929:
3215:
732:
2617:
99:
83:
2265:
1371:
924:{\displaystyle {\begin{array}{ccccccc}F_{\mathrm {A} _{0}}&-&F_{\mathrm {A} }&+&\displaystyle \int _{0}^{V}v\,dV&=&\displaystyle {\frac {dN_{\mathrm {A} }}{dt}}\\{\text{in}}&-&{\text{out}}&+&\left({{\text{generation }}- \atop {\text{consumption}}}\right)&=&{\text{accumulation}}\end{array}}}
1503:
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
1894:
and depend on the reaction mechanism. For an elementary (single-step) reaction, 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
1560:
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 (it may break bonds, and promote molecules to
1510:
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
3210:
Temperature is a measure of the average kinetic energy of the reactants. As temperature increases, the kinetic energy of the reactants increases. That is, the particles move faster. With the reactants moving faster this allows more collisions to take place at a greater speed, so the chance of
2259:
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
1435:
is used the reaction rate may be stated on a catalyst weight (mol g s) or surface area (mol m s) 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 and is called a turnover frequency.
1137:
532:
3812:
Silva, Camylla K. S.; Baston, Eduardo P.; Melgar, Lisbeth Z.; Bellido, Jorge D. A. (2019-10-01). "Ni/Al2O3-La2O3 catalysts synthesized by a one-step polymerization method applied to the dry reforming of methane: effect of precursor structures of nickel, perovskite and spinel".
551:
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 P by a constant factor (the reciprocal of its
3856:
Elizalde, Ignacio; Mederos, Fabián S.; del Carmen
Monterrubio, Ma.; Casillas, Ninfa; Díaz, Hugo; Trejo, Fernando (2019-02-01). "Mathematical modeling and simulation of an industrial adiabatic trickle-bed reactor for upgrading heavy crude oil by hydrotreatment process".
1875:, 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
2612:{\displaystyle {\begin{array}{rll}1)&\quad {\ce {2NO_{(g)}<=> N2O2_{(g)}}}&({\text{fast equilibrium}})\\2)&\quad {\ce {N2O2 + H2 -> N2O + H2O}}&({\text{slow}})\\3)&\quad {\ce {N2O + H2 -> N2 + H2O}}&({\text{fast}}).\end{array}}}
3252:
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
3512:
3646:
1561:
electronically or vibrationally excited states...) 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
1519:. 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
3401:
266:
556:) and for a reactant A 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
3257:, reaction rates for many reactions double for every ten degrees Celsius increase in temperature. For a given reaction, the ratio of its rate constant at a higher temperature to its rate constant at a lower temperature is known as its
3246:. The transition state or activated complex shown on the diagram is the energy barrier that must be overcome when changing reactants into products. The molecules with an energy greater than this barrier have enough energy to react.
2174:
347:
3988:
Vedyagin, Aleksey A.; Stoyanovskii, Vladimir O.; Kenzhin, Roman M.; Slavinskaya, Elena M.; Plyusnin, Pavel E.; Shubin, Yury V. (2019-06-01). "Purification of gasoline exhaust gases using bimetallic Pd–Rh/δ-Al2O3 catalysts".
3900:
Liu, Jiaqi; Shen, Meiqing; Li, Chenxu; Wang, Jianqiang; Wang, Jun (2019-10-01). "Enhanced hydrothermal stability of a manganese metavanadate catalyst based on WO3–TiO2 for the selective catalytic reduction of NOx with NH3".
154:
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.
3661:. 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
1906:
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
1915:
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
3944:
Li, Xiaoliang; Feng, Jiangjiang; Xu, Zhigang; Wang, Junqiang; Wang, Yujie; Zhao, Wei (2019-10-01). "Cerium modification for improving the performance of Cu-SSZ-13 in selective catalytic reduction of NO by NH3".
3058:
1911:
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.
680:
3189:
1366:{\displaystyle v={\frac {d\xi }{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)}
3286:-phase reactions (that is, when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice.
3417:
1511:
colliding particles will have the necessary activation energy resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the
1106:
2834:
2015:
1758:
3294:
3211:
reactants forming into products increases, which in turn results in the rate of reaction increasing. A rise of ten degrees
Celsius results in approximately twice the reaction rate.
1572:
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,
3553:
3207:
are dependent on the reaction. There are also more complex equations possible, which describe the temperature dependence of other rate constants that do not follow this pattern.
2933:
1583:
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
1030:
3249:
For a successful collision to take place, the collision geometry must be right, meaning the reactant molecules must face the right way so the activated complex can be formed.
1845:
2029:
1605:
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
4036:
2714:
2244:
195:
1646:
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
3798:
3751:
701:
and the number of times per second the transition state is approached by reactant molecules. When so defined, for an elementary and irreversible reaction,
2994:
1595:, 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.
3289:
The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex:
1599:
3651:
In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure.
2849:
of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants
4226:
4134:
3774:
3727:
2248:
As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is
527:{\displaystyle v=-{\frac {1}{a}}{\frac {d}{dt}}=-{\frac {1}{b}}{\frac {d}{dt}}={\frac {1}{p}}{\frac {d}{dt}}={\frac {1}{q}}{\frac {d}{dt}}}
581:
1771:), or if only the initial rate is analyzed (with initial vanishing product concentrations), this simplifies to the commonly quoted form
4165:
4081:
165:
that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used to deduce probable
3132:
2956:. In practice the rate equation is used to suggest possible mechanisms which predict a rate equation in agreement with experiment.
1921:
4201:
720:. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
1649:
4109:
4190:
3678:
3266:
1550:
reactions), tend to have anti-Arrhenius temperature dependence: the rate constant decreases with increasing temperature.
3070:
2852:
2621:
Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate-determining step. This is a
1469:
986:
3688:
1044:
288:
1776:
737:
2743:
4221:
3698:
1461:
178:
3507:{\displaystyle \Delta V^{\ddagger }={\bar {V}}_{\ddagger }-{\bar {V}}_{\mathrm {A} }-{\bar {V}}_{\mathrm {B} }}
3283:
3230:
The minimum kinetic energy required for a reaction to occur is called the activation energy and is denoted by
3641:{\displaystyle \left({\frac {\partial \ln k_{x}}{\partial P}}\right)_{T}=-{\frac {\Delta V^{\ddagger }}{RT}}}
2628:
2181:
4231:
3258:
1643:
1592:
1902:
For elementary reactions or reaction steps, the order and stoichiometric coefficient are both equal to the
1507:
The order of the reaction controls how the reactant concentration (or pressure) affects the reaction rate.
