# Why does the BET equation take into consideration a multimolecular-layer, even though it deals with chemisorption?

I came across the Brunauer-Emmet-Teller (BET) equation recently, and one thing that I found strange was an implicit reference to the formation of molecular multi-layer.

In the BET equation

\begin{align} \frac{P}{V(P^0 - P)} &= \frac{1}{CV_m} + \frac{C-1}{CV_m}\cdot \frac{P}{P^0}\, ; \tag{1}\\ C &= e^{(Q_1 - Q_2)/RT}\quad (C:\text{constant})\, ,\tag{2} \end{align}

where $V_m$ – monolayer adsorption amount, V – adsorption amount at the equilibrium pressure $P$, $Q_\mathrm{L}$ refers to the heat of adsorption of the second and higher layers of adsorbate onto the adsorbent.

Now according to my textbook, chemisorption only results in the formation of a molecular monolayer. Multilayers are formed by physisorption.

The thing is, I'm told the BET equation is an extension of Langmuir's adsorption isotherm for chemisorption at low pressures. If the BET equation applies only to chemisorption, then what is the point of including a term dependent on the formation of multilayers, when chemisorption doesn't even form a multilayer all by itself.

Is there something I'm overlooking here? The internet has not yielded any decent result in that regard.

• BET equation does not deal with chemisorption. May 31 '18 at 12:25

Brunauer–Emmett–Teller (BET) explains the physical adsorption of gas molecules on a solid surface, and doesn't address chemisorption. Even the wikipedia link that you provided, makes that quite explicit. However, you are correct to think that it is in a extension of the Langmuir adsorption model, which only accounts for monolayers.

The assumption that underscore this model are as follows:

1. Adsorptions occur only on well-defined sites of the sample surface (one per molecule)
2. The only molecular interaction considered is the following one: a molecule can act as a single adsorption site for a molecule of the upper layer.
3. The uppermost molecule layer is in equilibrium with the gas phase, i.e. similar molecule adsorption and desorption rates.
4. The desorption is a kinetically-limited process, i.e. a heat of adsorption must be provided:
• these phenomenon are homogeneous, i.e. same heat of adsorption for a given molecule layer.
• it is E1 for the first layer, i.e. the heat of adsorption at the solid sample surface
• the other layers are assumed similar and can be represented as condensed species, i.e. liquid state. Hence, the heat of adsorption is EL is equal to the heat of liquefaction.
5. At the saturation pressure, the molecule layer number tends to infinity (i.e. equivalent to the sample being surrounded by a liquid phase)

References: The original article

P.S: Good reading material on BET theory can be found here

My book (G. Wedler, H.-J. Freund, Lehrbuch der Physikalischen Chemie, 6. Edition ... obviously a German book on physical chemistry) begins with the following, when introducing the BET equation.

Besonders bei der Physisorption beobachtet man, dass häufig Adsorption in mehreren Schichten übereinander, eine sog. mehrmolekulare Adsorption eintritt.

Esp. during physisorption one can observe that often adsorption happens in multiple layers on top of each other, a so called multilayer adsorption occurs.

Further on it is mentioned that:

Als ersten gelang es Brunauer, Emmett und Teller, eine für die praktische Anwendung geeignete Adsorptionsisotherme für die Mehrscheichtenadsorption abzuleiten.

Brunauer, Emmett and Teller were the first who developed a useful adsorption isotherm for practical purposes regarding the multilayer adsorption.

From that point of view, I would assume, that the BET equation is used for physisorption.

• Wait, just confirming; the Langmuir adsorption isotherm ist für niedriger pressure, right? And it's used in the analysis of Chemisorption? Oct 10 '16 at 17:02
• a) Please write english and not a mix of different languages. While I understand what you want from me and I really appreciate your wish to use "my" words, that is not helpful for a lot of people. b) Why do you think that? Oct 10 '16 at 17:06
• Ah, well my German sucks, and I'm trying my best to practice using it. Trouble is most of the time I'm not able to form complete sentences in German every time (in this case it's because I don't know what German for 'Pressure' is). Also, my bad, I ended up putting more effort trying to transliterate what I was trying to convey, than in the actual content of what I was trying to convey. So correcting that: Langmuir's is for chemisorption at high (I know I said niedriger, my bad) pressure right? Oct 11 '16 at 9:56