Heavy Metal Adsorption onto Kappaphycus sp. from Aqueous Solutions: The Use of Error Functions for Validation of Isotherm and Kinetics Models

Table 1

Equations of the isotherm, kinetic, and thermodynamic models used in the study.

Model	Equation	Reference
Langmuir		[25]
		[26]
Freundlich		[27]
Temkin		[28]
D-R		[29]
		[30]
	PFO		[31]
PSO		[32]
	Elovich		[28]
			[33]
IpD		[34]
Thermodynamics		[35]

(mg L⁻¹): adsorbate initial concentration, (mg L⁻¹): adsorbate equilibrium concentration, (mg g⁻¹): observed biosorption capacity at equilibrium, (mg g⁻¹): maximum biosorption capacity, (L mg⁻¹): Langmuir constant related to the energy of adsorption, (): a dimensionless constant, known as separation factor, (mg g⁻¹) (L mg⁻¹): Freundlich isotherm constant related to the sorption capacity, : a constant which gives an idea of the grade of heterogeneity, (8.314 J mo⁻¹): universal gas constant, (°K): absolute temperature, (L mg⁻¹): equilibrium binding constant corresponding to the maximum binding energy, (J mol⁻¹): Temkin constant related to heat of sorption, (mol² kJ⁻²): Dubinin-Radushkevich isotherm constant, : Polanyi potential related to the equilibrium concentration, (kJ mol⁻¹): mean free energy of biosorption, (mg g⁻¹): equilibrium adsorption uptake at time, , (min⁻¹): pseudo-first-order rate constant of adsorption, (g mg⁻¹ min⁻¹): pseudo-second-order rate constant of adsorption, (mg g⁻¹ min⁻¹): initial adsorption rate, (min): half-adsorption time, (mg g⁻¹ min⁻¹): initial adsorption rate constant, β (g mg⁻¹): desorption constant, (mg g⁻¹): boundary layer diffusion effect, (mg g⁻¹ min^−0.5): rate constant for intraparticle diffusion, (kJ mol⁻¹): change in Gibbs free energy, (kJ mol⁻¹): change in enthalpy, (kJ mol⁻¹ K⁻¹): change in entropy, and : thermodynamic equilibrium constant.