Adsorption equilibrium
Gas on a surface.
Measure, fit, balance.
Compare Henry, Langmuir, Freundlich and BET isotherms. Fit your own observations, inspect temperature effects and estimate isosteric heat only where measurements overlap.
One temperature. Four models.
Uptake is absolute mol/kg of dry adsorbent (numerically equal to mmol/g). BET is shown only inside its specified P/P₀ window. The four parameter sets are independently specified, not calibrated to one another.
Closed-vessel equilibrium
p is adsorbate partial pressure. Inert gas is ideal and nonadsorbing. The gas volume stays fixed; adsorbed-phase volume is neglected. No kinetics or energy balance is calculated.
Bring your own observations
Fit isotherms. Compare temperatures.
All calculations stay in this browser. No files or data are uploaded. Export your study before leaving.
Paste measurements, confirm units and source, then fit. The synthetic example uses the same absolute loadings at 300, 320 and 340 K.
Reproduction of observations
Residual = predicted − observed q. Unweighted least squares in the original uptake scale. Compare RMSE only on the same observations: BET may use fewer rows. A good fit does not validate the adsorption mechanism or extrapolation.
Isosteric heat from overlapping data
Model equations and limitations q in mol/kg; P in kPa
Langmuir: q = qs bP/(1 + bP)
Freundlich: q = K(P/1 kPa)ᵐ
BET: q = qm C r / [(1 − r)(1 + (C − 1)r)], r=P/P₀
Henry describes the low-pressure linear limit. Langmuir represents a finite population of equivalent independent sites. Freundlich is empirical, has no finite saturation capacity, and generally lacks a finite Henry limit when m<1. This lab restricts 0<m≤1. BET describes multilayer adsorption under its assumptions and must not be extended to r≥1.
BET windows depend on the adsorbate and adsorbent. The displayed monolayer-pressure and q(1−r) checks are screening flags, not a complete IUPAC consistency assessment. No certified surface area, pore-size distribution or uncertainty interval is inferred. A high R² is not sufficient evidence of model validity.
The vessel solver uses the selected model only within the declared pressure window. It assumes absolute adsorption and an ideal gas and limits total pressure to 200 kPa as a teaching scope, not an accuracy guarantee. An out-of-range solution is reported unavailable. Competitive adsorption and IAST are not included.
Temperature and isosteric heat Do not extrapolate to missing loadings
Fits are independent at each measured temperature. No temperature law is inferred for the fitted parameters. For isosteric analysis, ln(P/kPa) is interpolated linearly in absolute q within each measured isotherm, then regressed against 1/T at nine common loadings. Positive Qst denotes exothermic adsorption under the ideal-gas approximation.
Every isotherm must have strictly increasing pressure and uptake, with a common positive-loading interval. Duplicate pressures, hysteresis or nonmonotone measurements block this analysis; they are not silently averaged or repaired. Fits can still be inspected. Two temperatures define a slope but cannot test its linearity; three or more are preferable. No confidence intervals are constructed from interpolated points.
Reported excess uptake is not interchangeable with absolute uptake, especially at high pressure. This lab requires an external, justified conversion before import. Amounts reported as gas volume at STP also require their stated reference conditions to convert.