A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events .
115-413: Chain reactions are one way that systems which are not in thermodynamic equilibrium can release energy or increase entropy in order to reach a state of higher entropy. For example, a system may not be able to reach a lower energy state by releasing energy into the environment, because it is hindered or prevented in some way from taking the path that will result in the energy release. If a reaction results in
230-463: A closed system at constant temperature and volume, without a build-up of reaction intermediates , the reaction rate v {\displaystyle v} is defined as where ν i is the stoichiometric coefficient for chemical X i , with a negative sign for a reactant. The initial reaction rate v 0 = v t = 0 {\displaystyle v_{0}=v_{t=0}} has some functional dependence on
345-402: A fractional order , and may depend on the concentration of an intermediate species. A reaction can also have an undefined reaction order with respect to a reactant if the rate is not simply proportional to some power of the concentration of that reactant; for example, one cannot talk about reaction order in the rate equation for a bimolecular reaction between adsorbed molecules : Consider
460-405: A thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium. The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact,
575-503: A thermodynamic operation . In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties , other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings. In systems that are at
690-903: A "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10 years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium." Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." According to L. Tisza : "... in
805-408: A chain reaction at the level of the nucleus. He did not envision fission as one of these neutron-producing reactions, since this reaction was not known at the time. Experiments he proposed using beryllium and indium failed. Later, after fission was discovered in 1938, Szilárd immediately realized the possibility of using neutron-induced fission as the particular nuclear reaction necessary to create
920-466: A chain-reaction, so long as fission also produced neutrons. In 1939, with Enrico Fermi, Szilárd proved this neutron-multiplying reaction in uranium. In this reaction, a neutron plus a fissionable atom causes a fission resulting in a larger number of neutrons than the single one that was consumed in the initial reaction. Thus was born the practical nuclear chain reaction by the mechanism of neutron-induced nuclear fission. Specifically, if one or more of
1035-409: A common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on
1150-507: A complete rate equation with a two-term denominator ( mixed-order kinetics ). The pyrolysis (thermal decomposition) of acetaldehyde , CH 3 CHO (g) → CH 4 (g) + CO (g), proceeds via the Rice-Herzfeld mechanism: The methyl and CHO groups are free radicals . This reaction step provides methane , which is one of the two main products. The product •CH 3 CO (g) of the previous step gives rise to carbon monoxide (CO), which
1265-517: A constant rate. In homogeneous catalysis zero order behavior can come about from reversible inhibition. For example, ring-opening metathesis polymerization using third-generation Grubbs catalyst exhibits zero order behavior in catalyst due to the reversible inhibition that occurs between pyridine and the ruthenium center. A first order reaction depends on the concentration of only one reactant (a unimolecular reaction ). Other reactants can be present, but their concentration has no effect on
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#17327838928381380-476: A constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it to compensate for
1495-425: A graph of ln v {\displaystyle \ln v} as a function of ln [ A ] {\displaystyle \ln[{\ce {A}}]} then corresponds to the order x {\displaystyle x} with respect to reactant A {\displaystyle {\rm {A}}} . However, this method
1610-514: A molecule excited by light, but could also start with two molecules colliding violently due to thermal energy as previously proposed for initiation of chemical reactions by van' t Hoff . Christiansen and Kramers also noted that if, in one link of the reaction chain, two or more unstable molecules are produced, the reaction chain would branch and grow. The result is in fact an exponential growth, thus giving rise to explosive increases in reaction rates, and indeed to chemical explosions themselves. This
1725-424: A natural thermodynamic process . It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It
1840-630: A non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface. Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse : "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium
1955-421: A particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential. A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for
2070-414: A path of release over friction. Chemically, the equivalent to a snow avalanche is a spark causing a forest fire. In nuclear physics, a single stray neutron can result in a prompt critical event, which may finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion. Another metaphor for a chain reaction is the domino effect , named after the act of domino toppling , where
2185-460: A reaction a ·A + b ·B → c ·C with rate law v 0 = k ⋅ [ A ] x ⋅ [ B ] y , {\displaystyle v_{0}=k\cdot [{\rm {A}}]^{x}\cdot [{\rm {B}}]^{y},} the partial order x {\displaystyle x} with respect to A {\displaystyle {\rm {A}}}
