Kinetic treatment of two-stage second-order consecutive reactions with a common factor

Riggs, NV

doi:10.1071/ch9580086

Cited by 5 publications

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“…The deviation was defined as (22) The zero of ( a D ) / ( a b ) was found by means of Newton's method. Figure 2 shows the variation of b with K, for K, values of zero, three, and five.…”

Section: Form Of the Approximate Solutionmentioning

confidence: 99%

“…ting the data obtained from the digitalcomputer integration to Equation (20), through the method of least squares. The deviation was defined as (22) The zero of ( a D ) / ( a b ) was found by means of Newton's method. Figure 2 shows the variation of b with K, for K, values of zero, three, and five.…”

Section: Substitution Of Equationmentioning

confidence: 99%

“…Experimental data have been used (5,21,24,29,30) to determine the individual rate constants for consecutive competitive reaction systems. By suitable treatment of the differental equations Fuoss (8), Natta and Mantica (18), and others (1,4,11,15,22,23,25,26) have derived formulas which describe the distribution of converted A among the products as a function of the rate constants. Product distribution studies for similar but more complex reaction systems have also been reported (2,3,9).…”

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A study of consecutive competitive reaction systems

Friedman

White

1962

AIChE Journal

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Experimental kinetic data are most conveniently correlated by the integrated form of the differential rate equations which the reactions are presumed to obey. A new method of obtaining an approximate integral solution of the differential equations is described and applied to a set of three consecutive competitive reactions.The approximote integral solution is used to correlate experimental data on systems whose stoichiometry would indicate a consecutive competitive mechanism. The compositions of the reaction mixes are predicted with a standard error of estimate of less than 4% of the original concentration of the initiating reactant, in most cases less than 2%. The estimates of the rate constants, found by fitting the approximate solution to the data, are within experimental error of the values obtained by differentiation of the published results.Consider a set of irreversible consecutive reactions carried out at constant temperature k, ( 1 )The differential equations governing the course of the reaction set areatdt Because many addition, substitution, and polymerization reactions are stoichiometrically characterized by Equation ( 1 ) an integrated solution of Equations ( 2 ) is desirable. In the discussion to follow it will be assumed that only A and B are originalIy present and that the density of the system does not change as the reaction proceeds.To date the equations above have not been solved for the general case of any initial composition and any set of rate constants. In fact no solution has been reached for the simpler case in which only A and B are originally present. The equations have been solved for certain initial molar ratios and for particular sets of rate constants (7, 27), but these solutions can- (5,21,24,29,30) to determine the individual rate constants for consecutive competitive reaction systems. By suitable treatment of the differental equations Fuoss (8), Natta and Mantica (18), and others (1,4,11,15,22,23,25,26) have derived formulas which describe the distribution of converted A among the products as a function of the rate constants. Product distribution studies for similar but more complex reaction systems have also been reported (2, 3, 9). Thus, given the rate constants for the reaction set, if the quantity of A in the reaction mix could be computed, product distribution studies could then be used to predict the entire composition of the reaction mix at any time, for any set of initial conditions. Once this can be done, practical problems involving systems of consecutive cometitive reactions can be solved. It will Ee possible to correlate the large body of experimental data on systems whose stoichiometry obeys Equation (1) to see whether the mechanism of the reactions is well represented by the differential rate equations and to find rate constants for the twin purposes of extrapolation and design. Hence the first purpose of this paper is the development of equations describing the time dependence of the concentration of A. M. H. Friedman is with the Minnesota APPROXIMATE S O L U T ...

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“…The deviation was defined as (22) The zero of ( a D ) / ( a b ) was found by means of Newton's method. Figure 2 shows the variation of b with K, for K, values of zero, three, and five.…”

Section: Form Of the Approximate Solutionmentioning

confidence: 99%

Section: Substitution Of Equationmentioning

confidence: 99%

mentioning

confidence: 99%

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A study of consecutive competitive reaction systems

Friedman

White

1962

AIChE Journal

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Maximale Raum‐Zeit‐Ausbeute bei Flüssigphase‐Reaktionen. Teil 2: Konkurrierende Folgereaktionen zweiter Ordnung

Gestrich

Krauß²

1990

Chemie Ingenieur Technik

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Irreversible Reaktion mit unendlich schnellem ersten SchrittHierbei (k,/k, < 0,01) handelt es sich praktisch um eine sehr rasche, vollstandige Vorreaktion des UnterschuRreaktanden S zum Monoester C, der dann (effektive Anfangskonzentration C', = Cg) mit dem Alkohol (effektive Anfangskonzentration Ca = C i -q) abreagiert: Ersetzt man hierin t nach GI. (7), so ergibt sich (9) Fur ein gegebenes Reaktionsvolumen V, ist in GI. (9) Irreversible Reaktion rnit unendlich schnellem zweiten SchrittHierbei (k2/kl > 100) handelt es sich um eine normale Reaktion zweiter Ordnung, r = k , CACs, bei der das Zwischenprodukt C sofort erneut mit A reagiert, so daR als Umsetzung resultiert:2 A + S k1 . P + 2 H,O .und E nach GI. (5) ergibt sich hier der GI. (7) entsprechende Zeitverlauf 1) Eine Zusammenstellung der Formelzeichen befindet sich am SchluB des Beitrags.

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Preparation and Diels‐Alder Reactivity of Tricarbonyliron Complexes of [2.2.2]Hericene

Hänisch¹,

Tagliaferri²,

Roulet³

et al. 1983

Helvetica Chimica Acta

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Treatment of [2.2.2]hericene 10 with Fe2(CO)9 in hexane gave a mixture of monometallic complex 14, two isomeric dimetallic complexes 15 and 16, and a trimetallic complex 19 in which all the three diene moieties of 10, are coordinated. The rate constants of the Diels‐Alder additions of tetracyanoethylene (TCE) and dimethyl acetylenedicarboxylate (DMAD) to the uncomplexed diene moieties of 14–16 have been evaluated and compared with those measured for the uncomplexed 10 and its monoadducts 11A, 11B and bis‐adducts 12A, 12B. The tricarbonyldieneiron function retards the cycloaddition of an homoconjugated, exocyclic s‐cis‐butadiene. The effect is significantly larger for TCE‐ than for DMAD‐additions. The origin of this effect is discussed briefly in terms of the valence‐bond model which is usually assumed to describe the properties of a tricarbonyldieneiron complex, and in terms of the inductive and steric factors of the Fe(CO)3‐group.

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Kinetic treatment of two-stage second-order consecutive reactions with a common factor

Cited by 5 publications

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A study of consecutive competitive reaction systems

A study of consecutive competitive reaction systems

Maximale Raum‐Zeit‐Ausbeute bei Flüssigphase‐Reaktionen. Teil 2: Konkurrierende Folgereaktionen zweiter Ordnung

Preparation and Diels‐Alder Reactivity of Tricarbonyliron Complexes of [2.2.2]Hericene

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