Adsorption Calculations: Surface Area and Activation Energy

The number of molecules that can form a complete monolayer on a surface is simply the total available surface area divided by the area each individual molecule occupies. For a spherical droplet, the total surface area is 4*π*r², using the RADIUS (half the given diameter), converted into the same area units as the per-molecule figure (here, square nanometres) before dividing. For a water droplet of diameter 3.5 mm (radius 1.75 x 10⁻³ m), the surface area works out to about 3.85 x 10¹³ nm²; dividing by 4.18 nm² per SLS molecule gives about 9.20 x 10¹² molecules. The general method — total surface area divided by area per adsorbed molecule, with careful unit conversion to a common area unit — applies to any monolayer-adsorption counting problem, not just this specific surfactant example.

The same relationship can be rearranged to calculate an ADSORBENT surface area from a measured mass of gas adsorbed: surface area S equals (mass of gas adsorbed / molar mass of the gas) x Avogadro number x cross-sectional area per molecule — essentially converting the adsorbed mass into a number of molecules (via moles and Avogadro number), then multiplying by the area each one covers. This is the standard way surface area of a porous solid (like silica or activated carbon) is measured experimentally, using a gas with a well-known molecular cross-sectional area (commonly nitrogen).

Physisorption (weak van der Waals attraction between adsorbate and surface) is generally EXOTHERMIC and DECREASES as temperature rises (higher temperature gives adsorbed molecules enough energy to escape the weak attractive forces holding them to the surface) — so a claim that physisorbed gas mass increases with temperature is false. The extent of physisorption also depends strongly on the specific gas involved (its boiling point, polarisability, molecular size all matter), so two different gases physisorbed on the same adsorbent at the same temperature generally do NOT show the same number of molecules adsorbed per unit mass — a claim that they would is also false. Chemisorption, by contrast, involves genuine chemical bond formation between adsorbate and surface, and this shows up as a much HIGHER activation energy than physisorption (physisorption activation energies are typically only a few kJ/mol; chemisorption activation energies are comparable to real bond energies, often tens to hundreds of kJ/mol) — an adsorption process reported with an activation energy of 96 kJ/mol (such as H₂ on a nickel surface) is therefore correctly classified as chemisorption, not physisorption.