Introduction
Materials and methods
Materials
Preparation of pomegranate peel adsorbent
Batch adsorption studies
Instrumental characterization procedures
Results and discussion
Instrumental characterizations
Fourier-transform infrared (FTIR) spectroscopy
X-ray diffraction (XRD)
Scanning electron microscopy (SEM)
Thermal analysis
Effect of process variables
Adsorption isotherm modeling
Two-parameter isotherm models | Parameters | Adsorption kinetic equations | Parameters |
---|---|---|---|
Langmuir \(q_{e} = \frac{{k_{L} .C_{e} }}{{1 + a_{L} .C_{e} }}\) | \({a}_{L}\) | Pseudo-first order \({q}_{t}={q}_{e}\left[1-exp\left({-k}_{1}t\right)\right]\) | k1 |
qe | |||
\({K}_{L}\) | |||
Freundlich \(q_{e} = K_{F} .C_{e}^{1/n}\) | 1/n | Pseudo-second order \({q}_{t}=\frac{{k}_{2}{q}_{e}^{2\bullet }t}{\left(1+{k}_{2}{q}_{e}t\right)}\) | K2 |
qe | |||
KF | |||
Temkin \({q}_{e}=\frac{RT}{{b}_{T}}\bullet ln\left({A}_{T}{C}_{e}\right)\) | AT | Intra-Particle Diffusion \({q}_{t}={k}_{id}{t}^{0.5}+{q}_{e}\) | Kid |
qe | |||
bT | |||
Dubinin–Radushkevich \(q_{e} = q_{D} .\exp ( - B_{D} [RT\ln (1 + \frac{1}{{C_{e} }})]^{2} )\) | \({q}_{D}\) | Bangham’s Equation \({q}_{t}={q}_{e}\left[1-exp\left({-k}_{b}{t}^{n}\right)\right]\) | qe |
n | |||
kb | |||
BD | |||
Elovich Equatio \({q}_{t}=\beta ln\left(\alpha \beta t\right)\) | α | ||
Β |
Error Function | Equation |
---|---|
Average relative error (ARE) | \(ARE = \sum\limits_{i = 1}^{n} {\left| {\frac{{(q_{e} )_{\exp .} - (q_{e} )_{calc.} }}{{(q_{e} )_{\exp .} }}} \right.} \left. {} \right|\) |
Average percentage error (APE) | \(APE\% = \frac{{\sum\limits_{i = 1}^{N} {\left| {[((q_{e} )_{\exp .} - (q_{e} )_{calc.} )/q_{\exp .} \left. ] \right|} \right.} }}{N}x100\) |
Sum squares error (ERRSQ/SSE) | \(ERRSQ = \sum\limits_{i = 1}^{n} {[(q_{e} )_{calc.} - (q_{e} } )_{\exp .} ]^{2}\) |
Hybrid fraction error function (Hybrid) | \(Hybrid = \frac{100}{{n - p}}\sum\limits_{i = 1}^{n} {[\frac{{((q_{e} )_{\exp .} - (q_{e} )calc.)^{2} }}{{(q_{e} )_{\exp .} }}} ]_{i}\) |
Marquardt’s percent standard deviation (MPSD) | \(MPSD = (\sqrt[{100}]{{\frac{1}{n - p}\sum\limits_{i = 1}^{n} {[\frac{{((q_{e} )_{\exp .} - (q_{e} )_{calc.} )}}{{(q_{e} )_{\exp .} }}} }}]^{2}\) |
Nonlinear chi-square test (χ2) | \(\chi^{2} = \sum {\frac{{(q_{e.\exp } - q_{e.theoretical} )^{2} }}{{q_{e.theoretical} }}}\) |
Coefficient of determination (R2) | \(R^{2} = \frac{{\sum\limits_{i = 1}^{n} {} (q_{e,calc} - \overline{{q_{e,\exp } }} )^{2} }}{{\sum\limits_{i = 1}^{n} {} (q_{e,calc} - \overline{{q_{e,\exp } }} )^{2} + \sum\limits_{i = 1}^{n} {} (q_{e,calc} - q_{e,\exp } )^{2} }}\) |
Langmuir | Freundlich | Temkin | D–R |
---|---|---|---|
qmax = 707.424 | 1/nF = 0.41 | KT = 73.95 | qD = 554.53 |
KL = 7.55 | KF = 49.16 | bT = 43.24 | βD = 1.2E-04 |
RL = 0.011 | R2 = 0.994 | R2 = 0.940 | R2 = 0.895 |
R2 = 0.999 | SNE = 1.026 | SNE = 1.013 | E = 64.55 |
SNE = 1.059 | SNE = 1.014 |
Langmuir model
Maximum adsorption capacity (mg/g) | Adsorbate | Refs |
---|---|---|
165.9 | Cr(VI) | [12] |
30.12 | Cu(II) | [17] |
3.31 | Cr(VI) | [18] |
20.87 | Cr(VI) | [11] |
9.45 | Cr(VI) | [19] |
23.05 | Cd(II) | [20] |
193.9 | Pb(II) | [21] |
7.54 | Ni(II) | [22] |
8.98 | Co(II) | [22] |
166.63 | Pb(II) | [23] |
47.17 | Cr(VI) | [24] |
18.5 | Fe(II) | [25] |
6.18 | NH4(I) | [26] |
600 | Pb(II) | Present work |
Freundlich model
Temkin model
Dubinin–Radushkevich (DR) model
Adsorption kinetics modeling
Pseudo-first-order | Pseudo-second-order | Elovich | Intra-particle diffusion |
---|---|---|---|
Co = 150 mg/L | |||
qe = 94.50 | qe = 104.66 | α = 32.696 | Kid = 11.870 |
k1 = 0.039 | k2 = 2.0E-04 | β = 0.020 | c = 83.658 |
R2 = 0.995 | R2 = 0.996 | R2 = 0.995 | R2 = 0.974 |
SNE = 1.058 | SNE = 1.095 | SNE = 1.090 | SNE = 1.056 |
Co = 300 mg/L | |||
qe = 151.86 | qe = 166.77 | α = 30.048 | Kid = 18.371 |
k1 = 0.040 | k2 = 1.18E-04 | β = 9.7E-03 | c = 134.883 |
R2 = 0.998 | R2 = 0.995 | R2 = 0.990 | R2 = 0.956 |
SNE = 1.111 | SNE = 1.068 | SNE = 1.029 | SNE = 1.038 |