Library

Notes: The program given here assembles and solves symmetric positive-definite equations as met in finite element applications. The technique is more involved than the standard band-matrix algorithms, but it is more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print-out.

Notes: In the design of a guyed mast the design specification often imposes limits on the allowable deflection of the mast under wind and other lateral loads. While the deflected form of a mast depends on many different design parameters, the guy erection tensions form one of the simplest means of controlling the lateral displacements. The paper describes a procedure for calculating these tensions in the case of a mast required to have a specified set of displacements under a given set of lateral loads. It also discusses the case where specified deflections are not to be exceeded under a number of different loading conditions.

Notes: This paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.

Notes: The transient field problem of the type encountered in heat conduction problems is formulated in terms of the finite element process using the Galerkin approach. Curved two-dimensional and three-dimensional, isoparametric elements are used in a time-stepping solution and their advantages illustrated by means of several examples.

Notes: The proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.

Notes: A numerical method for the analysis of field problems is described. The algorithm is based upon the generalized Betti-Maxwell theorem. Using a set of known solutions to problems with similar boundary conditions produces a set of ‘integral’ equations for the required solution. Using any convenient numerical integration formula reduces the problem to the solution of a set of simultaneous algebraic equations. The accuracy of the solution depends upon the accuracy of the integration formula as applied to the problem under consideration and is independent of the known auxiliary solutions. The method is described in detail as applied to harmonic problems.

Notes: Considerable attention has been devoted in the literature on numerical methods towards securing energy convergence of solutions for, say, linearly elastic plate bending problems. Although energy convergence is necessary it by no means follows that the derived bending moments and shearing forces converge uniformly at a given point and it is this kind of feature which the engineer is really seeking.This question is examined in the context of a problem which is of particular interest to the civil engineering field and concerns the bending of a square plate under uniformly distributed load; the plate has simply supported edges and contains a central square hole with free edges. The solution to this multiply connected and mixed boundary value problem is obtained through a recently developed modification to the Rayleigh-Ritz method which has very general application and renders the solution mathematically valid up to the internal corner points where the bending moments are singular. Use is made of triangular equilibrium finite elements in conjunction with continuous eigenfunctions. Although it is already known that the order (i.e. the eigenvalue) of the singularity at the internal corners is available by inspection, it is an interesting feature of the present solution that a good approximation to the amplitude is also obtained by an inspection of the finite element results.

Notes: The convergence rates of eigenvalue solutions using two finite plate bending elements are studied. The elements considered are the well-known 12 degree of freedom, non-conforming rectangular element and the 16 degree of freedom, conforming rectangular element. Three problems are analysed, a square plate simply supported on two opposite sides with the other two sides clamped, simply supported, or free. Closed form, finite element solutions for these problems are obtained by using shifting E-operators.With few exceptions, eigenvalue solutions found with the non-conforming element converge from below the exact answers at an asymptotic rate of n-2, where n is the number of elements on a side. However, since the array size needed for such convergence is very large, little can be said about the convergence rates for practical arrays. The conforming element solutions converge from above at an asymptotic rate of n-4. A comparison of the errors involved in using these two elements shows that the conforming element is far superior to the non-conforming element.

Notes: This paper presents a labour-saving method of discretizing irregular and inhomogeneous two-dimensional continua into triangular elements. The method uses a magnetic pen to record node point data and a computer program to generate element data. This technique eliminates the tedium in the manual generation of data and the delay due to mistakes which would otherwise arise frequently for a complex mesh.

Notes: A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.

Notes: A numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro-differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presented.

Notes: This paper is concerned with the development of general discrete models for the analysis of boundary-value problems in the first strain-gradient theory of elasticity. Extensions of the finite element method are constructed for this purpose, and general equations of motion are derived for finite elements of a class of micro-polar materials which are characterized by strain energy functions involving strains and second gradients of strains or displacements. The notion of generalized nodal doublets is introduced. The problem of a composite consisting of a strain-gradient sensitive microlayer embedded between semi-infinite bodies is examined as an example problem. Some of the results are compared with available exact solutions.

Notes: Methods for the analysis of complex, highly redundant structures subjected to intermittent loads causing biaxial membrane stress and stress reversal into the plastic range are presented. The Bauschinger effect in multi-axial stress is taken into account by the use of Ziegler's modification of Pragers kinematic hardening theory. The implementation of this plasticity theory in the discrete element methods involves the application of the loading in small increments. A linear relationship between increments of plastic strain and of stress, arising out of the theory, is used in conjunction with a linear matrix equation that governs the elastic behaviour of the structure. In the latter equation, plastic strains are interpreted as initial strains. A solution to the linear matrix equation, expressed in terms either of stress or of total strain, may be obtained by utilizing one of two alternative procedures. The methods are capable of treating materials which exhibit elastic-plastic behaviour involving ideal plasticity, linear or non-linear strain hardening, or limited strain hardening. Application is made to several representative structures. Comparison of some of the results with existing test data for both monotonic and reversed loading shows good correlation.

Notes: A general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi-storey building frames is outlined, and numerical results are presented for a simple test case and for a 19-storey frame.

Notes: A newly developed numerical Laplace transform inversion technique is described. A derivation of the method, termed the ‘multidata method’, is presented along with a description of a similar collocation method. Similarities and differences between the two numerical methods are described and discussed. Results of parameter studies of both methods are presented which demonstrate the sensitivity to error displayed by the collocation method and the magnitude of the improvement in accuracy obtainable with the multidata method as compared with the collocation method, especially when errors exist in the function to be inverted.

Notes: In this study, finite element solution procedures are developed for an elastica problem of inextensible beams. The element stiffness matrices are obtained by using Galerkin's method. Results of a numerical example compare reasonably well with those obtained by using the elliptical integral.Extensions of this research are currently being made to include membrane effects of beams and to develop plate element stiffness matrices for elastica problems of plate structures.

Notes: This report summarizes an experimental application of the finite element approach to two-dimensional inviscid fluid flow.The method results in a matrix equation relating the vector of velocities at the nodal points with the vector of singularities. The singularities, which are concentrated at the nodes, consist of a source and a vortex.On solution of this equation (defining the flow in the region), boundary conditions must te stipulated. This usually involves setting the internal singularities to zero and making certain modifications ro those lying on the boundary of the region.Some results of the application to a particular problem are included in the paper.

