Substitutional expression

Note that this expression reduces to Equation 74 on substituting expressions for W (Equation 77) and K " (Equation 79). 

One of the merits of the above treatment, which justifies its inclusion in this review, is that it allows a quantitative comparison of the selectivity of nucleophilic heteroaromatic substitution (expressed by the reaction constant) with that for the analogous reaction with nitro-activated systems. Values for the latter are in the range 3.6 to 6.0. The fact that in both cases high p-values of similar magnitude are found is consistent with the hypothesis of similar mechanisms for both classes of compounds. 

Before giving further motivations, it is worth noting here that = 0". This fact can readily be verified by substituting expression (36) into the formula... 

In case of the doped semiconductor of -type under consideration the situation gets simple due to large thickness of SCR if compared to the free path length of the carriers. Therefore, substituting expression (1.42) into (1.41) under condition of applicability of the Boltzmann statistics for the free electrons and holes leads to expression... 

Substituting expressions (Eq. 78) for and w2(q) into relationships Eqs. 73 and 74 we get a closed set of kinetic equations describing radical copolymerization in the framework of the simplest model in hand. The values of the rates of initiation in phases 1 and 2 entering in Eq. 74 are determined as follows... 

A We write the expression for Kc and then substitute expressions for molar concentrations. 

FIGURE 1. Diagram to show the effect of the increase in the initial concentration value of amine on the rate of substitution expressed as a second-order rate coefficient. Indicative [RNFLlo values and kjbs values are from reactions between 2,4-dinitrofluorobenzene and n-butylamine in toluene259... 

Fig. 12.20 Dissolution-time curves of synthetic Al substituted goethites in 6 M HCI at 25 °C. The figures at the curves indicate Al substitution expressed as AI/(Fe-i-AI) mol mol and the figures in () are surface areas in m g (EGME) (Schwertmann, 1991, with permission).

Both methods of standard addition can be analyzed with the graph in Figure 5-6. The theoretical response to the additions is derived by substituting expressions for [X]f and [S]f... 

By substituting expressions for [ML] and [ML2J into the mass balance, show that the master equation for a titration of metal by ligand is... 

Our strategy is to substitute expressions into the charge balance to obtain an equation in which the only variable is [H+l. For this purpose, we use the fractional composition equations for the triprotic acid, H,P04, which we abbreviate as H3P ... 

Substituting expressions for P 0 and P from Equations 18-7 and 18-8. we obtain a relation between incident irradiance and emission intensity ... 

By substituting expressions for the apparent acidity constants the two intrinsic surface acidity constants K J[ K for surface reactions are defined as... 

Substituting expressions of type (5.95) for T(0) and 7(0) into the system of equations (5.91) and (5.92), expanding over multipole moments and accounting for the orthogonality of spherical functions (B.3), we obtain the terms —7KaPg and —TxbpQ which have to be added to the righthand sides of (5.94) and (5.93). 

Substituting expression 14 for the size-dependent free-en-ergy term ii and eq 10 and 11 for the surface area A per amphiphile in eq 15a and 15b yields for thB inflection point... 

Substituting expression (18) into these equations, noting that H and si commute and that, p/2=j>/, and using equations (17) and (13), one arrives at the expressions... 

Substituting expression (2-57) for each analyte into equation (1-5), we get... 

Substituting expressions (4-33) and (4-34) into expression (4-31), we can write an expression for the equilibrium constant ... 

Substituting expressions (69) and (70) into Eqn. (67), we can write the transition rate constant in terms of the density matrices of phonon subsystem initial and final states, as in (54). Following the respective manipulations of... 

Substituting expression (6.10) back into formulae (6.8) and (6.9). we find... 

Substituting expression (8.36) for the electric field in the fourth Maxwell s equation (8.30),... 

Substituting expressions (8.135) through (8.137) into the Lorentz lemma (8.134), we find... 

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