Reactions, law of successive

Ostwald proposed that when two or more new phases may form from existing phase or phases, that is, when new phases are more stable than the existing phase(s), the least stable new phase would form first and then transform into more stable phases. This is called the Ostwald rule, the Ostwald step rule, or the law of successive reactions. An alternative statement of the Ostwald rule is as follows ... 

Closely allied with the concepts of metastable equilibrium and suspended transformations is Ostwald s rule (Ostwald s step rule or law of successive reactions). Essentially Ostwald s rule states that in all processes it is not the most stable state with the least amount of free energy that is initially obtained but the least stable state lying nearest to the original state in free energy (Ostwald 1897). It is easy to see how this rule and the concept of suspended transformations can explain the production of a metastable polymorph through crystallization from a melt or solution. 

Law of Successive Reactions.— When sulphur vapour is cooled at the ordinary temperature, it first of all condenses to drops of liquid, which solidify in an amorphous form, and only after some time undergo crystallisation or when phosphorus vapour is condensed, white phosphorus is first formed, and not the more stable form, violet phosphorus. It has also been observed that even at the ordinary temperature (therefore much below the transition point) sulphur may crystallise out from solution in benzene, alcohol, carbon disulphide, and other solvents, in the monoclinic form, the less stable crystals then undergoing transformation into the rhombic form a similar behaviour... 

On account of the great frequency with which the prior formation of the less stable form occurs, Ostwald has put forward the law of successive reactions which states that wb ft Aw system passes from -a, less. aot pass directly into the most stable of... 

Univariant Systems.—Equilibrium between liquid and vapour. Vaporisation curve. Upper limit of vaporisation curve. Theorems of van t Hoff and of Le Chatelier. The Clausius-Clapeyron equation. Presence of complex molecules. Equilibrium between solid and vapour. Sublimation curve. Equilibrium between solid and liquid. Curve of fusion. Equilibrium between solid, liquid, and vapour. The triple point. Complexity of the solid state. Theory of allotropy. Bivariant systems. Changes at the triple point. Polymorphism. Triple point Sj—Sg— V. Transition point. Transition curve. Enantiotropy and monotropy. Enantiotropy combined with monotropy. Suspended transformation. Metastable equilibria. Pressure-temperature relations between stable and metastable forms. Velocity of transformation of metastable systems. Metastability in metals produced by mechanical stress. Law of successive reactions. 

In crystallization processes involving a material that displays polymorphism, it is quite common for an unstable polymorph to appear first and then transform into a stable form. This observation is summarized by Ostwald s step rule, sometimes referred to as the Law of Successive Reactions, which says that in any process, the state which is initially obtained is not the stablest state but the least stable state that is closest in terms of free energy change, to the original state. What this means, therefore, is that a crystallization process, the initial solid phase, can be the least stable polymorph that will then transform into successively more stable forms until the stable form, at the conditions of the system, is reached. With some systems this can mean the formation of an... 

During the 19th century. Gay Lussac observed that, during crystallization, an unstable form is frequently obtained first that subsequently transforms into a stable form [13]. This observation was later explained thermodynamically by Ostwald [13,16-19], who formulated the law of successive reactions, also known as Ostwald s step rule. This... 

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

The theory of the steady state allows us to set up the rate laws for any assumed set of successive reactions in terms of the concentrations of reactants and resultants, in quantities that are determined by analysis. The rate law is first set up in terms of the concentration of the intermediate, and this is replaced by its value, from the steady-state equation, in terms of compounds present in large... 

Ostwald s law of successive transformation is very important in the consideration of zeolite s)mthesis. According to the law, the first phase formed during a reaction is thermodynamically the least stable, and is replaced by ever more stable phases until the most stable product is formed. However, in some instances, thermodynamically unfavourable products may persist if there is a significant activation energy barrier to the more stable phase. All zeolite structures are metastable with respect to more dense phases. 

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). 

The time required to convert a given fraction of the limiting reagent is a characteristic of the rate equation. A comparison of successive half-times, or any other convenient fractional time, reveals whether a reaction follows any simple-order rate law. Thus, the ratio of the time to reach 75 percent completion to that for 50 percent is characteristic of the reaction order. Values of this ratio for different orders are as follows ... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

The simple theories of reaction rates involve applying basic physical chemistry knowledge to calculate or estimate the rates of successful molecular encounters. In Section 6.3 we present important results from physical chemistry for this purpose in subsequent sections, we show how they are used to build rate theories, construct rate laws, and estimate the values of rate constants for elementary reactions. 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

The idea of in situ generation of known amounts of chemical reagents is an intriguing one that has occupied the attention of many chemists. Electrochemists, in particular, have been notably successful in this regard. The basis for this is, of course, Faraday s law of electrolysis, which states that the quantity of electricity passed (coulombs) is directly proportional to the amount of chemical reaction (equivalents) that takes place at an electrode. As we have seen in Chapter 3, a mathematical expression for this concept is readily apparent ... 

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