3536:
3113:
1580:
1515:. For example, coal burns in a fireplace in the presence of oxygen, but it does not when it is stored at
1588:
553:
339:
2256:
and second order in NO, even though the stoichiometric coefficients of both reactants are equal to 2.
147:
1553:
Many reactions take place in solution and the properties of the solvent affect the reaction rate. The
983:
When applied to the closed system at constant volume considered previously, this equation reduces to:
3521:
3080:
2846:
2737:
1481:
972:
548:
170:
71:
2736:
is an unstable intermediate whose concentration is determined by the fact that the first step is in
3765:
Petrucci, Ralph H.; Herring, F. Geoffrey; Madura, Jeffry D.; Bissonnette, Carey (4 February 2016).
3683:
3544:
1547:
1420:
When side products or reaction intermediates are formed, the IUPAC recommends the use of the terms
687:
683:
304:
131:
1484:), the complexity of the reaction and other factors can greatly influence the rate of a reaction.
4014:
3970:
3926:
3882:
3838:
3792:
3745:
3396:{\displaystyle {\ce {A + B <=>}}\ |{\ce {A}}\cdots {\ce {B}}|^{\ddagger }\ {\ce {-> P}}}
3117:
2986:
2976:
1876:
1512:
1129:
166:
162:
2963:
does not appear in the rate equation because it reacts in the third step, which is a rapid step
1128:
can be used, in order to avoid handling concentrations. It is defined as the derivative of the
261:{\displaystyle {\ce {{{\mathit {a}}A}+{{\mathit {b}}B}->{{\mathit {p}}P}+{{\mathit {q}}Q}}}}
4196:
4161:
4130:
4105:
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335:
158:
123:
1431:
Reaction rates may also be defined on a basis that is not the volume of the reactor. When a
4097:
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3998:
3954:
3910:
3866:
3822:
3693:
1908:
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rather than molar) in a given differential volume, integrated over the entire system volume
695:
4206:
3214:
1473:
4184:
1476:. Some reactions are naturally faster than others. The number of reacting species, their
3654:
Reactions can increase or decrease their rates with pressure, depending on the value of
1444:
Factors that influence the reaction rate are the nature of the reaction, concentration,
1554:
1477:
1849:
For gas phase reaction the rate equation is often alternatively expressed in terms of
1480:(the particles that form solids move much more slowly than those of gases or those in
4215:
4152:
4018:
3974:
3930:
3886:
3842:
3540:
3529:
3254:
2169:{\displaystyle {\ce {2H2_{(g)}}}+{\ce {2NO_{(g)}-> N2_{(g)}}}+{\ce {2H2O_{(g)}}},}
1618:
331:
127:
4046:
3274:
is commonly used as the ratio of rate constants that are ten degrees
Celsius apart.
2270:
3219:
3101:
1903:
724:
59:
2967:
the rate-determining step, so that it does not affect the overall reaction rate.
4041:
2622:
1453:
17:
4002:
3958:
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3826:
682:
is uniquely defined. An additional advantage of this definition is that for an
3870:
2937:
This agrees with the form of the observed rate equation if it is assumed that
1520:
174:
103:
4045:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
4010:
3966:
3922:
3878:
3834:
3784:
3737:
169:. The concepts of chemical kinetics are applied in many disciplines, such as
4054:
1584:
1569:
is put under diffused light. In bright sunlight, the reaction is explosive.
1500:
1496:
323:
151:
3218:
Reaction coordinate diagram for the bimolecular nucleophilic substitution (
705:
is the rate of successful chemical reaction events leading to the product.
98:
82:
1573:
1562:
1532:
1488:
1445:
1432:
1124:
For a single reaction in a closed system of varying volume the so-called
135:
1566:
1524:
1465:
1457:
292:
139:
138:
per unit time. Reaction rates can vary dramatically. For example, the
87:
48:
1576:
catalyzes the combustion of hydrogen with oxygen at room temperature.
4202:
Overview of
Bimolecular Reactions (Reactions involving two reactants)
3718:
McMurry, John; Fay, Robert C.; Robinson, Jill K. (31 December 2014).
2625:
elementary reaction whose rate is given by the second-order equation
1528:
3053:{\displaystyle k=A\exp \left(-{\frac {E_{\mathrm {a} }}{RT}}\right)}
675:{\displaystyle v=-{\tfrac {d}{dt}}=-{\tfrac {1}{3}}{\tfrac {d}{dt}}}
1565:
in the dark, the reaction rate is slow. It can be sped up when the
150:
is a slow reaction that can take many years, but the combustion of
319:
1032:, where the concentration is related to the number of molecules
1487:
Reaction rate increases with concentration, as described by the
143:
2790:
248:
233:
218:
203:
1762:
For reactions that go to completion (which implies very small
1598:
Stirring can have a strong effect on the rate of reaction for
1546:). Reactions without an activation barrier (for example, some
3184:{\displaystyle \exp \left({\tfrac {-E_{\rm {a}}}{RT}}\right)}
694:
is equal to the product of the probability of overcoming the
2985:
has a temperature dependency, which is usually given by the
134:
per unit time and to the decrease in the concentration of a
126:
takes place, defined as proportional to the increase in the
544:. The reaction rate thus defined has the units of mol/L/s.
4127:
Chemical
Kinetics:The Study of Reaction Rates in Solution
3535:
For the above reaction, one can expect the change of the
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2020:
Example of a complex reaction: hydrogen and nitric oxide
1609:(the coefficient in the rate equation of the reaction).
3226:) reaction between bromomethane and the hydroxide anion
3329:
3147:
2329:
1063:
643:
631:
595:
3767:
General chemistry: principles and modern applications
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2178:the observed rate equation (or rate expression) is
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57:
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37:
32:
4191:Reaction kinetics, examples of important rate laws
4151:
3640:
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3395:
3183:
3120:the number of collisions with energy greater than
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2009:
1839:
1752:
1538:Reaction rates can be independent of temperature (
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1100:
1024:
923:
674:
536:where denotes the concentration of the substance
526:
260:
3337:
3336:
3319:
3318:
3282:The pressure dependence of the rate constant for
2337:
2336:
2319:
2318:
4160:(2nd ed.). Harlow: Addison Wesley Longman.
1382:is the stoichiometric coefficient for substance
1101:{\displaystyle ={\tfrac {N_{\rm {A}}}{N_{0}V}}.}
4104:(3rd ed.). Harper & Row. p. 277.
