What is the true meaning of chemical activity in solutions?

[echandler]

Hello - I am wondering abut the meaning of chemical activity. Most definitions are something along the lines of "effective concentration," which is fine until you have a real concentration in a lab, and you don't know if you need to calculate the concentration or "effective" concentration of the species. Basically its too ambiguous a definition to be of real use.

Elsewhere you find activity being used in real equations, such as in the definition of p{H}, or in the definition of the equilibrium constant.

Finally after hours of reading on the side, I finally came across the definition in Hansen and McDonald's excellent book, "Theory of Simple Liquids," where they give the definition of activity as exp(μ/kT)*(mkT/2π(hbar^2))^1.5. I don't know about anyone else, but not being a statistical mechanisist, that definition doesn't help too much on the conceptual end. Wikipedia gives a similar definition, but without the multiplying factor (cube of the De Broglie length). The concept of propensity to undergo phase change across interfaces makes sense, but that seems too simple too.

I am currently reading literature on high ionic strength solutions, but everyone talks about the activity coefficient either in highly theoretical terms or as if it just exists and nothing more.

Can anyone give a middle of the road definition that's conceptual, not a series of equations, but not "effective concentration?" Why would a concentration have a real side and an effective side that are different?

Thanks in advance.

 

[Lord Jestocost]

Terms like “chemical activity” or “effective concentration” have been introduced in order to maintain the formal, thermodynamic description of ideal mixtures and solutions for the thermodynamic description of real mixtures and solutions.

 

[echandler]

Terms like “chemical activity” or “effective concentration” have been introduced in order to maintain the formal, thermodynamic description of ideal mixtures and solutions for the thermodynamic description of real mixtures and solutions.

Thanks for the reply!

Certainly, that makes sense, but I guess maybe a better way to ask my question is what are the practical meaning of activity? Assume we lived in a world where I could take a microsope and selectively look at aqueous copper and optically filter out all of the water (thought experiment), then I would see the concentration of copper, not the number indicated by activity.

So say for reaction mechanisms with this hypothetical copper solution. Does the activity maybe indicate the degree to which the hydration sheath around each copper will slow a reaction down, meaning the rate is based on a modified (lower) concentration, or if I find a species that promotes the reaction, the activity coefficient goes to greater than 1, and the effective concentration is higher, thus making the rate faster?

Or am I completely missing it?

Thanks again.

 

[Lord Jestocost]

Activity coefficient, in chemistry, the ratio of the chemical activity of any substance to its molar concentration. The measured concentration of a substance may not be an accurate indicator of its chemical effectiveness, as represented by the equation for a particular reaction, in which case an activity coefficient is arbitrarily established and used instead of the concentration in calculations. In solutions, the activity coefficient is a measure of how much a solution differs from an ideal solution—i.e., one in which the effectiveness of each molecule is equal to its theoretical effectiveness. (from the Encyclopaedia Britannica)

Maybe, these are of help:
[PDF]What is Activity?
[PDF]18. Solutions - Materials Science & Engineering

 

[Chestermiller]

Are you familiar with the subject of Thermodynamics, particularly the subject of thermodynamics of solution? This is critical to being able to quantify reaction equilibrium and reaction kinetics. The information you are looking for regarding solution thermodynamics is contained in Introduction to Engineering Thermodynamics by Smith and Van Ness, Chapters 10-12 (particularly chapter 12). You need to learn about the concepts of Gibbs Free Energy of solutions, partial molar properties, chemical potential, and activity. If you are dealing with aqueous electrolyte solutions, then I also suggest Handbook of Aqueous Electrolyte Solution Thermodynamics by Rafal et al.

The concepts of activity and activity coefficient come into play when you are dealing with deviations from ideal solution behavior, when the molecules of the various chemical species interact energetically with one another.

 

[zbikraw]

Historically, activity was introduced to rationalize behaviour of dilute aqueous solutions of electrolytes. When you add more electrolyte, properties of solution changes linearly with concentration of solute. After crossing some concentration, changes are less than stoichiometric, so one said that "some solute is present, but not active". It is denoted by diminishing its activity coefficient below 1. Now we know that "1" means situation when all solute ions and/or are fully solvated with water dipolar molecules and do not interact directly with other ones. That means infinite dilution. Molecular theory made possible to estimate activity coefficients in aqueous solutions under "normal" conditions. Change of temperature, pressure or solvent composition complicates situation. Sometimes it is sufficient to add corrections derived from other theories.
Quite another situation with activity is in chemical engineering. The "1" situation is usually defined as pure substance. Adding another one changes properties of starting substance, mainly by breaking interactions between their molecules and add new ones. For understanding such a situation one must know detailed structure of molecular interactions in pure solvent and solute and investigate it in mixture. Although generally not impossible, this is not met in practice. So there is no real sense in activity coefficient outside conditions where it was derived. Some industry-oriented scientists do such measurements and computations, mainly for binary solutions, mainly for simulation of distillation. There are trials to rationalize results, for example when coefficient of one solute exceeds 1, they say that molecules of of this solute are expelled to solution surface. The "activity" is sometimes named "volatility" or "fugacity". Real reason for such investigations is applying in practice simple thermodynamic techniques of computation, mainly the Clapeyron-Clausius equation. For many-component solutions use of activity is more than problematic.
In industrial practice any real distillation must be experimentally optimised, because inaccuracies from activity estimation may consume any profit margin in factory. Real distillations are far from thermodynamic equlibria, so applying "equilibrium" computing is senseless. There are companies that uses distillation techniques "close to equlilibrium" to economize lack of laboratory work for optimize more effective ones.
Large petrochemical distillations use rather "kinetic" difference in volatility of solute components and fractionation instead of pure component preparation. This is effective, but demands other theory and other modelling techniques.

 

[Merzhin]

Chiming in the discussion two years after the question was asked, maybe you have found your answer since?

I would like to preface by saying that I have an issue with the interpretation of chemical activity that is usually taught, that was mentioned by the previous answer:
"Some solute is present, but not active"

The main problem with this interpretation is that it crumbles at very high concentrations, where the activity coefficient can be above 1 (even goes up to 10 or more in the case of HCl for example).

To find a more satisfying interpretation of the activity coefficient, we need to look more closely at what happens to ions dissolved in solution.

Charged ions in solution are subject to two kind of interactions: long-range (first order) and short-range (higher orders). At relatively low concentrations, the average distance between two ions is sufficiently high, so that the dominant attractions are long-range. At higher concentrations, the average distance between ions decreases, and short-range interactions become dominant.

How does that impact "effective concentration" though?
Well, in thermodynamics, concentration is essentially a useful way to count the Gibbs free energy of a system (at constant temperature and pressure).
In chemical kinetics, concentration is a useful way to count the average frequency of collision of reactants.

Now, taking in account the short-range and long-range interactions effectively "correct" the concentration:

With increasing number of solute molecules, the Gibbs free energy of the system is no longer proportional to concentration only. We need to multiply it by an activity coefficient, because the useful work that can provide the molecules also depends on their interactions.

And the average frequency of collision no longer depends on concentration only, but also on the interaction of the reactants, since we can not make the assumption that solute molecules obey the laws of Brownian motion to collide (as would an uncharged solute)

In conclusion, if I was to sum up activity in one sentence, it would be "a corrective factor applied to concentration, which is useful to count the amount of work a system can provide, or the average collision frequency of the solute molecules, when taking in account solute-solute interactions"