Notes: Some typical results of an extensive series of evaluations of parallelogram-shaped plate bending elements with increasing levels of sophistication are presented. It is shown that, contrary to experience in other fields of stress analysis, this sophistication does not lead to striking improvements in accuracy in the solution of simple rectangular and skew plate problems. A computational procedure is described whereby stiffness matrices may be automatically generated from the minimum of input data specifying the displacement modes prescribed for the element.

Notes: A conforming plate bending solution using simple polynomial deflection functions of third-degree inside each triangular element is presented. In order to avoid normal slope discontinuities along the sides of the elements, the plate displacement parameters are subjected to ‘slope continuity conditions’ acting as constraints to the minimum potential energy problem. This is then solved by the classical method of Lagrange introducing multipliers as new auxiliary variables. If a special variational formulation of the problem is used, it can be shown that the Lagrangean multipliers are generalized stress parameters. The suggested solution is therefore basically a ‘mixed’ solution, the unknown variables of the problem being both displacement and stress parameters. Several numerical results are presented.

Notes: Approximate formulations of non-uniform beam element stiffness matrices for dynamic and elastic instability analysis are derived. Displacement functions for the uniform beam segment are employed in this development. Moment of inertia and area of the element are prescribed by arbitrary powers of the axial co-ordinate. Numerical results are obtained and compared with both analytical solutions and numerical solutions based upon stepped representations using uniform section elements. The significance of the inclusion of taper considerations within individual elements upon solution accuracy and convergence characteristics is also examined. This subject problem and solution approach demonstrates that the upper bound character of minimum energy solutions may be difficult to exploit under practical circumstances.

Notes: This article describes-a new method, suitable for use on a digital computer, for evaluating the singular double integral of Hayes which determines the transonic wave drag of a slender body. Comparison with known exact results and with an earlier computer program described by Eminton shows the present method to be accurate as well as economic in computer time.

Notes: The complementary variational principle has been used to derive the differential equations and the associated boundary conditions of the vibrating plate in terms of bending moments. It is shown that in this formulation, the plate possesses an infinite number of zero frequency modes in which the plate remains in a state of constant strain under a set of self-equilibrating bending moments. In applying the Rayleigh Ritz procedure for the non-zero frequency modes of the plate, it is shown that it the assumed functions are orthogonal to only a finite number of zero frequency modes, then one may obtain frequencies which are lower than the true frequencies of the plate. An iliustrative example is given in the paper.

Notes: Convergence of a finite element procedure for the solution of the fourth-order equations is proved. A generalization of this result is mentioned and some remarks concerning the numerical results obtained at the Computing Centre of the Technical University in Brno are given.

Notes: Digital filters are finding wide applications in signal processing aspects of such fields as engineering, geophysics and biosignal analysis. The design of a digital filter and its realization with near minima computer word length are two problems which can be solved by computer-aided design techniques In this paper, the automated design of the initial filter (recursive type) only is considered. Both of the basic design methods - the direct and indirect approaches - have been analysed, and compute programs have been written to implement the various design techniques. The present program are limited to the design of flat loss type filters specified by their gain rather than their phase character istics. although provision has been made to allow for other types of design in the indirect approach Design examples are given, and the results analysed with a view to the suitability and limitations of the different design techniques.

Notes: This paper demonstrates the applicability of general non-linear programming methods to the solution of buckling problems. The minimum energy formulation of the buckling condition is shown to yield an unconstrained non-linear programming problem, for which several numerical methods of solution are readily available. Some of these methods are discussed and numerical results are presented for stiffened plates with in-plane as well as lateral loads.

Notes: Stiffness matrices are formulated for the torsional and lateral stability analysis of structures composed of flexural members by the matrix displacement method. The formulations are based upon approximate displacement fields which represent the action of the element in simple flexure. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristics of the derived formulations.

Notes: A solution has been formulated, which allows one to analyse all the major performance characteristics in a chain of impacting elastic ‘rods’. By allowing one end of the elastic chain to impact against a surface which resists penetration according to a specified penetration law it is possible to analyse the impact system of a variety of mechanical devices such as percussive tools and squeeze film dampers. Virtually, unlimited variety in the number and geometry of the impacting rods, and virtually unlimited complexity in the form of the reaction of the terminal face is permitted. A computer program for treating one or two elastic rods has been developed. The program prints out all important stresses as well as the stress history at several selected points. It also prints out the depth of penetration, the energy transferred from rod to rod, the overall energy transfer into the receiver, rebound velocities and times of separation between rods and between rod and 4receiver. Agreement with exact solutions and experiments is demonstrated.

Notes: A technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method. The technique is applied to axisymmetric situations in which statically indeterminate conditions occur and is shown to provide a means for resolving these conditions in terms of contact stresses. Three typical engineering problems are analysed to demonstrate the technique in cases where body forces, thermal gradients and external applied forces are acting.

Notes: Recent advances in finite element techniques have enabled full three-dimensional stress analyses to be undertaken. Economy and accuracy can only be achieved simultaneously if the characteristics of the element are understood. Preparatory work is described in which suitable pitching and disposition of brick-type elements are established for the analysis of cylinders.The information derived is put to use in the analysis of a cylinder-cylinder intersection. A favourable comparison is made with an independently computed solution.

Notes: The velocity field of a semi-contained turbulent jet, as constructed by Abramovich, is used to arrive at the temperature distributions in the initial region of a turbulent flow film cooling situation taking into account both the development of the jet boundary layer and the wall boundary layer. After suitable profiles of eddy thermal conductivity are established, a finite difference form of the thermal energy equation is derived, shown to be unconditionally stable, and solved numerically with the aid of an IBM System 360 computer to yield the temperature distributions. Wieghardt's parameter for collapsing the temperature profiles onto a single curve in film cooling situations, when suitably modified, also collapse the analytical results to essentially a single curve even as near as 2·7 slot heights from the injection point, thus verifying the temperature similarity in film cooling which has been experimentally observed even very near the injection point. Results in graphical form are presented which allows one to construct the actual temperature profile for a fairly wide range of the relevant parameters.

Notes: A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation.A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation.A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations.Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used.The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.

Notes: A finite element method to determine unsteady aerodynamic influence coefficients, consistent with the stiffness and inertia properties of a lifting surface in supersonic flow, is described. This is basically a kinematic method, which reduces the dynamical equations of a non-conservative system to a simple and elegant form. It is illustrated by application to a delta wing using triangular elements to calculate steady and unsteady lift and moment coefficients. Throughout the calculations only a coarse grid system has been employed and the answers have been compared with available results.