3547:) with pressure at constant temperature to be:
2829:{\displaystyle {\ce {={\mathit {K}}_{1}^{2}}},}
189:Consider a typical balanced chemical reaction:
1523:. That is valid for many other fuels, such as
27:Speed at which a chemical reaction takes place
2010:{\displaystyle {\frac {d}{dt}}=k(T)^{n}^{m}.}
547:The rate of a reaction is always positive. A
8:
4185:Chemical kinetics, reaction rate, and order
4032:
4030:
4028:
3991:Reaction Kinetics, Mechanisms and Catalysis
3947:Reaction Kinetics, Mechanisms and Catalysis
3903:Reaction Kinetics, Mechanisms and Catalysis
3859:Reaction Kinetics, Mechanisms and Catalysis
3815:Reaction Kinetics, Mechanisms and Catalysis
3769:(Eleventh ed.). Toronto. p. 923.
1542:) or decrease with increasing temperature (
1495:. As reactant concentration increases, the
3797:: CS1 maint: location missing publisher (
3750:: CS1 maint: location missing publisher (
3532:) indicates the activation-state complex.
2725:is the rate constant for the second step.
1753:{\displaystyle v=k^{n}^{m}-k_{r}^{i}^{j}.}
574:is consumed three times more rapidly than
291:, while the capital letters represent the
3722:(Seventh ed.). Boston. p. 492.
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1557:also has an effect on the reaction rate.
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708:The above definition is only valid for a
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1591:, which take place, for example, during
97:
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3312:
3112:the molecules have energies given by a
2312:
1895:illustrated below for the reaction of H
330:for a chemical reaction occurring in a
3790:
3743:
1428:for products and reactants, properly.
967:is the instantaneous reaction rate of
29:
1642:, the rate equation or rate law is a
1426:rate of the decrease of concentration
1422:the rate of increase of concentration
7:
4064:
4062:
1402:in the typical reaction above. Also
110:reaction rate. This process is fast.
94:reaction rate. This process is slow.
3069:, is the pre-exponential factor or
2928:{\displaystyle v=k_{2}K_{1}^{2}\,.}
4042:Compendium of Chemical Terminology
3614:
3586:
3565:
3498:
3474:
3421:
3159:
3029:
1990:
1972:
1935:
1820:
1802:
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1715:
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1666:
1413:is the concentration of substance
1071:
1052:
883:
832:
772:
747:
653:
605:
506:
465:
424:
380:
25:
4207:pressure dependence Can. J. Chem.
1025:{\displaystyle v={\frac {d}{dt}}}
2981:Each reaction rate coefficient
2519:
2411:
2281:
1840:{\displaystyle v=k(T)^{n}^{m}.}
4129:. VCH Publishers. p. 14.
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1406:is the volume of reaction and
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376:
227:
1:
4227:Chemical reaction engineering
3679:Diffusion-controlled reaction
1504:pressure dependence is weak.
723:For an open system, the full
326:definition the reaction rate
727:must be taken into account:
3689:Isothermal microcalorimetry
289:stoichiometric coefficients
4248:
4158:Physical Organic Chemistry
4003:10.1007/s11144-019-01573-1
3959:10.1007/s11144-019-01621-w
3915:10.1007/s11144-019-01624-7
3827:10.1007/s11144-019-01644-3
3699:Steady state approximation
3669: −0.025 L/mol).
2974:
1616:
4125:Connors, Kenneth (1990).
3871:10.1007/s11144-018-1489-7
3094:is the activation energy,
2252:overall: first order in H
1869:reaction rate coefficient
1462:electromagnetic radiation
179:environmental engineering
4150:Isaacs, Neil S. (1995).
2959:The second molecule of H
2709:{\displaystyle v=k_{2},}
2239:{\displaystyle v=k^{2}.}
1623:For a chemical reaction
950:in molecules per second;
338:, without a build-up of
122:is the speed at which a
4072:; Meiser, J.H. (1982).
4055:10.1351/goldbook.R05156
3405:the activation volume,
3259:temperature coefficient
1644:mathematical expression
1600:heterogeneous reactions
1593:heterogeneous catalysis
271:The lowercase letters (
3642:
3537:reaction rate constant
3508:
3397:
3227:
3185:
3129:to be proportional to
3114:Boltzmann distribution
3054:
2971:Temperature dependence
2929:
2830:
2710:
2613:
2240:
2170:
2011:
1841:
1754:
1581:kinetic isotope effect
1367:
1132:with respect to time.
1102:
1026:
946:is the inflow rate of
925:
676:
528:
340:reaction intermediates
262:
111:
95:
4193:(lecture with audio).
4076:. Benjamin/Cummings.
3643:
3509:
3398:
3217:
3186:
3108:Since at temperature
3055:
2930:
2831:
2711:
2614:
2241:
2171:
2012:
1842:
1755:
1589:reactions on surfaces
1368:
1103:
1027:
926:
677:
554:stoichiometric number
529:
263:
101:
85:
4187:(needs flash player)
3554:
3522:partial molar volume
3418:
3295:
3133:
3081:exponential function
2995:
2853:
2847:equilibrium constant
2744:
2629:
2266:
2182:
2030:
1922:
1909:number of collisions
1890:are called reaction
1777:
1650:
1138:
1045:
987:
973:number concentration
733:
582:
348:
196:
171:chemical engineering
3684:Dilution (equation)
3545:molar concentration
3325:
3278:Pressure dependence
2898:
2803:
2777:
2764:
2698:
2685:
2664:
2584:
2568:
2552:
2533:
2489:
2470:
2454:
2438:
2425:
2384:
2360:
2325:
2307:
2210:
2161:
2140:
2118:
2091:
2061:
1856:In these equations
1440:Influencing factors
800:
167:reaction mechanisms
66:mol⋅m⋅s
53:mol⋅L⋅s
4074:Physical Chemistry
3638:
3504:
3393:
3344:
3228:
3181:
3175:
3050:
2987:Arrhenius equation
2977:Arrhenius equation
2925:
2886:
2826:
2787:
2765:
2752:
2706:
2686:
2673:
2652:
2609:
2607:
2572:
2556:
2540:
2521:
2477:
2458:
2442:
2426:
2413:
2361:
2348:
2344:
2287:
2236:
2198:
2166:
2141:
2128:
2095:
2071:
2038:
2007:
1877:Arrhenius equation
1837:
1750:
1513:Arrhenius equation
1363:
1130:extent of reaction
1126:rate of conversion
1098:
1093:
1022:
979:at a given moment.
