Is the Nernst equation limited to dilute ionic solutions?

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As the link states the Nernst equation is for activity. Concentration and activity are approximately equal when small. Do you know any thermodynamics? It is common in thermodynamics to make some approximations. When the conditions are not met we need do adjust the variables. For example often (as here) we define a new variable that behaves in the idealized way, then we must calculate it. Often a variable has dependence that we cannot always ignore.

http://en.wikipedia.org/wiki/Thermodynamic_activity
 
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my chemistry teacher told me that we can't make approximations, when we are dealing with calculations consisting of each and every particle...
please help me on this...
 
Yes so in thermodynamics activity is defined. Activity can be used in the Nernst equation when concentration cannot. The trouble is experimental data is often needed for the activity in this case.
 
Nernst equation using concentration and partial pressures is approximate; Nernst equation using activity and fugacity is exact as far as I know.

Concentration can be converted exactly to activity for ionic species in solution by Robinson-Stokes equation. For cases besides ionic species in solution it is trickier, fugacity is trickier also.