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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.

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  • $\begingroup$ It sounds like the book is focussing on the ratios of molecules. This is the same idea as moles or partial pressures in a gas: they measure the ratios of the compounds present. $\endgroup$ – matt_black Sep 3 '16 at 11:50
  • $\begingroup$ Okay, but why? Can you please elaborate? $\endgroup$ – user33789 Sep 3 '16 at 13:13
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    $\begingroup$ Well, I want to mention that activity might be intuitively understood by its usage in radioactivity: the activity of the given substance determines how fast it is disintegrating and how much radiation it is generating, analogous to how "reactive" a particular reagent is in the reaction. However, I am not sure if activity and active mass are the same thing... $\endgroup$ – FreezingFire Sep 28 '16 at 10:14
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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.

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  • $\begingroup$ Sir, in my study material, it's written that, active is actually a dimensionless quantity, and for our convenience and purposes we take them with the dimensions of molarity, partial pressure, etc. $\endgroup$ – Adesh Tamrakar Dec 28 '16 at 11:36
  • $\begingroup$ @AdeshTamrakar "activity" is dimensionless. "active mass" is a historical term that professional chemists do not use anymore. The correct historical meaning of "active mass" is mass per volume, such as mass per cubic centimeter. The term "active mass" is older than the term "molarity". $\endgroup$ – DavePhD Jan 2 '17 at 0:23
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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

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    $\begingroup$ I'm afraid I don't understand how taking the ratio functions as a correction factor. Additionally, when using "activity" in the expression for equilibrium constant, the final value does end up having some units. How is this so? Why do we settle for using molarity in place of activity? Can you please further elaborate on all this? $\endgroup$ – user33789 Sep 23 '16 at 11:21
  • $\begingroup$ @JM97 I don't think "active mass" and "chemical activity" are interchangeable terms. The idea behind them is the same though, I agree. $\endgroup$ – getafix Sep 23 '16 at 11:22
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    $\begingroup$ @KaumudiHarikumar the equilibrium constant is dimensionless $\endgroup$ – getafix Sep 23 '16 at 11:24
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    $\begingroup$ @KaumudiHarikumar "molarity" is used because it is a readily measurable physical thing, and using it is usually approximately correct. "activity" is artificially defined mathematically to make the equilibrium constant exactly constant for all concentrations iupac.org/goldbook/A00115.pdf goldbook.iupac.org/S05915.html It is as if we say, for all people (body weight)/(brain weight) = 27, and when we realize it isn't exactly true, we define something called pseudoweight to make the equation always be true. $\endgroup$ – DavePhD Sep 23 '16 at 16:32
  • $\begingroup$ Um, OK. I don't know about pseudoweight though. $\endgroup$ – user33789 Sep 24 '16 at 2:07
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Kaumudi there is no need of any confusion regarding the Active mass. In simplest way it is the actual number of entities taking part in a reaction at a particular instance. For example, suppose u have given x gms of a substance to participate in a reaction and the reaction takes y mts. In the above regard it is very obvious that the whole x gms will not participate in the reaction at any instance. The actual participation of substantial atoms will be less than x, otherwise the reaction would be rather instant. Hence, this actual amount of substantial atoms participating in the reaction per unit time is active mass. Now, as this quantity is comparative and dynamic that's why we can consider it "dimensionless". Secondly, you can't replace it with terms like Molarity which although give definite quantity but are Static in nature.

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