Superscripts with chemical reactions

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.)... 

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

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. 

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... 

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. 

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.)... 

In Eq. (5.8), is the absorbing potential operator for all chemical arrangements and Et)) is a reference scattering state with incoming-wave boundary conditions in channel (u,j, /, J, M Et). The reaction probabihties are independent of the quantum number M, to be defined below. In what follows, we omit the ABC superscript with the understanding that we are using the ABC formulation. 

Note that CD is the second species on the AB side of the reaction (equation 33). The element is then found by permuting B with D in the superscripted chemical labels and b with d in the spin product subscripts in equation 38, right hand side giving equations 39 and 40. Notice the summation is over all terms that are diagonal in c and d (equations 39 and 40). 

It is customary to work with the equilibrium constants Kx, Kc, Km that are related to standard conditions, i.e., to standard rather than reference chemical potentials. Then the superscripts in AG X, AGdc, AG refer to the differential Gibbs free energy changes accompanying the reaction - 0 in... 

AG is considered negative. AG° for the burning of graphite under standard temperature (25°C) and pressure (1 atm), indicated by the superscript °, is -394.4kJ mol-1. Tables of AG° for various reactions are widely available and values of AG° for different reactions can be calculated by simple arithmetic combination of tabulated values. Any reaction with a negative AG value will in theory proceed spontaneously—the chemical equivalent of water flowing downhill —releasing energy. 

By convention, a nuclide is specified as X, where X is the chemical symbol for the element, the superscript A denotes the mass number, and the subscript Z the atomic number of the nuclide. When particles or radiations interact with a nucleus, nuclear reactions occur. For example, a neutron may interact with the nucleus of the nuclide isAl according to... 

In addition, the Pt serves as the electrical conductor to the external circuit. Under standard state conditions, that is, when the H2 pressure equals 1 atm and the ideal concentration of the HCl is 1 M, and the system is at 25°C, the reduction potential for the reaction given in Eq. (15.8) is exactly 0 V. (The potential actually depends on the chemical activity of the HCl, not on its concentration. The relationship between activity and concentration is discussed subsequently. For an ideal solution, concentration and activity are equal.) The potential is symbolized by where the superscript zero means standard state conditions. The term standard reduction potential means that the ideal concentrations of all solutes are 1 M and all gases are at 1 atm other solids or liquids present are pure (e.g., pure Pt solid). By connecting the SHE half-cell with any other standard half-cell and measuring the voltage difference developed, we can determine the standard reduction potential developed by the second half-cell. 

Figure 1 Schematic of the multi-step process of organic degradation in anaerobic systems, indicating the influence of H2. Boxes indieate major chemical pools, arrows with text indicate microbially-mediated process. Superscripts on arrow text indicate the mode of control by H2 (F)—facultative interspecies H2 transfer (O)—obligate interspecies H2 transfer (B)—H2 can be a by-product, shifting the product yield (U)— the reaction becomes thermodynamically unfavorable when H2 concentrations are too low (R)—the process is demonstrated or hypothesized to be reversible, based on H2 concentrations. Note ( ) important inorganic oxidants may include NO, Mn , Fe , and various oxidized sulfur speeies (e.g., S04 ) Xred corresponds to the redueed form (e.g., H2S). Adpated from Ref. [19].

The superscript T in (3.4)-(3.5) denotes a triplet state. Reaction (3.4) is treated in a coherent manner (hyperfine-induced) rather than with the usual chemical kinetics rate constant formalism. Reactions (3.3) - (3.6) have also been investigated in quinone-free reaction centers, to remove the complications of extra interactions of the Q" spin with those of the other radicals. We focus later on whether (3.1)-(3.2) involves one or two steps. 

A radical species is a species with an un-accommodated electron. These species, such as radical ions, are mainly found in organic chemistry as reaction intermediates. They are unstable and react very quickly to form a different, more stable species. This free electron is symbolized by a superscript point beside the chemical symbol. 

Photosensitized oxidation reactions involve a process in which the excited state of a photosensitizer produces a highly reactive oxygen specie such as an excited singlet oxygen ( O2), a superoxide anion (O2 ) or a free radieal (these are neutral chemical species with an unpaired electron, often represented by a dot as a superscript on the right hand side) such as a hydroxyl radical (OH ). In fact, a photosensitized oxidation reaction often involves a chain reaction as shown below (Niemz, 1996) ... 

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