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International Journal of
eISSN: 2475-5559

Petrochemical Science & Engineering

Research Article Volume 7 Issue 1

Kinetics of the bioremoval of selected heavy metal ions from wastewater by the application of modified Nigerian Bambara groundnuts shells

Ibifuro A,1 Akuma O,2 Tonye O. E2

1Chemical/Petrochemical Engineering Department, Rivers State University, Port Harcourt, Nigeria
2CCentre for Gas, Refining and Petrochemical Engineering Department, University of Port Harcourt, Nigeria

Correspondence: Akuma O, Centre for Gas, Refining and Petrochemical Engineering Department, University of Port Harcourt, Nigeria, Tel +2348036766966

Received: April 18, 2024 | Published: April 30, 2024

Citation: Ibifuro A, Akuma O, Tonye OE. Kinetics of the bioremoval of selected heavy metal ions from wastewater by the application of modified Nigerian Bambara groundnuts shells. Int J Petrochem Sci Eng. 2024;7(1):8-18. DOI: 10.15406/ipcse.2024.07.00138

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Abstract

Nigerian Bambara Groundnut Shells (BGS) were modified to obtain Raw Bambara Groundnut Shell (RBGS), Carbonized Bambara Groundnut Shell (CBGS) and Bambara Groundnut Shell Lignin (BGSL) and used as bio-adsorbents to remove Lead (Pb), Nickel (Ni) and Cadmium (Cd) ions from industrial wastewater. The adsorption study investigated the effects of bio-adsorbent dosage, wastewater pH and contact time. Preliminary analyses which include: an Atomic Adsorption Spectrophotometer (AAS) on the wastewater and Scanning Electron Microscopy (SEM) were carried out on the different modified BGS, while the mechanism of adsorption was described using adsorption kinetic models. AAS analysis revealed that the concentrations of the heavy metals of interest were above WHO permissible limits in wastewater. SEM analysis revealed that the microspores of the bio-adsorbents were covered after the adsorption process. After the adsorption process, 85 – 91% Pb and 80 – 85% Ni and 92 - 98% Cd were removed by the different bio-adsorbents at optimum conditions of adsorption capacity which occurred at 0.8g dosage, pH of 7 and 120 min contact time. Generally, equilibrium occurred within 90 minutes. The mechanism of Pb, Ni and Cd ions adsorption onto RBGS, CBGS and BGSL bio-adsorbents can be described with diffusion and chemisorption processes. Pseudo-second-order kinetics fitted the adsorption process, implying that it is the rate-controlling step. This study found that the modified Bambara groundnut shell bio-adsorbents can be used as an alternative to conventional adsorbents used to treat industrial wastewater effluent

Keywords: bio–adsorbents, wastewater, dosage, adsorption, heavy metals

Abbreviations

RGBS, raw Bambara groundnut shells; CBGS, carbonized Bambara groundnut shells; BGSL, Bambara groundnut shells; Pb, lead; Ni, nickel; Cd, cadmium; AAS, atomic adsorption spectrophotometer; SEM, scanning electron microscopy; WHO, World Health Organization; H2SO4, sulphuric acid; NaOH, sodium hydroxide.

Introduction

In Nigeria, the issue of water availability and the pursuit of sustainable clean water solutions have been complicated by the detrimental impact of pollution stemming from municipal, industrial, and anthropogenic activities.1,2 The rise in urbanization and industrialization has contributed to the contamination of both ground and surface water sources with heavy metals such as Lead (Pb), Nickel (Ni) and Cadmium (Cd) resulting in a decline in water quality due to the excessive generation of waste.3,4 Consequently, water bodies have become tainted with untreated or insufficiently treated effluents from various sources, including industrial, commercial, pharmaceutical, agricultural, and domestic sources.5

In an effort to mitigate the adverse impacts of water contaminants with these heavy metals in the environment and human health, regulatory authorities establish regulations and limits for the discharge of wastewater into the environment. However, these measures often prove insufficient, necessitating the treatment of wastewater.6 Various treatment methods are available for the removal of water pollutants, but some of these approaches are associated with high costs and limited effectiveness.7 Conventional techniques employed to eliminate heavy metals from water include chemical precipitation, flotation, flocculation, sedimentation, solvent extraction, oxidation/reduction, dialysis/electro-dialysis, reverse osmosis, ultra-filtration, electrochemical deposition, ion exchange, and adsorption.8

The choice of a suitable technique is predicated on its efficacy and cost-effectiveness.7 Among the various methods, adsorption has emerged as an effective means of removing heavy metals owing to its numerous advantages. These advantages encompass cost-effectiveness and the ready availability of adsorbents, minimized sludge production, ease of operation, and the potential for adsorbent reuse after undergoing subsequent treatment steps. Adsorption technology operates on a surface-based mechanism, wherein contaminants present in the solution interact with a solid material termed as adsorbents. The porous surface structure of the adsorbent facilitates the adherence of solute molecules, or adsorbate, from the solution onto the adsorbent surface.7,8