2300-424: A single concentration squared, the time dependence of the concentration is given by The unit of k is mol dm s . The time dependence for a rate proportional to two unequal concentrations is if the concentrations are equal, they satisfy the previous equation. The second type includes nucleophilic addition-elimination reactions , such as the alkaline hydrolysis of ethyl acetate : This reaction
2415-404: A single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes
SECTION 20
#17327838928382530-407: A small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released. A macroscopic metaphor for chain reactions is thus a snowball causing a larger snowball until finally an avalanche results (" snowball effect "). This is a result of stored gravitational potential energy seeking
2645-574: A special term 'thermal equilibrium'. J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its " full thermodynamic equilibrium state". Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all
2760-586: A state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a "meta-stable equilibrium". Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when an isolated body of material starts from an equilibrium state, in which portions of it are held at different states by more or less permeable or impermeable partitions, and
2875-433: A strong electric field causes them to gain energy, and when they impact other atoms, the energy causes release of new free electrons and ions (ionization), which fuels the same process. If this process happens faster than it is naturally quenched by ions recombining, the new ions multiply in successive cycles until the gas breaks down into a plasma and current flows freely in a discharge. Electron avalanches are essential to
2990-437: A system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some intensive variables . For example, a relatively dense component of a mixture can be concentrated by centrifugation. Order of reaction#Mixed order In chemistry , the rate equation (also known as the rate law or empirical differential rate equation ) is an empirical differential mathematical expression for
3105-557: A system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, not only is there an absence of macroscopic change, but there is an “absence of any tendency toward change on a macroscopic scale.” Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal , mechanical , chemical , and radiative equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by
3220-418: A thermodynamic operation removes or makes the partitions more permeable, then it spontaneously reaches its own new state of internal thermodynamic equilibrium and this is accompanied by an increase in the sum of the entropies of the portions. Classical thermodynamics deals with states of dynamic equilibrium . The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential
3335-426: A thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example,
3450-420: A typical chemical reaction in which two reactants A and B combine to form a product C: This can also be written The prefactors −1, −2 and 3 (with negative signs for reactants because they are consumed) are known as stoichiometric coefficients . One molecule of A combines with two of B to form 3 of C, so if we use the symbol [X] for the molar concentration of chemical X, If the reaction takes place in
3565-653: A wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when
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3680-434: A wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and
3795-400: Is mol dm s . This may occur when there is a bottleneck which limits the number of reactant molecules that can react at the same time, for example if the reaction requires contact with an enzyme or a catalytic surface. Many enzyme-catalyzed reactions are zero order, provided that the reactant concentration is much greater than the enzyme concentration which controls the rate, so that
3910-537: Is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero. R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that
4025-541: Is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory , and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example,
4140-421: Is constant then v 0 = k [ A ] [ B ] = k ′ [ A ] , {\displaystyle v_{0}=k[{\ce {A}}][{\ce {B}}]=k'[{\ce {A}}],} where the pseudo–first-order rate constant k ′ = k [ B ] . {\displaystyle k'=k[{\ce {B}}].} The second-order rate equation has been reduced to
4255-463: Is defined as the average number of times the propagation cycle is repeated, and equals the overall reaction rate divided by the initiation rate. Some chain reactions have complex rate equations with fractional order or mixed order kinetics. The reaction H 2 + Br 2 → 2 HBr proceeds by the following mechanism: As can be explained using the steady-state approximation , the thermal reaction has an initial rate of fractional order (3/2), and
4370-418: Is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in
4485-538: Is determined using a large excess of B {\displaystyle {\rm {B}}} . In this case v 0 = k ′ ⋅ [ A ] x {\displaystyle v_{0}=k'\cdot [{\rm {A}}]^{x}} with k ′ = k ⋅ [ B ] y , {\displaystyle k'=k\cdot [{\rm {B}}]^{y},} and x {\displaystyle x} may be determined by
4600-483: Is essential for the strict meaning of thermodynamic equilibrium. A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium. " A monograph on classical thermodynamics by H.A. Buchdahl considers
4715-444: Is first-order in each reactant and second-order overall: If the same hydrolysis reaction is catalyzed by imidazole , the rate equation becomes The rate is first-order in one reactant (ethyl acetate), and also first-order in imidazole, which as a catalyst does not appear in the overall chemical equation. Another well-known class of second-order reactions are the S N 2 (bimolecular nucleophilic substitution) reactions, such as