921:
919:
849:
811:
786:
672:
670:
640:
622:
524:
258:
163:physical chemistry
148:Earth's atmosphere
112:
96:
61:SI base units
4222:Chemical kinetics
4197:Rates of reaction
4136:978-0-471-72020-1
4102:Chemical Kinetics
3776:978-0-13-293128-1
3729:978-0-321-94317-0
3636:
3593:
3539:(based either on
3524:of a species and
3493:
3469:
3447:
3391:
3384:
3368:
3360:
3351:
3346:
3307:
3301:
3174:
3043:
2909:
2889:
2811:
2792:
2768:
2755:
2689:
2676:
2655:
2597:
2587:
2575:
2559:
2543:
2536:
2524:
2502:
2492:
2480:
2473:
2461:
2445:
2429:
2416:
2394:
2375:
2364:
2351:
2346:
2298:
2290:
2221:
2201:
2152:
2144:
2131:
2109:
2098:
2082:
2074:
2052:
2041:
2024:For the reaction
1951:
1851:partial pressures
1491:and explained by
1356:
1323:
1288:
1268:
1232:
1212:
1185:
1165:
1119:Avogadro constant
1092:
1020:
915:
899:
897:
888:
869:
857:
847:
699:activation energy
669:
639:
621:
522:
494:
481:
453:
440:
412:
396:
368:
342:, is defined as:
255:
250:
240:
235:
225:
220:
210:
205:
185:Formal definition
159:Chemical kinetics
140:oxidative rusting
124:chemical reaction
80:
79:
76:L⋅T⋅N
16:(Redirected from
4239:
4172:
4171:
4155:
4147:
4141:
4140:
4122:
4116:
4115:
4094:
4088:
4087:
4066:
4057:
4047:Rate of reaction
4034:
4023:
4022:
3985:
3979:
3978:
3941:
3935:
3934:
3897:
3891:
3890:
3853:
3847:
3846:
3809:
3803:
3802:
3796:
3788:
3762:
3756:
3755:
3749:
3741:
3715:
3694:Rate of solution
3668:
3660:
3647:
3645:
3644:
3639:
3637:
3635:
3627:
3626:
3625:
3612:
3604:
3603:
3598:
3594:
3592:
3584:
3583:
3582:
3563:
3527:
3519:
3513:
3511:
3510:
3505:
3503:
3502:
3501:
3495:
3494:
3486:
3479:
3478:
3477:
3471:
3470:
3462:
3455:
3454:
3449:
3448:
3440:
3433:
3432:
3411:
3402:
3400:
3399:
3394:
3392:
3389:
3382:
3381:
3380:
3375:
3369:
3366:
3361:
3358:
3356:
3349:
3348:
3347:
3345:
3343:
3342:
3335:
3327:
3326:
3324:
3317:
3309:
3305:
3299:
3264:
3245:
3238:
3206:
3197:
3190:
3188:
3187:
3182:
3180:
3176:
3173:
3165:
3164:
3163:
3162:
3148:
3128:
3111:
3099:
3093:
3078:
3071:frequency factor
3068:
3059:
3057:
3056:
3051:
3049:
3045:
3044:
3042:
3034:
3033:
3032:
3022:
2984:
2955:
2934:
2932:
2931:
2926:
2920:
2919:
2910:
2907:
2899:
2897:
2894:
2887:
2881:
2880:
2871:
2870:
2844:
2835:
2833:
2832:
2827:
2822:
2821:
2820:
2815:
2809:
2802:
2799:
2794:
2793:
2786:
2781:
2776:
2773:
2766:
2763:
2760:
2753:
2724:
2715:
2713:
2712:
2707:
2699:
2697:
2694:
2687:
2684:
2681:
2674:
2665:
2663:
2660:
2653:
2647:
2646:
2618:
2616:
2615:
2610:
2608:
2598:
2595:
2588:
2585:
2583:
2580:
2573:
2567:
2564:
2557:
2551:
2548:
2541:
2534:
2532:
2529:
2522:
2503:
2500:
2493:
2490:
2488:
2485:
2478:
2471:
2469:
2466:
2459:
2453:
2450:
2443:
2437:
2434:
2427:
2424:
2421:
2414:
2395:
2393:fast equilibrium
2392:
2385:
2383:
2380:
2379:
2373:
2362:
2359:
2356:
2349:
2347:
2345:
2343:
2342:
2335:
2327:
2326:
2324:
2317:
2309:
2306:
2303:
2302:
2296:
2288:
2245:
2243:
2242:
2237:
2232:
2231:
2222:
2219:
2211:
2209:
2206:
2199:
2175:
2173:
2172:
2167:
2162:
2160:
2157:
2156:
2150:
2142:
2139:
2136:
2129:
2119:
2117:
2114:
2113:
2107:
2096:
2090:
2087:
2086:
2080:
2072:
2062:
2060:
2057:
2056:
2050:
2039:
2016:
2014:
2013:
2008:
2003:
2002:
1993:
1985:
1984:
1975:
1952:
1950:
1942:
1938:
1926:
1889:
1885:
1866:
1846:
1844:
1843:
1838:
1833:
1832:
1823:
1815:
1814:
1805:
1770:
1759:
1757:
1756:
1751:
1746:
1745:
1736:
1728:
1727:
1718:
1710:
1709:
1697:
1696:
1687:
1679:
1678:
1669:
1641:
1607:rate coefficient
1517:room temperature
1493:collision theory
1468:, surface area,
1416:
1412:
1405:
1401:
1397:
1393:
1389:
1385:
1381:
1372:
1370:
1369:
1364:
1362:
1358:
1357:
1355:
1347:
1339:
1337:
1336:
1324:
1322:
1314:
1313:
1312:
1299:
1289:
1287:
1286:
1274:
1269:
1267:
1259:
1252:
1251:
1235:
1233:
1231:
1230:
1218:
1213:
1211:
1203:
1202:
1201:
1188:
1186:
1184:
1183:
1171:
1166:
1164:
1156:
1148:
1116:
1107:
1105:
1104:
1099:
1094:
1091:
1087:
1086:
1076:
1075:
1074:
1064:
1055:
1040:
1031:
1029:
1028:
1023:
1021:
1019:
1011:
997:
978:
970:
966:
960:
949:
945:
930:
928:
927:
922:
920:
916:
913:
904:
900:
898:
895:
893:
889:
887:generation
886:
870:
867:
858:
855:
848:
846:
838:
837:
836:
835:
821:
799:
794:
777:
776:
775:
758:
757:
756:
755:
750:
704:
696:transition state
693:
681:
679:
678:
673:
671:
668:
660:
656:
644:
641:
632:
623:
620:
612:
608:
596:
577:
573:
569:
562:
543:
539:
533:
531:
530:
525:
523:
521:
513:
509:
497:
495:
487:
482:
480:
472:
468:
456:
454:
446:
441:
439:
431:
427:
415:
413:
405:
397:
395:
387:
383:
371:
369:
361:
329:
314:
310:
302:
298:
286:
282:
278:
274:
267:
265:
264:
259:
257:
256:
253:
252:
251:
241:
238:
237:
236:
226:
223:
222:
221:
211:
208:
207:
206:
