4. Linear and non-linear fitting application

#### 4.1 Dyes

Dyes are organic substances that cause a permanent or temporary change in colour of a material; they are resistant to detergents. Dyes are widely employed in leather, food, textile, paper, rubber, and plastic industries. When dyes are released in the hydrosphere, they can block sunlight penetration, thus affecting the marine life. In addition, they give unpleasant colour to water making it unsafe for human consumption. To reduce the impact of dyes on the ecosystem, adsorption method has been employed to remove dyes from wastewater. Different kinetic models have been employed to study the adsorption of dyes from solution, these include; PFO, PSO, Elvoich, and IP models. The suitability of any model depends on error functions. Table 2 summarises the non-linear adsorption kinetics of different adsorbent.


While using a linear model of kinetics, based on R2

AC 2,4-D R<sup>2</sup>

DOI: http://dx.doi.org/10.5772/intechopen.80495

MIEX resin 2,4-D R<sup>2</sup>

AC 2,4-D R<sup>2</sup>

MWCNT Atrazine R2

Trimethylsilylated Gemfibrozil R2

Photocatalytic Indomethacin R<sup>2</sup>

Human hair Tetracycline R2

Sibunit 2,4-D R<sup>2</sup> PFO\*

Modelling of Adsorption Kinetic Processes—Errors,Theory and Application

Peanut Atrazine R<sup>2</sup> PFO\*

Biochars Atrazine R<sup>2</sup> PFO, PSO\*

R2

195

\*

acid.

Table 2.

Non-linear adsorption kinetics.

adsorption [61–65].

4.2 Other organic materials

of Rhodamine B by Mg3Si2O5(OH)4 followed second order system; however, expending non-linear analysis, R<sup>2</sup> of PFO jumped from 0.67 to 0.99 [26]. Using non-linear approach to analyse the kinetics of dye adsorption, the goodness fit of PFO increases drastically to an average of 0.90. The fitting of R<sup>2</sup> ≥ 0.9 is statistically good and can be used to make conclusions. Most error functions have been based on

Best model, NSD: normalised standard deviation, X<sup>2</sup> : chi-square, SE: standard error, SSE: sum of error squared, ARE: average relative error, RMSE: root-mean-square error, AC: activated carbon, 2,4-D: 2,4-dichlorophenoxyacetic

Adsorbent Solute Error function Kinetic Ref. AC Carbofuran R<sup>2</sup> PFO, PSO\* [50]

—this has forced researchers to conclude that both PFO and PSO explain the adsorption of dye. However, further analysis using different error functions can help to solve the puzzle. The adsorption of Methylene blue onto activated carbon fitted PFO and PSO well (R<sup>2</sup> > 0.9); however, the analysis of NSE, PFO had the least value [21]—thus the adsorption of methylene blue is best described by PFO. Linearization of PFO worsens the adsorption parameter—to have a better fitting of PFO during dye adsorption, the non-linear model should be used while studying dye adsorption. Therefore as more dye adsorption studies are being carried, non-linear model and error functions should be explored to avoid misleading conclusions. Similar trends have been observed by different research groups working on dye

A number of organic material have been classified as emerging contaminates, these include; pesticide, pharmaceuticals, disinfection by-products, fertilisers, and biological toxins. All these organic materials affect our ecosystem in a diverse way. The cheap and effective method of removing these materials from the solution is adsorption; however, there has been mixed results about the adsorption kinetics of these pollutants. Carbofuran is a pesticide, ranked among the most dangerous carbamate insecticides. Albeit its bioaccumulation is less, its mammalian toxicity potential is high. When consumed for a prolonged period of time at elevated concentrations (more than 0.09 mg/L), it disrupts the endocrine, breathing, devel-

opment and reproduction systems [50]. This necessitates its removal from

, it was evident the adsorption

, ARE, NSD PFO, PSO\*

, RMSE PFO, PSO\*

, ARE PFO, PSO\*

, ARE PFO\*

, IP [51]

, IP [52]

, [53]

, PSO\* [55]

, IP, Elovich\*

, PSO, IP [60]

