Effective constant

Given that the concentration of both the copper atoms and the electrons m the copper metal will be effectively constant, so that two of the activity tenns can be neglected, we finally have, on rearranging A2.4.107,... 

An increase in the time required to form a visible precipitate under conditions of low RSS is a consequence of both a slow rate of nucleation and a steady decrease in RSS as the precipitate forms. One solution to the latter problem is to chemically generate the precipitant in solution as the product of a slow chemical reaction. This maintains the RSS at an effectively constant level. The precipitate initially forms under conditions of low RSS, leading to the nucleation of a limited number of particles. As additional precipitant is created, nucleation is eventually superseded by particle growth. This process is called homogeneous precipitation. ... 

Demonstrating that a reaction obeys the rate law in equation A5.11 is complicated by the lack of a simple integrated form of the rate law. The kinetics can be simplified, however, by carrying out the analysis under conditions in which the concentrations of all species but one are so large that their concentrations are effectively constant during the reaction. For example, if the concentration of B is selected such that [B] [A], then equation A5.11 simplifies to... 

Equation 39 can often be simplified by adopting the concept of a mass transfer unit. As explained in the film theory discussion eadier, the purpose of selecting equation 27 as a rate equation is that is independent of concentration. This is also tme for the Gj /k aP term in equation 39. In many practical instances, this expression is fairly independent of both pressure and Gj as increases through the tower, increases also, nearly compensating for the variations in Gj. Thus this term is often effectively constant and can be removed from the integral ... 

If other reagents affect the rate, then setting their concentrations much higher may sometimes be desirable. They would remain effectively constant during the course of... 

The buildup of very low concentrations of product, if it can be monitored, will provide the initial rate. During this time the concentrations of the reactants remain effectively constant. A family of such determinations provides both the form of the kinetic expression and the value of the rate constant. 

When both A] and A2 are present in large excess over B, and [Ai] and [A2] are thus effectively constant, it follows that the ratio of final and initial concentrations gives the rate constant ratio ... 

Assuming that each reaction follows second-order kinetics, use the following data to evaluate ki/k. four of the 20 original experiments being given.17 Note that [N lo = 0.010 M. so that [CPLCT J and [Phi], present at much higher concentrations, remain effectively constant in each determination. Methanol is the solvent, so umcoh = 1 ... 

Bi very small, (say, <0.1). Here the main resistance to heat transfer lies within the fluid this occurs when the thermal conductivity of the particle in very high and/or when the particle is very small. Under these conditions, the temperature within the particle is uniform and a lumped capacity analysis may be performed. Thus, if a solid body of volume V and initial temperature Oo is suddenly immersed in a volume of fluid large enough for its temperature 0 to remain effectively constant, the rate of heat transfer from the body may be expressed as ... 

If temperature gradients are small, Cr may be regarded as effectively constant. Furthermore, Kart is a function of composition, being approximately proportional to the product x, Xr. It is therefore useful to work in terms of the thermal diffusion factor a, where ... 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

For another set of field-effect constants, based on a different premise, see Draffehn, J. Ponsold, K. J. Prakt. Chem., 1978, 320, 249. 

The half-cell potentials of the two reference electrodes are constant sample solution conditions can often be controlled so that E,j is effectively constant and the composition of the internal solution can be maintained so that (ai)i , ai is fixed. Consequently Eq. (3) can be simplified to give... 

In the case of sound waves, which are of very low intensity, the pressure and density of the medium remain effectively constant throughout the process. Therefore, all parts of a sound wave are transmitted at the same velocity, so that a sinusoidal (sine) wave, for example, remains sinusoidal indefinitely during propagation. 

Fig. 2.8. The variation of stability constants, K, for the complexes of M2+ ions of the Irving-Williams series, ox, oxalate en, ethylenediamine (note that the constants plotted are absolute, not effective constants at pH = 7).

Catalyst Reaction a Order b Activation Energy a, kJ/mol Water Effect Constant m Reaction Rate Constant k, mol/g-cat/h/MPa(a+b)... 

Figure 2. Nonlinear dielectric effect constant ( 10 scm7SC 2moF ) of Br(CH2)n, Br at 25 °C. Points represent the experimental results of Chelkowski (19, 20). The solid and dashed lines are calculated with 4>s, = 120 ° and +80 °, respectively, for thefirst and last C-C bonds. (Reproduced with permission from Ref 6. Copyright 1981, American...

To determine (/f) it may be assumed known for K > 2Kc, where should not be very large and relatively easy to calculate. Next suppose that Kc < K < 2Kc and construct a sequence of effective constants Ki, K2, etc. to satisfy Kn+i = f(Kn), with Ki = f K). Kadanoff s formula then implies... 

Somewhat unusual pressure dependence of the nature of the spin transition curve has been found for chain-like SCO systems containing substituted bridging triazole ligands [163, 164]. Although the transition is displaced to higher temperatures with increase in pressure, the shape of the transition curve, unusually, is effectively constant, i.e. there is no significant change in the hysteresis width and the transition remains virtually complete. This has been taken to indicate that the cooperativity associated with the transitions in these and related systems is confined within the iron(II) triazole chains. 

The DP of the polymers too was independent of the quantity of monomer and of the amount of catalyst solution added, but increased with decreasing temperature from 103 at -35° to 2.8 x 103 at -98°, giving a linear Arrhenius plot with EDP - -1.3 kcal/mole. These observations indicate that the DP is controlled by transfer reactions, and it seems likely that under the conditions of these experiments the most important of these is monomer transfer. The fact that the DP was independent of conversion is difficult to interpret since the polymer was precipitated during the reaction and therefore the concept of monomer concentration is ambiguous if the growing chain ends remained in the unreacted monomer its concentration would remain effectively constant. 

The choice of about 2% is made to ensure that the composition of the analyte solution remains effectively constant. A constant-composition solution is useful in irdiibiting side reactions since, commonly, the reac-tion(s) at the mercury drop vary with solution composition. In particular, the electrode reaction alters as depletion of the solution approaches completeness, i.e. as all cations of analyte are removed from solution. 

It has been argued (Appendix 3, Eq. A.21) that the collapse time for a bubble, initially of radius R, is considerably shorter than the time period of the compression cyde. Thus the external pressure Pj (= P + Pjj), in the presence of an acoustic field, maybe assumed to remain effectively constant (Pj ) during the collapse period. Neglecting surface tension, assuming adiabatic compression (i. e. very short compression time), and replacing R, by R, the size of the bubble at the start of collapse, the motion of the bubble wall becomes... 

In addition, the molar mass (which is proportional to the intrinsic viscosity, [t]]. Tab. 6.17) of the copolymer decreases with increasing potential in the silent system, whereas in the sonicated case it is effectively constant. Overall ultrasound also appears to produce a more uniform reaction system in that in the silent system the reactivity ratio (determined by infra red spectroscopy) increases with electrode potential, whilst under sonication it remains fairly constant. 

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