Fundamentals of adsorption onto activated carbon

Consider a volume of solution loaded with a molecule (A) that is in contact with a mass of adsorbent. The system is continuously stirred for a time. Assuming there is no chemical or biological reaction but only a mass transfer ftom the liquid phase to the solid surface, the mass balance can be written  

Consider fee same situation as above. A new adsrabent is used, and the experiment is performed at constant temperature. The concentration of fee solute (A) is analyzed as a function of time. A kinetic curve is obtained lor fee molecule being removed from the solution. An example of an azo dye (Acid Red 18) adsorption in aqueous solution is ven in Fig.l. From fee previous data and the mass balance equation, the adsorption capacity is found as a function of time as presented in the same figure. 

The Langmuir theory assumes that the adsorption is an equilibrated reaction between a solute (A) and a surfk (0) following the equation  

Langmuir proposes a relation to model the evolution of the amount adsorbed  

Coupling Eq. (4) with mass balance enables a normalized initial adsorption coefficient to be calculated  

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