, IP [56]

[57]

, PSO\*

, RMSE PFO, PSO\* [54]

, SE PFO, PSO\* [58]

, SE, SSE PFO, PSO\* [59]


#### Modelling of Adsorption Kinetic Processes—Errors,Theory and Application DOI: http://dx.doi.org/10.5772/intechopen.80495

\* Best model, NSD: normalised standard deviation, X<sup>2</sup> : chi-square, SE: standard error, SSE: sum of error squared, ARE: average relative error, RMSE: root-mean-square error, AC: activated carbon, 2,4-D: 2,4-dichlorophenoxyacetic acid.

#### Table 2.

Adsorbent Solute Error function Kinetic Ref. Activated carbon Acid red R<sup>2</sup> PFO, PSO\* [19]

, PSO\* [20]

, PSO [21]

, IP, Elovich\*

, PSO\* [24]

, PSO [25]

, PSO\* [26]

, PSO Elovich\*

, PSO Elovich [31]

PFO, PSO\* Elovich [35]

, PSO, IP, Elovich

, IP, Elovich

, X<sup>2</sup> PFO, PSO\* [37]

, RMSE PFO, PSO\* IP [42]

, NSD PFO, PSO\* IP [44]

, NSD PFO, PSO\* [47]

, ARE PFO, PSO\* [48]

, RMSE PFO, PSO\* [49]

, PSO IP, Elovich

, Avrami

, Elovich

, PSO, IP [46]

, IP [33]

[36]

[38]

[43]

[2]

[45]

, IP, [39]

, PSO\* [40]

, X<sup>2</sup> PFO, PSO\* Elovich [30]

, ARE PFO, PSO\* Elovich [32]

, IP [22]

[23]

[28]

, NSD PFO\*

, X<sup>2</sup> PFO, PSO\*

, X<sup>2</sup> PFO, PSO\*

, NSD PFO\*

, SSE PFO\*

, X<sup>2</sup> PFO, PSO\*

, SSE, ARE

, X<sup>2</sup> PFO\*

, RMSE, ARE PFO, PSO\*

, SSE PFO\*

, RMSE PFO\*

, ARE PFO, PSO\*

, SSE PFO, PSO\*

, X<sup>2</sup>

, X<sup>2</sup>

, ARE PFO, PSO\*

R2

, X<sup>2</sup>

Crystal violet R<sup>2</sup> PFO\*

Activated carbon Methylene blue R<sup>2</sup> PFO\*

Methylene blue R2

Fe3C/Fe3O4/C Methylene blue R<sup>2</sup> PFO, PSO\* [27]

Clinoptilolite Pb R<sup>2</sup> PFO, PSO\* [29]

Nano-TiO2 As NSD, R<sup>2</sup> PFO, PSO\* [34]

Tourmaline P R<sup>2</sup> PFO, PSO\* [41]

F R<sup>2</sup>

Mg3Si2O5(OH)4 Rhodamine B R<sup>2</sup> PFO\*

Fruit peels Cu R<sup>2</sup> PFO\*

Basic red 46

Activated carbon Methylene blue R2

Sugarcane bagasse Auramine-O, Safranin-T R<sup>2</sup>

Clinoptilolite Pb NSD, R2

Wheat straw Cu R2

Chitosan Cu R<sup>2</sup>

Rape straw Cu R2

Nano-iron As NSD, R2

Graphene oxide As R2

Nanocellulose Hg R2

Almond shell Hg R2

Zn-Al P R<sup>2</sup>

Iron N R2

Chitosan-Fe N R2

Cellulose N R2

Quintinite F R<sup>2</sup>

Mg-Al-Fe F R<sup>2</sup>

Coconut Carbofuran R2

AC Carbofuran R<sup>2</sup>

Chitosan P R<sup>2</sup> PFO\*

MCM-41 Hg R2

Mn2O3 nanofibres Methylene blue, malachite green,

Advanced Sorption Process Applications

Polyhedral oligomeric

MWCNTs hydrogel

Manganese carbonate

194

Non-linear adsorption kinetics.

