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While reading a book on Instrumental analysis by Skoog, in appendix part they explain activity of a species.

The relationship between activity of a species and it's molar concentration $[X]$ is given as $a_x=\gamma_x[X]$ where $\gamma_x$ is a dimensionless quantity called the activity coefficient of $X$.

Basically $\gamma_x$ tells about measure of effectiveness with which that species influence the equilibrium in which it is a participant.They say that in the expression of equilibrium constant, activity of the compound is used instead of its concentration.

In high school, we use the concentration of the compound and the activity of a compound is not introduced at that time. But it is also the fact that the concentration of compounds given at that time is very low for which $\gamma_x \to 1$. So $a_x \approx [X]$.

Basically, the question is that what is the need of the concept of activity for using in the expression of equilibrium constant? Without using this concept when the concentration of compounds is high (in this case $\gamma_x<1$ and $a_x<[X]$), what contradicting result we would get?

Also please tell me some reference where I get the derivation of mean activity coefficient ($\gamma_{+-}$) of an electrolyte $A_mB_n$, given as $\gamma_{+-}=(\gamma^m_A \gamma^n_B)^\frac{1}{m+n}$.

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  • $\begingroup$ A physical chemistry textbook like Atkins introduces how mean activity coefficients arise naturally when dealing with the thermodynamics of electrolytes. $\endgroup$ – Buck Thorn Jun 11 at 17:31
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    $\begingroup$ Regarding your question on activity, the concept is introduced to deal with non-ideal behavior that might be encountered in non-ideal solutions such as non-dilute or electrolyte solutions. You can approximate activity with concentration in ideal dilute solutions. $\endgroup$ – Buck Thorn Jun 11 at 17:34
  • $\begingroup$ Basically, the value of equilibrium constant for a weak electrolyte can be found by calculating the degree of dissociation which is derivable using Kohlrausch law($\alpha=$(Conductivity at concentration C)/(Conductivity at infinite dilution)) and then we can calculate K. But the value which we get does it is in accordance to activity of the electrolyte not the concentration (when high concentration of electrolyte is taken because then $a_x\neq [X]$), so the concept of activity is introduced? $\endgroup$ – Manu Jun 12 at 3:29
  • $\begingroup$ This paragraph might have confused some people: "Basically, the question is that what is the need of the concept of activity for using in the expression of equilibrium constant, without using this concept when high concentration of compounds are taken (in this case γx<1 and ax<[X]), what contradicting result we would get?" I think I understood it after rereading, but you may want to edit it to make it clearer (perhaps by breaking it up into two sentences?) $\endgroup$ – Buck Thorn Jun 15 at 15:01
  • $\begingroup$ You may want to try a small change: "Basically, the question is that what is the need of the concept of activity for using in the expression of equilibrium constant? Without using this concept when the concentration of compounds is high (in this case γx<1 and ax<[X]), what contradicting result we would get?" $\endgroup$ – Buck Thorn Jun 15 at 15:03

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