Hello to everyone.

I am working on the adsorption of Cu2+ from aqueous solution onto the biochar.

I found a strange result in thermodynamic analysis. At low temperature (15C), ∆G is 2 kJ/mol (∆G is positive). it means that the process is not spontaneous, and in fact, it shouldn't happen. But, adsorption happens in reality based on the experimental results.

At higher temperature, ∆G is negative.

I found ∆G > 0 results in a few papers but there is no explanations except that: adsorption is not easy if ∆G > 0.

{Yargic et. al., Assessment of toxic copper(II) biosorption from aqueous solution by chemically-treated tomato waste, Journal of Cleaner Production 88 (2015) 152-159

Hajjaji et. al., Adsorption of blue copper on a natural and electrochemically treated bentonite, Appl Water Sci (2016) 6:11–23}

I have used following equations found in literature:

∆G = ∆H - T∆S (equation 1)

∆G = -RTln(Keq) (equation 2)

Keq = (Qeq) / (Ceq) (equation 3)

Qeq is the amount of copper adsorbed divided by the mass of adsorbent (mg / g)

Ceq is the concentration of copper in the solution at equilibrium (mg/L)

Combining equations and the linearization will give:

lnKeq = ∆S / R - ∆H / (RT)

This equation was used for linear regression to estimate the values of ∆S and ∆H. ∆G was calculated by the definition.

I tried to find a reason. I really appreciate it if you could help me.

Explanation 1) Regression error

R2 is 0.96 in linear regression. There is an error in estimation of ∆S and ∆H, and therefore ∆G. Especially the value of ∆G is small.

Explanation 2) Physical adsorption

The equation (2) is defined for a reversible chemical reaction (Gibbs free energy isotherm equation). But, what if the adsorption is physisorption?

Is it necessary for ∆G to be negative even in case of physical adsorption? Especially, the formula used is defined for a reversible chemical reaction.

The value of ∆H is 30.2 kJ/mol. Based on literature, if the ∆H is less that 40 kJ/mol, the dominant mechanism is physical adsorption. It means that, in my experiment, adsorption is physical.

Explanation 3) Definition of Keq

if ∆G > 0, based on equation 2, Keq < 1 which means that:

Qeq < Ceq.

On the contrary, if ∆G < 0, Qeq > Ceq.

But, there is not any rule or limitation in the adsorption regarding the relationship between Qeq and Ceq. Especially, there quantities have different units and dimensions, and it is not possible to compare them.

It seems that the definition of Keq in adsorption is not appropriate. Based on equation (2), equilibrium constant must be dimensionless. Ln is a natural logarithm and therefore Keq must be a pure number and cannot have a dimension, since logarithms can only be taken of pure numbers. But, in adsorption, Keq is not dimensionless.

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There is another confusing issue for me. If the assumption is equilibrium, ∆G must be zero. But, in all papers that I read, ∆G has a value either negative or positive. So, why?

Thank you very much for your time and patience to read such a long question.