The application of Rumex abyssinicus based activated carbon for Brilliant Blue Reactive dye adsorption from aqueous solution

Table 3 Adsorption isotherm models with linear and non- linear forms

Isotherm model	Non-linear form	Linear form	References
Langmuir	${\text{Qe}} = \frac{QmaxKLCe}{{1 + KLCe}}$	$\frac{1}{Qe} = \frac{1}{Qmax} + \frac{1}{KLQmaxCe}$	[45,46,47]
Freundlich	Qe = KFCe^1/n	Log Qe = log KF + $\frac{1}{n} $ log Ce	[46, 48, 49]
Temkin	Qe = $\frac{RT}{b}$ ln($K_{T}$ Ce)	Qe = $\frac{RT}{b}lnCe + \frac{RT}{b}lnK_{T}$	[46, 48, 50]
Sips	Qe = $\frac{{Qmax(KCe)^{n} }}{{(1 + KCe)^{n} }}$	ln $\left( {{\raise0.7ex\hbox{${Qe}$} \!\mathord{\left/ {\vphantom {{Qe} {Qmax}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Qmax}$}} - Qe} \right)$ = ${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {ns}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${ns}$}}$ ln Ce + ln $(Ks)^{ns}$	[32, 45]

ISSN: 2661-801X

Isotherm model	Non-linear form	Linear form	References
Langmuir	\({\text{Qe}} = \frac{QmaxKLCe}{{1 + KLCe}}\)	\(\frac{1}{Qe} = \frac{1}{Qmax} + \frac{1}{KLQmaxCe}\)	[45,46,47]
Freundlich	Qe = KFCe^1/n	Log Qe = log KF + \(\frac{1}{n} \) log Ce	[46, 48, 49]
Temkin	Qe = \(\frac{RT}{b}\) ln(\(K_{T}\) Ce)	Qe = \(\frac{RT}{b}lnCe + \frac{RT}{b}lnK_{T}\)	[46, 48, 50]
Sips	Qe = \(\frac{{Qmax(KCe)^{n} }}{{(1 + KCe)^{n} }}\)	ln \(\left( {{\raise0.7ex\hbox{${Qe}$} \!\mathord{\left/ {\vphantom {{Qe} {Qmax}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Qmax}$}} - Qe} \right)\) = \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {ns}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${ns}$}}\) ln Ce + ln \((Ks)^{ns}\)	[32, 45]