Apparently, the issue of water pollution, arising from the introduction of heavy metals due to industrial activities and the convectional techniques used for the treatment of industrial wastewater is experiencing a significant concern on a global scale. This is because some convectional adsorbents require synthetic chemicals to reactivate after its use and these chemicals have negative impacts on the environment.1 Consequently, the quest for environmentally-friendly, cost-effective treatment methodologies to eliminate pollutants has become a prominent area of academic investigations. Biomass, encompassing a wide range of organisms resulting from photosynthesis, comprising animals, plants, and microorganisms, emerges as a valuable biological resource and they are abundant in nature, low pollution and sustainable.2

Hence,numerous researchers have used the adsorption technique to remove contaminants from water by using affordable adsorbents prepared locally from plant and animal waste, such as palm fibre,11 bamboo,12 soursop,13 rice husk,14 garlic and ginger.2 Locally formulated adsorbent can be modified by means of physical or chemical activation. The activation of these wastes increases the carbon content to over 70% when pyrolised into charcoal with high porosity and large surface area. 9-10 Bambara groundnut shells, an agricultural waste readily available in the local setting, represent an under-utilized resource. The Bambara groundnut, a legume indigenous to Africa, is a significant crop on the continent, with its total annual production surpassing 300,000 tons.15 Additionally, it serves as a low-cost source of high-quality protein. Leveraging Bambara shell as a natural, cost-effective, safe, and environmentally friendly alternative, it offers promising potential for conventional remediation systems16 Lignin, extracted from agricultural residues, exhibits notable adsorption capacity and a strong affinity for removing heavy metal.17,18

Consequently,16 investigated carbonized Bambara groundnut shell as an adsorbent for removal of paraquat dichloride from aqueous solution. The authors described the adsorption process as chemisorption, and the kinetics followed the pseudo-second-order kinetics with an R2 value of 0.999. Also,20 conducted research on the use of biosorbents derived from the leaves of Ziziphus spina-christi for removing cadmium (Cd2+) ions from aqueous solutions through adsorption. It was discovered that the adsorption process followed the Langmuir isotherm model more closely.

The study conducted by21 explored the efficacy of biosorbents derived from the leaves and stems of Calotropis procera for eliminating chromium ion from aqueous solutions. The adsorption behaviour of chromium ion by the biosorbents was best described by the Freundlich isotherm model and pseudo-second-order kinetic model, as revealed by an evaluation of the isotherm and kinetics of the adsorption process. Also, the authors in18 used chemically activated carbon from Bambara groundnut shell to remove pendimethalin (PE) (herbicides) and paraquat dichloride (PQ) from aqueous solution. It was found that pseudo-second-order kinetics provided better explanation of PE and PQ removal suggesting that the adsorption was chemisorption.

Similarly, 22 examined how chitosan-modified bamboo charcoal adsorbent could be used to simultaneously adsorb Pb (II) and Cd (II) ions from an aqueous solution. The results revealed that the adsorption kinetics followed the pseudo-second-order model while the adsorption isotherm was best described by the Langmuir isotherm model. Also, 23 investigated the adsorption capacity and optimum condition for adsorption of Arsenic ion (As (V)) onto grapefruit peel biosorbent. They varied the solution pH, temperature, adsorbent dosage, and initial concentration of As (V) to obtain the optimal condition for best removal. The kinetic data indicated that the pseudo-second order model was more appropriate than other kinetic models evaluated in the study.

Therefore, the purpose of this study is to modify Bambara groundnut shells into various forms: Raw Bambara Groundnut Shells (RBGS), Carbonized Bambara Groundnut Shells (CBGS) and Bambara Groundnut Shell Lignin (BGSL). The adsorption capacities of the different Bambara groundnut shell formulations were tested for their ability to remove heavy metals in industrial wastewater collected from a petrochemical plant. Adsorption variables such as the initial concentration of metals, pH level and contact time were studied and the efficiency of the adsorbents and the level of contaminants that can be removed were observed. Furthermore, the understanding of adsorption mechanisms frequently involves the interpretation of kinetic characteristics governing the interplay between the adsorbent and the liquid phase. In this study, the interaction mechanism between the metals (Pb, Ni and Cd) and the modified Bambara adsorbents was assessed using models such as pseudo-first order kinetics, pseudo-second order kinetics, and the intra-particle diffusion model.

Methodology

Collection and preparation of samples

The preparation of Bambara groundnut shells for experimental analysis followed the method described in the work of 16–18 for processing bio-adsorbents intended for use in the adsorption process. The collected shells were thoroughly washed and cleaned with fresh tap water to remove any impurities. Subsequently, they were spread out on a clean surface and allowed to naturally dry for 3 days under ambient conditions. Further drying of the shells was achieved by placing them in an oven at a controlled temperature range of 70 - 100°C for 45 minutes. The dried Bambara groundnut shells were then divided into three portions and subjected to additional processing to obtain the raw sample, carbonized material, and lignin.Top of Form

Raw Bambara groundnut shell adsorbent

The dried Bambara groundnut shells were cooled and subsequently milled into fine particles to obtain the RBGS adsorbent. These particles were immersed in a 0.1M NaOH solution for a duration of 9 hours. Following this step, they were washed with distilled water and subjected to drying once again. Next, the dried particles underwent a 9-hour immersion in a 0.1M H2SO4 solution to eliminate any remaining traces of alkalinity. Subsequently, the particles were thoroughly washed with distilled water and then dried within a desiccator. The resulting dried samples were sieved to achieve a maximum particle size of 1.18mm and were then stored in an airtight container, ready for use in the adsorption process.