Notes: A simple program carrying out various vector operations in two- or three-dimensional spaces is presented. The listings are given in A.S.A. FORTRAN IV. The program is of particular application in various forms of three-dimensional and shell analysis as it can create and transform locally orthogonal co-ordinates, etc. While these applications motivated its design, it is of very general use one such application is illustrated by applying the program to general perspective projection.

Notes: A procedure is presented for the automatic renumbering of network type equations prior to solution by sparse matrix techniques. The method takes an arbitrary input sequence and creates an order which makes possible solution of complex network systems by reducing demand for computer storage and time.Examples are presented to demonstrate the procedure in action and show that, even in cases where the system has been carefully numbered, considerable improvement can be achieved. The procedure is also applicable to band matrix solution techniques.

Notes: This paper deals with solving two-dimensional variational problems of second- and third-order by the finite element method. To each meshpoint are associated three or six basic functions of class C1 or C2. The expression of the admissible functions on a triangular and rectangular element are given here in a general form which is specially suitable for computation.

Notes: The eigenvalue method is well-known as an aid to the solution of a wide range of engineering problems. In power system analysis it has relevance to travelling wave phenomena,1 sensitivity and dynamic stability in synchronous multimachine2 systems, critical speed calculation, vibration of structures and other related topics. The method of numerical solution of eigenvalues depends on the size and nature of the problem and often where large matrices are involved presents great difficulties.This paper describes in detail the application of the escalator method and diakoptics to large eigenvalue problems. The escalator method is a well-established one which consists of a systematic way of escalating from a 2 × 2 matrix up to any desired order in steps of one row and column at a time. The diakoptical method reduces computer storage, calculation time and improves accuracy. This results in the more economical solution of large and complicated problems which cannot be conveniently solved by any orthodox method. The paper deals with problems of degeneracy and means of overcoming these by simple routine processes. It concludes by indicating the particular advantages of the method and its usefulness for a wide variety of general engineering problems.

Notes: In any mesh, rules exist that interrelate the number of internal and external sides, vertices, etc. and the total number of elements. These are given explicitly for plane meshes of triangles and quadrilaterals, and for solid meshes of tetrahedra and cuboidal elements. The method is quite general and discovers all such independent rules that exist. Thus, for a plane mesh of T elements having Vi internal and Vb boundary vertices and Si internal and Sb boundary sides, then \documentclass{article}\pagestyle{empty}\begin{document}$$\begin{array}{l} T = \frac{1}{3}\left({S_b + 2S_i} \right) = V_b + 2V_i + 2H - 2\quad{\rm (for\,triangular\,elements)}\\ T = \frac{1}{4}\left({S_b + 2S_i} \right) = \frac{1}{2}\left({V_b + 2V_i} \right) + H - 1\quad{\rm (for\,quadrilateral\,elements)} \\ \end{array} $$\end{document} where H is the number of internal boundaries (holes) there might be. For solid meshes, these two-dimensional equations relating elements to sides generalize to \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} T = \frac{1}{6}\left({F_b + 2Fi} \right){\rm\quad (for\,cuboid\,elements)} \\ T = \frac{1}{4}\left({F_b + 2Fi} \right){\rm\quad (for\,tetrahedral\,elements)} \\ \end{array} $$\end{document} where there are Fb boundary and Fi internal faces. Unfortunately, there is no direct generalization of the two-dimensional equations relating vertices and elements: it is only possible to do this by including the Ei internal and Eb boundary edges: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} T = \frac{1}{8}E_b + \frac{1}{2}\left({E_i - V_i + H - h - 1} \right){\rm\quad (for\,cuboid\,elements)} \\ T = \frac{1}{3}E_b + E_i - V_i + H - H - 1{\rm\quad (for\,tetrahedral\,elements)} \\ \end{array} $$\end{document} where there are H through holes and h cavities.

Notes: The stiffness equation is derived for curved elements of orthotropic axi-symmetric thin shells, and equivalent applied loads are found for shells subjected to initial strains, applied surface loads and body forces. The Lure approximation of thin shells and displacement field approximation by polynomials of arbitrary degree are included in the formulae derived.

Notes: A computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.

Notes: A novel integral equation technique is employed for the analysis of dynamic stability problems. The governing equation of the linearized parametric resonance problem is transformed into an integral equation. The kernel of the integral equation is computed as the influence function for the deflection and/or bending moment of a corresponding beam.The highest derivative of the governing function (in our case fourth derivative of the displacement function) is chosen as the basic unknown. Using the formal analogy with the differential equation of the beam flexure this highest derivative is comprehended as some unknown transverse ‘load’. The distribution of this ‘load’ is a priori assumed to be polygonal. Using elementary methods of structural analysis, the displacements due to the assumed ‘load’ are determined. These displacements, arrayed into a square matrix, approximate the kernel of the governing integral equation.The subsequent procedure via Hill's determinant is a conventional one. The results prove to be accurate enough even for a very modest number of points of integration. This reflects the fact that the method is based on numerical integration rather than on numerical differentiation.

Notes: The feasibility of achieving a preassigned stress state by changing the stiffness of determinate and indeterminate pin connected structures is presented. A new force method with all element forces (or stresses or areas) as independent variables is developed. The possibility but futility of getting the element areas by inverting and pre-multiplying the coefficient matrix with the external load vector when areas are chosen as variables is shown. The relationship existing between the compatibility equations and the plastic strength of pin connected structures is illustrated. Possible design methods for trusses under single or multiplicity of load conditions, the design of truss geometry and the relations between fully stressed and minimum weight structures are examined and illustrated through several examples.

Notes: The gas-phase dehydrogenation of cyclopentene to cyclopentadiene catalyzed by iodine in the range 178-283°C has been found to obey a rate law consistent with the slow rate-determining step, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm I} + {\rm c} - {\rm C}_5 {\rm H}_8 \stackrel{4}{\rightarrow}{\rm HI} + {\rm c} - {\rm C}_5 {\rm H}_7 $\end{document}, log [k4/(1 mole-1 sec-1)] = 10.25 ± 0.08 - (12.26 ± 0.18)/θ, where θ = 2.303RT in kcal/mole. Surface effects are not important. This value of E4 leads to a value of DHf2980 = 82.3 ± 1 kcal/mole and ΔHf298 = 38.4 ± 1 kcal/mole. From difference in bond strengths in the alkane and the alkene, the allylic resonance stabilization in the cyclopentenyl radical is 12.6 ± 1.0 kcal/mole, in excellent agreement with the value for the butenyl radical.Arrhenius parameters for the other steps in the mechanism are evaluated. The low value of A4 (compared with A4 for cyclopentane) suggests a “tighter” transition state for H-atom abstraction from alkenes than from alkanes.