120:rate of reaction
62:
30:
21:
18:Rate of reaction
4247:
4246:
4242:
4241:
4240:
4238:
4237:
4236:
4212:
4211:
4181:
4176:
4175:
4168:
4153:"Section 2.8.3"
4149:
4148:
4144:
4137:
4124:
4123:
4119:
4112:
4096:
4095:
4091:
4084:
4068:
4067:
4060:
4035:
4026:
3987:
3986:
3982:
3943:
3942:
3938:
3899:
3898:
3894:
3855:
3854:
3850:
3811:
3810:
3806:
3789:
3777:
3764:
3763:
3759:
3742:
3730:
3717:
3716:
3712:
3707:
3675:
3662:
3655:
3628:
3617:
3613:
3585:
3574:
3564:
3558:
3557:
3552:
3551:
3525:
3517:
3483:
3459:
3437:
3424:
3416:
3415:
3406:
3370:
3293:
3292:
3280:
3272:
3262:
3240:
3237:
3231:
3223:
3205:
3199:
3195:
3194:The values for
3166:
3153:
3149:
3142:
3131:
3130:
3127:
3121:
3109:
3097:
3092:
3086:
3076:
3066:
3035:
3023:
3017:
3013:
2993:
2992:
2982:
2979:
2973:
2962:
2954:
2948:
2938:
2911:
2872:
2862:
2851:
2850:
2843:
2837:
2804:
2742:
2741:
2735:
2731:
2723:
2717:
2638:
2627:
2626:
2606:
2605:
2589:
2517:
2508:
2507:
2494:
2409:
2400:
2399:
2386:
2279:
2264:
2263:
2255:
2223:
2180:
2179:
2028:
2027:
2022:
1994:
1976:
1943:
1927:
1920:
1919:
1898:
1887:
1883:
1857:
1824:
1806:
1775:
1774:
1769:
1763:
1737:
1719:
1701:
1688:
1670:
1648:
1647:
1624:
1621:
1615:
1474:diffusion limit
1442:
1414:
1411:
1407:
1403:
1399:
1395:
1391:
1387:
1383:
1380:
1376:
1348:
1340:
1328:
1315:
1304:
1300:
1294:
1290:
1278:
1260:
1243:
1236:
1222:
1204:
1193:
1189:
1175:
1157:
1149:
1136:
1135:
1115:
1109:
1078:
1077:
1065:
1043:
1042:
1039:
1033:
1012:
998:
985:
984:
976:
968:
964:
959:
953:
947:
944:
943:
935:
918:
917:
910:
905:
884:
878:
876:
871:
864:
859:
851:
850:
839:
826:
822:
817:
812:
783:
778:
766:
764:
759:
745:
740:
731:
730:
718:constant volume
710:single reaction
702:
691:
661:
645:
613:
597:
580:
579:
575:
571:
564:
557:
541:
537:
514:
498:
473:
457:
432:
416:
388:
372:
346:
345:
336:constant volume
327:
312:
308:
300:
296:
284:
280:
276:
272:
194:
193:
187:
161:is the part of
60:
40:
28:
23:
22:
15:
12:
11:
5:
4245:
4243:
4235:
4234:
4232:Temporal rates
4229:
4224:
4214:
4213:
4210:
4209:
4204:
4199:
4194:
4188:
4180:
4179:External links
4177:
4174:
4173:
4166:
4142:
4135:
4117:
4110:
4098:Laidler, K. J.
4089:
4082:
4070:Laidler, K. J.
4058:
4024:
3997:(1): 137–148.
3980:
3953:(1): 163–174.
3936:
3909:(1): 175–191.
3892:
3848:
3821:(1): 251–269.
3804:
3775:
3757:
3728:
3709:
3708:
3706:
3703:
3702:
3701:
3696:
3691:
3686:
3681:
3674:
3671:
3649:
3648:
3634:
3631:
3624:
3620:
3616:
3610:
3607:
3602:
3597:
3591:
3588:
3581:
3577:
3573:
3570:
3567:
3561:
3500:
3492:
3489:
3482:
3476:
3468:
3465:
3458:
3453:
3446:
3443:
3436:
3431:
3427:
3423:
3388:
3379:
3374:
3364:
3355:
3341:
3334:
3323:
3316:
3304:
3279:
3276:
3270:
3235:
3221:
3203:
3179:
3172:
3169:
3161:
3156:
3152:
3145:
3141:
3138:
3125:
3118:one can expect
3106:
3105:
3095:
3090:
3084:
3074:
3048:
3041:
3038:
3031:
3026:
3020:
3016:
3012:
3009:
3006:
3003:
3000:
2975:Main article:
2972:
2969:
2960:
2952:
2946:
2924:
2918:
2914:
2905:
2902:
2893:
2884:
2879:
2875:
2869:
2865:
2861:
2858:
2841:
2825:
2819:
2814:
2808:
2798:
2785:
2780:
2772:
2759:
2751:
2733:
2729:
2721:
2705:
2702:
2693:
2680:
2671:
2668:
2659:
2650:
2645:
2641:
2637:
2634:
2604:
2601:
2593:
2590:
2579:
2571:
2563:
2555:
2547:
2539:
2528:
2518:
2516:
2513:
2510:
2509:
2506:
2498:
2495:
2484:
2476:
2465:
2457:
2449:
2441:
2433:
2420:
2410:
2408:
2405:
2402:
2401:
2398:
2390:
2387:
2378:
2372:
2368:
2355:
2341:
2334:
2323:
2316:
2301:
2295:
2285:
2280:
2278:
2275:
2272:
2271:
2253:
2235:
2230:
2226:
2217:
2214:
2205:
2196:
2193:
2190:
2187:
2165:
2155:
2149:
2135:
2126:
2122:
2112:
2106:
2102:
2094:
2085:
2079:
2069:
2065:
2055:
2049:
2045:
2036:
2021:
2018:
2006:
2001:
1997:
1992:
1988:
1983:
1979:
1974:
1970:
1967:
1964:
1961:
1958:
1955:
1949:
1946:
1941:
1937:
1933:
1930:
1896:
1882:The exponents
1836:
1831:
1827:
1822:
1818:
1813:
1809:
1804:
1800:
1797:
1794:
1791:
1788:
1785:
1782:
1767:
1749:
1744:
1740:
1735:
1731:
1726:
1722:
1717:
1713:
1708:
1704:
1700:
1695:
1691:
1686:
1682:
1677:
1673:
1668:
1664:
1661:
1658:
1655:
1617:Main article:
1614:
1611:
1555:ionic strength
1544:anti-Arrhenius
1478:physical state
1450:reaction order
1441:
1438:
1409:
1378:
1361:
1354:
1351:
1346:
1343:
1335:
1331:
1327:
1321:
1318:
1311:
1307:
1303:
1297:
1293:
1285:
1281:
1277:
1272:
1266:
1263:
1258:
1255:
1250:
1246:
1242:
1239:
1229:
1225:
1221:
1216:
1210:
1207:
1200:
1196:
1192:
1182:
1178:
1174:
1169:
1163:
1160:
1155:
1152:
1146:
1143:
1113:
1097:
1090:
1085:
1081:
1073:
1068:
1061:
1058:
1054:
1050:
1037:
1018:
1015:
1010:
1007:
1004:
1001:
995:
992:
981:
980:
962:
957:
951:
941:
939:
911:
909:
906:
903:
892:
881:
877:
875:
