Calculating surface area from BET results

Question

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.

Answer 1

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 $1 \times 10^9~\mathrm{nm/m}$.