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A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry. It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by an atom or group. [1] [2] [3] It can be represented generically as: + +
a solution of hydrogen peroxide and an iron catalyst that is used to oxidize contaminants or waste waters Formaldehyde: the simplest aldehyde; an important precursor to many other chemical compounds, such as polymers and polyfunctional alcohols Formic acid: the simplest carboxylic acid; often used as a source of the hydride ion Grignard reagents
In an aqueous solution the hydrogen ions (H +) and hydroxide ions (OH −) are in Arrhenius balance ([H +] [OH −] = K w = 1 x 10 −14 at 298 K). Acids and bases are aqueous solutions, as part of their Arrhenius definitions. [1] An example of an Arrhenius acid is hydrogen chloride (HCl) because of its dissociation of the hydrogen ion when ...
A thermite reaction using iron(III) oxide. The sparks flying outwards are globules of molten iron trailing smoke in their wake. A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. [1]
The material stiffness properties of these elements are then, through linear algebra, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure’s unknown displacements and forces can then be determined by solving this equation.
The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on simply connected bodies. More precisely, the problem may be stated in the following manner. [5] Figure 1. Motion of a continuum body. Consider the deformation of a body shown in Figure 1.
The equations are written only for the small domain of individual elements of the structure rather than a single equation that describes the response of the system as a whole (a continuum). The latter would result in an intractable problem, hence the utility of the finite element method.
In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.