While using a linear model of kinetics, based on R2 , it was evident the adsorption of Rhodamine B by Mg3Si2O5(OH)4 followed second order system; however, expending non-linear analysis, R<sup>2</sup> of PFO jumped from 0.67 to 0.99 [26]. Using non-linear approach to analyse the kinetics of dye adsorption, the goodness fit of PFO increases drastically to an average of 0.90. The fitting of R<sup>2</sup> ≥ 0.9 is statistically good and can be used to make conclusions. Most error functions have been based on R2 —this has forced researchers to conclude that both PFO and PSO explain the adsorption of dye. However, further analysis using different error functions can help to solve the puzzle. The adsorption of Methylene blue onto activated carbon fitted PFO and PSO well (R<sup>2</sup> > 0.9); however, the analysis of NSE, PFO had the least value [21]—thus the adsorption of methylene blue is best described by PFO. Linearization of PFO worsens the adsorption parameter—to have a better fitting of PFO during dye adsorption, the non-linear model should be used while studying dye adsorption. Therefore as more dye adsorption studies are being carried, non-linear model and error functions should be explored to avoid misleading conclusions. Similar trends have been observed by different research groups working on dye adsorption [61–65].

#### 4.2 Other organic materials

A number of organic material have been classified as emerging contaminates, these include; pesticide, pharmaceuticals, disinfection by-products, fertilisers, and biological toxins. All these organic materials affect our ecosystem in a diverse way. The cheap and effective method of removing these materials from the solution is adsorption; however, there has been mixed results about the adsorption kinetics of these pollutants. Carbofuran is a pesticide, ranked among the most dangerous carbamate insecticides. Albeit its bioaccumulation is less, its mammalian toxicity potential is high. When consumed for a prolonged period of time at elevated concentrations (more than 0.09 mg/L), it disrupts the endocrine, breathing, development and reproduction systems [50]. This necessitates its removal from

wastewater. The adsorption kinetics of carbofuran have been studied in almost every adsorption study. The analysis of non-linear and linear kinetic functions using the error parameters—the adsorption of carbofuran generally follows PSO. The experimental data for adsorption of carbofuran on coconut were almost in perfect correlation with PSO model [48]. Therefore, PSO should be given a priority while designing adsorption system for carbofuran adsorption.

Weber and Morris intra-particle diffusion model, Bangham model and Boyd kinetic

Modelling of Adsorption Kinetic Processes—Errors,Theory and Application

During metal adsorption, the best kinetic model is evaluated by assessing the error function after plotting linear or and linear model. In addition, qe must match reasonably well with experimental values, qecal at all initial concentrations of adsorbate with maximum R<sup>2</sup> and minimum χ<sup>2</sup> values. The adsorption of lead by pretreated clinoptilolite using the non-linear kinetics was best described by PFO [28]. Both raw and treated clinoptilolite PFO had R2 above 0.98 in addition to having the least values of SSE—the experimental values agreed well with the calculated values. The rate constant increased with the increase in the initial solute concentration. Using almost similar adsorbent, bentonite to adsorbed Pb from solution was best described by PSO than any other kinetic model [29]. This observation was based on the linear format of the kinetics—therefore, to make conclusive meaning, both non-