Notes: The absolute rate constants have been measured for several gas-phase chlorine atom-molecule reactions at 25°C by resonance fluorescence. These reactions and their corresponding rate constants in units of cm3 mole-1 sec-1 are: The effects of varying the substrate pressure, total pressure, light intensity and chlorine-atom source on the value of the bimolecular rate constants have been investigated for all these reactions. Conditions under which no competing side reaction occurs were established and the reported rate constants were measured under these conditions. For reactions (2), (5), (6), (7), and 8, there is a discrepancy of a factor of two between the rate constants measured in this work and values in the literature; it is suggested that this is due to an error in the previously measured value of kCH4/kH2 upon which the relative measurements in the literature ultimately depend.

Notes: The kinetics and absolute rate constants for the free-radical chain reaction of tri-n-butyltin hydride with di-t-butyl disulfide have been measured in cyclohexane at 30°. The rate controlling step for chain propagation involves the cleavage of the disulfide bond by an attacking tributyltin radical. The rate constant for this bimolecular homolytic substitution at sulfur is ∼8 × 104 Mole-1 sec-1. Chain termination involves the self-reaction of two tributyltin radicals.The rate constants for attack of tributyltin radicals on some other disulfides and on elemental sulfur have also been measured. The results are compared with literature data for homolytic substitutions on these compounds by a variety of radicals which have their unpaired electron centered on carbon.

Notes: O(1D), produced from the photolysis of N2O at 2139 Å, reacts with N2O in accord with: \documentclass{article}\pagestyle{empty}\begin{document} $$ \begin{array}{*{20}c} {(2)} & {{\rm O}(^1 D) + N_2 {\rm O} \to {\rm N}_2 + {\rm O}_2 } \\ \end{array} $$ \end{document}\documentclass{article}\pagestyle{empty}\begin{document} $$ \begin{array}{*{20}c} {(3)} & { \to 2{\rm NO}} \\ \end{array} $$ \end{document}We have used the method of chemical difference to obtain an accurate measure of k2/k3 = 0.59 ± 0.01. Furthermore, the quantum yield of production of O(3P), either on direct photolysis or on deactivation of O(1D) by N2O, is less than 0.02 and probably zero.

Notes: A method for constructing potential energy surfaces previously proposed by the author has been extended to hydrogen transfer reactions between halide, oxygen, and carbon atoms. A qualitative relation was found between the repulsive energy and the number of anti-bonding electrons. In general, the calculated kinetic isotope effect is in satisfactory agreement with observed values and the contributions by H-atom tunneling to the rate of reaction is smaller than that obtained from other surfaces.

Notes: The kinetics of the nitric oxide catalyzed, homogeneous, gas-phase isomerization of 1,trans-3,trans-5-heptatriene have been studied for temperatures ranging between 130°C and 241°C. The very clean reaction involves exclusive geometrical isomerization about the 5,6-π-bond. The observed rate constants for \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm NO} + trans - {\rm 3,}trans{\rm - 5}\stackrel{1}{\rightarrow}trans - 3,cis - 5 + {\rm NO} $\end{document} can be represented (with standard errors) by log k1 = (7.18 ± 0.06) - (16.75 ± 0.12)/θ, where θ = 2.303 RT in kcal/mole. The consecutive-step reaction mechanism involves addition of NO to the double bond (Ka, b = ka/kb), followed by rotation of the 5,6-C—C bond in the adduct radical (kc.)Analysis of the observed activation parameters shows, that kc is rate-controlling and consequently k1 = kcKa, b. Estimates of kc and Ka, b lead to a value of k1 in good agreement with experiment.Comparing our data with those previously obtained for the similar 1,3-pentadiene system results in a value for the extra stabilization energy generated in the 1,3-heptadienyl radical of 18.5 ± 1.7 kcal/mole. This value is discussed in view of comparable data in the literature.

Notes: Arrhenius parameters have been measured for the abstraction of hydrogen from the C Si, Ge, and Sn tetramethyls: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {k({\rm ml m}^{ - {\rm 1}} {\rm s}^{ - {\rm 1}} )} \hfill & {{\rm for}} \hfill & {{\rm C}({\rm CH}_{\rm 3} )_4 = {{10^{12.0} {\rm e}^{ - 8370} } \mathord{\left/ {\vphantom {{10^{12.0} {\rm e}^{ - 8370} } {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \hfill \\ {k({\rm ml m}^{ - {\rm 1}} {\rm s}^{ - {\rm 1}} )} \hfill & {{\rm for}} \hfill & {{\rm Si(CH}_{\rm 3} {\rm )}_{\rm 4} = {{10^{11.9} {\rm e}^{ - 7300} } \mathord{\left/ {\vphantom {{10^{11.9} {\rm e}^{ - 7300} } {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \hfill \\ {k({\rm ml m}^{ - {\rm 1}} {\rm s}^{ - {\rm 1}} )} \hfill & {{\rm for}} \hfill & {{\rm Ge(CH}_{\rm 3} {\rm )}_{\rm 4} = {{10^{11.7} {\rm e}^{ - 7370} } \mathord{\left/ {\vphantom {{10^{11.7} {\rm e}^{ - 7370} } {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \hfill \\ {k({\rm ml m}^{ - {\rm 1}} {\rm s}^{ - {\rm 1}} )} \hfill & {{\rm for}} \hfill & {{\rm Sn(CH}_{\rm 3} {\rm )}_{\rm 4} = {{10^{11.7} {\rm e}^{ - 7250} } \mathord{\left/ {\vphantom {{10^{11.7} {\rm e}^{ - 7250} } {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \hfill \\ \end{array} $$\end{document} The rate constants correlate with the proton chemical shift, which is related to a polar effect. In all cases except carbon, a hot-molecule β-fluorine rearrangement-elimination reaction occurs following radical combination: \documentclass{article}\pagestyle{empty}\begin{document} $$ ({\rm CF}_3 {\rm CH}_2 {\rm M}({\rm CH}_3 )_3 )^* \to {\rm CF}_2 {\rm CH}_2 + {\rm FM}({\rm CH}_3 )_3 $$ \end{document} We suggest the occurrence of a radical exchange reaction for the Si, Sn, and Ge systems, \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm CF}_3 + {\rm M}({\rm CH}_3 )_4 \rightleftharpoons{\rm CF}_3 {\rm M}({\rm CH}_3 )_4 \to {\rm CH}_3 + {\rm CF}_3 {\rm M}({\rm C}{\rm H}_3 )_3 $$\end{document} with kexchange (CF3 + Sn(Me)4) ∼ 107 ml m-1 s-1.