Carbonized Bambara groundnut shell adsorbent

A measured quantity of 1.5 kg of dried Bambara groundnut shells was precisely weighed using an analytical weighing balance and introduced into a Pyrolysizer. The pyrolysis process was carried out within a temperature range of 500ºC to 800ºC. Specifically, pyrolysis was conducted at 800ºC, and at approximately 32 minutes into the process. Subsequent to the completion of pyrolysis, the resulting carbonaceous materials were subjected to crushing using a ball mill crusher to achieve fine particles, which were then sieved to obtain a maximum particle size of 1.18mm. These particles were subsequently stored in containers until ready for use in the adsorption process.

Bambara groundnut shell lignin adsorbent

Lignin was isolated from the dried Bambara groundnut shell through a series of steps. Initially, 30g of the dried shells were placed in a beaker, and a 1.0M solution of NaOH was added. The resulting mixture was then subjected to boiling at a temperature of 120 ºC for a duration of 4 hours. After cooling, the mixture underwent filtration, and the pH of the filtrate was adjusted to 2 by the addition of 98% H2SO4. The resulting lignin cake was then recovered through oven drying. The obtained lignin was allowed to cool and stored in an airtight container. Following this extraction process, the isolated lignin was utilized as an adsorbent without any further modification.

Initial wastewater analysis

Atomic adsorption spectrophotometer and scanning electron microscopy

The Atomic Adsorption Spectrophotometer (AAS) was used to determine the concentrations of heavy metal (Pb, Ni and Cd ions) contaminants in the wastewater. Scanning Electron Microscopy (SEM, FEI ESEM Quanta 200) was employed to analyze the structural arrangement and pore coverage of the particles before and after the adsorption process, providing insight into the morphology of the raw and carbonized Bambara groundnut shell as well as the lignin.

Batch adsorption experiments

Adsorption experiments followed the procedures recorded in16–18 as follows:  

Effect of dosage

150ml of wastewater was carefully measured and placed into a conical flask. Subsequently, 0.2g of powdered particles of the RBGS was introduced into the flask. The pH of the solution adjusted to 7.0 by the addition of sulphuric acid (H2SO4). The flask was then positioned on a rotary disc and stirred magnetically at a rotational speed of 100 rpm for 2 hours to ensure thorough contact between the particles and contaminants in the solution. Following the 2-hour stirring period, the mixture was filtered using filter paper, and the resulting filtrate was subjected to analysis with AAS to determine the concentrations of Pb, Ni, and Cd ions remaining in the solution. This procedure was repeated using dosages of 0.4g, 0.6g, and 0.8g while maintaining the solution pH at 7 and contact time at 2 hours. Likewise, the same procedures were conducted using CBGS and BGSL.

Effect of pH

The impact of wastewater pH on the adsorption process was explored with the modified BGS across four pH levels: 3, 7, 9, and 12. To achieve the desired pH for the wastewater, H2SO4 and NaOH were employed for pH adjustment. The investigation followed the same procedures as in the dosage effect study, with a fixed adsorbent dosage of 0.8g while varying the water pH. Additionally, the contact time for each experimental run remained constant at 120 minutes. Upon the completion of the 120-minute contact period, the solution underwent filtration to facilitate the analysis of Pb, Ni, and Cd ion concentrations, which was performed using an AAS.

Effect of contact time

The adsorption processes were examined at varying contact intervals of 30, 60, 90, and 120 minutes with the modified BGS bio-adsorbents. The procedures described earlier for the examination of dosage and pH effects were replicated for all experimental runs at a constant pH of 7.0 and dosage 0.8g. Following a 30-minute contact time, the solution underwent filtration, and the filtrate was subjected to analysis for the concentrations of lead, nickel, and cadmium ions using AAS. A detailed breakdown of the various batch experiments conducted for each formulated adsorbent is outlined in Table 1.

 

RBGS

CBGS

BGSL

 

m(g)

pH

t(min)

m(g)

pH

t(min)

m(g)

pH

t(min)

Effect of dosage

0.2

7

120

0.2

7

120

0.2

7

120

 

0.4

7

120

0.4

7

120

0.4

7

120

 

0.6

7

120

0.6

7

120

0.6

7

120

 

0.8

7

120

0.8

7

120

0.8

7

120

Effect of pH

0.8

3

120

0.8

3

120

0.8

3

120

 

0.8

7

120

0.8

7

120

0.8

7

120

 

0.8

9

120

0.8

9

120

0.8

9

120

 

0.8

12

120

0.8

12

120

0.8

12

120

Effect of contact time

0.8

7

30

0.8

7

30

0.8

7

30

 

0.8

7

60

0.8

7

60

0.8

7

60

 

0.8

7

90

0.8

7

90

0.8

7

90

 

