after the reactants have been mixed at the temperature of interest.
Fast reactions
For faster reactions, the time required to mix the reactants and bring them to a specified temperature may be comparable or longer than thehalf-life of the reaction.[9] Special methods to start fast reactions without slow mixing step include
Stopped flow methods, which can reduce the mixing time to the order of a millisecond[9][10][11] The stopped flow methods have limitation, for example, we need to consider the time it takes to mix gases or solutions and are not suitable if the half-life is less than about a hundredth of a second.
Chemical relaxation methods such astemperature jump andpressure jump, in which a pre-mixed system initially at equilibrium is perturbed by rapid heating or depressurization so that it is no longer at equilibrium, and the relaxation back to equilibrium is observed.[9][12][13][14] For example, this method has been used to study theneutralization H3O+ + OH− with a half-life of 1 μs or less under ordinary conditions.[9][14]
While chemical kinetics is concerned with the rate of a chemical reaction,thermodynamics determines the extent to which reactions occur. In areversible reaction, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal (the principle ofdynamic equilibrium) and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, theHaber–Bosch process for combining nitrogen and hydrogen to produce ammonia.Chemical clock reactions such as theBelousov–Zhabotinsky reaction demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium.
Free energy
In general terms, thefree energy change (ΔG) of a reaction determines whether a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be veryexothermic and have a very positiveentropy change but will not happen in practice if the reaction is too slow. If a reactant can produce two products, the thermodynamically most stable one will form in general, except in special circumstances when the reaction is said to be underkinetic reaction control. TheCurtin–Hammett principle applies when determining the product ratio for two reactants interconverting rapidly, each going to a distinct product. It is possible to make predictions about reaction rate constants for a reaction fromfree-energy relationships.
Thekinetic isotope effect is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of itsisotopes.
The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performingcatalytic cracking of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur.
In some cases, equations are unsolvable analytically, but can be solved using numerical methods if data values are given. There are two different ways to do this, by either using software programmes or mathematical methods such as theEuler method. Examples of software for chemical kinetics are i) Tenua, aJava app which simulates chemical reactions numerically and allows comparison of the simulation to real data, ii)Python coding for calculations and estimates and iii) the Kintecus software compiler to model, regress, fit and optimize reactions.
-Numerical integration: for a 1st order reaction A → B
The differential equation of the reactant A is:
It can also be expressed as which is the same as
To solve the differential equations with Euler and Runge-Kutta methods we need to have the initial values.
We can approximate the differentials as discrete increases:
The unknown part of the equation isy(x+Δx), which can be found if we have the data for the initial values.
Runge-Kutta methods → it is more accurate than the Euler method.In this method, an initial condition is required:y =y0 atx =x0. The problem is to find the value ofy whenx =x0 +h, whereh is a given constant.
It can be shown analytically that the ordinate at that moment to the curve through(x0,y0) is given by the third-order Runge-Kutta formula.
In first-order ordinary equations, the Runge-Kutta method uses a mathematical model that represents the relationship between the temperature and the rate of reaction. It is worth it to calculate the rate of reaction at different temperatures for different concentrations. The equation obtained is:
Stochastic methods → probabilities of the differential rate laws and the kinetic constants. In an equilibrioum reaction with direct and inverse rate constants, it is easier to transform from A to B rather than B to A.As for probability computations, at each time it choose a random number to be compared with a threshold to know if the reaction runs from A to B or the other way around.
^C.M. Guldberg and P. Waage,"Studies Concerning Affinity"Forhandlinger i Videnskabs-Selskabet i Christiania (1864), 35
^P. Waage, "Experiments for Determining the Affinity Law" ,Forhandlinger i Videnskabs-Selskabet i Christiania, (1864) 92.
^C.M. Guldberg, "Concerning the Laws of Chemical Affinity",Forhandlinger i Videnskabs-Selskabet i Christiania (1864) 111
^Hoff, J. H. van't (Jacobus Henricus van't); Cohen, Ernst; Ewan, Thomas (1896-01-01).Studies in chemical dynamics. Amsterdam : F. Muller; London : Williams & Norgate.
