Linear and Nonlinear Regression Methods for Equilibrium Modelling of p-Nitrophenol Biosorption by Rhizopus oryzae: Comparison of Error Analysis Criteria

Table 1

Mathematical equations of the applied single component isotherm models.

Isotherm model		Nonlinear form		Linear expression	Plot
Langmuir [36]	(1)	𝑞𝑒=𝐾𝐿𝑐𝑒1+𝑎𝐿𝑐𝑒,	(2)	𝑐𝑒𝑞𝑒=1𝐾𝐿+𝑎𝐿𝐾𝐿𝑐𝑒	𝑐𝑒𝑞𝑒 versus 𝑐𝑒
Freundlich [37]	(3)	𝑞𝑒=𝐾𝐹⋅𝑐^𝑛𝐹𝑒	(4)	log𝑞𝑒=log𝐾𝐹+𝑛𝐹⋅log𝑐𝑒.	log𝑞𝑒 versus log𝑐𝑒.
Redlich and Peterson [38]	(5)	𝑞𝑒=𝐾𝑅⋅𝑐𝑒1+𝑎𝑅𝑐𝑒^𝑏	(6)	ln𝐾𝑅𝑐𝑒𝑞𝑒−1=𝑏ln(𝑐𝑒)+ln(𝑎𝑅).	ln𝐾𝑅𝑐𝑒𝑞𝑒−1 versus ln(𝑐𝑒)
Multilayer [39]	(7)	𝑞𝑒=𝑄𝑚𝐾1𝑐𝑒1−𝐾2𝑐𝑒1+𝐾1−𝐾2𝑐𝑒,		Second-order polynomial form	𝑐𝑒𝑞𝑒 versus 𝑐𝑒
			(8)	𝑐𝑒𝑞𝑒=𝑐^2𝑒𝐾^22−𝐾1𝐾2+𝑐𝑒𝐾1−2𝐾2+1𝑄𝑚𝐾1
Fritz and Schluender [40]	(9)	𝑞𝑒=𝐴⋅𝑐𝑒^𝛼1+𝐵⋅𝑐𝑒^𝛽		—	—