0.8

7

120

0.8

7

120

0.8

7

120

Table 1 Batch adsorption design for each formulated adsorbent

Estimation of Adsorption Capacity

The formula used to calculate the percentage of heavy metal adsorbed by the modified Bambara adsorbents is given as:

Adsorbed metal ( % ) = C i C f C i ×100% MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaqGbb GaaeizaiaabohacaqGVbGaaeOCaiaabkgacaqGLbGaaeizauaabeqa beaaaOqaaKqzGeGaaeyBaiaabwgacaqG0bGaaeyyaiaabYgaaaqbae qabeqaaaGcbaqcfa4aaeWaaOqaaKqzGeGaaiyjaaGccaGLOaGaayzk aaaaaKqzGeGaeyypa0tcfa4aaSaaaOqaaKqzGeGaam4qaKqbaoaaBa aaleaajugWaiaadMgaaSqabaqcLbsacqGHsislcaWGdbqcfa4aaSba aSqaaKqzadGaamOzaaWcbeaaaOqaaKqzGeGaam4qaKqbaoaaBaaale aajugWaiaadMgaaSqabaaaaKqzGeGaey41aqRaaGymaiaaicdacaaI WaGaaiyjaaaa@5BD6@   (1)

The formula used to calculate the adsorption capacity of the modified Bambara adsorbents at any time is expressed as:

Q t =( C i C t ) V m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9Kqbaoaa bmaakeaajugibiaadoeajuaGdaWgaaWcbaqcLbmacaWGPbaaleqaaK qzGeGaeyOeI0Iaam4qaKqbaoaaBaaaleaajugWaiaadshaaSqabaaa kiaawIcacaGLPaaajuaGdaWcaaGcbaqcLbsacaWGwbaakeaajugibi aad2gaaaaaaa@4B0C@   (2)

The formula used to calculate the adsorption capacity of the modified Bambara adsorbents at equilibrium is expressed as:

Q e =( C i C e ) V m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamyzaaWcbeaajugibiabg2da9Kqbaoaa bmaakeaajugibiaadoeajuaGdaWgaaWcbaqcLbmacaWGPbaaleqaaK qzGeGaeyOeI0Iaam4qaKqbaoaaBaaaleaajugWaiaadwgaaSqabaaa kiaawIcacaGLPaaajuaGdaWcaaGcbaqcLbsacaWGwbaakeaajugibi aad2gaaaaaaa@4AEE@   (3)

Where:

C i = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGdb qcfa4aaSbaaSqaaKqzadGaamyAaaWcbeaajuaGcqGH9aqpaaa@3BC2@  Concentration of heavy metal analysed in wastewater before treatment (mg/l)

Cf= Concentration of heavy metal analysed in wastewater after treatment (mg/l)

Ct= Concentration of heavy metal analysed in wastewater after time, t (mg/l)

Ce= Concentration of heavy metal analysed in wastewater at equilibrium (mg/l)

Qt= Concentration of heavy metal on the surface of adsorbent at time, t (mg/g)

Qe= Concentration of heavy metal on the surface of adsorbent at equilibrium (mg/g)

V = Volume of the wastewater (l)

m = Weight of the modified Bambara formulations (g) 23,24,25.

Adsorption kinetics of the modified Bambara groundnut shell bio-adsorbents

Pseudo first-order kinetic model

The rate of adsorption of lead, nickel, and cadmium ions by the modified Bambara bio-adsorbents was studied using the pseudo first-order kinetic model developed by,26 which is expressed by27 as:

d Q t dt = k 1 ( Q e Q t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamizaiaadgfajuaGdaWgaaWcbaqcLbmacaWG0baaleqa aaGcbaqcLbsacaWGKbGaamiDaaaacqGH9aqpcaWGRbqcfa4aaSbaaS qaaKqzadGaaGymaaWcbeaajugibuaabeqabeaaaOqaaKqbaoaabmaa keaajugibiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqzGe GaeyOeI0IaamyuaKqbaoaaBaaaleaajugWaiaadshaaSqabaaakiaa wIcacaGLPaaaaaaaaa@4F46@   (4)

Where:

k1= Pseudo first order rate constant (min-1)

Qe= Concentration of heavy metal adsorbed by the adsorbent at equilibrium (mg/g)

Qt= Concentration of heavy metal adsorbed by the adsorbent with time (mg/g)

t = Contact time (min)

The adsorption capacity at equilibrium and the first-order kinetic rate constant were estimated after integrating equation (4) and linearizing the resulting solution. By integration, we have as follows:

