**Abstract**

Adsorption is a process in which a substance that is in a liquid phase accumulates on a solid surface and is then removed from the liquid phase. An adsorption isotherm describes the equilibrium of adsorption of a substance on a surface at a constant temperature. It represents the amount of material bound to the surface as a function of the material present in the solution. In the adsorption process, the compound to be removed is called the adsorbate and the solid on which the compound is adsorbed is called the adsorbent. The affinity of the adsorbate for the adsorbent is quantified using adsorption isotherms. Adsorption isotherms are mathematical equations that describe the relationship between the amount of adsorbate adsorbed on an adsorbent and the concentration of adsorbate in solution when equilibrium has been reached at constant temperature. Adsorption isotherms are performed by giving a volume-determined solution containing a known amount of adsorbate along with various dosages of the adsorbent. The mixture is held at constant temperature with stirring until it reaches equilibrium. When this is the case, the concentration of the adsorbate in the aqueous phase is measured and the adsorption capacity at equilibrium for each experiment is calculated from the mass balance.

**Keywords:** isotherms, Henry's, Langmuir, Freundlich, Temkin, Dubinin–Radushkevich, Redlich–Peterson, sips, Halsey, Harkin–Jura, Elovich, Flory–Huggins, fowler–Guggenheim, Jovanovic and Kiselev

## **1. Introduction**

Wastewater treatment has become one of the most important issues for the development of nations. During treatment, contamination can be found that cannot be treated by biological means, but there are also other recalcitrant compounds such as heavy metals that, in certain concentrations, can make biological treatment of wastewater difficult. Treatment of these compounds requires a different type of treatment: chemical precipitation, reverse osmosis, filtration, ion exchange, electrochemical degradation, photocatalytic degradation, nanofiltration, irradiation [1], and

adsorption, to name a few. There are processes that are very efficient in removing impurities at trace concentrations, such as reverse osmosis. However, they have the disadvantage that the initial cost is very high and the consumables, such as membranes and maintenance, are very expensive. One of the most promising methods for removing recalcitrant compounds such as heavy metals is adsorption. This is because it is cheap, easy to implement, and environmentally friendly [2]. To understand adsorption mechanisms, it is important to obtain equilibrium data, commonly known as adsorption isotherms. The adsorption isotherms are important for describing how the adsorbate molecules or ions interact with the surface adsorption sites. Therefore, correlation of the equilibrium data using a theoretical or empirical equation is essential for interpretation and prediction of adsorption [3]. An adsorption isotherm is an equation expressing the relationship between the amount of solute adsorbed by the adsorbent and the solute concentration in the liquid phase [4–14]. They are important because they describe how an adsorbate interacts with an adsorbent, and they are critical to the design of an adsorption process. Several equilibrium models have been developed to describe the relationship of isotherms at equilibrium. The models used are those of Henry, Langmuir, Freundlich, Temkin, Dubinin–Radushkevich (DR), Redlich– Peterson (RP), Sips, Halsey, Harkin–Jura, Elovich, Flory–Huggins, Fowler– Guggenheim, Jovanovic, and Kiselev.