Notes: The thermal decomposition of 1,2-dichloropropane at atmospheric pressure has been studied in the temperature range 227-590°C, in a flow system. Above 450°C, the reaction is homogenous and unimolecular with a rate constant: \documentclass{article}\pagestyle{empty}\begin{document}$$k = 10^{12.95 \pm 0.15} \exp (- 53,070 \pm 500/RT)\sec ^{ - 1}$$\end{document}Below 450°C, a low activation energy, probably heterogenous process competes with the gas phase reactionThe primary reaction products are HCl and the monochloropropene isomers; the relative amounts of each isomer depend on the temperature in the low but not in the high temperature region. The direction of the HCl elimination is discussed in terms of substituent effects at the α- and β-carbon positions and compared with literature data on similar reactionsSecondary products are formed principally by further pyrolysis of allyl chloride. The first-order rate constant of this reaction is given by: \documentclass{article}\pagestyle{empty}\begin{document}$$ k = 10^{8.54 \pm 0.2} \exp (- 37,275 \pm 700/RT)\sec ^{ - 1} $$\end{document}.

Notes: A record of the time dependence of the difference between two signals, one proportional to the concentration of a reactant or product in one reaction mixture and the other proportional to the concentration of the same or a corresponding substance in another mixture in which the reaction is initiated at the same time as the first, makes it possible to obtain not only the ratio, but also the individual values, of the rate constants for the two reactions. The effects of the experimental variables on a number of measurable parameters are examined, the errors associated with a number of different ways of evaluating the rate constants and their ratio are discussed, and it is shown how conditions can be selected that should provide values whose precisions compare favorably with those attainable by other techniques.

Notes: At 540°C, H2S (0.1 to 5 mm Hg) diminishes the initial rate of pyrolysis of C2H6 (50 mm Hg) into C2H4 + H2 and, even more strongly, the rate of appearance of the traces of nC4H10; on the contrary, the initial rate of formation of the traces of CH4 is practically not modified.A mechanism is proposed in order to interpret these experimental facts.

Notes: A check of the data from comparative rate single-pulse shock tube experiments have been carried out through the use of a new standard reaction, the decyclization reaction of ethylcyclobutane. The rate expressions for cyclohexene and 2,2,3-trimethylbutane have been found to be \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} k({\rm C}_{\rm 6} {\rm H}_{{\rm 10}} \to 1,3 - {\rm C}_4 {\rm H}_6 + {\rm C}_2 {\rm H}_4 ) = 10^{15.3} \exp ( - 33,690/T)\sec ^{ - 1} ,950^ \circ - 1100^ \circ {\rm K,2} - {\rm 6atm} \\ k(t{\rm C}_4 {\rm H}_9 - {\rm iC}_3 {\rm H}_7 \to t{\rm C}_{\rm 4} {\rm H}_{\rm 9} \cdot + {\rm iC}_{\rm 3} {\rm H}_7 \cdot ) = 10^{16.5} {{\exp ( - 36,830} \mathord{\left/ {\vphantom {{\exp ( - 36,830} T}} \right. \kern-\nulldelimiterspace} T})\sec ^{ - 1} ,1000^ \circ - 1100^ \circ {\rm K,2} - {\rm 6atm} \\ \end{array} $$\end{document} in excellent agreement with previously published results. Most of the small discrepancy that does exist is apparently due to the differences between the present and earlier (decomposition of isopropyl bromide) "standard" reaction. For the latter process, the present study yields \documentclass{article}\pagestyle{empty}\begin{document}$$ k({\rm iC}_{\rm 3} {\rm H}_7 {\rm Br} \to {\rm C}_{\rm 3} {\rm H}_6 + {\rm HBr}) \to 10^{13.73} {\rm exp(}{{ - 23,970} \mathord{\left/ {\vphantom {{ - 23,970} {T\sec ^{ - 1} ,800^ \circ - 1000^ \circ {\rm K,2} - {\rm 6}}}} \right. \kern-\nulldelimiterspace} {T\sec ^{ - 1} ,800^ \circ - 1000^ \circ {\rm K,2} - {\rm 6}}}{\rm atm)} $$\end{document} These results confirm the correctness of previously published comparative rate single-pulse shock tube experiments. They demonstrate once again that for the decomposition of paraffin hydrocarbons, calculated preexponential factors are at least an order of magnitude higher than the directly measured number and that the accepted value of the heat of formation of t-butyl radicals ΔHf300(tC4H9·) = 29 kJ (6.8 kcals) is at least 10 kJ too low. Finally, attention is called to recent studies on neopentane decomposition in flow and static systems which are in complete agreement with the present conclusions.

Notes: Dilute mixtures of 4-methyl-l-pentyne have been pyrolyzed in a single-pulse shock tube. The decomposition process involves bond breaking: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm HC} \equiv {\rm C} - {\rm CH}_2 ({\rm i - C}_{\rm 3} {\rm H}_{\rm 7} )\stackrel{k_B}{\longrightarrow}{\rm HC} \equiv {\rm C} - {\rm CH}_2 \cdot ({\rm propynyl}) + {\rm i - C}_{\rm 3} {\rm H}_{\rm 7} \cdot $$\end{document} as well as a molecular reaction: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm HC}\equiv {\rm C} - {\rm CH}_{\rm 2} ({\rm \rm i - C}_{\rm 3} {\rm H}_{\rm 7} )\stackrel{k_M}{\rightarrow}{\rm C}_{\rm 3} {\rm H}_4 ({\rm allene}) + {\rm C}_3 {\rm H}_6 . $$\end{document} The rate parameters are: \documentclass{article}\pagestyle{empty}\begin{document}$$k_{\bf B} = 10^{15.56} \exp {\rm (} - 34,940/T){\rm (sec}^{ - {\rm 1}}) $$ $$\begin{array}{*{20}c} k_{\rm M} = 10^{13.1} \exp {\rm (} - {\rm 29,670/}T){\rm (sec}^{ - {\rm 1}})&{\rm 1100}^ \circ {\rm K, 1}{\rm .5} - 5{\rm atm}\end{array}$$\end{document} The heat of formation of propynyl radical is thus ΔHf300 = 338 kJ mol-1 (80.7 kcal mol-1)· This leads to a propynyl resonance energy of 40 kJ mol-1 (9.6 kcal mol-1).