Q to Q t d Q t ( Q e Q t ) = k 1 0 t dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa8qCaO qaaKqbaoaalaaakeaajugibiaadsgacaWGrbqcfa4aaSbaaSqaaKqz adGaamiDaaWcbeaaaOqaaKqzGeqbaeqabeqaaaGcbaqcfa4aaeWaaO qaaKqzGeGaamyuaKqbaoaaBaaaleaajugWaiaadwgaaSqabaqcLbsa cqGHsislcaWGrbqcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaaaOGaay jkaiaawMcaaaaaaaaaleaajugWaiaadgfalmaaBaaameaajugWaiaa dshacaWGVbaameqaaaWcbaqcLbmacaWGrbWcdaWgaaadbaqcLbmaca WG0baameqaaaqcLbsacqGHRiI8aiabg2da9iaadUgajuaGdaWgaaWc baqcLbmacaaIXaaaleqaaKqbaoaapehakeaajugibiaadsgacaWG0b aaleaajugWaiaaicdaaSqaaKqzadGaamiDaaqcLbsacqGHRiI8aaaa @6443@   (5)

ln Q e ln ( Q e Q t ) = k 1 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaciGGSb GaaiOBaiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqzGeGa eyOeI0IaciiBaiaac6gafaqabeqabaaakeaajuaGdaqadaGcbaqcLb sacaWGrbqcfa4aaSbaaSqaaKqzadGaamyzaaWcbeaajugibiabgkHi TiaadgfajuaGdaWgaaWcbaqcLbmacaWG0baaleqaaaGccaGLOaGaay zkaaaaaKqzGeGaeyypa0Jaam4AaKqbaoaaBaaaleaajugWaiaaigda aSqabaqcLbsacaWG0baaaa@51F7@   (6)

Rearranging equation (6) gives:

ln ( Q e Q t ) =ln Q e k 1 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaciGGSb GaaiOBauaabeqabeaaaOqaaKqbaoaabmaakeaajugibiaadgfajuaG daWgaaWcbaqcLbmacaWGLbaaleqaaKqzGeGaeyOeI0IaamyuaKqbao aaBaaaleaajugWaiaadshaaSqabaaakiaawIcacaGLPaaaaaqcLbsa cqGH9aqpciGGSbGaaiOBaiaadgfajuaGdaWgaaWcbaqcLbmacaWGLb aaleqaaKqzGeGaeyOeI0Iaam4AaKqbaoaaBaaaleaajugWaiaaigda aSqabaqcLbsacaWG0baaaa@51F7@   (7)

A plot of ln ( Q e Q t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaciGGSb GaaiOBauaabeqabeaaaOqaaKqbaoaabmaakeaajugibiaadgfajuaG daWgaaWcbaqcLbmacaWGLbaaleqaaKqzGeGaeyOeI0IaamyuaKqbao aaBaaaleaajugWaiaadshaaSqabaaakiaawIcacaGLPaaaaaaaaa@4429@  against time, t gives the slope of the graph, which corresponds to k 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGRb qcfa4aaSbaaSqaaKqzadGaaGymaaWcbeaaaaa@3A23@  and intercept which corresponds to ln Q e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaciGGSb GaaiOBaiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaaaa@3C1C@ .

Expressing equation (7) in terms of Q t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaaaaa@3A47@ , we obtained an exponential function given as:

Q e Q t = Q e e k 1 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamyzaaWcbeaajugibiabgkHiTiaadgfa juaGdaWgaaWcbaqcLbmacaWG0baaleqaaKqzGeGaeyypa0JaamyuaK qbaoaaBaaaleaajugWaiaadwgaaSqabaqcLbsacaWGLbqcfa4aaWba aSqabeaajugWaiabgkHiTiaadUgalmaaBaaameaajugWaiaaigdaaW qabaqcLbmacaWG0baaaaaa@4E51@   (8)

By factorization, we obtain

Q t = Q e ( 1 e kt ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9iaadgfa juaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqzGeqbaeqabeqaaaGcba qcfa4aaeWaaOqaaKqzGeGaaGymaiabgkHiTiaadwgajuaGdaahaaWc beqaaKqzadGaeyOeI0Iaam4AaiaadshaaaaakiaawIcacaGLPaaaaa aaaa@4A3E@   (9)

The exponential model, expressed in Equation (9), is used to predict the concentration of heavy metal adsorbed by the modified Bambara bio-adsorbents at any given time.

Pseudo second-order kinetic model

The rate of adsorption of lead, nickel, and cadmium ions by the modified Bambara adsorbents was also studied using the pseudo second-order kinetic model.27 expressed the pseudo second-order kinetics as:

d Q t dt = k 2 ( Q e Q t ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamizaiaadgfajuaGdaWgaaWcbaqcLbmacaWG0baaleqa aaGcbaqcLbsacaWGKbGaamiDaaaacqGH9aqpcaWGRbqcfa4aaSbaaS qaaKqzadGaaGOmaaWcbeaajugibuaabeqabeaaaOqaaKqbaoaabmaa keaajugibiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqzGe GaeyOeI0IaamyuaKqbaoaaBaaaleaajugWaiaadshaaSqabaaakiaa wIcacaGLPaaaaaqcfa4aaWbaaSqabeaajugWaiaaikdaaaaaaa@51EC@   (10)

Where:

k 2 = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGRb qcfa4aaSbaaSqaaKqzadGaaGOmaaWcbeaajuaGcqGH9aqpaaa@3BB8@  Pseudo second order adsorption rate constant (g/mg.min)

Definition of other parameter remained the same. The adsorption capacity at equilibrium and the second-order kinetic rate constant were estimated after integrating equation (10) and linearizing the resulting solution. By integration, we have as follows:

