The parameter q>> is by definition a quotient of two rate constants. Therefore, its temperature dependence should follow the Arrhenius equation (Figure 10). [Pg.177]

The equilibrium constant, K, is determined by the concentrations of reactants and products at equilibrium for a constant temperature. Therefore, of a reaction is always constant at a definite temperature. However, the value for reaction quotient Q is not constant. It is determined by the instantaneous concentrations of reactants and products. The reaction quotient expression is written as the same as expression for a reaction. For example, for the reaction [Pg.70]

As expected from Table 5.7, this environmental quotient for conventional oxo processes (basis Co catalysts) and for the manufacture of the bulk chemical -butanal is actually about 0.6-0.9, depending on the definition of the term "target" product. The range 0.6-0.9 [Pg.132]

In this section, we shall see that the quotient in Theorem 3.23 is, in fact, a hyper-Kahler quotient. Let us review on the hyper-Kahler structure and hyper-Kahler quotients briefly. The interested reader should read Hitchin s book [38]. First, we recall the definition of Kahler manifolds. [Pg.32]

Recall that in the sixth chapter, we defined a closed subset to be schurian if it is faithfully embedded in itself. From this definition we easily obtain that a scheme is schurian if and only if it is isomorphic to a quotient scheme of a thin scheme. [Pg.292]

In this terminology, our definition of projective fullerenes amounts to selection of cell-complex projective-planar 3-valent maps with only 5- and 6-gonal feces. As noted above, P5 — 6 for these maps. Thus, the Petersen graph is die smallest projective fullerene. In general, the projective fullerenes are exactly the antipodal quotients of the centrally symmetric spherical fullerenes. [Pg.42]

A subset R of S is called naturally valenced if each element of R has finite valency. The present chapter starts with the observation that naturally valenced schemes give rise to quotient schemes over finite closed subsets. After the definition of quotient schemes we shall always assume S to be naturally valenced. [Pg.63]

In Equation (18b), the activity quotient is separated into the terms relating to the silver electrode and the hydrogen electrode. We assume that both electrodes (Ag+/Ag and H+/H2) operate under the standard condition (i.e. the H+/H2 electrode of our cell happens to constitute the SHE). This means that the equilibrium voltage of the cell of Figure 3.1.6 is identical with the half-cell equilibrium potential E°(Ag+l Ag) = 0.80 V. Furthermore, we note that the activity of the element silver is per definition unity. As the stoichiometric number of electrons transferred is one, the Nemst equation for the Ag+/Ag electrode can be formulated in the following convenient and standard way [Pg.146]

When X = C2, X can be identified with the set of GLJl(C)-orbits of (Hi, B2, i) where Bi, B2 are commuting n x n-matrices and i is a cyclic vector (Theorem 1.14). Many properties of (C2) are derived from this description. In Chapter 3, we shall regard the description as a geometric invariant theory quotient and a hyper-Kahler quotient. This description is very similar to the definition of quiver varieties which were studied in [62]. [Pg.1]

The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K° in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K° [Equation (3)]. However, there exists no justification for using the numerical value of a solvent s molar concentration as an approximation for the pure solvent s activity, which is unity by definition.76,77 [Pg.348]

If the reaction mixture is very dilute in the reactants and the products, the activity coefficients can all be approximated by unity. Then the last term on the right hand side of Eq. (2.20) vanishes, and the left hand side can be written as AG° = -RT n ATsolution, the equilibrium quotient becoming the equilibrium constant. Under ordinary conditions, however, the activity coefficient term must be taken into account, since there are solvent effects on all the terms on the right hand side except -RTIn K". The fact that different numbers of solvent molecules may specifically associate with the reactants and the products and that solvent molecules may be released or consumed in the reaction should not be included explicitly, since this effect is already covered by the terms in AG s of solvation of the reactants and products according to our definition of this concept. [Pg.102]

© 2019 chempedia.info