Copper is another mineral that has received considerable attention over the past

Ranked in top five among the most dangerous metal, the occurrence of Arsenic in wastewater is on raise due to increased usage of paintings, dyes, mining and smelting activities. The consumption of arsenic contaminated materials (above 10 parts per billion) causes muscle cramping, blood and hair loss—thus it is necessary to remove arsenic from water before it is consumed. The adsorption kinetics of arsenic vary from one experiment to another. While comparing the non-linear and linear kinetics of arsenic adsorption by nano-TiO2, both non-linear form of PFO and PSO yielded good fit (>0.90) [34]. The linear model of PFO yielded a very poor fit—thus basing on the linear model only can lead to poor judgement. Although there is no clear cut point on the best kinetic model, the recent adsorption studies of arsenic favour PSO (Table 2). Mercury is another heavy metal that has been investigated extensively due to its toxicity to animals. Although Hg is widely used in teeth amalgam, consumption of water levels with more 0.01 mg/L of Hg causes neuronal disorders and damages cardiovascular system [67]. This has called the development of cheap and efficient adsorbents to remove Hg from solution. While modelling the linear adsorption of Hg using MCM-41, PFO yielded a poor coefficient; however, when non-linear models were applied, PFO error functions improved [38]. Table 2 summaries the adsorption kinetics of Hg onto different adsorbents—the non-linear PSO model has been preferred over the other models. Metals in wastewater are always accompanied by anions like phosphate, sulphate, carbonate, and chloride. Among these, phosphate is the most crucial element. Phosphorus is a vital element in our ecosystem, without it life would be impossible. Phosphorus support bone and tooth growth, nerves and muscles. Phosphorus is vital during the formation and maintenance of DNA and cell membranes. However,

decades. Copper nanoparticles have been employed in lubricates to reduce the friction, tear and mend torn surfaces. Because of its good charge-discharge property, copper nanoparticles have been used in lithium batteries to improve coulombs efficiency. Due to numerous application of copper, it is mostly likely to enter into human bodies via the food and water chain. Excessive exposer of animals to copper destruct lipid profile, malfunction of the renal, and hepatocirrhosis [33]; this calls its removal from solution before it is consumed by humans. The removal of copper by adsorption process has been studied by different research groups. Although there are some studies that have favoured the adsorption of copper to be PFO nature [31], the assessment non-linear and linear adsorption kinetics of copper favours PSO—regardless of the adsorbent (Table 2). Comparing the error functions that determine the suitability of the kinetic model, PSO error parameters possess minimal variations. For example, the adsorption of copper onto chitosan followed

linear and linear model should be investigated.

DOI: http://dx.doi.org/10.5772/intechopen.80495

PSO mechanism [32].

197

model.

2,4-Dichlorophenoxyacetic acid (2,4-D) is herbicide that is globally used as a selective regulator of plants. 2,4-D is non-volatile but highly soluble in water. Thus exposure of groundwater to 2,4-D can lead to contamination. Long-time exposure of 100 μg/L of 2,4-D to humans can lead its accumulation in the seminal plasma and follicular mucus—increasing the risk of infertility. The removal of 2,4-D from solution using adsorption technique is mainly dominated by carbon related adsorbents [66]. Although the adsorption of 2,4-D using Sibunit raised a mixed observation as the initial concentration of changed [53], from Table 2, the assessment of error functions shows that adsorption of 2,4-D is mainly governed by PSO kinetics. Both non-linear and linear functions sorption kinetics favour PSO model. Another common herbicide expended in broadleaf weeds regulation is atrazine. Because of its high solubility in water, it has been detected in a number of groundwater wells, thus its ban in European countries; however, atrazine is extensively used in developing economies as pre and post-emergent herbicide to control weeds in crops. As 2,4-D, atrazine is an endocrine disruptor [56]. Several non-linear and linear kinetic studies have indicated that the adsorption of atrazine to be PSO in nature (Table 2).

Pharmaceuticals are organic compounds used to prevent, treat, and restore organ function. After restoring the damaged organ, they are flashed out of the body into the environment. In addition, pharmaceutical companies release numerous amount of waste into the water streams. The widely employed wastewater treatment technologies cannot remove pharmaceuticals wastes—thus the escalated presence of pharmaceutical products in the environment. Estrone, 17β-estradiol, 17α-ethinylestradiol, estriol, and acetaminophen are among the most alkaloids, steroid hormones and primary estrogens present in wastewater. As pesticides and herbicides, pharmaceuticals danger the nervous system. Most of the pharmaceuticals that are harmful to human nervous system tend to be lipophilic in nature, binding to solids. Nanofiltration, advanced oxidation, and adsorption are some of the main methods that are used to remove pharmaceuticals from wastewater. To effectively remove pharmaceuticals from solution, mesopore adsorbents with considerable surface area must be used. The adsorption kinetics of anionic, neutral, and cationic pharmaceutical onto mesopore trimethylsilylated all followed PSO model [58].