872:
865:
863:
860:
853:
852:
845:
842:
834:
829:
825:
818:
816:
813:
810:
807:
803:
798:
793:
789:
784:
782:
779:
774:
769:
765:
763:
760:
754:
749:
743:
739:
738:
667:
664:
659:
655:
651:
648:
638:
635:
629:
626:
619:
616:
611:
607:
603:
600:
593:
590:
587:
520:
517:
512:
508:
504:
501:
493:
490:
485:
479:
476:
471:
467:
463:
460:
452:
449:
444:
438:
435:
430:
426:
422:
419:
411:
408:
403:
400:
394:
391:
386:
382:
378:
375:
367:
364:
359:
356:
353:
269:
268:
244:
229:
214:
186:
183:
78:
77:
74:
68:
67:
64:
55:
54:
51:
45:
44:
41:
39:Common symbols
38:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4244:
4233:
4230:
4228:
4225:
4223:
4220:
4219:
4217:
4208:
4205:
4203:
4200:
4198:
4195:
4192:
4189:
4186:
4183:
4182:
4178:
4169:
4167:9780582218635
4163:
4159:
4154:
4146:
4143:
4138:
4132:
4128:
4121:
4118:
4113:
4107:
4103:
4099:
4093:
4090:
4085:
4083:0-8053-5682-7
4079:
4075:
4071:
4065:
4063:
4059:
4056:
4052:
4048:
4044:
4043:
4038:
4033:
4031:
4029:
4025:
4020:
4016:
4012:
4008:
4004:
4000:
3996:
3992:
3984:
3981:
3976:
3972:
3968:
3964:
3960:
3956:
3952:
3948:
3940:
3937:
3932:
3928:
3924:
3920:
3916:
3912:
3908:
3904:
3896:
3893:
3888:
3884:
3880:
3876:
3872:
3868:
3864:
3860:
3852:
3849:
3844:
3840:
3836:
3832:
3828:
3824:
3820:
3816:
3808:
3805:
3800:
3794:
3786:
3782:
3778:
3772:
3768:
3761:
3758:
3753:
3747:
3739:
3735:
3731:
3725:
3721:
3714:
3711:
3704:
3700:
3697:
3695:
3692:
3690:
3687:
3685:
3682:
3680:
3677:
3676:
3672:
3670:
3666:
3659:
3652:
3632:
3629:
3622:
3618:
3608:
3605:
3600:
3595:
3589:
3579:
3575:
3571:
3568:
3559:
3550:
3549:
3548:
3546:
3542:
3541:mole fraction
3538:
3533:
3531:
3530:double dagger
3523:
3514:
3487:
3480:
3463:
3456:
3451:
3441:
3434:
3429:
3425:
3413:
3410:
3403:
3377:
3362:
3332:
3321:
3302:
3290:
3287:
3285:
3277:
3275:
3273:
3269:
3260:
3256:
3255:rule of thumb
3250:
3247:
3244:
3234:
3225:
3216:
3212:
3208:
3202:
3192:
3177:
3170:
3167:
3154:
3150:
3143:
3139:
3136:
3124:
3119:
3115:
3103:
3096:
3089:
3085:
3082:
3075:
3072:
3065:
3064:
3063:
3060:
3046:
3039:
3036:
3024:
3018:
3014:
3010:
3007:
3004:
3001:
2998:
2990:
2988:
2978:
2970:
2968:
2966:
2957:
2951:
2945:
2941:
2935:
2922:
2916:
2891:
2877:
2873:
2867:
2863:
2859:
2856:
2848:
2840:
2823:
2817:
2796:
2783:
2770:
2757:
2739:
2726:
2720:
2703:
2691:
2678:
2657:
2643:
2639:
2635:
2632:
2624:
2619:
2602:
2577:
2569:
2561:
2545:
2537:
2526:
2511:
2482:
2474:
2463:
2447:
2439:
2431:
2418:
2403:
2366:
2353:
2332:
2321:
2283:
2273:
2261:
2257:
2251:
2246:
2233:
2228:
2203:
2191:
2188:
2185:
2176:
2163:
2133:
2124:
2120:
2100:
2067:
2063:
2043:
2034:
2025:
2019:
2017:
2004:
1999:
1981:
1962:
1956:
1953:
1947:
1944:
1928:
1917:
1913:
1910:
1905:
1900:
1893:
1880:
1878:
1874:
1873:rate constant
1870:
1864:
1860:
1854:
1852:
1847:
1834:
1829:
1811:
1792:
1786:
1783:
1780:
1772:
1766:
1760:
1747:
1742:
1724:
1706:
1702:
1698:
1693:
1675:
1659:
1656:
1653:
1645:
1639:
1635:
1631:
1627:
1620:
1619:Rate equation
1613:Rate equation
1612:
1610:
1608:
1603:
1601:
1596:
1594:
1590:
1586:
1582:
1577:
1575:
1570:
1568:
1564:
1558:
1556:
1551:
1549:
1545:
1541:
1540:non-Arrhenius
1536:
1534:
1530:
1526:
1522:
1518:
1514:
1508:
1505:
1502:
1498:
1494:
1490:
1485:
1483:
1479:
1475:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1439:
1437:
1434:
1429:
1427:
1423:
1418:
1373:
1359:
1352:
1349:
1344:
1341:
1333:
1329:
1325:
1319:
1316:
1309:
1305:
1301:
1295:
1291:
1283:
1279:
1275:
1270:
1264:
1261:
1253:
1248:
1244:
1237:
1227:
1223:
1219:
1214:
1208:
1205:
1198:
1194:
1190:
1180:
1176:
1172:
1167:
1161:
1158:
1153:
1150:
1144:
1141:
1133:
1131:
1127:
1122:
1120:
1112:
1095:
1088:
1083:
1079:
1066:
1059:
1036:
1016:
1013:
1005:
999:
993:
990:
974:
963:
956:
952:
938:
934:
933:
932:
907:
901:
890:
879:
873:
861:
843:
840:
827:
823:
814:
808:
805:
801:
796:
791:
787:
780:
767:
761:
752:
741:
728:
726:
721:
719:
715:
714:closed system
711:
706:
700:
697:
689:
685:
665:
662:
646:
636:
633:
627:
624:
617:
614:
598:
591:
588:
585:
567:
560:
555:
550:
549:negative sign
545:
534:
518:
515:
499:
491:
488:
483:
477:
474:
458:
450:
447:
442:
436:
433:
417:
409:
406:
401:
398:
392:
389:
373:
365:
362:
357:
354:
351:
343:
341:
337:
333:
332:closed system
325:
321:
318:According to
316:
306:
294:
290:
242:
212:
192:
191:
190:
184:
182:
180:
176:
172:
168:
164:
160:
156:
153:
149:
145:
141:
137:
133:
129:
128:concentration
125:
121:
117:
116:reaction rate
109:
105:
100:
93:
89:
84:
75:
73:
69:
65:
63:
56:
52:
50:
46:
42:
36:
33:Reaction rate
31:
19:
4157:
4145:
4126:
4120:
4101:
4092:
4073:
4040:
3994:
3990:
3983:
3950:
3946:
3939:
3906:
3902:
3895:
3865:(1): 31–48.
