Reciprocal rule

The product (N02) and the reactants (N2 and 02) have switched sides (reciprocal rule). 

Applying the reciprocal rule (page 327), we can deduce the equilibrium constant expression for the reverse reaction... 

Coefficient rule Reciprocal rule Multiple equilibrium... 

The equation just written is the reverse of that for the ionization of water, so the equilibrium constant can be calculated by using the reciprocal rule (Chapter 12). 

Notice that this reaction is the reverse of the reaction of the weak base QH - (the acetate ion) with water (Chapter 13). It follows from the reciprocal rule that for this reaction,... 

Equation 9.126, known as the reciprocity relationship or reciprocal rule, then leads to the equation ... 

Real surfaces, radiation 441,443 RbavblI.. B. N, 274, 302, 3 1 Reboilers 494, 495, 496 Reciprocal rule 448 Reciprocating piston compressor 347... 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

If z(x, y), then x(y, z) and y(z, x). Each of these functions permits the definition of two partial derivatives. What are the relationships between the six partial derivatives formed from three variables If two partial derivatives hold the same variable constant, we only have two variables and can use the reciprocal rule from ordinary calculus ... 

There is the assumption that the surfaces are flat or convex. The reciprocity rule gives... 

A local thermodynamic state is determined as elementary volumes at individual points for a nonequilibrium system. These volumes are small such that the substance in them can be treated as homogeneous and contain a sufficient number of molecules for the phenomenological laws to be apphcable. This local state shows microscopic reversibility that is the symmetry of all mechanical equations of motion of individual particles with respect to time. In the case of microscopic reversibility for a chemical system, when there are two alternative paths for a simple reversible reaction, and one of these paths is preferred for the backward reaction, the same path must also be preferred for the forward reaction. Onsager s derivation of the reciprocal rules is based on the assumption of microscopic reversibility. 

Onsager s reciprocal rules are valid for systems that are sufficiently close to global equilibrium. It is crucial to determine under what conditions the assumption of linearity will hold. Onsager s reciprocal rules hold if the flows and forces are independent of one another and are identified from the rate entropy production or dissipation function. 

Equations (6.299) and (6.300) show that Onsager s reciprocal rules hold. The Js eq and Jweq have a microscopic definition represented by perturbation matrix elements and a macroscopic definition represented by the equilibrium exchange rate. As long as the criteria of linearization are satisfied, the statistical rate theory may be used to describe systems with temperature differences at an interface besides the driving forces of pressure and concentration differences. 

Table 7.8 shows the thermal diffusion ratios and thermal diffusion coefficients obtained from Onsager s reciprocal rules for toluene, chlorobenzene, and bromobenzene at 1 atm and at 298 and 308 K. Thermal diffusion or heats of transport may be extremely sensitive to the molecular interactions in solutions (Rowley et al., 1988). 

Table 7.11. Thermal diffusion ratios from Onsagefs reciprocal rules for toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm and 35oa...

Table 7.11 shows the thermal diffusion ratios obtained from Onsager s reciprocal rules for toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm and 35°C. The heats of transport for the ternary mixtures are shown in Tables 7.12 and 7.13. For the ternary mixture of toluene (l)-chlorobenzene (2)-bromobenzene (3), the heats of transport are tabulated at 298 and 308 K. The temperature- and composition-dependent heats of transport values are fitted by the following equations by Platt et al. (1982) with a deviation below 5% ... 

Here, the reciprocal rules hold, and we have Ln = L2. The introduction of the explicit form of chemical potential for a single component... 

Consider the Seebeck effect resulting from two junctions maintained at two different temperatures as shown in Figure 7.5. Assume that points 1 and 4 are at the same temperature T0. These points are connected to a potentiometer so that the electromotive force E can be measured with zero current Je = 0. Under these conditions and using the reciprocal rules, Eq. (7.287) yields... 

This is known as the second equation of Thomson. This relation is based on the Onsager reciprocal rules, and the experimental verification of Eq. (302) would be additional confirmation of Onsager s rules. 

If Onsager s reciprocal rules hold, the rate of entropy production for two simultaneous chemical reactions is... 

The above phenomenological equations obey Onsager s reciprocal rules, and hence there would be six instead of nine coefficients to be determined. 

According to the Onsager reciprocal rules, we have LqB = LBq. If we replace the chemical potential in terms of the concentration (instead of activity), we transform Eqs. (a) and (b)... 

As Eq. (10.84) is an appropriately derived dissipation function consisting of the conjugate flows and forces, the Onsager s reciprocal rules states that /.( = LJt. 

Lu and L1 are the straight and cross-coefficients, respectively. By Onsager s reciprocal rules, we have LtJ = L. The electrochemical potential differences between internal i and external e regions are defined by... 

This relation is referred to as the reciprocity relation or the reciprocity rule, and it enables us to determine the counterpart of a view factor from a knowledge of the view factor itself and the areas of the two surfaces. When determining the pair of view factors Fj >j and it makes sense to evaluate first the easier one directly and then the more difficult one by applying the reciprocity relation. 

Thc sumniation rule can be applied to each surface of an enclosure by varying i from 1 to /V. Therefore, the summation rule applied to each of the N surfaces of an enclosure gives N relations for the determination of the view factors. Also, the reciprocity rule gives N(N — 1) additional relations. Then the total number of view factors that need to be evaluated directly for an /V-suiface enclosure becomes... 

The symmetry rule can also be expressed as if the surfaces j and k are symmetric. about the surface i then F, >y = F, >. Using the reciprocity rule, we can show that the relation F is also true in thi.s case. 

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