requiring constant equilibrium adsorption. In practice, keeping an adsorbent-adsorbate system at constant temperature is simplest and so the adsorption isotherm is the most widely used method to represent the equilibrium state of an adsorbent-adsorbate system. 5.1.2.1 Adsorption Isotherm The adsorption isotherm can be used to derive many different properties of the adsorbent and adsorbate such as the surface area, pore volume and size distribution, relative adsorbability and the enthalpy of adsorption. Many adsorption isotherm equations have been derived including the Langmuir, the Freundlich, the Brunauer-Emmett-Teller (BET) and the Dubinin equations. These are some of the most widely used isotherms but for the purposes of this project we will be using the Langmuir isotherm equations to represent the equilibrium state of our systems. According to Bansal and Goyal, there are three theoretical approaches for the derivation of an adsorption isotherm: The kinetic approach The statistical approach The thermodynamic approach Of these we will be using the kinetic approach to derive the Langmuir isotherm considering the kinetic approach uses the condition of equilibrium which states that the rate of adsorption must be equal to the rate of desorption. 5.1.2.2 Langmuir Isotherm Derivation If it is assumed that the number of filled at equilibrium is and the number of sites not filled θ is such that then rate of adsorption, denoted as can be written as, + = 1, rabs θo θ θo equ. 5.1 where is the adsorption coefficient, the fraction of molecules adsorbed onto the surface of the a
requiring constant equilibrium adsorption. In practice, keeping an adsorbent-adsorbate system at constant temperature is simplest and so the adsorption isotherm is the most widely used method to represent the equilibrium state of an adsorbent-adsorbate system. 5.1.2.1 Adsorption Isotherm The adsorption isotherm can be used to derive many different properties of the adsorbent and adsorbate such as the surface area, pore volume and size distribution, relative adsorbability and the enthalpy of adsorption. Many adsorption isotherm equations have been derived including the Langmuir, the Freundlich, the Brunauer-Emmett-Teller (BET) and the Dubinin equations. These are some of the most widely used isotherms but for the purposes of this project we will be using the Langmuir isotherm equations to represent the equilibrium state of our systems. According to Bansal and Goyal, there are three theoretical approaches for the derivation of an adsorption isotherm: The kinetic approach The statistical approach The thermodynamic approach Of these we will be using the kinetic approach to derive the Langmuir isotherm considering the kinetic approach uses the condition of equilibrium which states that the rate of adsorption must be equal to the rate of desorption. 5.1.2.2 Langmuir Isotherm Derivation If it is assumed that the number of filled at equilibrium is θ and the number of sites not filled is θo such that θ + θo = 1, then rate of adsorption, denoted as rabs can be written as, equ. 5.1 where a is the adsorption coefficient, the fraction of molecules adsorbed onto the surface of the
Characterization_of_Activated_Carbon_sample-_Cu+2_Adsorption_Isotherm_.docx