# Why we have mass of adsorbent in Freundlich equation?

In Freundlich equation why we have $m$ the mass of adsorbent. I mean it is surface chemistry and on the surface of adsorbent the adsorption takes place so why we have mass of adsorbent in that equation.

Let us understand my problem by an example.

In my book it is given that when we add charcoal to a solution of acetic acid in water then the acidity of the solution is decreased because charcoal has adsorbed some amount of acid.

Now let us have two beakers with acetic acid in water with same concentration and let us have $m$ gram of charcoal. In the first beaker you add the charcoal in shape of a cube and in the second beaker you add the charcoal in the powdered form.

Since the surface area of charcoal available for adsorption in second case is more and so there will be more adsorption and this means the final concentration of the second beaker will be less as compared to the first beaker.

Please tell me why we have mass of adsorbent in Freundlich equation rather than surface area? In the example above we were having same mass of adsorbent but the extend of adsorption was different and this is the reason why I think that mass of adsorbent in useless. If there is some use of mass of adsorbent in the Freundlich equation then please tell me.

EDIT

In the above example of acetic acid we have considered two cases in one we adding charcoal in the shape of cube and in the second one we are adding charcoal in powdered form.

In both the situation adsorbate and adsorbent are same and are at same temperature so the value of $K$ and $n$ is same for both situations. Also we have taken concentration to be same in both the situation so $c$ is also same for both the situations. Mass of the adsorbate that is mass of the acetic acid is also same in both the situations.

Also take the same mass of charcoal. Now according to the Freundlich equation the concentration of acetic acid in water after adsorption has to be same in both the situations because in both the case we have same value of $K,n,c,x,m$. But this is not true since we know that more the surface area more will be the adsorption therefore in the second case when we have added the charcoal in the powdered form then it will adsorb more acetic acid as compared to the first case where we have added the charcoal in the shape of a cube.

Sir I don't have equipments to perform this experiment but I have some logic.

Statement 1 Freundlich equation is true.

Statement 2 More the surface area more will be the adsorption.

Now here I can say without any doubt that one of the above statement is clearly wrong.

I request the readers to please see the example and please try to understand what I mean to say.

• It seems from your example that you are considering charcoal to be non porous? In any case, physical adsorption depends on the physical nature of the adsorbent, and so one does not expect a powdered adsorbate to behave the same as a monolith of the same material. The Frueundlich model is expressed as mass adsorbed per mass adsorbate because that's how Freundlich decided to express it. It's not clear to me what you are asking really, as the accessible surface area can be directly related to $K$ in each system, which are physically different as you point out – repurposer Dec 23 '15 at 15:22
• @repurposer Sir thank you for you time, I have edited the question and I hope that it will be clear this time. So please have a look. – Singh Dec 24 '15 at 5:38
• $K$ and $n$ are not the same for both situations. You may be using the same material, but the surface area matters. Thus they are not the same adsorbent – repurposer Dec 24 '15 at 14:03