Activities and molar concentrations I would be really happy if someone would clarify the term "chemical activity" and its implications for me, and also how it is related to the concept of molar concentration. My textbook fails at explaining this clearly and, sadly, the Internet is filled with vague definitions and scientific verbiage that's too difficult for me to grasp. Also, why are activities included in various formulae, and what are their uses?

I never quite actually understood what are activities and how do they differ from molar concentrations, nor how are they used. In addition, when working with the Nernst equation, why are we allowed to compute the activities of the reactants and the equilibrium concentrations of the products? This is the stuff that really baffled me and I'd be highly appreciative if you could clarify it.
Most thermodynamic equations are derived assuming a perfect gas or ideal solution. However, for real a solution the chemical potential $\mu_i=\mu^0_i +RT\ln(x_i)$ may not be accurate for the solvent where $\mu^0_i$ is the chemical potential of the liquid solvent at 1 atm and $x_i$ is the mole fraction. The solute may, similarly, not follow ideal behaviour.  The activity is introduced to allow us to use the familiar equations but now as $\mu=\mu^0_{liq} +RT\ln(\gamma x_i)$ where $\gamma$ is the activity coefficient thus $\mu_i=\mu^0_{liq} +RT\ln(a_i)$ where $a=\gamma x$. Thus we can think of activity as effective concentration or effective pressure (now called fugasity) relative to its standard state.  The activity coefficient is unity in the ideal case. The activity has to be measured experimentally because $\gamma$ depends on exactly what intermolecular interactions exits as any temperature and pressure and cannot be easily calculated.  As an example, naphthalene dissolved in benzene behaves almost ideally and the activity coefficient $\gamma = 1$ but when dissolved in hexane this is not the case and $\gamma=2.5$. A positive deviation from Raoult's law indicates that the vapour pressure is larger than that expected from perfect behaviour and so the activity is larger than the mole fraction and $\gamma &gt;1$.