Science
BET Adsorption Isotherm: Monolayer Capacity, Constant C & Surface Area
Calculate Brunauer-Emmett-Teller (BET) energetic constant C = 1 + (s / i), monolayer capacity n_m = 1 / (s + i), and N2 specific surface area S_BET (m^2/g) from linearized isotherm slope and intercept.
Convert linearized 77 K nitrogen physisorption plots into m^2/g catalyst area!
Over the classical relative pressure window 0.05 <= P / P_0 <= 0.30, plotting 1 / (n * ((P_0 / P) - 1)) against P / P_0 yields a straight Brunauer-Emmett-Teller (BET) line with slope s = (C - 1) / (n_m * C) and y-intercept i = 1 / (n_m * C) (both in g/mmol when adsorbed gas n is reported in mmol/g)!
Adding slope + intercept immediately isolates monolayer molar capacity n_m = 1 / (s + i) (mmol/g), while dividing gives the dimensionless BET adsorption enthalpy constant C = 1 + (s / i) (which must be positive—a negative intercept signals micropore filling outside the valid BET range)! Multiplying n_m (in mol/g) by Avogadro's constant N_A = 6.02214e23 and the 77 K nitrogen molecular cross-section sigma_N2 = 0.162 nm^2 = 0.162e-18 m^2 delivers Specific Surface Area S_BET in m^2/g!
| Porous Solid Sample | BET Slope s (g/mmol) | Intercept i (g/mmol) | BET Constant C & S_BET (m^2/g) |
|---|---|---|---|
| Calcined Ceramic Support | 38.50 | 0.50 | C = 78.00 | S_BET = 2.50 m^2/g |
| Mesoporous Silica Catalyst | 4.80 | 0.20 | C = 25.00 | S_BET = 19.51 m^2/g |
| Microporous Zeolite (Invalid Fit) | 0.95 | -0.02 (<= 0!) | Invalid Negative BET Intercept |
Specific Surface Area S_BET (m^2/g) from N2 77 K BET Slope & Intercept
Evaluates n_m = 1 / (s + i) in mmol/g, converts to mol/g (* 1e-3), and multiplies by N_A (6.02214e23) * sigma_N2 (0.162e-18 m^2), guarding against negative or zero slope/intercept.
=IF(OR(B2 <= 0, B3 <= 0), "Invalid BET Fit (Intercept <= 0)", ROUND((1 / (B2 + B3)) * 0.001 * 6.02214E23 * 0.162E-18, 2))Dimensionless BET Energetic Constant C = 1 + (s / i)
Quantifies first-layer heat of adsorption relative to multilayer liquefaction heat.
=IF(B3 <= 0, "Invalid BET Fit (Intercept <= 0)", ROUND(1 + (B2 / B3), 2))Try the example
Use the original values or change them to test your understanding.