*3.9. Adsorption Isotherms*

The Langmuir model is expressed according to Equation (5) as:

$$\frac{\mathbf{C\_e}}{\mathbf{q\_e}} = \frac{1}{\mathbf{q\_m}\mathbf{b}} + \frac{\mathbf{C\_e}}{\mathbf{q\_m}} \tag{5}$$

where Ce is the equilibrium concentration of metal ions solution, qe is the amount of equilibrium adsorbed metal ions, qm is maximum adsorption capacity and b is the Langmuir isotherm constant. The separation factor RL of Langmuir isotherm was examined by using Equation (6) as:

$$\mathbf{R\_L} = \frac{1}{1 + \mathbf{b} \times \mathbf{C\_0}}\tag{6}$$

where Co represent the initial concentration of metal ions. The RL values show the nature of adsorption i.e. irreversible (RL = 0), linear (RL = 1), unfavorable (RL > 1) and favorable (0 < RL < 1). The Freundlich isotherm model is given by Equation (7) as:

$$
\ln \mathbf{q}\_{\text{e}} = \ln \mathbf{K}\_{\text{F}} + \frac{1}{\mathbf{n}} \ln \mathbf{C}\_{\text{e}} \tag{7}
$$

where KF and n are Freundlich constants and indicate the adsorption capacity and adsorption intensity of adsorbent respectively.

The interaction between adsorbent (GT-cl-poly(DMA) hydrogel and GT-cl-poly(DMA)/RGO hydrogel composite) and adsorbate (Hg2<sup>+</sup> and Cr6<sup>+</sup>) was explained through isotherms model Equations (5) and (7). The Langmuir parameters were calculated from the graph between Ce/qe and Ce (Figure 8a–d) and presented in Table 5. The Freundlich parameters were determined from the graph of lnqe vs lnCe (Figure 9a–d) and depicted in Table 5. For the Langmuir isotherm, the higher R<sup>2</sup> suggests that the Langmuir isotherm was best suited for the removal of Hg2<sup>+</sup> and Cr6<sup>+</sup> ions on GT-cl-poly(DMA) hydrogel and GT-cl-poly(DMA)/RGO hydrogel composite. For Hg2+, GT-cl-poly(DMA) and GT-cl-poly(DMA)/RGO showed higher removal capacity of 625 mg g−<sup>1</sup> and 666.6 mg g−<sup>1</sup> respectively. Similarly, for Cr6<sup>+</sup>, the maximum reported removal capacities were 401.6 mg g−<sup>1</sup> and 473.9 mg g−<sup>1</sup> by GT-cl-poly(DMA) hydrogel and GT-cl-poly(DMA)/RGO hydrogel composite respectively.

**Figure 8.** Langmuir isotherm model for Hg2<sup>+</sup> adsorption by (**a**) gum tragacanth-cl-*N,N*dimethylacrylamide (GT-cl-poly(DMA)) hydrogel (**b**) reduced graphene oxide incorporated gum tragacanth-cl-*N,N*-dimethylacrylamide (GT-cl-poly(DMA)/RGO) hydrogel composite, Langmuir isotherm model for Cr6<sup>+</sup> adsorption by (**c**) gum tragacanth-cl-*N,N*-dimethylacrylamide (GT-cl-poly(DMA)) hydrogel (**d**) reduced graphene oxide incorporated gum tragacanth-cl-*N,N*dimethylacrylamide (GT-cl-poly(DMA)/RGO) hydrogel composite. (Experimental conditions for Hg2<sup>+</sup>: adsorbent dose—0.035 g, pH—5.5, metal ion concentration—20–300 ppm, rpm = 200 and for Cr6+: adsorbent dose—0.045 g, pH—3.5, metal ion concentration—20–500 ppm, rpm = 200).

**Figure 9.** Freundlich isotherm model for Hg2<sup>+</sup> adsorption by (**a**) gum tragacanth-cl-*N,N*dimethylacrylamide (GT-cl-poly(DMA)) hydrogel (**b**) reduced graphene oxide incorporated gum tragacanth-cl-*N,N*-dimethylacrylamide (GT-cl-poly(DMA)/RGO) hydrogel composite, Freundlich isotherm model for Cr6<sup>+</sup> adsorption by (**c**) gum tragacanth-cl-*N,N*-dimethylacrylamide (GT-cl-poly(DMA)) hydrogel (**d**) reduced graphene oxide incorporated gum tragacanth-cl-*N*,*N*dimethylacrylamide (GT-cl-poly(DMA)/RGO) hydrogel composite, (Experimental conditions for Hg2<sup>+</sup>: adsorbent dose—0.035 g, pH—5.5, metal ion concentration—20−300 ppm, rpm = 200 and for Cr6+: adsorbent dose—0.045 g, pH—3.5, metal ion concentration—20−500 ppm, rpm = 200).