#### 4.3 Metals and anions

In allowable range, metals are vital elements that support human life—without them, life could be impossible. Among all the major contaminants, metals top the list because of their wide applicability in electricity, construction, and medicine. Accumulation of heavy metals in human bodies is dangerous. For example, thallium and manganese damages nervous system, while cobalt and nickel are carcinogenic. Different adsorbents have been developed to remove these metals from wastewater. These include; industrial waste, peat, wood, brown rice, straw, peanut shell, hazelnut shell, soybean filament, cotton seed pulp, sugar beet pulp, leaves. The adsorption of metals is affected by pH of the solution, contact time, the initial concentration of metal and ambient temperature are affected. The adsorption mechanism is evaluated by various kinetic models such as PFO, PSO, Elovich,

Modelling of Adsorption Kinetic Processes—Errors,Theory and Application DOI: http://dx.doi.org/10.5772/intechopen.80495

Weber and Morris intra-particle diffusion model, Bangham model and Boyd kinetic model.

During metal adsorption, the best kinetic model is evaluated by assessing the error function after plotting linear or and linear model. In addition, qe must match reasonably well with experimental values, qecal at all initial concentrations of adsorbate with maximum R<sup>2</sup> and minimum χ<sup>2</sup> values. The adsorption of lead by pretreated clinoptilolite using the non-linear kinetics was best described by PFO [28]. Both raw and treated clinoptilolite PFO had R2 above 0.98 in addition to having the least values of SSE—the experimental values agreed well with the calculated values. The rate constant increased with the increase in the initial solute concentration. Using almost similar adsorbent, bentonite to adsorbed Pb from solution was best described by PSO than any other kinetic model [29]. This observation was based on the linear format of the kinetics—therefore, to make conclusive meaning, both nonlinear and linear model should be investigated.

Copper is another mineral that has received considerable attention over the past decades. Copper nanoparticles have been employed in lubricates to reduce the friction, tear and mend torn surfaces. Because of its good charge-discharge property, copper nanoparticles have been used in lithium batteries to improve coulombs efficiency. Due to numerous application of copper, it is mostly likely to enter into human bodies via the food and water chain. Excessive exposer of animals to copper destruct lipid profile, malfunction of the renal, and hepatocirrhosis [33]; this calls its removal from solution before it is consumed by humans. The removal of copper by adsorption process has been studied by different research groups. Although there are some studies that have favoured the adsorption of copper to be PFO nature [31], the assessment non-linear and linear adsorption kinetics of copper favours PSO—regardless of the adsorbent (Table 2). Comparing the error functions that determine the suitability of the kinetic model, PSO error parameters possess minimal variations. For example, the adsorption of copper onto chitosan followed PSO mechanism [32].

Ranked in top five among the most dangerous metal, the occurrence of Arsenic in wastewater is on raise due to increased usage of paintings, dyes, mining and smelting activities. The consumption of arsenic contaminated materials (above 10 parts per billion) causes muscle cramping, blood and hair loss—thus it is necessary to remove arsenic from water before it is consumed. The adsorption kinetics of arsenic vary from one experiment to another. While comparing the non-linear and linear kinetics of arsenic adsorption by nano-TiO2, both non-linear form of PFO and PSO yielded good fit (>0.90) [34]. The linear model of PFO yielded a very poor fit—thus basing on the linear model only can lead to poor judgement. Although there is no clear cut point on the best kinetic model, the recent adsorption studies of arsenic favour PSO (Table 2). Mercury is another heavy metal that has been investigated extensively due to its toxicity to animals. Although Hg is widely used in teeth amalgam, consumption of water levels with more 0.01 mg/L of Hg causes neuronal disorders and damages cardiovascular system [67]. This has called the development of cheap and efficient adsorbents to remove Hg from solution. While modelling the linear adsorption of Hg using MCM-41, PFO yielded a poor coefficient; however, when non-linear models were applied, PFO error functions improved [38]. Table 2 summaries the adsorption kinetics of Hg onto different adsorbents—the non-linear PSO model has been preferred over the other models.