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4830-430: Is in great excess with respect to the other reactants), its concentration can be included in the rate constant, leading to a pseudo–first-order (or occasionally pseudo–second-order) rate equation. For a typical second-order reaction with rate equation v 0 = k [ A ] [ B ] , {\displaystyle v_{0}=k[{\ce {A}}][{\ce {B}}],} if the concentration of reactant B
4945-544: Is minimized (in the absence of an applied voltage), or for which the entropy ( S ) is maximized, for specified conditions. One such potential is the Helmholtz free energy ( A ), for a closed system at constant volume and temperature (controlled by a heat bath): Another potential, the Gibbs free energy ( G ), is minimized at thermodynamic equilibrium in a closed system at constant temperature and pressure, both controlled by
5060-412: Is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined. This local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles . In a radiating gas, the photons being emitted and absorbed by the gas do not need to be in a thermodynamic equilibrium with each other or with
5175-478: Is not always reliable because The tentative rate equation determined by the method of initial rates is therefore normally verified by comparing the concentrations measured over a longer time (several half-lives) with the integrated form of the rate equation; this assumes that the reaction goes to completion. For example, the integrated rate law for a first-order reaction is where [ A ] {\displaystyle [{\rm {A]}}}
5290-430: Is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium. Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other. For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in
5405-488: Is physical damage to the crystal). Certain devices, such as avalanche diodes , deliberately make use of the effect. Examples of chain reactions in living organisms include excitation of neurons in epilepsy and lipid peroxidation . In peroxidation, a lipid radical reacts with oxygen to form a peroxyl radical (L• + O 2 → LOO•). The peroxyl radical then oxidises another lipid, thus forming another lipid radical (LOO• + L–H → LOOH + L•). A chain reaction in glutamatergic synapses
5520-420: Is responsible for the formation of as many as 10 molecules of the product HCl . Nernst suggested that the photon dissociates a Cl 2 molecule into two Cl atoms which each initiate a long chain of reaction steps forming HCl. In 1923, Danish and Dutch scientists J. A. Christiansen and Hendrik Anthony Kramers , in an analysis of the formation of polymers, pointed out that such a chain reaction need not start with
5635-486: Is said to be second order when the overall order is two. The rate of a second-order reaction may be proportional to one concentration squared, v 0 = k [ A ] 2 , {\displaystyle v_{0}=k[{\ce {A}}]^{2},} or (more commonly) to the product of two concentrations, v 0 = k [ A ] [ B ] . {\displaystyle v_{0}=k[{\ce {A}}][{\ce {B}}].} As an example of
5750-540: Is second order and the reaction of the energized molecule which is unimolecular and first order. The rate of the overall reaction depends on the slowest step, so the overall reaction will be first order when the reaction of the energized reactant is slower than the collision step. The half-life is independent of the starting concentration and is given by t 1 / 2 = ln ( 2 ) k {\textstyle t_{1/2}={\frac {\ln {(2)}}{k}}} . The mean lifetime
5865-457: Is the cause of synchronous discharge in some epileptic seizures. Thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics . It is an internal state of a single thermodynamic system , or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls . In thermodynamic equilibrium, there are no net macroscopic flows of matter nor of energy within
SECTION 50
#17327838928385980-435: Is the concentration at time t {\displaystyle t} and [ A ] 0 {\displaystyle [{\rm {A]_{0}}}} is the initial concentration at zero time. The first-order rate law is confirmed if ln [ A ] {\displaystyle \ln {[{\ce {A}}]}} is in fact a linear function of time. In this case
6095-428: Is the mechanism of a Geiger counter and also the visualization possible with a spark chamber and other wire chambers . An avalanche breakdown process can happen in semiconductors, which in some ways conduct electricity analogously to a mildly ionized gas. Semiconductors rely on free electrons knocked out of the crystal by thermal vibration for conduction. Thus, unlike metals, semiconductors become better conductors
6210-481: Is the overall order of reaction. In a dilute solution, an elementary reaction (one having a single step with a single transition state ) is empirically found to obey the law of mass action . This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using mathematical product notation is: Where: The natural logarithm of
6325-496: Is the second main product. The sum of the two propagation steps corresponds to the overall reaction CH 3 CHO (g) → CH 4 (g) + CO (g), catalyzed by a methyl radical •CH 3 . This reaction is the only source of ethane (minor product) and it is concluded to be the main chain ending step. Although this mechanism explains the principal products, there are others that are formed in a minor degree, such as acetone (CH 3 COCH 3 ) and propanal (CH 3 CH 2 CHO). Applying
6440-410: Is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings. The various types of equilibriums are achieved as follows: Often the surroundings of
