What is active mass?

Question

I'm aware of the fact that active mass is defined as the molarity of a substance, but my textbook states that

"Active masses are dimensionless quantities but for our purposes we generally take them with dimensions of molarity, partial pressures etc."

What point is my textbook trying to get across to me? Why do active masses have no dimensions? Why have we defined this quantity in the first place, if we use it interchangeably with the term "molarity"?

Edit: Please keep in mind that I have only just graduated high school and would be very grateful if you could explain this concept to me in simple terms.

Answer 1

The term "active mass" is a historical term.

The concept of an equilibrium constant was developed by Cato Maximilian Guldberg and Peter Waage. The Law of Mass Action has also been referred to as the Law of Guldberg and Waage, historically.

Guldberg and Waage defined the term "active mass" in the 1867 Études sur les affinitès chimiques.

l'on peut choisir un volume arbitraire, par exemple un centimètre cube. Les quantités d'un corps qui se trouvent dans lcc du volume total se nomment la masse active du corps.

or roughly translated:

One can choose an arbitrary volume, for example a cubic centimeter. The amounts of a body located in 1cc of total volume are called the active mass of the body.

And as stated in The Laws of Reaction Rates and of Equilibrium J. Chem. Ed. 1956, 33 (4), p 178 :

Guldberg and Waage in their study of chemical affinity formulated the law of the rate of chemical reactions as proportional to the "active mass" of the reagents. This they called the law of mass action and very clearly defined "active mass" as amount per unit volume. (emphasis added)

So, from a historical point of view, it is false that "active mass" is dimensionless.

However, in relating Gibbs energy to the equilibrium constant, it is necessary for the equilibrium constant to be dimensionless, because only the logarithm of a dimensionless quantity is logical. For this reason, the text mentioned in the OP redefines "active mass" to be dimensionless.

Answer 2

Active mass implies that amount of mass which is taking part in a reaction, that it is the effective concentration of a substance.

It's other names are reactive mass or chemical activity.

Units: The units of activity are nominal, rather than real, because chemical activity is formally defined as the ratio of the actual chemical activity of a substance to its chemical activity under some defined standard conditions, and ratios have no units because the units divide out. Or simply it's the ratio of concentration at required conditions to standard condition.The difference between activity and other measures of composition arises because molecules in non-ideal gases or solutions interact with each other, either to attract or to repel each other. The activity of an ion is particularly influenced by its surroundings.

For example : with the hydrogen ion, we use pH = − log10 [H+ ] where [H+ ] is the concentration, i.e. the number of particles (in moles) divided by the volume (in litres). Once you get a lot of these particles, they bang into each other and take up room (think of billiard balls on a pool table or a room full of tennis balls flying around). In these circumstances we talk about ‘activity’, which is a way to correct for this. Basically it is what the concentration or amount appears to be if we were using the simplified laws (the effective concentration). For the hydrogen ion, it is also what the concentration appears to be to physiological systems. In other words it uses a correction factor for the simplified laws.

Also Wikipedia says:

In a solution of potassium hydrogen iodate [KH(IO3)2] at 0.02 M the activity is 40% lower than the calculated hydrogen ion concentration, resulting in a much higher pH than expected