Notes: The kinetics of the ethane pyrolysis have been studied at temperatures from 550 to 596°C and with 0 to 62% of added nitric oxide. The rates of production of various products were studied by gas chromatography; ethylene, hydrogen, methane, nitrogen, water, nitrous oxide and acetonitrile were found as primary products, with hydrogen cyanide, carbon monoxide, acetaldehyde, n-butane, 1-butene, cis- and trans-2-butene and 1,3-butadiene as secondary products. For all the primary products the orders with respect to C2H6and NO were determined, as were the activation energies at two different percentages of NO (15.7 and 45.5%).Nitric oxide was found to be rapidly consumed with a finite initial rate, and the rate of production of H2O was close to that of C2H4 at higher nitric oxide pressures.A mechanism is proposed which gives good agreement with all of the observed results. Its main features are: (1) Initiation takes place mainly by the unimolecular dissociation of ethane; there is no evidence for or against the process NO + C2H6 → HNO + C2H5; (2) NO scavenges ethyl radicals to form acetaldoxime which decomposes, and in this way the breakdown of C2H5 is hastened; (3) termination takes place mainly by the unimolecular decomposition of acetaldoxime to give inactive products. Some of the relevant rate parameters are evaluated. Reactions are proposed to account for the formation of the secondary products observed.

Notes: Nitrogen quantum yields are reported for the photolysis of C2F5N=NC2F5 at 3660 Å over the pressure range 2-10 cm from 25° to 150°c. The Stern-Volmer plots obtained are discussed and compared with those obtained with azoethane and azoisopropane.

Notes: The kinetics of the decomposition of benzotrifluoride was studied from 720°c to 859°c in a flow system with and without carrier gas. Consideration of the product distribution made possible the study of the decomposition into CF3 and C6H5 radicals, which appeared to be truly homogeneous in character. The first-order rate constant of the C—C bond fission, log k (sec-1) = (17.9 ± 0.5) (99.7 ± 2.5)/θ, did not change with change of initial concentration, pressure of the carrier gas, or contact time. The Arrhenius parameters have been related to the appropriate thermodynamic data. Assumption of 0 kcal/mole for the activation energy of the reverse combination reaction yielded DH298°(C6H5—CF3) = 103.6 ± 2.5 kcal/mole and ΔHf298°(C6H5) = 77.1 ± 3.0 kcal/mole.Applicability of the simple first-order formula to calculation of the rate constant has been also dealt with.

Notes: Combination reactions of the methyl radical have been studied by following the decay of the absorbance of the methyl radical during the course of the reaction by means of kinetic spectroscopy. The limiting values of the second-order rate constants at high pressure were determined for two reactions at room temperature: \documentclass{article}\pagestyle{empty}\begin{document}$ \begin{array}{*{20}c} {{\rm CH}_{\rm 3} + {\rm CH}_{\rm 3} ( + {\rm M}) \to {\rm CH}_{\rm 3} {\rm CH}_{\rm 3} ( + {\rm M}):k_1 = (2.6 \pm 0.3) \times 10^{10} 1{\rm mole}^{ - {\rm 1}} \sec ^{ - 1} } \\ {{\rm CH}_{\rm 3} + {\rm NO }( + {\rm M}) \to {\rm CH}_{\rm 3} {\rm NO }( + {\rm M}):k_2 = (2.4 \pm 0.2) \times 10^9 1{\rm mole}^{ - {\rm 1}} \sec ^{ - 1} } \\ \end{array} $\end{document} The extinction coefficient of the methyl radical was found to have a maximum value of (1.02 ± 0.06) X 104 1 mole-1 cm-1 at 216.4 nm. Integration of the extinction coefficient over the absorption band of the methyl radical gave an oscillator strength of 1.0 X 10-2.

Notes: A simple electrostatic model of point dipoles is used which permits direct calculation of the activation energies for the addition of the molecules H2O, H2S, H3N, and H3P to olefins. These calculated values agree with the known experimental data to within ±2 kcal/mole on the average. It was found that the best fit could be obtained with a polar transition state that corresponded to a reduction in bond order from 1 to ½ for the bond-breaking coordinates and an increase in bond order from 0 to 0.18 for the bond-forming coordinates. The replacement of a hydrogen atom of the species H2O, H2S, H3N, or H3P by a polarizable methyl group is expected to stabilize the charge on the central atoms. The following stabilization energies for the pairs H2O—CH3OH, H2S—CH3SH, H3N—CH3NH2, H3P—CH3PH2 were calculated: -4.8 kcal/mole, -0.7 kcal/mole, -1.9 kcal/mole, -0.8 kcal/mole, respectively.

Notes: The reaction of trifluoromethyl radicals with ammonia in the gas phase has been studied in the temperature range 30-352°. Product formation is not explicable simply in terms of the reactions: \documentclass{article}\pagestyle{empty}\begin{document}$\begin{array}{*{20}c} {{\rm CF}_{\rm 3} + {\rm NH}_{\rm 3} \to {\rm CF}_3 {\rm H} + {\rm NH}_2 } \\ {2{\rm CF}_3 \to {\rm C}_2 {\rm F}_6 } \\\end{array}$\end{document} and curvature of the Arrhenius plot at high and low temperatures suggests that there are additional sources of fluoroform.

Notes: The quantitative kinetics of pyrolysis of some cyclic and polycyclic compounds are examined from the point of view of biradical intermediates. Transition state methods for estimating the Arrhenius parameters of the lowest free energy biradical pathway to products in cyclic and polycyclic compound reactions are described and illustrated. A large number of the polycyclic reactions are found to have Arrhenius parameters consistent with the biradical mechanism estimates. Other reactions are found to have much faster experimental rates and must therefore be concerted. The value of activation energy and activation entropy estimates as discriminatory tests of mechanism, i.e., single step (concertedness) or consecutive step processes, is discussed.

Notes: The kinetics of the gas-phase reaction CH3COCH3 + I2 ⇄ CH3COCH2I + HI have been measured spectrophotometrically in a static system over the temperature range 340-430°. The pressure of CH3COCH3 was varied from 15 to 330 torr and of I2 from 4 to 48 torr, and the initial rate of the reaction was found to be consistent with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm COCH}_3 + {\rm I}^{\rm .} \stackrel{1}{\rightarrow}{\rm CH}_{\rm 3} {\rm COCH} + {\rm HI} $\end{document} as the rate-determining step. An Arrhenius plot of the variation of k1 with temperature showed considerable scatter of the points, depending on the conditioning of the reaction vessel. After allowance for surface catalysis, the best line drawn by inspection yielded the Arrhenius equation, log [k1/(M-1 sec-1)] = (11.2 ± 0.8) - (27.7 θ 2.3)/θ, where θ = 2.303 RT in kcal/mole. This activation energy yields an acetone C—H bond strength of 98 kcal/mole and δHf0 (CH3COĊH2) radical = -5.7 ± 2.6 kcal/mole. As the acetone bond strength is the same as the primary C—H bond strength in isopropyl alcohol, there is no resonance stabilization of the acetonyl radical due to delocalization of the radical site. By contrast, the isoelectronic allyl resonance energy is 10 kcal/mole, and reasons for the difference are discussed in terms of the π-bond energies of acetone and propene.

