Dear Ahmad,

of course both are correct that you like they are inter convertible  units. But to me the mg/g seems reasonable

Uptake capacity can be calculated in terms of mg/g or mmol/g both are correct. But mg/g is most commonly used. 

In Adsorption studies, q basically represents efficiency of adsorption which is expressed as q=(amount of adsorbate adsorbed in mg)/(amount of adsorbent used for adsorption expressed in gm). 

Now we use the formula q=[(Ci-Cf)*V] / W. 

for example:-

 Ci=10 mg/L, Cf=0.01 mg/L, V=25 ml or 0.025 L, W=0.01 gm.

Putting these values in the equation we get,

q=[(10-0.01)mg/L * 0.025 L]/0.01 gm or

q=[9.99 mg *0.025]/0.01 gm {Note that the L gets cancelled} or

q=[0.24975 mg/0.01 gm] or 

q=24.975 mg / gm 

Thus 24.975 mg of  ions are adsorbed by 1 gm adsorbent. This q value you have got for the contact time which may be decide earlier .

You must do a contact time study for 5, 10, 15, 20, 30, 45, 60, 120, 180,.... and so on minutes. Find the q values for all the contact time.Plot q vs time. You will find that a particular time your q value saturates. That is your qe or q at equilibrium. [Note that the initial concentration should be same for all the sets]

The qt will correspond to q values for the respective time t.

All the best.

 Salah

U said i agree: but in case of comparison like HG>Pb>Cu as 52, 47 and 16 mg/g respectively. but when we convert into mmol/g it will become reverse as the molecular weight of 200,207 and 63 respectively. if we divide it with molecular weight it will be reverse. please explain me...

Both description make sense mg/g and mmol/g. And as already said they can be transfered into each other. If you want to do a a direct comparison it depends what you want to look at, the gravimetric uptake or the molar uptake or what you want to emphasis.

As you said for the ions Hg, Pb and Cu you have a gravimetric uptake in this order for your material. However, converted into molar values the trend is changed, which simply tells you that per gram material only a certain number of atoms can be adsorbed and having the same material you can store e.g 0.259 (Hg), 0.227 (Pb) and 0.252 (Cu) now mmol per gram. This means you can store more Hg than Cu and Pb ions in the same amount of material. Whatever unit you need, you can take. Usually to make a material more comparable towards uptake of e.g. different gases molar uptake is better for comparison. Because as you said a compound with a high molecular mass may seem to yield in a better uptake but actually you can store less ions or molecules etc in it. I hope I could help you a bit out.

As mentioned in the other answers both mg/g and mmol/g can be used. However, mmol/g counts the number of adsorbed ions and this makes it the favorable unit.

When one deals with the same solid and different metal ions and an adsorption model is used to find the capacities, then it is better to use mmol/g, because this counts the number of moles (molecules, ions) that can be accomodated on the surface. When the solid has a given number of adsorption sites per g, then for different small simple molecules the capacity in mmol/g should be the same and equal to the number of moles of sites/g. For molecules or ions that are larger than the surface sites, geometrical restrictions and lateral repulsion result in a lower capacity than corresponding to the number of sites. Other problems will occur when the solid contains pores that that cannot be entered by larger molecules.

For metal ions (positive) the capacity of surfaces with a constant (negative) charge (clay surfaces with a small edge surface fraction) is often given by the cation exchange capacity expressed as mmol univalent cations/g. The capacity of a given ion now depends on its valence.

Most charged surfaces have however, a charge that is dependent on the solution conditions such as pH and background electrolyte concentration. In this situation the cation exchange capacity of a given solid is thus a function of the solution conditions. Therefore, one has to control pH and background electrolyte concentration next to control of the (mostly low) metal ion concentration. Comparisons of different metal ions (mmol/g) should be made at constant pH and salt concentration. With metal ions adsorption the observed plateau values are often notan indication of the site capacity, but due to lateral electrstatic repulsion between the adsorbed metal ions. This repulsion is screened by the background eletrolyte concentration and becomes most important when the  surface charge is overcompensated by the metal ion charge (super equivalent adsorption).

Note also that, in general, the Langmuir equation only consideres adsorption to adsorption sites and not the lateral interaction. In case of application of the L eq. to ion adsorption the "saturation" adscorption or capacity is often primarily due to the lateral repulsion and not to real surface saturation. See for more detail on simple ion binding models the reference indicated below. 

Chapter Chapter 11, Interface Science 2008: Adsorption of charged components