3862:
3858:
3851:
3818:
3814:
3807:
3766:
3760:
3719:
3713:
3664:
3657:
3653:
3650:
3534:
3520:denotes the
3515:
3414:
3408:
3404:
3291:
3288:
3281:
3267:
3251:
3248:
3242:
3232:
3229:
3209:
3200:
3193:
3122:
3107:
3102:gas constant
3087:
3061:
2991:
2980:
2964:
2958:
2949:
2943:
2939:
2936:
2838:
2727:
2718:
2620:
2262:
2258:
2247:
2177:
2026:
2023:
1918:
1914:
1904:molecularity
1901:
1881:
1872:
1868:
1862:
1858:
1855:
1848:
1773:
1764:
1761:
1637:
1633:
1629:
1625:
1622:
1604:
1597:
1578:
1571:
1559:
1552:
1543:
1539:
1537:
1509:
1506:
1486:
1464:, catalyst,
1443:
1430:
1425:
1421:
1419:
1374:
1134:
1125:
1123:
1110:
1034:
982:
961:the outflow;
954:
936:
914:accumulation
729:
725:mass balance
722:
717:
713:
709:
707:
688:irreversible
565:
558:
546:
538:X (= A, B, P
535:
344:
317:
287:) represent
270:
188:
157:
119:
115:
113:
107:
91:
49:SI unit
2738:equilibrium
2623:bimolecular
2250:third order
1454:temperature
1386:, equal to
896:consumption
4216:Categories
4111:0060438622
2740:, so that
1521:exothermic
690:reaction,
684:elementary
303:) and the
175:enzymology
104:combustion
4019:145994544
4011:1878-5204
3975:189874787
3967:1878-5204
3931:199078451
3923:1878-5204
3887:105735334
3879:1878-5204
3843:199407594
3835:1878-5204
3793:cite book
3785:951078429
3746:cite book
3738:889577526
3720:Chemistry
3623:‡
3615:Δ
3609:−
3587:∂
3572:
3566:∂
3491:¯
3481:−
3467:¯
3457:−
3452:‡
3445:¯
3430:‡
3422:Δ
3387:⟶
3378:‡
3363:⋯
3340:⇀
3333:−
3322:−
3315:↽
3284:condensed
3151:−
3140:
3019:−
3011:
2728:However N
2554:⟶
2456:⟶
2340:⇀
2333:−
2322:−
2315:↽
2093:⟶
1699:−
1585:deuterium
1501:collision
1497:frequency
1280:ν
1224:ν
1177:ν
1154:ξ
891:−
862:−
788:∫
762:−
628:−
592:−
402:−
358:−
324:Gold Book
293:reactants
228:⟶
152:cellulose
72:Dimension
4100:(1987).
3673:See also
1899:and NO.
1574:platinum
1563:chlorine
1533:hydrogen
1489:rate law
1482:solution
1470:stirring
1466:isotopes
1446:pressure
1433:catalyst
305:products
136:reactant
3100:is the
3079:is the
3062:where
2845:is the
1867:is the
1567:mixture
1548:radical
1525:methane
1458:solvent
1117:is the
931:where
712:, in a
132:product
88:rusting
4164:
4133:
4108:
4080:
4017:
4009:
3973:
3965:
3929:
3921:
3885:
3877:
3841:
3833:
3783:
3773:
3736:
3726:
3543:or on
3516:where
3412:, is:
3383:
3350:
2836:where
2716:where
1892:orders
1531:, and
1529:butane
1472:, and
1398:, and
578:, but
283:, and
146:under
106:has a
90:has a
4037:IUPAC
4015:S2CID
3971:S2CID
3927:S2CID
3883:S2CID
3839:S2CID
3705:Notes
2965:after
1587:. In
1375:Here
1108:Here
570:then
320:IUPAC
130:of a
102:Wood
86:Iron
4162:ISBN
4131:ISBN
4106:ISBN
4078:ISBN
4007:ISSN
3963:ISSN
3919:ISSN
3875:ISSN
3831:ISSN
3799:link
3781:OCLC
3771:ISBN
3752:link
3734:OCLC
3724:ISBN
3265:).
3198:and
2596:fast
2501:slow
1886:and
1636:P +
1632:B →
1628:A +
1579:The
1424:and
971:(in
686:and
563:and
311:and
299:and
177:and
144:iron
114:The
108:high
4051:doi
4049:".
3999:doi
3995:127
3955:doi
3951:128
3911:doi
3907:128
3867:doi
3863:126
3823:doi
3819:128
3528:(a
3261:, (
3239:or
3137:exp
3077:exp
3008:exp
1871:or
1499:of
1041:by
868:out
716:of
568:= 3
561:= 1
540:or
334:at
322:'s
315:).
142:of
118:or
92:low
58:In
4218::
4156:.