Notes: Reinvestigation of the gas phase thermal reaction of 1,1,2,2-tetramethylcyclopropane (699-759°K) gave for the unimolecular disappearance of reactant, k(TMC) = 1015.27-63.93/θ sec-1, in good agreement with the original results of Frey and Marshall. However, evidence for a high activation energy (E = 79 ± 5 kcal/mole), competitive unimolecular decomposition to 2,3-dimethyl-1 and -2-butenes was also obtained. It is proposed that the serious discrepancy noted [1] between the experimentally observed Arrhenius parameters for the overall reaction kinetics, and those predicted by transition state calculations assuming a biradical mechanism for the isomerization reactions (previously believed to be the only primary reaction mode) can be explained in terms of the increasing importance of the decomposition reactions at higher reaction temperatures.

Notes: The kinetics of the gas-phase dehydrogenation of cyclopentane to cyclopentene is found to be consistent with a slow attack by an I atom (step 4, text) on cyclopentane in the range 282-382°C. The measured rate constants fit the Arrhenius equation, log k4 = 11.95 ± 0.08 - (24.9 ± 0.23)/θ 1 mole-1 sec-1, where θ = 2.303RT in kcal/mole. This leads to a value of ΔHf,2980 = 24.3 ± 1 kcal/mole and a bond dissociation energy DH = 94.9 ± 1 kcal/mole. The latter value is identical with DH0(i-Pr-H) = 95 ± 1 kcal/mole and signifies that cyclopentane and the cyclopentyl radical have the same strain energy. Arrhenius parameters are deduced for all six steps in the reaction mechanism. Surface reactions are shown to be unimportant.Cyclopentyl iodide is an unstable intermediate in the reaction and the rate constant for its bimolecular formation from HI + cyclopentene is found to be log k6 = 8.40 ± 0.29 - (26.9 ± 0.8)/θ 1 mole-1 sec-1. Together with the equilibrium constant, this yields for the unimolecular elimination of HI from cyclopentyl iodide, the rate constant, log k5 = 13.3 ± 0.3 - (42.8 ± 1.2)/θ sec-1.

Notes: The competitive reactions of Br atoms with CH4 and CD4 were studied over the temperature range of 562° to 637°K. Over this temperature interval, the kinetic isotope effect, kH/kD, varied from 3.05 to 2.47 for the reactions \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {{\rm Br} + {\rm CH}_{\rm 4} \stackrel{k_H}{\rightarrow}{\rm HBr} + {\rm CH}_3 } \\ {{\rm Br} + {\rm CD}_{\rm 4} \stackrel{k_D}{\rightarrow}{\rm DBr} + {\rm CD}_3 } \\ \end{array} $$\end{document} The rate constant ratio kH/kD, expressed in Arrhenius form, was found to equal (1.10 ± 0.05) exp (1030 ± 60/RT). A comparison is presented between the experimental result and the result obtained theoretically from absolute rate theory using the London-Eyring-Polanyi-Sato (LEPS) method of constructing the potential energy surface of the reaction. The agreement between theory and experiment is very poor, and this is believed to arise from the highly unsymmetrical nature of the potential energy surface involved in these reactions. A comparison is also presented between the kH/kD values obtained in the Br + CH4-CD4 experiments and the available data on the corresponding Cl + CH4-CD4 reactions.

Notes: The reversible isomerization of cis-hepta-1,3-diene to cis-2-trans-4-heptadiene via a 1,5 hydrogen shift has been investigated kinetically at nine temperatures in the range of 475° to 531°K. Equilibrium is reached near 94% reaction. Some cis-2-cis-4-heptadiene is also formed, but at a rate some 60 times slower than the cis,trans isomer. A least-squares analysis of the data yielded the Arrhenius equation for the isomerization of the cis-hepta-1,3-diene: \documentclass{article}\pagestyle{empty}\begin{document}$$ {{\log k_1 } \mathord{\left/ {\vphantom {{\log k_1 } {\sec ^{ - 1} = {{(11.110 \pm 0.087) - ([33,210 \pm 200]{\rm cal mole}^{ - {\rm 1}} )} \mathord{\left/ {\vphantom {{(11.110 \pm 0.087) - ([33,210 \pm 200]{\rm cal mole}^{ - {\rm 1}} )} \theta }} \right. \kern-\nulldelimiterspace} \theta }}}} \right. \kern-\nulldelimiterspace} {\sec ^{ - 1} = {{(11.110 \pm 0.087) - ([33,210 \pm 200]{\rm cal mole}^{ - {\rm 1}} )} \mathord{\left/ {\vphantom {{(11.110 \pm 0.087) - ([33,210 \pm 200]{\rm cal mole}^{ - {\rm 1}} )} \theta }} \right. \kern-\nulldelimiterspace} \theta }}} $$\end{document} Possible errors in the equilibrium constant measurements are discussed, and employing an equilibrium constant calculated by using group additivity estimates together with the values of k1, we obtained for the reverse reaction \documentclass{article}\pagestyle{empty}\begin{document}$$ {{\log k_2 } \mathord{\left/ {\vphantom {{\log k_2 } {\sec ^{ - 1} = (11.1 \pm 0.15) - ([35,800 \pm 300])}}} \right. \kern-\nulldelimiterspace} {\sec ^{ - 1} = (11.1 \pm 0.15) - ([35,800 \pm 300])}}{{{\rm cal mole}^{ - {\rm 1}} )} \mathord{\left/ {\vphantom {{{\rm cal mole}^{ - {\rm 1}} )} \theta }} \right. \kern-\nulldelimiterspace} \theta } $$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$$ \theta = 2.303RT $$\end{document}.

