What is the Difference Between Activity and Concentration in Chemical Laws?

[rohanprabhu]

Many of the chemical laws/concepts we deal with which relate some number to the 'quantity' of the reactants and/or products or the quantity of these substances among themselves, talk about 'activity'. For example, the law of mass action, or the Equilibrium constant.

But I've seen that they use concentration and active mass interchangeably. So.. my question is what exactly is activity? How does it differ from concentration and why is it that activity becomes approximately equal to concentration for very dilute solutions.

and.. also.. why is the activity of solids taken to be unity?

thanks

 

[lightarrow]

Many of the chemical laws/concepts we deal with which relate some number to the 'quantity' of the reactants and/or products or the quantity of these substances among themselves, talk about 'activity'. For example, the law of mass action, or the Equilibrium constant.

But I've seen that they use concentration and active mass interchangeably. So.. my question is what exactly is activity? How does it differ from concentration and why is it that activity becomes approximately equal to concentration for very dilute solutions.

and.. also.. why is the activity of solids taken to be unity?

thanks

Let's make an example. We know that, for example, PbCl2 is not soluble (at cold) in water (Kps ~ 10^(-5)). You add a great amount of KNO3 to the solution and, magically, the PbCl2 precipitate dissoles. Why?

The fact is that, a priori, there is actually not a clear reason for the fact that if you increase the concentration of Pb++ or Cl- ions you must have the formation of a precipitate (for mass-action law): what counts is actually the attraction of the ions and how this attraction, or, in general, interaction, depends on the ion concentrations, is not so immediate; you have to remember that we don't have ions in the gaseous state, they are immersed in a solvent which, actually, does partake in the process; our Pb++ and Cl- ions interact with H2O molecules and not in a simple way; a first way of coming out of this problem simplifying it, is to simply consider how the presence of generic ions of specific charge changes the dielectric constant of the solvent. This is summarized by the concept of "ionic strength":

$$I\ =\ 1/2\ \Sigma_i c_iz_i^2$$

where c_i is the concentration of the i-esim ion with charge number z_i (-1 for Cl-, +2 for Pb++, ecc.).

http://en.wikipedia.org/wiki/Ionic_strength

Ionic strenght affect the way in which our ions interact, because the higher I, the less they will attract; this is quantitatively expressed by the "Debye-Hückel equation":

http://en.wikipedia.org/wiki/Debye-Hückel_equation

which provides you (for dilute solutions) the activity coefficients of Pb++ and Cl- which, multiplied by their concentrations, gives you the "activity" of the ions, which are the correct quantity to consider in the product equation of Kps.
A similar reasoning applies to other kinds of reactions.

 

[Mapes]

Coming from a materials science perspective: the concentration of A in B tells you how many A atoms there are in a total of A and B atoms. Simple enough. But the activity gives you much more information: it tells you about the bonding between A and B atoms. If the activity of A is less than one, then A and B will tend to mix, because the A-B bond is more stable than A-A and B-B bonds. If the activity of A is more than one, the reverse is true; A-B bonds are less favored than A-A and B-B bonds. In this case, the mixture will tend to phase separate, like oil and water.

This is why it's convenient to consider the activity of of a solid or liquid (which is equivalent to a mixture of A in A) to be one.