Chemical equations defined

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

A A//-value assigned to a chemical equation defines the enthalpy change occurring when the number of moles of each reactant consumed is equal to its coefficient in the balanced equation. 

For a PVnr system of uniform T and P containing N species and 7T phases at thermodynamic equiUbrium, the intensive state of the system is fully deterrnined by the values of T, P, and the (N — 1) independent mole fractions for each of the equiUbrium phases. The total number of these variables is then 2 + 7t N — 1). The independent equations defining or constraining the equiUbrium state are of three types equations 218 or 219 of phase-equiUbrium, N 7t — 1) in number equation 245 of chemical reaction equiUbrium, r in number and equations of special constraint, s in number. The total number of these equations is A(7t — 1) + r -H 5. The number of equations of reaction equiUbrium r is the number of independent chemical reactions, and may be deterrnined by a systematic procedure (6). Special constraints arise when conditions are imposed, such as forming the system from particular species, which allow one or more additional equations to be written connecting the phase-rule variables (6). 

We will first explore what salt effect is expected for k and k2, and then examine the general situation. It is convenient to proceed by defining the net activation process.15 This is the chemical equation for the hypothetical process in which the transition state is formed from the predominant forms of the reagents, and not from the reactive entities. For the two pathways implicit in Eq. (9-47), these are the net activation processes ... 

This is the relaxation time of the polymer oxidation under electro-chemically stimulated conformational relaxation control. So features concerning both electrochemistry and polymer science are integrated in a single equation defining a temporal magnitude for electrochemical oxidation as a function of the energetic terms acting on this oxidation. A theoretical development similar to the one performed for the Butler-Volmer equation yields... 

A model is one of the main outcomes of ary scientific enquiry and hence is a major contributor to philosophy of science. A model may be defined as a simplified representation of a phenomenon (an object, system, event, process) or idea produced for the specific purpose of providing an explanation of that entity, the most important outcomes of which are the production of successful predictions of how it will behave under a range of circumstances (Gilbert, Boulter, Elmer, 2000). Entities can be modelled at the three levels at the macroscopic, by representing some of the aspects of the entity that can be seen at the sub-microscopic, by representing the ideas produced to explain the constitution and behaviour of the particles that constitute the entity and at the symbolic, by representing the symbols created to simplify the reference to such particles (as, for instance, chemical formulae and chemical equations). 

A hazard can be defined as a situation which may lead to harm, whilst risk is the probability that harm will occur. From the point of view of harm being caused by exposure to a chemical. Equation 1.3 is applicable. 

Both proposed mechanisms for NO2 decomposition contain chemical species produced in the first step and consumed in the second step. This is the defining characteristic of an intermediate. An intermediate is a chemical species produced In an early step of a mechanism and consumed in a later step. Intermediates never appear in the overall chemical equation. Notice that neither the O atoms of Mechanism I nor the NO3 molecules of Mechanism II appear In the balanced chemical equation for NO2 decomposition. 

Mole ratios can be used to determine the amount of one substance needed to react with a given amount of another substance. In this experiment, you will react a substance called an acid with another substance called a base. Acids can be defined as substances that dissociate and produce hydrogen (H+) ions when dissolved in water. Bases are substances that ionize to produce hydroxide (OH ) ions when they dissolve in water. When acids and bases react with each other, the H+ ions and OH ions join to form water (H20). The resulting solution no longer has an excess of either H+ ions or OH- ions. The solution has become neutral. This process is called neutralization. By using the mole ratio of hydrogen ions and hydroxide ions in the balanced chemical equation, you can predict the point at which a solution becomes neutral. 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

A complex reacting system is defined as one that requires more than one chemical equation to express the stoichiometric constraints contained in element balances. In such a case, the number of species usually exceeds the number of elements by more than 1. Although in some cases a proper set of chemical equations can be written by inspection, it is useful to have a universal, systematic method of generating a set for a system of any complexity, including a simple system. Such a method also ensures the correct number of equations (R), determines the number (C) and a permissible set of components, and, for convenience for a very large number of species (to avoid the tedium of hand manipulation), can be programmed for use by a computer. 

Another stoichiometric variable that may be used is the extent of reaction, , defined by equation 2.3-6 for a simple system. For a complex system involving N species and represented by R chemical equations in the form... 

A complete chemical reaction in which no fuel and no oxygen is left is called a stoichiometric reaction. This is used as a reference, and its corresponding stoichiometric oxygen to fuel mass ratio, r, can be determined from the chemical equation. A useful parameter to describe the state of the reactant mixture is the equivalence ratio, d, defined as... 

You are starting with moles of iron and want grams of Fe203 so we ll first convert from moles of iron to moles of Fe203 using the ratio of moles of Fe203 to moles of iron as defined by the balanced chemical equation ... 

