Chemical equations deduction

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... 

When the chemical equation is more complex, the equilibrium constant expression is also more complex and the deductions about the equilibrium concentrations of reactants and products are more involved too. 

The equilibrium law can be deduced by assuming that the order of the forward and backward reactions matches the coefficient in the chemical equation. What is the roie of deductive reasoning in science ... 

In short, we may say that there is evidence that the deviations from the relations predicted by the characteristic equations may be due to chemical changes in the substances, which are not taken into consideration in the kinetic deduction of the equations. Weinstein loc. cit.) considers that it is possible to deduce an equation which takes account of these chemical changes as well. It will be sufficient here to re-einphasise the fact that there is at present no characteristic equation known which agrees accurately with the behaviour of a single substance, let alone various substances, over a wide range of temperature. 

These laws lead tlirough mathematical deduction to a network of equations which find application in all branches of science and engineering. Tlie chemical engineer copes with a particularly wide variety of problems. Among them are calculation of heat and work requirements for physical and chemical processes, and the detemiiiiation of equilibrium conditions for chemical reactions and for tlie transfer of chemical species between pliases. 

Classical tliennody namics is a deductive science, in which the general features of macroscopic-system beliaviorfollow from a few laws and postulates. However, the practical application of thermodynamics requires values for the properties of individual chemical species and their mixtures. These may be presented either as numerical data (e.g., the steam tables for water) or as correlating equations (e.g., a P VT equation of state and expressions for the temperatnre dependence of ideal-gas heat capacities). 

Several approaches are suggested for the deduction of information on the causal chemical connectivity of the species, on the elementary reactions among the species, and on the sequence of the elementary reactions that constitute the reaction pathway and the reaction mechanism. Chemical reactions occur by the collisions of molecules, and such an event is called an elementary reaction for specified reactant and product molecules. A balanced stoichiometric equation for an elementary reaction yields the number of each type of molecule according to conservation of atoms, mass, and charge. Figure 1.1 shows a relatively simple reaction mechanism for the decomposition of ozone by light, postulated to occur in a series of three elementary steps. (The details of collisions of molecules and bond rearrangements are not discussed.) All approaches are based on the measurements of the concentrations of chemical species in the whole reaction system, not on parts, as has been the practice. 

Johannes Jacobus van Laar (The Hague, ii July 1860-Tavel sur Clarens, Lake Geneva, 9 November 1938), lecturer in physics in Amsterdam, published an enormous number of papers, mostly providing strict proofs of well-known thermodynamic and other results, criticising the simple but adequate deductions of van t Hoff, Nernst, and other physical chemists. His particular aversion was osmotic pressure. He produced a modified van der Waals equation in which the constants a and b are functions of temperature. His small book on thermodynamics is clear and interesting but disfigured by unnecessary polemics printed in heavy type. Max Planck used a function - /r in chemical thermodynamics. 

Deduction of the mechanism (5.1) and of the rate equations (5.2) is greatly simplified if the various decay processes occur at vastly different rates. Analysis of the case n = 2 exhibits all chemically significant features of the general mechanism. To introduce the ideas of time-scale separation and of a trace intermediate assume that the reactions go to completion, i.e., k = kJ 0. Then, if initially only A is present, the concentrations of A, B, and C are found by direct integration of the rate equations... 

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