6555-531: Is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within
6670-523: Is τ = 1/k. Examples of such reactions are: In organic chemistry, the class of S N 1 (nucleophilic substitution unimolecular) reactions consists of first-order reactions. For example, in the reaction of aryldiazonium ions with nucleophiles in aqueous solution, ArN + 2 + X → ArX + N 2 , the rate equation is v 0 = k [ ArN 2 + ] , {\displaystyle v_{0}=k[{\ce {ArN2+}}],} where Ar indicates an aryl group. A reaction
6785-635: The Steady State Approximation for the intermediate species CH 3 (g) and CH 3 CO(g), the rate law for the formation of methane and the order of reaction are found: The rate of formation of the product methane is ( 1 ) . . . d [ CH 4 ] d t = k 2 [ CH 3 ] [ CH 3 CHO ] {\displaystyle (1)...{\frac {d{\ce {[CH4]}}}{dt}}=k_{2}{\ce {[CH3]}}{\ce {[CH3CHO]}}} For
6900-446: The dielectric breakdown process within gases. The process can culminate in corona discharges , streamers , leaders , or in a spark or continuous electric arc that completely bridges the gap. The process may extend huge sparks — streamers in lightning discharges propagate by formation of electron avalanches created in the high potential gradient ahead of the streamers' advancing tips. Once begun, avalanches are often intensified by
7015-459: The molar concentrations of the species A {\displaystyle \mathrm {A} } and B , {\displaystyle \mathrm {B} ,} usually in moles per liter ( molarity , M {\displaystyle M} ). The exponents x {\displaystyle x} and y {\displaystyle y} are
SECTION 60
#17327838928387130-418: The rate constant k {\displaystyle k} is equal to the slope with sign reversed. The partial order with respect to a given reactant can be evaluated by the method of flooding (or of isolation) of Ostwald . In this method, the concentration of one reactant is measured with all other reactants in large excess so that their concentration remains essentially constant. For
7245-440: The reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as where [ A ] {\displaystyle [\mathrm {A} ]} and [ B ] {\displaystyle [\mathrm {B} ]} are
7360-413: The "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium ." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely,
7475-481: The "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition , which apparently was suggested by Fowler .) Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by
7590-477: The body remains sufficiently nearly in thermodynamic equilibrium during the process. A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium . This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium
7705-404: The bottom wall, but the temperature is the same everywhere. A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within
7820-469: The concentrations of the reactants, and this dependence is known as the rate equation or rate law . This law generally cannot be deduced from the chemical equation and must be determined by experiment. A common form for the rate equation is a power law: The constant k {\displaystyle k} is called the rate constant . The exponents, which can be fractional, are called partial orders of reaction and their sum
7935-411: The conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium". P.M. Morse writes that thermodynamics is concerned with " states of thermodynamic equilibrium ". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining
8050-413: The contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another. If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have
8165-443: The creation of photoelectrons as a result of ultraviolet radiation emitted by the excited medium's atoms in the aft-tip region. The extremely high temperature of the resulting plasma cracks the surrounding gas molecules and the free ions recombine to create new chemical compounds. The process can also be used to detect radiation that initiates the process, as the passage of a single particles can be amplified to large discharges. This
8280-416: The criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory! " J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems." Another author, cited by Callen as giving
8395-540: The discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common." The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it
8510-436: The enzyme is saturated . For example, the biological oxidation of ethanol to acetaldehyde by the enzyme liver alcohol dehydrogenase (LADH) is zero order in ethanol. Similarly reactions with heterogeneous catalysis can be zero order if the catalytic surface is saturated. For example, the decomposition of phosphine ( PH 3 ) on a hot tungsten surface at high pressure is zero order in phosphine, which decomposes at
8625-401: The equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement
8740-410: The experimental rate equation has been determined, it is often of use for deduction of the reaction mechanism . The rate equation of a reaction with an assumed multi-step mechanism can often be derived theoretically using quasi-steady state assumptions from the underlying elementary reactions, and compared with the experimental rate equation as a test of the assumed mechanism. The equation may involve
8855-400: The first type, the reaction NO 2 + CO → NO + CO 2 is second-order in the reactant NO 2 and zero order in the reactant CO. The observed rate is given by v 0 = k [ NO 2 ] 2 , {\displaystyle v_{0}=k[{\ce {NO2}}]^{2},} and is independent of the concentration of CO. For the rate proportional to
8970-429: The glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and
