Wait, can you specify what you did exactly? Did you calculate a theoretical Langmuir adsorption isotherm with statistical mechanics and it soesn't match the experiments?

Different models give a different answer for the maximum adsorption because the models extrapolate the measurements to higher concentrations in a different way.

The experimental maximum is often a pseudo maximum. Plot your results versus a log c scale and check wether there is a real maximum.

Langmuir isotherm equation is obtained from first-order (or pseudo-first order) kinetics. So, it will fit well this kind of kinetic data, but it may not fit data that do not follow this mechanism. As Luuk K. Koopal stated, different models give a different answer.

Hello Tamim Alia,

From my experience, Langmuir usually predicts higher qmax value than the experimental one. Firstly, please do understand the basic here;

Models are created to help us predict the behaviour of a certain mechanism. If our data fit any model (using R2 value as an indicator), we assume that its the mechanism is mostly in-par with the model. However, we also need to consider the assumption of that model.

Now, I do not recommend comparing the q values of pseudo-order and Langmuir model, for the former is derived from the adsorption capacity and time. It "assumed" mostly the physical or chemical adsorption process using these 2 parameters. Please be careful when referring to physi- and chemi-sorption.

On the other hand, the isotherm model like Langmuir uses the data of adsorption capacity over a range of final concentration. It also has its own assumption. For instance, it assumes monolayer coverage and equal energy for all adsorption sites (this reflected in how the equation is derived). So, the qmax can be much higher than that of experimental results. It is the model prediction over the range of the experimental concentration. Maybe try fitting the linear equation of other models (Freundlich, Temkin) and see the R2 values. It is more useful to compare different isotherms.

I hope this is not too confusing.

Only when the kinetic model corresponds directly with the isotherm model the same result may be expected.

Different isotherm equations may give different qmax, but you still need an addition critirion to decide which is best.

By plotting the isotherm models and the measured isotherm vs log c gives you an impression of the correspondence of the shape of the measured isotherm with the model isotherms and a good idea about the concentration range the measurements span and which range is requird for the model isotherms.

A good agreement between kinetics and eq. can be just accidental.