I want to calculate ∆G, ∆H and ∆S values for an adsorption isotherm using the following formulae:
1. Adsorption equilibrium constant (Kd) = qe/Ce
where,
qe=equilibrium adsorption capacity (mg/g) and
Ce=equilibrium concentration of the adsorbate (mg/L)
2. qe = {(Co-Ce)*V}/m
where,
Co = initial concentration of the adsorbate (mg/L)
V = Volume of the bathing solution (L)
m = mass of the adsorbent (g)
3. ln(kd) = (∆S/R)-(∆H/RT)
4. ∆G = ∆H - T∆S
I have used seven initial concentrations of the adsorbate (Co) (viz. 2, 6, 8, 10, 20, 40 and 80 ppm As) for conducting the adsorption isotherm experiment under two temperatures (i.e., two sets of adsorption reactions, each with seven levels of Co).
The problem I am facing is that I am getting seven different Kd (Adsorption equilibrium constant) values for seven 'Co's under each set of adsorption experiment.
Which Kd value should I take for further calculation of the thermodynamic parameters (∆G, ∆H and ∆S)? Do I need to average all the seven Kd values for a specific temperature? Or should I take the Kd value corresponding to the highest initial concentration (i.e., 80 ppm As) of the adsorbate? Or something else?
Kd should be dimensionless in order to get ∆G with the right units. Since Kd =qe/Ce in ( mg/g)/(mg/L) gives Kd in (L/g). To do the conversion, you should multiply the obtained values of Kd expressend in (L/g) by (the molecular weight of the considered pollutant (g/mol) x ( the number of moles of water per L of solurion (55 moles/L) . Once, you do this, you will get Kd without dimension and ∆G, ∆H and ∆S values with the right units. GOOD LUCK. Benaouda BESTANI
Hi Bestani Benaouda , thanks for telling me the way of making Kd correct and dimensionless.
However, the values of the rectified Kds are still varying with varying Co (initial concentration of sorbate) and I am confused about which value (or average value) of Kd to consider under a specific temperature for further thermodynamic calculations.
Of course you get for each Co a new Ceq at different T. Even you keep Co constant, you get a new Ce because you change T.
It is so easy to do it: Run 3 different adsorption tests at 3 different temperatures. After , you should get Ce and qe for each test, calculate 3 values of Kd in (L/g), do the conversion to Kd ( domensionless) to get 3 values of new Kd. Plot lnKd ( domensionless) versus 1/T will give you straight line from which you can get the thermodynamic property such as deltaG
For each Co you get Ce and qe for each T
3 or 4 values of T are enough to pot Ln Kd vs 1/T@
Bestani Benaouda thanks for trying to answer my question.
I have run 2 sets of adsorption tests for 2 different temperatures.
Under each set (for a single temperature), I have seven graded doses of arsenic or 7 "Co"s.
My problem is, under a single temperature, I am getting 7 Ce and & 7 qe, thus 7 values of Kd, for the said 7 Co.
I am wondering Kd corresponding to which Co to consider so that I get 2 Kds (from the total obtained 14 Kds) for 2 temperatures?
Hi Bestani Benaouda , could you please also share an article where you have calculated the Kd using the procedure you described? It would be a good reference for a detailed understanding.
Arkaprava Roy The adsorption equilibrium constant (Kd) is a measure of the extent of adsorption under specific conditions. In your case, you have conducted adsorption isotherm experiments at two different temperatures with seven different initial concentrations of the adsorbate (Co). This has resulted in different Kd values for each concentration and temperature.
The choice of which Kd value to use for further calculations of thermodynamic parameters (∆G, ∆H, and ∆S) depends on the specific requirements of your study and the assumptions of your model. Here are a few approaches:
Remember, the choice of approach should be guided by the specifics of your study and the assumptions of your model.
Hope it helps
Jajati Mandal sir, thanks for answering my question.
I think I have to go with the Kd for the highest initial concentration.
Best regards
Dear Arkaprava Roy,
Kindly use the attached document as a guide.
Rather than using the formula, Kd = Ce/Co, first, it is better to determine the isotherm that fits with the experimental data. Then you can calculate the value of Kc at different temperature using the fitted isotherm model.
For further information refer this article, Article Facile synthesis of bismuth and iron co-doped hydroxyapatite...
Dagne Bayih Adamu , Thanks for answering my question. This is going to help me a lot!
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