Combination of the electrostatic equations with the chemical equations then completely defines the interface. 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

The equivalent to the law of mass action, as encountered in the previous chapter (e.g. in equation (3.22)), are systems of differential equations, defined by the chemical model or the reaction mechanism and the corresponding rate constants. We start with a general chemical reaction, just to practise the notation — it is not a realistic example ... 

The potential of these reactions for methane production can be compared in terms of theoretical yields and heat recovery efficiencies. Theoretical methane yield is defined by the chemical equations. Theoretical heat recovery efficiency is defined as the percent of the higher heating value of the coal which is recovered in the form of methane product. These idealized parameters provide a measure of the ultimate capability of conversion systems and are useful for evaluating actual conversion processes. 

To do this, a model compovind is defined to represent an average molecule of organic matter. This compound is then used in chemical equations to illustrate how metabolic processes act on organic matter and its constituent elements. 

A mathematical simplification of rate behavior of a multistep chemical process assuming that over a period of time a system displays little or no change in the con-centration(s) of intermediate species (i.e., d[intermedi-ate]/df 0). In enzyme kinetics, the steady-state assumption allows one to write and solve the differential equations defining fhe rafes of inferconversion of various enzyme species. This is especially useful in initial rate studies. 

In the reaction, one mole of hydroxide generates one mole of alcohol and one mole of carboxylate ion from one mole of ester. Based on this stoichiometry (the mole relationship as defined by the balanced chemical equation), if the number of moles of base is known, then the amount of ester is known. 

We wish here to obtain the thermodynamic equations defining the liquidus surface of a solid solution, (At BB)2, ). It is assumed that the A and atoms occupy the sites of one sublattice of the structure and the C atoms the sites of a second sublattice. For the specific systems considered here Sb and play the role of C in the general formula above. It is also assumed that the composition variable is confined to values near unity so that the site fractions of atomic point defects is always small compared to unity. This apparently is the case for the solid solutions in the two systems considered. Then it can be shown theoretically (Brebrick, 1979), as well as experimentally for (Hgj CdJ2-yTe)l(s) (Schwartz et al, 1981 Tung et al., 1981b), that the sum of the chemical potentials of A and C and that of and C in the solid are independent of the composition variable y ... 

The said allows us to understand the importance of the kinetic approach developed for the first time by Waite and Leibfried [21, 22]. In essence, as is seen from Fig. 1.15 and Fig. 1.26, their approach to the simplest A + B —0 reaction does not differ from the Smoluchowski one However, coincidence of the two mathematical formalisms in this particular case does not mean that theories are basically identical. Indeed, the Waite-Leibfried equations are derived as some approximation of the exact kinetic equations due to a simplified treatment of the fluctuational spectrum a complete set of the joint correlation functions x(rJ) for kinds of particles is replaced by the only function xab (a t) describing the correlation of chemically reacting dissimilar particles. Second, the equation defining the correlation function X = Xab(aO is linearized in the function x(rJ)- This is analogous to the... 

The practical characteristic of a dyestuff is that when a textile is immersed in a solution containing a dye. the dye preferentially adsorbs onto and diffuses into the texiile. The thermodynamic equations defining this process have been reviewed in detail. The driving force for this adsorption process is the difference in chemical potential between the dye In the solution phase and the dye in the fiber phase. In practice it is only necessary to consider changes in chemical potential and to understand that the driving force is the reduction in free energy associated with the dye molecule moving from one phase to the other, as the molecule always moves to the siate of lowest chemical potential. 

To avoid the ambiguity of more than one rate, chemists have defined a general rate of reaction equal to the rate of consumption of a reactant or formation of a product divided by its coefficient in the balanced chemical equation. Thus, for the reaction... 

In equations 27-29, P(j is the partial distribution coefficient of component ij, Tij is the ratio of activity coefficients, 0 is the reduced standard-state chemical potential difference, xiop is the standard-state chemical potential of component i in phase p, and yf and yxjp are the activity coefficients of components i and ij, respectively, in phase p. The working equations (equations 23-26) describing phase equilibria, along with the equation defining a mole fraction, are implicitly complex relations for T, P, x, y, xAC, xA, xc, and xD but involve only two thermodynamic quantities, 0 and Tiy Equations 23-25 are implicit in composition only through the term, which is itself only a weak function of composition. 

We note from Equation 3.4 that the changing concentrations of the components in the reaction with time are, strictly speaking, only proportional to the rate of reaction, as rigorously defined in Equations 3.1 and 3.2. Experimentally, the instantaneous rates of changes of the concentrations of the components in a chemical equation are usually proportional to the instantaneous concentrations of the components themselves, each raised to some power. Such a relationship is called the rate law, or rate equation, of the reaction. For example, the rate law for the reaction of Equation 3.3 might be Equation 3.5 ... 

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