Chemical reactions superscripts

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

The student is expected to appreciate that the presence of a term that does not relate to a substance ( 2e ) shows that this particular equation cannot stand for a chemical reaction. (The student is also expected not to confuse superscripts used to denote charge with those showing mass numbers of isotopes.)... 

The reaction is exothermic and the enthalpy change AH° is therefore negative. The heat of reaction —AH° is positive. The superscript ° denotes a value at standard conditions and the subscript r implies that a chemical reaction is involved. 

The total number of atoms on one side of the equation must balance the total number of atoms on the other side. This rule is simply an expression of the well-known chemical fact that atoms are neither created nor destroyed during a chemical reaction. Remember that subscripts and superscripts are labels describing charges and sites and are not counted in evaluating the atom balance. 

Chemical reactions are designated as C, so if the product of electron transfer undergoes a homogeneous chemical reaction we say that it is an EC reaction. The C terms are often given a superscript or subscript to show why type of chemical reaction occurs, e.g. disproportionation, dimerization or catalytic. Table 6.4 lists many of the commonly encountered Reinmuth terms. 

Chemical reactions with one or more intermediates separated by transition states (usually indicated by the superscript symbol t) ... 

When a superscript is used as in AtIH°, it indicates that the change in H is considered for a transition under standard pressure, which usually is chosen as 1 bar. In the case of chemical reactions, the superscript ° refers to standard pressure and to reactants and products in their pure state or otherwise defined standard states such as infinitely dilute solutions. 

To express the heat absorbed or evolved in any chemical reaction, the symbol AH°S is used in which the superscript 0 indicates a standard state and the subscript specifies the temperature at which the reaction occurs. The standard state for a gas is 1 atm pressure and the standard state for liquids is the pure liquid under the same conditions. For solids, it refers customarily to a crystalline state at 1 atm. Unless otherwise denoted, 25°C is the standard state for temperature. 

Now we have two functions that can be used to predict spontaneity the entropy of the universe, which applies to all processes and free energy, which can be used for processes carried out at constant temperature and pressure. Since so many chemical reactions occur under the latter conditions, the free The superscript degree symbol (°) in- energy function is more useful to chemists. 

In order to prove equation (51), it is convenient to consider first the case in which N chemical components are present in each of the P phases and there are no chemical reactions or subsidiary conditions. In writing the thermodynamic properties, the phase will be identified by superscripts and the species will be identified by subscripts. If p, 7, and are known for i 1,..., and for y = 1,..., P, then the state of the system is completely determined (except for the total mass of material in each phase, knowledge of which is seldom wanted). Since... 

Here k" is the rate constant with SI units (mol / m2s) / (mol / m3)n. The rate constant k" for a first order reaction has SI units m/s. The superscript indices " indicate that the reaction takes place at the surface. The minus sign makes hA0 negative, as substance A is consumed in the chemical reaction. If substance A had been generated (2.353) would have a positive sign. 

The superscript c emphasizes that we refer to a chemical reaction. We can also define as the integral of the differential re-... 

In the following the chemical reactions will be described being induced by increasing CO exposure the superscript gas means gaseous, ads means adsorbed in any way. For a better comparison all formulae were referenced to a total of four CO molecules. 

As follows from the assertions in regularity assumptions 2, 3 (see end of Sect. 4.6 and Rem. 19), the matrix of both derivatives in (4.310) has the (maximal) rankn — h (equilibrium values are stressed here by the zero superscript, i.e. these are the values of corresponding quantities at p", T ). Therefore using now zero reaction rates (4.302) in the result (4.310) we obtain a system of homogeneous linear equations torn —h equilibrium affinities with the matrix of rank n - h formed by the equilibrium values of derivatives dJp/dpy. Therefore chemical affinities of independent chemical reactions (and, consequently, also of dependent reactions) must be zero in equilibrium... 

Flere the superscript gen refers to generation of species i, con refers to consumption, and acc refers to accumulation of i in the system. When chemical reactions are occur-ring, the difference between the generation and consumption terms reflects the net effect of reactions (rxn). Moreover, we already have an expression (7.4.15) for the change in species mole numbers due to reactions here we write (7.4.15) in the form... 

The production or source terms are due to the spray droplets and the chemical reactions, as well as to turbulence production and dissipation. The spray source terms are identifled with a superscript, s, and the chemical source terms with a superscript c. In the mass and species equations, the spray source term is which indicates the mass transfer between the liquid and gas phases, e.g., due to evaporation. The Kronecker delta, in the species equation indicates when fuel vapor is transferred to the gas phase, i.e., = 1 if m is a fuel species and... 

The net charge on an ion is represented by a superscript. The superscripts -b, 2-b, and 3-I-, for instance, mean a net charge resulting from the loss of one, two, and three electrons, respectively. The superscripts —, 2—, and 3— represent net charges resulting from the ain of one, two, and three electrons, respectively. Chlorine, with 17 protons and 17 electrons, for example, can gain an electron in chemical reactions, producing the CP ion ... 

Figure 6.12 uses the term AG°. We might also have used AG and AS. This can cause confusion, unless you refer to Figure 4.12 to see that there is no lexical problem, just a difference in how explicit we wish to be. That is, A G° is just a special case of AG. In this case, we are dealing with a chemical reaction (subscript r ), and with pure phases in their (high T) standard states (superscript °), so A,G° is correct, but AG° or AG is not incorrect. 

Superscript i denotes the homogeneous phase for x<0, while o denotes the homogeneous phase for x>0. The fluxes are the values of the normal components of the fluxes in the homogeneous phases. Mass conservation in the presence of chemical reactions is given by ... 

The change in Gibbs free energy of a system, when reactants in their standard states are converted to products in their standard states, is called the molar standard free energy change (AG ) for the reaction. The superscript zero to the G indicates the standard state and the overbar indicates that the molar amounts of the reactants and products given by the numerical coefficients in the balanced chemical equation for the reaction are involved. For the forward reaction of the general chemical reaction (1.5)... 

Standard enthalpy of formation data is employed to calculate the energy liberated (usually) or absorbed during a chemical reaction. If the reactants and products are at the same temperature and in a standard (or reference) state, the enthalpy (heat) of reaction is termed the standard enthalpy (heat) of reaction. For engineering purposes, the standard state of a chemical may be taken as the pure chemical at 1 atm pressure. A superscript zero is often employed to identify a standard heat of reaction, e.g., Af/ . A T subscript (A// ) is sometimes used to indicate the temperature standard heat of reaction data are meaningless unless the temperatures are specified. data (i.e.,... 

These equations illustrate two important conservation laws that must be obeyed when writing equations for nuclear reactions. Just as we do in an ordinary chemical reaction, we balance the number of atoms of each element on both sides of the equation. In a nuclear reaction, we also balance subscripts and superscripts on both sides of the equation. (Unlike the practice in an ordinary reaction, we do not concern ourselves with balancing charges in a nuclear reaction since in a nuclear reaction we are ignoring the electrons anyway and only indicating the nuclei of the atoms.)... 

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