Q to Q t d Q t ( Q e Q t ) 2 = k 2 0 t dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa8qCaO qaaKqbaoaalaaakeaajugibiaadsgacaWGrbqcfa4aaSbaaSqaaKqz adGaamiDaaWcbeaaaOqaaKqzGeqbaeqabeqaaaGcbaqcfa4aaeWaaO qaaKqzGeGaamyuaKqbaoaaBaaaleaajugWaiaadwgaaSqabaqcLbsa cqGHsislcaWGrbqcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaaaOGaay jkaiaawMcaaaaajuaGdaahaaWcbeqaaKqzadGaaGOmaaaaaaaaleaa jugWaiaadgfalmaaBaaameaajugWaiaadshacaWGVbaameqaaaWcba qcLbmacaWGrbWcdaWgaaadbaqcLbmacaWG0baameqaaaqcLbsacqGH RiI8aiabg2da9iaadUgajuaGdaWgaaWcbaqcLbmacaaIYaaaleqaaK qbaoaapehakeaajugibiaadsgacaWG0baaleaajugWaiaaicdaaSqa aKqzadGaamiDaaqcLbsacqGHRiI8aaaa@66E9@   (11)

1 ( Q e Q t ) = k 2 t+C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcfa4aaeWaaOqaaKqzGeGaamyuaKqbaoaa BaaaleaajugWaiaadwgaaSqabaqcLbsacqGHsislcaWGrbqcfa4aaS baaSqaaKqzadGaamiDaaWcbeaaaOGaayjkaiaawMcaaaaajugibiab g2da9iaadUgajuaGdaWgaaWcbaqcLbmacaaIYaaaleqaaKqzGeGaam iDaiabgUcaRiaadoeaaaa@4C03@   (12)

Letting t=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG0b Gaeyypa0JaaGimaaaa@393E@ in equation (12), we have Q t =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9iaaicda aaa@3C96@ . Hence C= 1 Q e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGdb Gaeyypa0tcfa4aaSaaaOqaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqc fa4aaSbaaSqaaKqzadGaamyzaaWcbeaaaaaaaa@3E91@ ,

Replacing C = 1/Qe, equation (12) results to:

1 Q e Q t = k 2 t+ 1 Q e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGa amyzaaWcbeaajugibiabgkHiTiaadgfajuaGdaWgaaWcbaqcLbmaca WG0baaleqaaaaajugibiabg2da9iaadUgajuaGdaWgaaWcbaqcLbma caaIYaaaleqaaKqzGeGaamiDaiabgUcaRKqbaoaalaaakeaajugibi aaigdaaOqaaKqzGeGaamyuaKqbaoaaBaaaleaajugWaiaadwgaaSqa baaaaaaa@4F4E@   (13)

By rearranging equation (13) and simplifying further, we obtained:

1 Q e Q t 1 Q e = k 2 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGa amyzaaWcbeaajugibiabgkHiTiaadgfajuaGdaWgaaWcbaqcLbmaca WG0baaleqaaaaajugibiabgkHiTKqbaoaalaaakeaajugibiaaigda aOqaaKqzGeGaamyuaKqbaoaaBaaaleaajugWaiaadwgaaSqabaaaaK qzGeGaeyypa0Jaam4AaKqbaoaaBaaaleaajugWaiaaikdaaSqabaqc LbsacaWG0baaaa@4FE8@
Q t Q e ( Q e Q t ) = k 2 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamyuaKqbaoaaBaaaleaajugWaiaadshaaSqabaaakeaa jugibiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqbaoaabm aakeaajugibiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqz GeGaeyOeI0IaamyuaKqbaoaaBaaaleaajugWaiaadshaaSqabaaaki aawIcacaGLPaaaaaqcLbsacqGH9aqpcaWGRbqcfa4aaSbaaSqaaKqz adGaaGOmaaWcbeaajugibiaadshaaaa@51A2@   (14)

The pseudo second-order constant and the adsorption capacity at any given time was obtained after rearrangement of equation (14) as follows.

Q t = k 2 t Q e 2 Q t Q e k 2 t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9iaadUga juaGdaWgaaWcbaqcLbmacaaIYaaaleqaaKqzGeGaamiDaiaadgfaju aGdaqhaaWcbaqcLbmacaWGLbaaleaajugWaiaaikdaaaqcLbsacqGH sislcaWGrbqcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiaadg fajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaKqzGeGaam4AaKqbaoaa BaaaleaajugWaiaaikdaaSqabaqcLbsacaWG0baaaa@55D7@   (15)

By dividing both sides of equation (15) by Q t Q e 2 k 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiaadgfajuaGdaqh aaWcbaqcLbmacaWGLbaaleaajugWaiaaikdaaaqcLbsacaWGRbqcfa 4aaSbaaSqaaKqzadGaaGOmaaWcbeaaaaa@44A2@ , we have:

1 Q e 2 k 2 = t Q t t Q e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqcfa4aa0baaSqaaKqzadGa amyzaaWcbaqcLbmacaaIYaaaaKqzGeGaam4AaKqbaoaaBaaaleaaju gWaiaaikdaaSqabaaaaKqzGeGaeyypa0tcfa4aaSaaaOqaaKqzGeGa amiDaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGaamiDaaWcbe aaaaqcLbsacqGHsisljuaGdaWcaaGcbaqcLbsacaWG0baakeaajugi biaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaaaaaaa@5265@   (16)