Notes: The kinetics of the acetaldehyde pyrolysis have been studied at temperatures from 450° to 525°C, at an acetaldehyde pressure of 176 torr and at 0 to 40 torr of added nitric oxide. The following products were identified and their rates of formation measured: CH4, H2, CO, CO2, C2H4, C2H6, H2O, C3H6, C2H5CHO, CH3COCH3, CH3COOCH=CH2, N2, N2O, HCN, CH3NCO, and C2H5NCO. Acetaldehyde vapor was found to react with nitric oxide slowly in the dark at room temperature, the products being H2O, CH3COOCH3, CO, CO2, N2, NO2, HCN, CH3NO2, and CH3ONO2. The rates of formation of N2 and C2H5NCO depend on how long the CH3CHO-NO mixture is kept at room temperature before pyrolysis; the rates of formation of the other products depend only slightly on the mixing period.The pyrolysis of “clean” CH3CHO-NO mixtures (i.e., the results extrapolated to zero mixing time, which are independent of products formed in the cold reaction) are interpreted as follows: (1) There are two chain carriers, CH3 and CH2CHO, their concentrations being interdependent and influenced by NO in different ways: the CH3 radical is both generated and removed by reactions directly involving NO, whereas CH2CHO is generated only indirectly from CH3 but is also removed by direct reaction with NO. (2) An important mode of initiation by NO is its addition to the carbonyl group with the formation of which is converted into ; this splits off OH with the formation of CH3NCO or CH3 + OCN. (3) Important modes of termination are \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {{\rm CH}_3 + {\rm NO} \to {\rm CH}_3 {\rm NO} \to {\rm CH}_2 {\rm NOH} \to {\rm HCN} + {\rm H}_2 {\rm O}} \\ {{\rm CH}_{\rm 2} {\rm CHO} + {\rm NO} \to {\rm CH}_2 ({\rm NO}){\rm CHO} \to {\rm CH}({\rm NOH}){\rm CHO} \to {\rm HCN} + {\rm H}_2 {\rm O} + {\rm CO}} \\ \end{array} $$\end{document} The steady-state equations derived from the mechanism are shown to give a good fit to the experimental rate versus [NO] curves and, in particular, explain why there is enhancement of rate by NO at higher CH3CHO pressures and, at lower CH3CHO pressures, inhibition at low [NO] followed by enhancement at higher [NO].The cold reaction is explained in terms of chain-propagating and chain-branching steps resulting from the addition of several NO molecules to CH3CHO and the CH3CO radical. In the “unclean” reaction it is found that the rates of N2 and C2N5NCO formation are increased by CH3NO2, CH3ONO, and CH3ONO2 formed during the cold reaction. A mechanism is proposed, involving the participation of α-nitrosoethyl nitrite, CH3CH(NO)ONO.It is suggested that there are two modes of behavior in pyrolyses in the presence of NO: (1) In the paraffins, ethers, and ketones, the effects are attributed to the addition of NO to a radical with the formation of an oxime-like compound. (2) In the aldehydes and alkenes, where there is a hydrogen atom attached to a double-bonded carbon atom, the behavior is explained in terms of addition of NO to the double bond followed by the formation of an oxime-like species.

Notes: Equilibrium constants for the reaction CH3COCH2CH3 + I2 ⇌ CH3COCHICH3 + HI have been computed to fit the kinetics of the reaction of iodine atoms with methyl ethyl ketone. From a calculated value of S2980(CH3COCHICH3) = 93.9 ± 1.0 gibbs/mole and the experimental equilibrium constants, ΔHf0(CH3COCHICH3) is found to be -38.2 ± 0.6 kcal/mole. The Δ(ΔHf2980) value on substitution of a hydrogen atom by an iodine atom in the title compound is compared with that for isopropyl iodide. The relative instability of 2-iodo-3-butanone (3.4 kcal/mole) is presented as further evidence for intramolecular coulombic interaction between partial charges in polar molecules. The unimolecular decomposition of 2-iodo-3-butanone to methyl vinyl ketone and hydrogen iodide was also measured in the same system. This reaction is relatively slow compared to the formation of the above equilibrium. Rate constants for the reaction over the temperature range 281°-355°C fit the Arrhenius equation: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm log(}{{k_{\rm 3} } \mathord{\left/ {\vphantom {{k_{\rm 3} } {{\rm sec}^{ - 1} }}} \right. \kern-\nulldelimiterspace} {{\rm sec}^{ - 1} }}{\rm )} = {\rm 13}{\rm .4} - {{(41.9 \pm 0.5)} \mathord{\left/ {\vphantom {{(41.9 \pm 0.5)} \theta }} \right. \kern-\nulldelimiterspace} \theta } $$\end{document} where θ = 2.303RT kcal/mole. The stability of both the ground and transition states is discussed in comparing this activation energy with that reported for the unimolecular elimination of hydrogen iodide from other secondary iodides. The kinetics of the reaction of hydrogen iodide with methyl vinyl ketone were also measured. The addition of HI to the double bond is not rate controlling, but it may be shown that the rate of formation of 1-iodo-3-butanone is more rapid than that for 2-iodo-3-butanone. Both four- and six-center transition complexes and iodine atom-catalyzed addition are discussed in analyzing the relative rates.

Notes: Numerical Methods were used to solve the differential equation for diffusion of a trace gas into a flowing carrier gas having a parabolic velocity profile in a cylindrical tube. Steady state solutions are given in the form of contour diagrams of constant trace gas concentration.

Notes: The reaction of nitrogen atoms with methylacetylene has been studied using a fast-flow low-pressure reactor coupled to a mass spctrometer by a nozzle-beam sampling system. Hydrogen atom concentrations were measured by ESR analysis. Experimental second-order rate constants for the consumption of N atoms, of C3H4, and for the formation of N2 were determined in the temperature range of 283° to 485°K. Product profiles of all stable species and of hydrogen atoms and methyl radicals were obtained for different initial concentrations of the reactants. Two different reaction pathways can be distinguished: one provides for recombination of N atoms, and the second leads to the formation of cyano compounds and other hydrocarbons. Only the latter process is influenced by the addition of hydrogen atoms. Mechanisms for the two pathways are discussed.

Notes: The vibrationally excited molecules CF3CH3* and CF3CD3* have been synthesized by radical combination (produced by ketone photolysis), and HF and DF elimination from them studied as a function of temperature and pressure. Using RRK theory many calculations have recently been made of critical energies for the decomposition of "hot" fluoroethane molecules. Taking CF3CH3* as an example, it is concluded that the empiricism involved in such calculations renders results of doubtful significance. The non-equilibrium kinetic isotope effect is kH/kD = 3.1 at 470°K. Arrhenius parameters are also presented for radical abstraction reactions from the ketone source molecules.