9085-421: The higher the temperature. This sets up conditions for the same type of positive feedback—heat from current flow causes temperature to rise, which increases charge carriers, lowering resistance, and causing more current to flow. This can continue to the point of complete breakdown of normal resistance at a semiconductor junction, and failure of the device (this may be temporary or permanent depending on whether there
9200-509: The integral method. The order y {\displaystyle y} with respect to B {\displaystyle {\rm {B}}} under the same conditions (with B {\displaystyle {\rm {B}}} in excess) is determined by a series of similar experiments with a range of initial concentration [ B ] 0 {\displaystyle [{\rm {B]_{0}}}} so that
9315-488: The intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field. J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with
9430-1766: The intermediates ( 2 ) . . . d [ CH 3 ] d t = k 1 [ CH 3 CHO ] − k 2 [ CH 3 ] [ CH 3 CHO ] + k 3 [ CH 3 CO ] − 2 k 4 [ CH 3 ] 2 = 0 {\displaystyle (2)...{\frac {d{\ce {[CH_3]}}}{dt}}=k_{1}{\ce {[CH3CHO]}}-k_{2}{\ce {[CH3]}}{\ce {[CH3CHO]}}+k_{3}{\ce {[CH3CO]}}-2k_{4}{\ce {[CH3]}}^{2}=0} and ( 3 ) . . . d [ CH 3 CO ] d t = k 2 [ CH 3 ] [ CH 3 CHO ] − k 3 [ CH 3 CO ] = 0 {\displaystyle (3)...{\frac {d{\ce {[CH3CO]}}}{dt}}=k_{2}{\ce {[CH3]}}{\ce {[CH3CHO]}}-k_{3}{\ce {[CH3CO]}}=0} Adding (2) and (3), we obtain k 1 [ CH 3 CHO ] − 2 k 4 [ CH 3 ] 2 = 0 {\displaystyle k_{1}{\ce {[CH3CHO]}}-2k_{4}{\ce {[CH3]}}^{2}=0} so that ( 4 ) . . . [ CH 3 ] = k 1 2 k 4 [ CH 3 CHO ] 1 / 2 {\displaystyle (4)...{\ce {[CH3]}}={\frac {k_{1}}{2k_{4}}}{\ce {[CH3CHO]}}^{1/2}} Using (4) in (1) gives
9545-423: The massive particles of the gas for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist. As an example, LTE will exist in a glass of water that contains a melting ice cube . The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of
9660-889: The melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous. Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated. For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice,
9775-585: The molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature. Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have
9890-412: The parent molecules with a far larger probability than the initial reactants. (In the new reaction, further unstable molecules are formed besides the stable products, and so on.) In 1918, Walther Nernst proposed that the photochemical reaction between hydrogen and chlorine is a chain reaction in order to explain what is known as the quantum yield phenomena. This means that one photon of light
10005-416: The partial orders of reaction for A {\displaystyle \mathrm {A} } and B {\displaystyle \mathrm {B} } and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which
10120-526: The power-law rate equation is This can be used to estimate the order of reaction of each reactant. For example, the initial rate can be measured in a series of experiments at different initial concentrations of reactant A {\displaystyle {\rm {A}}} with all other concentrations [ B ] , [ C ] , … {\displaystyle [{\rm {B],[{\rm {C],\dots }}}}} kept constant, so that The slope of
10235-428: The pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work. A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when
10350-438: The produced neutrons themselves interact with other fissionable nuclei, and these also undergo fission, then there is a possibility that the macroscopic overall fission reaction will not stop, but continue throughout the reaction material. This is then a self-propagating and thus self-sustaining chain reaction. This is the principle for nuclear reactors and atomic bombs . Demonstration of a self-sustaining nuclear chain reaction
10465-399: The rate law ( 5 ) d [ CH 4 ] d t = k 1 2 k 4 k 2 [ CH 3 CHO ] 3 / 2 {\displaystyle (5){\frac {d{\ce {[CH4]}}}{dt}}={\frac {k_{1}}{2k_{4}}}k_{2}{\ce {[CH3CHO]}}^{3/2}} , which is order 3/2 in
10580-533: The rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. The constant k {\displaystyle k} is the reaction rate constant or rate coefficient and at very few places velocity constant or specific rate of reaction . Its value may depend on conditions such as temperature, ionic strength, surface area of an adsorbent , or light irradiation . If
10695-464: The rate. The rate law for a first order reaction is The unit of k is s . Although not affecting the above math, the majority of first order reactions proceed via intermolecular collisions. Such collisions, which contribute the energy to the reactant, are necessarily second order. However according to the Lindemann mechanism the reaction consists of two steps: the bimolecular collision which
10810-649: The reactant CH 3 CHO. A nuclear chain reaction was proposed by Leo Szilard in 1933, shortly after the neutron was discovered, yet more than five years before nuclear fission was first discovered. Szilárd knew of chemical chain reactions, and he had been reading about an energy-producing nuclear reaction involving high-energy protons bombarding lithium, demonstrated by John Cockcroft and Ernest Walton , in 1932. Now, Szilárd proposed to use neutrons theoretically produced from certain nuclear reactions in lighter isotopes, to induce further reactions in light isotopes that produced more neutrons. This would in theory produce
10925-457: The reaction goes to completion, the rate equation for the reaction rate v = k [ A ] x [ B ] y {\displaystyle v\;=\;k[{\ce {A}}]^{x}[{\ce {B}}]^{y}} applies throughout the course of the reaction. Elementary (single-step) reactions and reaction steps have reaction orders equal to the stoichiometric coefficients for each reactant. The overall reaction order, i.e.