This is further rearranged as:

t Q t = t Q e + 1 Q e 2 k 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamiDaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGa amiDaaWcbeaaaaqcLbsacqGH9aqpjuaGdaWcaaGcbaqcLbsacaWG0b aakeaajugibiaadgfajuaGdaWgaaWcbaqcLbmacaWGLbaaleqaaaaa juaGcqGHRaWkdaWcaaGcbaqcLbsacaaIXaaakeaajugibiaadgfaju aGdaqhaaWcbaqcLbmacaWGLbaaleaajugWaiaaikdaaaqcLbsacaWG Rbqcfa4aaSbaaSqaaKqzadGaaGOmaaWcbeaaaaaaaa@51CB@   (17)

A plot of t Q t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamiDaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGa amiDaaWcbeaaaaaaaa@3C81@  against time, t gives the slope of the graph, which corresponds to 1 Q e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqcfa4aaSbaaSqaaKqzadGa amyzaaWcbeaaaaaaaa@3C34@  and intercept which corresponds to 1 Q e 2 k 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaGymaaGcbaqcLbsacaWGrbqcfa4aa0baaSqaaKqzadGa amyzaaWcbaqcLbmacaaIYaaaaKqzGeGaam4AaKqbaoaaBaaaleaaju gWaiaaikdaaSqabaaaaaaa@424D@ .

Further simplification equation (17) gives

Q t = k 2 Q e 2 t 1+ k 2 Q e t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9Kqbaoaa laaakeaajugibiaadUgajuaGdaWgaaWcbaqcLbmacaaIYaaaleqaaK qzGeGaamyuaKqbaoaaDaaaleaajugWaiaadwgaaSqaaKqzadGaaGOm aaaajugibiaadshaaOqaaKqzGeGaaGymaiabgUcaRiaadUgajuaGda WgaaWcbaqcLbmacaaIYaaaleqaaKqzGeGaamyuaKqbaoaaBaaaleaa jugWaiaadwgaaSqabaqcLbsacaWG0baaaaaa@5406@   (18)

Equation (18) is the solution to pseudo second-order kinetic model and it was used to predict the concentration of heavy metal adsorbed by the modified Bambara groundnut shell bio-adsorbents at any given time.

Intra-particle diffusion model

The intra-particle diffusion model is another useful equation for evaluation of adsorption rate, and this is expressed in the work of28 as:

Q t = K d t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9iaadUea juaGdaWgaaWcbaqcLbmacaWGKbaaleqaaKqbaoaakaaakeaajugibi aadshaaSqabaaaaa@41C3@   (19)

Where:

Q t = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaajugibiabg2da9aaa@3BDC@ The amount adsorbed at time t (mg/g)

K d = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb qcfa4aaSbaaSqaaKqzadGaamizaaWcbeaajuaGcqGH9aqpaaa@3BC5@ Weber and Morris intra-particle diffusion rate constant (mg/g.min0.5)

t = Time of adsorption (min)

A plot of Q t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGrb qcfa4aaSbaaSqaaKqzadGaamiDaaWcbeaaaaa@3A47@  against t 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG0b WcdaahaaqabeaadaWcgaqaaKqzadGaaGymaaWcbaqcLbmacaaIYaaa aaaaaaa@3B9F@ gives the slope of the graph, which corresponds to K d MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb qcfa4aaSbaaSqaaKqzadGaamizaaWcbeaaaaa@3A31@ . According to several studies, such as12 and 25, if the plot is linear, this suggests that the adsorption process is governed by intra-particle diffusion. Nonetheless, if the linear graph does not intersect the origin, then it indicates that intra-particle diffusion is not the rate-limiting step.

Results and discussion

Top of FormAAS and SEM analysis of Bambara groundnut shell

The results of preliminary analysis carried out on the industrial wastewater effluent sample are given in Table 2.

Parameter

Concentration (mg/l)

WHO limit (mg/l)

Lead

1.27

0.01

Nickel

1.14

0.02

Cadmium

1.06

0.003

Table 2 Concentrations of ions in the wastewater

AAS analysis revealed that all the metals of interest (Pb, Ni and Cd) had levels exceeding the permissible limits specified by the World Health Organization (WHO) for water and wastewater as shown in Table 2. SEM images in Figures 1a–3a exhibited the rough surfaces of RBGS, CBGS and BGSL samples before the adsorption process. These surfaces displayed an irregular pattern of microspores with varying sizes, which contributed to the enhanced adsorption of metals.29 However, as depicted in Figures 1b–3b, the pores on the surfaces, which were visible prior to the adsorption process, became filled up. This observation suggested that the Pb, Ni and Cd) ions had bonded to the vacant sites on the surfaces of the bio-adsorbents after the adsorption process. Upon careful examination of the images before and after adsorption, it was evident that the surfaces appeared smoother following the adsorption.30

Figure 1 Morphology of Raw Bambara Groundnut Shells before adsorption (a) and after adsorption (b).

Figure 2 Morphology of Carbonized Bambara Groundnut Shell before (a) and after adsorption (b).