4061:^
4039:,
4027:^
4013:.
4005:.
3993:.
3969:.
3961:.
3949:.
3925:.
3917:.
3905:.
3881:.
3873:.
3861:.
3837:.
3829:.
3817:.
3795:}}
3791:{{
3779:.
3748:}}
3744:{{
3732:.
3569:ln
3518:V̄
3271:10
3191:.
3116:,
2989::
2942:=
2908:NO
2810:NO
2289:NO
2220:NO
2073:NO
1879:.
1853:.
1602:.
1535:.
1527:,
1460:,
1456:,
1452:,
1448:,
1417:.
1394:,
1390:,
1121:.
856:in
542:Q)
279:,
275:,
181:.
173:,
4170:.
4139:.
4114:.
4086:.
4053::
4021:.
4001::
3977:.
3957::
3933:.
3913::
3889:.
3869::
3845:.
3825::
3801:)
3787:.
3754:)
3740:.
3667:=
3665:V
3663:Δ
3658:V
3656:Δ
3633:T
3630:R
3619:V
3606:=
3601:T
3596:)
3590:P
3580:x
3576:k
3560:(
3526:‡
3499:B
3488:V
3475:A
3464:V
3442:V
3435:=
3426:V
3409:V
3407:Δ
3390:P
3373:|
3367:B
3359:A
3354:|
3306:B
3303:+
3300:A
3268:Q
3263:Q
3243:G
3241:Δ
3236:a
3233:E
3224:2
3222:N
3220:S
3204:a
3201:E
3196:A
3178:)
3171:T
3168:R
3160:a
3155:E
3144:(
3126:a
3123:E
3110:T
3104:.
3098:R
3091:a
3088:E
3083:,
3073:,
3067:A
3047:)
3040:T
3037:R
3030:a
3025:E
3015:(
3005:A
3002:=
2999:k
2983:k
2961:2
2953:1
2950:K
2947:2
2944:k
2940:k
2923:.
2917:2
2913:]
2904:[
2901:]
2892:2
2888:H
2883:[
2878:1
2874:K
2868:2
2864:k
2860:=
2857:v
2842:1
2839:K
2824:,
2818:2
2813:]
2807:[
2797:1
2791:K
2784:=
2779:]
2771:2
2767:O
2758:2
2754:N
2750:[
2734:2
2732:O
2730:2
2722:2
2719:k
2704:,
2701:]
2692:2
2688:O
2679:2
2675:N
2670:[
2667:]
2658:2
2654:H
2649:[
2644:2
2640:k
2636:=
2633:v
2603:.
2600:)
2592:(
2586:O
2578:2
2574:H
2570:+
2562:2
2558:N
2546:2
2542:H
2538:+
2535:O
2527:2
2523:N
2515:)
2512:3
2505:)
2497:(
2491:O
2483:2
2479:H
2475:+
2472:O
2464:2
2460:N
2448:2
2444:H
2440:+
2432:2
2428:O
2419:2
2415:N
2407:)
2404:2
2397:)
2389:(
2377:)
2374:g
2371:(
2367:2
2363:O
2354:2
2350:N
2300:)
2297:g
2294:(
2284:2
2277:)
2274:1
2254:2
2234:.
2229:2
2225:]
2216:[
2213:]
2204:2
2200:H
2195:[
2192:k
2189:=
2186:v
2164:,
2154:)
2151:g
2148:(
2143:O
2134:2
2130:H
2125:2
2121:+
2111:)
2108:g
2105:(
2101:2
2097:N
2084:)
2081:g
2078:(
2068:2
2064:+
2054:)
2051:g
2048:(
2044:2
2040:H
2035:2
2005:.
2000:m
1996:]
1991:B
1987:[
1982:n
1978:]
1973:A
1969:[
1966:)
1963:T
1960:(
1957:k
1954:=
1948:t
1945:d
1940:]
1936:P
1932:[
1929:d
1897:2
1888:m
1884:n
1865:)
1863:T
1861:(
1859:k
1835:.
1830:m
1826:]
1821:B
1817:[
1812:n
1808:]
1803:A
1799:[
1796:)
1793:T
1790:(
1787:k
1784:=
1781:v
1768:r
1765:k
1748:.
1743:j
1739:]
1734:Q
1730:[
1725:i
1721:]
1716:P
1712:[
1707:r
1703:k
1694:m
1690:]
1685:B
1681:[
1676:n
1672:]
1667:A
1663:[
1660:k
1657:=
1654:v
1640:Q
1638:q
1634:p
1630:b
1626:a
1415:i
1410:i
1408:C
1404:V
1400:q
1396:p
1392:b
1388:a
1384:i
1379:i
1377:ν
1360:)
1353:t
1350:d
1345:V
1342:d
1334:i
1330:C
1326:+
1320:t
1317:d
1310:i
1306:C
1302:d
1296:V
1292:(
1284:i
1276:1
1271:=
1265:t
1262:d
1257:)
1254:V
1249:i
1245:C
1241:(
1238:d
1228:i
1220:1
1215:=
1209:t
1206:d
1199:i
1195:n
1191:d
1181:i
1173:1
1168:=
1162:t
1159:d
1151:d
1145:=
1142:v
1114:0
1111:N
1096:.
1089:V
1084:0
1080:N
1072:A
1067:N
1060:=
1057:]
1053:A
1049:[
1038:A
1035:N
1017:t
1014:d
1009:]
1006:A
1003:[
1000:d
994:=
991:v
977:V
969:A
965:v
958:A
955:F
948:A
942:0
940:A
937:F
908:=
902:)
880:(
874:+
844:t
841:d
833:A
828:N
824:d
815:=
809:V
806:d
802:v
797:V
792:0
781:+
773:A
768:F
753:0
748:A
742:F
703:v
692:v
666:t
663:d
658:]
654:B
650:[
647:d
637:3
634:1
625:=
618:t
615:d
610:]
606:A
602:[
599:d
589:=
586:v
576:A
572:B
566:b
559:a
519:t
516:d
511:]
507:Q
503:[
500:d
492:q
489:1
484:=
478:t
475:d
470:]
466:P
462:[
459:d
451:p
448:1
443:=
437:t
434:d
429:]
425:B
421:[
418:d
410:b
407:1
399:=
393:t
390:d
385:]
381:A
377:[
374:d
366:a
363:1
355:=
352:v
328:v
313:Q
309:P
307:(
301:B
297:A
295:(
285:q
281:p
277:b
273:a
254:Q
249:q
243:+
239:P
234:p
224:B
219:b
213:+
209:A
204:a
43:ν
20:)
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