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^q k q ²

 ( ¹ )t

q

^t 2 e ^e
The initial sorption rate (t = 0) is found as follows

k q

2
h  _{2 e}
In this equation, k₂-constant velocity, q_e – the amount of metal absorbed in the sorbent of a given mass (mg g^-1), t-time (minutes) [8]. Study of adsorption equilibrium: Adsorption isotherms are the most important thing for the analysis of equilibrium processes. Of the many models used to represent equilibrium processes in liquid and solid systems, the most widely used and most convenient are the Langmuir and Freundlich models [9].
Langmuir adsorption isotherm model: It is represented by the equation below.

q  q
K_LC_e

e max _{1  K}
L^Ce

Here: q_e - the amount of metal absorbed into the sorbent of a certain mass (mg g^-1), C_e
– the equilibrium concentration of the solution (mg l^-1), q_max - the maximum amount of metal absorbed into the sorbent of a certain mass (mg g^-1).
In order to find the Langmuir constant (K_L), the Langmuir equation (2) can be converted to a linear form. The values of q_max and K_L can be determined from the C_e dependence graph of C_e/q_e.

С_{e }
q_e
1
q_e К_L
 1
^qmax
 C_e

An important feature of the Langmuir isotherm parameters is that the separation coefficient “R_L” can be used to draw conclusions about the relationship between the adsorbent and the adsorbate.

R_L 
1
1  К_L

 C₀

In this regard(4): It represents 0 ˂ R_L ˂ 1 comfortable, R_L ˃ 1 uncomfortable, R_L
= 1 linear and R_L = 0 irreversible for the adsorption process [10].
Freundlich adsorption isotherm model It is represented by the equation (5) below.

n
q_e  K_F C_e
It is possible to study the sorption processes that take place in different (non- ideal) solutions by using the Freundlich isotherm equation [11]. The linear equation of this model can be expressed as follows:

logq_e
 log K_F

•