11040-419: The reaction of n-butyl bromide with sodium iodide in acetone : This same compound can be made to undergo a bimolecular (E2) elimination reaction , another common type of second-order reaction, if the sodium iodide and acetone are replaced with sodium tert-butoxide as the salt and tert-butanol as the solvent: If the concentration of a reactant remains constant (because it is a catalyst , or because it
11155-499: The respective intensive parameters of the system and surroundings are equal. This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state. M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When
11270-525: The simple action of toppling one domino leads to all dominoes eventually toppling, even if they are significantly larger. Numerous chain reactions can be represented by a mathematical model based on Markov chains . In 1913, the German chemist Max Bodenstein first put forth the idea of chemical chain reactions. If two molecules react, not only molecules of the final reaction products are formed, but also some unstable molecules which can further react with
11385-481: The sum of stoichiometric coefficients of reactants, is always equal to the molecularity of the elementary reaction. However, complex (multi-step) reactions may or may not have reaction orders equal to their stoichiometric coefficients. This implies that the order and the rate equation of a given reaction cannot be reliably deduced from the stoichiometry and must be determined experimentally, since an unknown reaction mechanism could be either elementary or complex. When
11500-511: The surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to
11615-593: The surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables. It can be useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges . Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout
11730-406: The surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency ; a system in thermodynamic equilibrium is inanimate. Otherwise, a thermodynamic operation may directly affect a wall of the system. It is often convenient to suppose that some of
11845-405: The surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called
11960-468: The surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy. Another textbook author, J.R. Partington , writes: "(i) An equilibrium state is one which is independent of time ." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that
12075-633: The surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied. A thermodynamic system consisting of
12190-408: The surroundings: where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system. In other words, Δ G = 0 {\displaystyle \Delta G=0} is a necessary condition for chemical equilibrium under these conditions (in the absence of an applied voltage). Thermodynamic equilibrium
12305-421: The system must be isolated; Callen does not spell out what he means by the words "intrinsic factors". Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with
12420-410: The system was in equilibrium . In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium,
12535-454: The system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there
12650-419: The system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than
12765-425: The two systems have the same temperature. The A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called
12880-583: The variation of k ′ {\displaystyle k'} can be measured. For zero-order reactions, the reaction rate is independent of the concentration of a reactant, so that changing its concentration has no effect on the rate of the reaction. Thus, the concentration changes linearly with time. The rate law for zero order reaction is − d [ A ] d t = k [ A ] 0 = k , {\displaystyle -{d[A] \over dt}=k[A]^{0}=k,} The unit of k
12995-471: The whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point. If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and
13110-465: Was accomplished by Enrico Fermi and others, in the successful operation of Chicago Pile-1 , the first artificial nuclear reactor, in late 1942. An electron avalanche happens between two unconnected electrodes in a gas when an electric field exceeds a certain threshold. Random thermal collisions of gas atoms may result in a few free electrons and positively charged gas ions, in a process called impact ionization . Acceleration of these free electrons in
13225-478: Was the first proposal for the mechanism of chemical explosions. A quantitative chain chemical reaction theory was created later on by Soviet physicist Nikolay Semyonov in 1934. Semyonov shared the Nobel Prize in 1956 with Sir Cyril Norman Hinshelwood , who independently developed many of the same quantitative concepts. The main types of steps in chain reaction are of the following types. The chain length
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