Metals in wastewater are always accompanied by anions like phosphate, sulphate, carbonate, and chloride. Among these, phosphate is the most crucial element. Phosphorus is a vital element in our ecosystem, without it life would be impossible. Phosphorus support bone and tooth growth, nerves and muscles. Phosphorus is vital during the formation and maintenance of DNA and cell membranes. However,

wastewater. The adsorption kinetics of carbofuran have been studied in almost every adsorption study. The analysis of non-linear and linear kinetic functions using the error parameters—the adsorption of carbofuran generally follows PSO. The experimental data for adsorption of carbofuran on coconut were almost in perfect correlation with PSO model [48]. Therefore, PSO should be given a priority while

2,4-Dichlorophenoxyacetic acid (2,4-D) is herbicide that is globally used as a selective regulator of plants. 2,4-D is non-volatile but highly soluble in water. Thus exposure of groundwater to 2,4-D can lead to contamination. Long-time exposure of 100 μg/L of 2,4-D to humans can lead its accumulation in the seminal plasma and follicular mucus—increasing the risk of infertility. The removal of 2,4-D from solution using adsorption technique is mainly dominated by carbon related adsorbents [66]. Although the adsorption of 2,4-D using Sibunit raised a mixed observation as the initial concentration of changed [53], from Table 2, the assessment of error functions shows that adsorption of 2,4-D is mainly governed by PSO kinetics. Both non-linear and linear functions sorption kinetics favour PSO model. Another common herbicide expended in broadleaf weeds regulation is atrazine. Because of its high solubility in water, it has been detected in a number of groundwater wells, thus its ban in European countries; however, atrazine is extensively used in developing economies as pre and post-emergent herbicide to control weeds in crops. As 2,4-D, atrazine is an endocrine disruptor [56]. Several non-linear and linear kinetic studies have indicated that the adsorption of atrazine to be PSO in nature (Table 2). Pharmaceuticals are organic compounds used to prevent, treat, and restore organ function. After restoring the damaged organ, they are flashed out of the body into the environment. In addition, pharmaceutical companies release numerous amount of waste into the water streams. The widely employed wastewater treatment technologies cannot remove pharmaceuticals wastes—thus the escalated presence of pharmaceutical products in the environment. Estrone, 17β-estradiol, 17α-ethinylestradiol, estriol, and acetaminophen are among the most alkaloids, steroid hormones and primary estrogens present in wastewater. As pesticides and herbicides, pharmaceuticals danger the nervous system. Most of the pharmaceuticals that are harmful to human nervous system tend to be lipophilic in nature, binding to solids. Nanofiltration, advanced oxidation, and adsorption are some of the main methods that are used to remove pharmaceuticals from wastewater. To effectively remove pharmaceuticals from solution, mesopore adsorbents with considerable surface area must be used. The adsorption kinetics of anionic,

neutral, and cationic pharmaceutical onto mesopore trimethylsilylated all followed

In allowable range, metals are vital elements that support human life—without them, life could be impossible. Among all the major contaminants, metals top the list because of their wide applicability in electricity, construction, and medicine. Accumulation of heavy metals in human bodies is dangerous. For example, thallium and manganese damages nervous system, while cobalt and nickel are carcinogenic. Different adsorbents have been developed to remove these metals from wastewater. These include; industrial waste, peat, wood, brown rice, straw, peanut shell, hazelnut shell, soybean filament, cotton seed pulp, sugar beet pulp, leaves. The adsorp-

tion of metals is affected by pH of the solution, contact time, the initial concentration of metal and ambient temperature are affected. The adsorption mechanism is evaluated by various kinetic models such as PFO, PSO, Elovich,

PSO model [58].

196

4.3 Metals and anions

designing adsorption system for carbofuran adsorption.

