In general, activity is what is important when doing any equlibrium calculations. In all possible places - dissociation constants, solubility products, complexation constants, Nernst equation and so on - it is activity that is important, not the concentration.

In diluted solutions that makes no difference, the more concentrated the solution, the worse the situation.

For the diluted solutions there is no problem, but once the solutions get more concentrated discrepancy between calculated and observed concentrations in equlibrium rises. That's why the activity concept was introduced. Look for Debye-Huckel theory, activity coefficients and ionic strength of the solution. Formulas for the calculations are presented on my web site (try info on pH calculation), but for the explanation you have to either find a book or google the web.

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basically because concentration is an approximate concept.

c_B is the number of molecules of specie B. In phase space (ideal gas), there is no quantum correlations between molecules and each molecule is a well-defined specie. In real phase (gas, and specially solutions and solids) there is not real molecules. There is a global system formed by N particles. The situation is even worse in electrochemical systems because there is charges and electrostatic Coulomb forces are large correlation ones.

Therefore it is difficult to define c_B in a system where B (in the usual chemical sense) really does not exist  .

However in some sense "B" is inside the total system of N particles and therefore it is natural to believe in some substitute for c_B: e.g. activity a_B

Some books attempt to claim that one may always substitute c_B by a_B in non ideal phases. This is not true.

In fact, that ad hoc rule was source (and continue to be) of confusion in the past. E.g. if one follows that "standard rule" one obtains from chemical kinetics

B + D ---> products

part a_B / part t = - ka_Ba_D                            (wrong)

but this equation does not work. The correct is

part c_B / part t = - ka_Ba_D and, therefore, some textbooks do

part c_B / part t = - k'c_Bc_D and introduces nonideal effects (e.g. strengh of an external electric field directly in the rate constant).

From macroscopic canonical science one obtains the correct answers to these questions without adtitional asumptions or wrong reasoning. Moreover, at equilibrium the rate part "collapses" and survives only the activity part (right part) and by this reason in equilibrium formulas it appears the activity instead of concentration. For instance the equlibrium constant is computed from both products and products^-1 of activities instead of concentrations.

Moreover, from microscopic canonical science, one obtain the details of why. There is no real molecules in the ideal gas sense, therefore there is not typical concentration.

Perhaps some chemists are perplexed of that molecules (in the usual "chemical" sense of individual entities) do not exist, but let me remember that usual quantum chemistry computations are only valid for idealized phases, where each individual molecule is a well-defined entity.

In fact, my profesor of quantum mechanics said us an anecdote (i believe is real one)of an inorganic chemist that using the Gaussian computed an entalpy, apply it, and find a sound discrepancy. He just forgot that computed "Gaussian entalpy" was valid only for ideal gas of that molecule. In condensed matter situations, one may introduce solvent effects and in more sophisticated approaches simply ignore the language of wavefunctions, Schrödinger equation, and all that.

I said "because concentration is an approximate concept."

It read ambigous. As said, the chemical specie is really therein, Of course

I mean that the use of concentration in the typical chemical of a "molecule forever" sense like a "source" for several dynamics properties (including equilibrium ones) is incorrect.

I wait now it is more clear my previous post. Thanks!!

It occured to me that when the electrode is really very small (and we were using ones with the radius measured in Angstroms), when the concentration of reacting electrolyte is small, and when there is very fast potential sweep (measured in kV or even in MV per second) diffusion is no longer continuous process. In fact it never is, but usually we have enough particles so that statistics is on our side.

Whow!! Really difficult problem.

When the system is small there are superfitial and quantum effects to be studied. Chemical thermodynamics (and kinetics) are only valid for macroscopic bodies. In my work in nanothermodynamics I show that there are addittional thermal effects of the order of (1/N).

When the potential is very fast you are basically outside of the limit of application of linear-slow approximation (i.e. chemical kinetics and thermodynamics) and you need more general formulations (basically nonlinear ones). Canonical thermodynamics is nonlinear and study those effects. A special formulation rather developed (it was formulated the last century) is extended thermodynamics. The basic idea is that the fluxes are also thermodynamical variables to be introduced in the fundamental equation. Extended thermodynamics would permit you to compute correction terms for very, very fast processes.

From extended thermodynamics (canonical thermodynamics is more general still!!) one can derive generalizations to the usual law of diffusion. In fact, it is usually ignored ("hidden") in physical chemistry textbooks that usual laws of transport are valid only in very constrained situations (linear, average, slow processes, macroscopic bodies, etc.).

E.g. Fourier law for heat transport violates relativistic theory and it is only valid for small temperature gradients.

i haven't seen any rate equation takes in account of activity. must we do so for chemical reactions taking place in highly concentrated solutions?

Every equilibrium is in fact dynamic and kinetically controlled.