NationMaster - Encyclopedia: Extent of reaction

In a chemical reaction system the stoichiometric coefficient of the i–th component is defined as A chemical reaction occurs when vapours of hydrogen chloride and ammonia meet to form a cloud of a new substance, ammonium chloride Chemical reaction is a process that results in the interconversion of chemical substances [1]. The substance or substances initially involved in a chemical reaction are called reactants. ... System (from the Latin (systÄ“ma), and this from the Greek (sustÄ“ma)) is an assemblage of entity/objects, real or abstract, comprising a whole with each and every component/element interacting or related to another one. ...

where N_i is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37 & 62). The extent of reaction can be regarded as a real (or hypothetical) product, one molecule of which is produced each time the reaction event occurs. In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. ...

The stoichiometric coefficient ν_i represents the degree to which a chemical species participates in a reaction. The convention is to assign negative coefficients to "reactants" (which are consumed) and positive ones to "products". However, any reaction may be viewed as "going" in the reverse direction, and all the coefficients then change sign (as does the free energy). Whether a reaction actually will go in the arbitrarily selected forward direction or not depends on the amounts of the substances present at any given time, which determines the kinetics and thermodynamics; i.e. whether equilibrium lies to the "right" or the "left". The free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ... Water and steam are two different forms of the same chemical substance A chemical substance is any material with a definite chemical composition, no matter where it comes from. ... In physical chemistry, chemical kinetics or reaction kinetics study reaction rates in a chemical reaction. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... Chemical equilibrium is the state in which the concentrations of the reactants and products have no net change over time. ...

If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since elementary reactions always involve whole molecules. If one uses a composite representation of an "overall" reaction, some may be rational fractions. There are often chemical species present which do not participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species which is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero. In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs. ... The integers are commonly denoted by the above symbol. ... In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ... A cake divided into four equal quarters. ... It has been suggested that this article or section be merged into Catalysis. ...

The simplest possible case is an isomerism In chemistry, isomers are molecules with the same chemical formula and often with the same kinds of bonds between atoms, but in which the atoms are arranged differently. ...

in which ν_B = 1 since one molecule of B is produced each time the reaction occurs, while ν_A = −1 since one molecule of A is necessarily consumed. In any chemical reaction, not only is the total mass conserved, but also the numbers of atoms of each kind, and this imposes a corresponding number of constraints on possible values for the stoichiometric coefficients. Of course, only a small subset of the possible atomic rearrangements will occur. (The Lomonosov-Lavoisier law) states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... Properties For other uses, see Atom (disambiguation). ... The periodic table of the chemical elements is a tabular method of displaying the chemical elements, first devised in 1869 by the Russian chemist Dmitri Mendeleev. ... A is a subset of B, and B is a superset of A. In mathematics, especially in set theory, a set A is a subset of a set B, if A is contained inside B. The relationship of one set being a subset of another is called inclusion. ...

There are usually multiple reactions proceeding simultaneously in any natural reaction system, including those in biology. Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i–th component in the k–th reaction is defined as Galunggung in 1982, showing a combination of natural events. ... Biology (from Greek Î²Î¯Î¿Ï‚ Î»ÏŒÎ³Î¿Ï‚, see below) is the branch of science dealing with the study of living organisms. ... In general, a things components are its parts; the things that compose it. ...

so that the total (differential) change in the amount of the i–th component is

Extents of reaction provide the clearest and most explicit way of representing compositional change, although they are not yet widely used.

With complex reaction systems, it is often useful to consider both the representation of a reaction system in terms of the amounts of the chemicals present { N_i } (state variables), and the representation in terms of the actual compositional degrees of freedom, as expressed by the extents of reaction { ξ_k }. The transformation from a vector expressing the extents to a vector expressing the amounts uses a rectangular matrix whose elements are the stoichiometric coefficients [ ν_i k ]. The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ... In mathematics, a vector space (or linear space) is a collection of objects (known as vectors) which may be scaled and added; all linear combinations of vectors are themselves vectors. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...

The maximum and minimum for any ξ_k occur whenever the first of the reactants is depleted for the forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the reverse direction. This is a purely kinematic restriction on the reaction simplex, a hyperplane in composition space, or N‑space, whose dimensionality equals the number of linearly independent chemical reactions. This is necessarily less than the number of chemical components, since each reaction manifests a relation between at least two chemicals. The accessible region of the hyperplane depends on the amounts of each chemical species actually present, a contingent fact. Different such amounts can even generate different hyperplanes, all of which share the same algebraic stoichiometry. The largest and the smallest element of a set are called extreme values, or extreme records. ... This article or section may be confusing for some readers, and should be edited to be clearer or more simplified. ... In geometry, a simplex (plural: simplices) or n-simplex is an n-dimensional analogue of a triangle. ... A hyperplane is a concept in geometry. ... :For other senses of this word, see dimension (disambiguation). ... In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. ... [[Media:[[Media: == Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry) is the calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations). ...

In accord with the principles of chemical kinetics and thermodynamic equilibrium, every chemical reaction is "reversible", at least to some degree, so that each equilibrium point must be an interior point of the simplex. Consequently, extrema for the ξ's will not occur unless an experimental system is prepared with zero initial amounts of some products. In physical chemistry, chemical kinetics or reaction kinetics study reaction rates in a chemical reaction. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... In mathematics, the interior of a set S consists of all points which are intuitively not on the edge of S. A point which is in the interior of S is an interior point of S. The notion of interior is in many ways dual to the notion of closure. ...

The number of physically independent reactions can be even greater than the number of chemical components, and depends on the various reaction mechanisms. For example, there may be two (or more) reaction paths for the isomerism above. The reaction may occur by itself, but faster and with different intermediates, in the presence of a catalyst.

The (dimensionless) "units" may be taken to be molecules or moles. Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules. The N's and ξ's are reduced to molar units by dividing by Avogadro's number. While dimensional mass units may be used, the comments about integers are then no longer applicable. In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... The mole and its simple conversions into different units of measurements. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... Unsolved problems in physics: What causes anything to have mass? Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to. ...

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Non-equilibrium thermodynamics is a branch of thermodynamics concerned with studying time-dependent thermodynamic systems, irreversible transformations and open systems. ...

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