Advanced Sorption Process Applications

excessive presence of phosphorus in the ecosystem promotes bacteria growth. This affects marine life which in turn disorganises the ecosystem. Also, white phosphorus has been reported to cause stomach cramps, nausea, and drowsiness [68]. Various approaches are used in phosphate removal from wastewater including ion exchange, chemical precipitation, biological, and adsorption. The later has received considerable attention due to its efficiency and cost benefit. The adsorption kinetics of vanadium have been extensively studied in almost every study. There are mixed results about the adsorption kinetics of phosphorus. The adsorption of phosphorus onto tourmaline was best described by linear PSO; however, analysis of the nonlinear models produced better fitting for both models (R<sup>2</sup> > 0.95) [41]. Thus, before any conclusion is made about the kinetic model, non-linear kinetics should be investigated. There is no clear model that governs the adsorption of phosphorus (Table 2).

Acknowledgements

Author details

and Serdar Aydın1

199

George William Kajjumba<sup>1</sup>

\*

provided the original work is properly cited.

, Serkan Emik<sup>2</sup>

\*Address all correspondence to: saydin@istanbul.edu.tr

1 Department of Environmental Engineering, Istanbul University, Istanbul, Turkey

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 Department of Chemical Engineering, Istanbul University, Istanbul, Turkey

, Atakan Öngen<sup>1</sup>

, H. Kurtulus Özcan1

UZURI Advisory for the suggestions and advice.

DOI: http://dx.doi.org/10.5772/intechopen.80495

This study was funded by Istanbul University with project number BYP-2017-22921. Thanks to Joseph Wasswa, Laura Milillo and Michael Kayemba of

Modelling of Adsorption Kinetic Processes—Errors,Theory and Application

Nitrates are another ions that affect ecosystem extensively. The mechanisation of agriculture has promoted the use of nitrogen infused fertilisers at large scale. Excessive nitrogen promotes eutrophication—a condition that promotes algal growth. Algal growth cuts off oxygen supply in the aquatic system [69]. Therefore, before nitrate infused wastewater is released into the atmosphere, it must be treated. In addition, elevated amount of nitrate cause blue-baby syndrome. Adsorption has been employed to remove nitrates from wastewater. The adsorption of nitrate onto iron particles was best described by PFO [43]. However, during the adsorption of nitrate onto chitosan-Fe, PSO was favoured model [44]. There is more need to investigate the non-linear kinetics of nitrate adsorption. Fluorine is an essential element in our daily life—it is used in toothpaste to prevent teeth from decay. However, long term consumption of water with over 1.5 mg/L causes fluorosis, a condition that affects teeth, bones ossification, and neurological damage under extreme conditions [70]. To remove fluorine from water, precipitation and adsorption have been employed extensively. The adsorption kinetics of fluoride are complex, they depend on solute-adsorbent interaction. For example, the adsorption of fluoride onto manganese carbonate was second order in nature [47]; however, the analysis of a non-linear model of fluoride adsorption by Mg-Al-Fe, PFO controlled the reaction [46].

#### 5. Conclusion

Since the late C20th, majority of the adsorption studies have favoured PSO than PFO. This is attributed to the fact that, most of the plots of PSO include values as the system approaches equilibrium—the values of <sup>t</sup> =qt ≈ <sup>t</sup> =qe . The incorporation of values close to equilibrium produces a fitting index close to one. For PFO, as the system approaches equilibrium, the qt qe slant to zero, thus ln qe qt becomes abnormally large at equilibrium reducing the accuracy. In all adsorption studies sampled, R<sup>2</sup> has is used to test goodness fit. However, to have a better comparison of R<sup>2</sup> , the scale must be the same. Therefore, to understand the adsorption mechanism of any solute, non-linear models should be applied, and to assess the best fit model, non-linear least squares must be applied. Many linear forms of PFO, PSO and Elovich have been developed, but most of them are based on erroneous assumptions. Consequently, while studying the adsorption kinetics, the above given equations should be used. Using PSO model to conclude that the adsorption kinetics is chemisorption is misleading. The models should also be checked with diffusion models to best describe the adsorption mechanism.

Modelling of Adsorption Kinetic Processes—Errors,Theory and Application DOI: http://dx.doi.org/10.5772/intechopen.80495
