# Calculating surface area from BET results

I have been trying to work out the workings of the BET method and I have come to a standstill.

The surface area of a sample is given by

$$S_{\text{BET}} = \frac{\nu_{\text{m}}Ns}{V}$$

where $\nu_{\text{m}}$ is the amount in the monolayer (given in $\mathrm{cm^3/g}$), $N$ is Avogadro's constant, $s$ is the adsorption cross-section of the adsorbate ($\pu {0.162 nm^3}$ for $\ce{N2}$) and $V$ is the molar volume of the gas ($\pu {22.4 L/mol}$).

If I run this sample through a commercial software that comes with the adsorption equipment, for a given mesoporous sample, it gives me $\nu_{\text{m}} = 209.6160~\mathrm{cm^3/g}$, and a final result of $S_{\text{BET}} = 912.5 ~\mathrm{m^2/g}$.

If I try to calculate this myself (converting everything into SI units), however, I get that same result, but divided by a factor of $1\times 10^9$.

I think I'm making some stupid unit conversion mistake, but I can't see it.

Your problem is not the unit conversion, but the units you have used. The adsorption cross-section of $\ce{N2}$ ($s$) has been found using BET method is $\pu{0.162 nm^2}$ (Langmuir). Yet, you have used $\pu{0.162 nm^3}$, more than a factor of $1 \times 10^9~\mathrm{nm/m}$.

• It is always a good idea to use dimensional anaylsis to check an equation if something seems to be "going wrong". Also you can use it to check equations if you are not sure if the equation is right. May 4, 2018 at 5:10
• Thanks, I knew it was something stupid that I failed to check. Thanks also for the edits, I'm not very familiar with S-X's LaTeX markup so I wasn't sure how to enter units. May 4, 2018 at 11:43