Table 5.

Batch and column adsorption models and its parameters.

Adsorption model	Linear equation	Plot	Parameters of model	Heavy metals
				Pb	Cu	Cd	Zn	Ni	Cr
Batch isotherm
Langmuir	$\frac{1}{q_e}=\frac{1}{q_m{K}_L{C}_e}+\frac{1}{q_m}$	$\frac{1}{q_e}vs.\frac{1}{C_e}$	KL (L/mg)	0.0678	0.0604	0.0554	0.0454	0.0401	0.0381
			qm (mg/g)	174.7	154.5	144.2	133.4	122.5	111.5
			R2	0.9984	0.9985	0.9963	0.9987	0.9948	0.9981
Freundlich	$log{q}_e=log{K}_F+\frac{1}{n}log{C}_e$	$log{q}_{e}vs.log{C}_e$	KF (L/mg)	19.2514	17.4514	15.1424	10.1578	7.1212	6.0287
			n (-)	0.2451	0.3125	0.3525	0.3747	0.4001	0.4212
			R2	0.9875	0.9884	0.9825	0.9810	0.9840	0.9864
Temkin isotherm	$q_e=\frac{\mathit{RT}}{b}ln{K}_T-\frac{\mathit{RT}}{b}ln{C}_e$	$q_{e}vs.ln{C}_e$	b (kJ/mol)	750.25	725.12	645.45	640.12	632.2	603.1
			KT (L/gm)	45.45	56.45	75.45	80.12	85.12	89.23
			R2	0.9758	0.9721	0.9756	0.9752	0.9745	0.9762
Column isotherm
Thomas model	$ln\left[\left(\frac{C_O}{C_t}\right)-1\right]=\frac{k_{\mathit{TH}}{q}_{o}m}{Q}-\frac{k_{\mathit{TH}}{C}_o{V}_{\mathit{eff}}}{Q}$	$ln\left[\left(\raisebox{1ex}{$C_o$}\!\left/ \!\raisebox{-1ex}{$C_t$}\right.\right)-1\right]$ vs. time	kTH (mL/mg·min)	0.6112	0.5124	0.5714	0.6555	0.5457	0.5252
			q0 (mg/g)	205.6	185.8	154.5	133.3	120.6	110.9
			R2	0.9858	0.9812	0.9898	0.9878	0.9852	0.9811
Bed depth service time model	$t=\frac{N_O}{C_{0}U}Z-\frac{1}{k_{\mathit{BDST}}{C}_0}ln\left(\frac{C_0}{C_t}-1\right)$	Bed-height vs. time	kBDST (mL/mg·min)	0.3787	0.3353	0.3232	0.3425	0.2785	0.3011
			No (mg/g)	9784.5	9524.5	9455.5	9335.6	9248.0	9025.3
			R2	0.9788	0.9699	0.9787	0.9785	0.9758	0.9785
Adam and Bohart model	$ln\left[\left(\frac{C_O}{C_t}\right)-1\right]=K_{\mathit{AB}}{N}_O\frac{Z}{u}-K_{\mathit{AB}}{C}_{t}t$	$ln\left[\left(\raisebox{1ex}{$C_o$}\!\left/ \!\raisebox{-1ex}{$C_t$}\right.\right)-1\right]$ vs. time	kAB × 10–5 (1/mg·min)	8.7822	7.4521	8.0127	7.8784	6.4510	6.2122
			No (mg/L)	9557.5	9218.2	9025.2	8956.1	8356.9	8124.5
			R2	0.9757	0.9787	0.9752	0.9788	0.9745	0.9756