Thanks Mr. Alexandre A.S Goncalves for the valuable answer.

Sir I understand the basic procedure, but my doubt is that:

The equilibrium concentration depends upon the initial concentration and uptake qt is also depend upon initial and equilibrium concentration as per formula: qe=((C0-Ce)/m) * V

• qe is the amount of dye absorbed per unit mass of adsorbent (mg g-1), C0 is initial concentration and Ce is concentration of dye (mg L-1) at time t. m is mass of adsorbent in g and V is volume of dye solution in L.

But in plotting graph(attached) they used both dependent variables i..e,  qe and Ce.

Please suggested, the reason behind the problem. 

Hi Jagdeep Singh,

Several solutions with different concentrations at same temperature must be tested. This is performed aiming to determine the surface capacity of the adsorbent at certain temperature. To find the value of the adsorption constant ''k'', you need to repeat such procedure at different temperatures. Therefore, the initial concentration will change at constant temperature. Later on, same concentrations will be used at different temperatures. The equilibrium concentration is dependent upon the value of initial concentration. I have attached links of papers that I believe it will be helpful to you.

Best Regards,

Alexandre.

http://pubs.acs.org/doi/pdf/10.1021/acsami.5b06951

http://www.sciencedirect.com/science/article/pii/000186869080006L?via%3Dihub

Thanks Mr. Alexandre A.S Goncalves for the valuable answer.

Sir I understand the basic procedure, but my doubt is that:

The equilibrium concentration depends upon the initial concentration and uptake qt is also depend upon initial and equilibrium concentration as per formula: qe=((C0-Ce)/m) * V

• qe is the amount of dye absorbed per unit mass of adsorbent (mg g-1), C0 is initial concentration and Ce is concentration of dye (mg L-1) at time t. m is mass of adsorbent in g and V is volume of dye solution in L.

But in plotting graph(attached) they used both dependent variables i..e,  qe and Ce.

Please suggested, the reason behind the problem. 

Yes, the equilibrium concentration depends on initial one. But regardless the absolute value of both of them, the point will fit in the same curve at the same temperature.  If you increase the initial concentration, the equilibrium one will go high  but on the equilibrium curve and if you decrease the initial concentration, the equilibrium concentration will go down but still on the same curve.

1- Adsorption isotherm is an equilibrium relation that relates (qe) the equilibrium amount of dye absorbed per unit mass of adsorbent (mg g-1) and equilibrium concentration( Ce) so you should plot (qe) versus (Ce)

2- You should insure that you reached equilibrium in your experiments

3- Initial concentration affects adsorption kinetics 

You can read some textbooks and references in mass transfer such as "Trybal: Mass transfer operations" and "Seader, Henley and Hoper: Separation Process Principles" to further understand the phenomenon and its mathematical relations and calculations 

Thanks, Ibrahim Ismail  and Eslam Gomaa ِAl-Sakkari  for valuable suggestion 

Adsorption isotherm is, by definition, the adsorbed amount (usually in weight of adsorbate per weight of adsorbent) as a function of the equilibrium concentration of adsorptive (the molecule being adsorbed) at constant temperature.

Then, you need to know all concentrations in solution and do that calculation. If the amount of adsorbent changes, then you need to correct it in the adsorbed amount (remember it is weight of adsorbate/weight of adsorbent).

Hi Jagdeep, my experience is in gas adsorption, but I will try to explain what I think is happening.  Also the following article may be of interest.

http://pubs.acs.org/doi/abs/10.1021/am4055657?journalCode=aamick .

In your experiment you have a volume V of solution containing dye at an initial concentration Co.  You bring this into contact with a mass m of adsorbent and agitate for 24 hours.  This results in mass transfer of dye into the adsorbent (hydrogel) and concentration Ct in the solution which will fall with time.

Eventually there should be negligible change in Ct and this indicates no more dye can be adsorbed at the prevailing concentration Ct.  The concentration of dye remaining in the solution is Ce and is in equilibrium with the dye adsorbed (qe).

By material balance the amount adsorbed, qe must be the amount removed from solution, = volume of solution (V) x change on concentration (Co-Ce). 

so qe = V.(Co-Ce).

The adsorbent has a very large but finite capacity on the internal surface within its pores to accommodate dye.  Equilibrium exists when the tendency (rate) of the dye to enter and stick to the interior of the adsorbent is exactly balanced by the tendency or rate at which it escapes and diffuses back into the bulk external solution.

So an equilibrium isotherm curve simply represents (at the stated fixed temperature) how various fixed initial amounts of adsorbate (dye) distribute between the liquid solution and the adsorbed phase.

I think I had better stop as you probably know all this already.  One unusual characteristic - the isotherms show a higher capacity at higher temperature, which is contrary to my experience on gas adsorption.  Perhaps you can explain this.