Hi Mobina,

With the simplest approach I can say that your findings better fit the second degree kinetic model. It's best to think simple. Each kinetic model has a description. You can find them from sources.

Kind Regards.

Mrs/Ms Mobina,

I mean it's enough to make a statement based on second order model because your findings are more fit than the first order kinetic model.

I think your data was not sufficient , or the process is more likely a second order kinetics , and there are many references with 2nd order kinetics with metal ion adsorption

Mobina,

First order kinetic is approach the natural behavior. There are many influence factors with it. You should to separate the physical adsorption and first order kinetic through experimental design. You need to rethink the difference between different chemical kinetics.  Have a nice day.    

Thank you for your interest in this question.

I guess that you used two following models to describe the adsorption process:

logaritmic

t = 1/k ln((qe-qt)/qe)     (  ln(qe-qt) = ln qe – k t  )     (a)

hyperbolic

t = 1/k qt/(qe(qe-qt))      (  t/qt = 1/(k qe2) + t/qe  )  (b)

The adsorption curve usually looks as follows: at the beginning a rapid increase of qt and then slow asymptotic growth to equilibrium. This explains receiving similar values of r2 closed to 1 for the two different models.

There is strong correlation between qe and k in eq. a. If we use least square method (or any numerical method)  to determine the value of qe and k we may get many solutions (qe,k) for almost the same value of r2. This is the reason the qe value determining with the use of eq. a may differ significantly from experimental value.

Regards

Thanks Miroslaw to provide the difference between adsorption models. While, I am try to explain with mass transfer resistances in the first order kinetic model. This is a simple variable resistances with chemistry and physics. There are many model with experiment to correct the firsr order kinetic adsorption model.

With Best Regards.

Neither the logarithmic function (qt = f(t) exponential) nor the hyperbolic function have anything to do with the mass transfer resistance (external or internal). These are only functions (with no physical meaning) that are used to approximate individual kinetic curves. Regards,

I Think your process fits best to the pseudo-second-order kinetic model showing the chemical nature of the adsorption process.