Figure 3 Morphology of Bambara Groundnut Shell Lignin before (a) and after adsorption (b).

Batch adsorption studies

Effect of adsorbent dosage

Figures 4a–4c revealed that as the dosage increased from 0.2g to 0.8g, the percentage of Pb, Ni and Cd ions removed from the wastewater showed an upward trend. The increment in Pb, Ni and Cd ions removal with the increased dosage of the adsorbent can be predominantly attributed to the greater availability of exchangeable binding sites, facilitating the sorption of metal ions. The higher performance observed in the BGSL bio -adsorbent can be attributed to its finer microstructures relative to CBGS and RBGS. This observation is consistent with findings from 15,18 regarding the Bambara groundnut husk adsorbent.

Figure 4a Lead ion removal at various dosages.

Figure 4b Nickel ion removal at various dosages.

Figure 4c Cadmium ion removal at various dosages.

The outcomes of the investigation demonstrate that increasing the dosage of RBGS, CBGS, and BGSL substantially bolstered their efficacy in removing Pb, Ni and Cd ions from the wastewater.

Effect of solution pH

Figures 5a–5c illustrates that the percentage of Pb, Ni and Cd ions removed increased as the solution pH ranged from 3.0 to 7.0 for RBGS, CBGS, and BGSL bio-adsorbents. However, the removal efficiency decreased with increasing pH from 9.0 to 12.0. The observed increase in metal adsorption with increasing pH from 3.0 to 7.0 indicates that the surfaces of the adsorbents become more negatively charged, leading to a favorable electrostatic force of attraction with the positively charged metal ions.34 As explained by 34,35 the pH of a solution influences the chemical state of the binding sites. At low pH values, there is an increased concentration and mobility of hydrogen ions (H+), favoring the adsorption of H+ over metal ions. This creates a competitive scenario between protons and metal ions for the binding sites on the adsorbent.

Figure 5a Lead ion removal at various pH of solution.

Figure 5b Nickel ion removal at various pH of solution.

Figure 5c Cadmium ion removal at various pH of solution.

Effect of Contact Time

As depicted in Figures 6a–6c, an increase in contact time, ranging from 30 to 120 minutes, increased Pb, Ni and Cd ion removal. During the initial 30 to 60 minutes of contact time, there was a rapid increase in the percentage removal of Pb, Ni and Cd ions, after which the rate of increase slowed down as the contact time extended further to 120 minutes. Equilibrium adsorption was achieved at approximately 90 minutes for RBGS and CBGS adsorbents and at around 80 minutes for BGSL. After attaining equilibrium, a subsequent increase in contact time did not lead to substantial adsorption. These results indicate that the optimal adsorption onto the modified adsorbents occurred at 120 minutes. A similar study by 16–18,34 reported a maximum adsorption of Pb ions onto Bambara groundnut husk at a contact time of 120 minutes.

Figure 6a Lead ion removal at various contact time.

Figure 6b Nickel ion removal at various contact time.

Figure 6c Cadmium ion removal at various contact time.

The adsorption method demonstrated the effective removal of Pb, Ni and Cd ions from wastewater under optimal conditions as shown in Table 3. However, the values obtained after the adsorption were above the recommended limits set by WHO for drinking water quality. Despite this, the considerable removal levels of Pb, Ni and Cd ions observed after 120 minutes of adsorption suggest that the formulated bio-adsorbents are effective in removing these heavy metals from industrial water. To achieve concentrations of heavy metals below acceptable limits, additional measures can be taken, such as prolonging the contact time or increasing the dosage of the adsorbent. Previous studies have indicated that both contact time and dosage play crucial roles in promoting the removal of water contaminants. 37-39

Parameter

Initial value

After adsorption

WHO limit

Removal (%)

RBGS

CBGS

BGSL

RBGS

CBGS

BGSL

Pb (mg/l)

1.27

0.1948

0.1205

0.1575

0.01

84.66

87.6

90.51

Ni (mg/l)

1.14

0.2177

0.1557

0.1865

0.02

79.46

82.41

85.31

Cd (mg/l)

1.06

0.0868

0.0201

0.0533

0.003

92.39

95.32

98.24

Table 3 Industrial wastewater contamination and removal level

Adsorption kinetics

The kinetic evaluation was performed on results obtained from the investigation of contact time influence between 30 and 120 minutes at wastewater pH of 7.0 and 0.80g dosage of the three formulated Bambara groundnut shell bio-adsorbents.

Plots for determination of kinetic constants

The kinetic constants were determined by fitting results obtained from the experiment into pseudo first-order kinetics, pseudo second-order rate kinetic and intra-particle diffusion model as shown in Figures 7a–7c for RBGS, Figures 8a–8c for CBGS and Figures 9a–9c for BGSL.

Figure 7a Pseudo-first-order kinetics for adsorption on RBGS.

Figure 7b Pseudo second-order kinetics for adsorption on RBGS.

Figure 7c Intra-particle diffusion kinetics for adsorption on RBGS.

Figure 8a Pseudo first order kinetics for adsorption on CBGS.

Figure 8b Pseudo second order kinetics for adsorption on CBGS.

Figure 8c Intra-particle diffusion kinetics for adsorption on CBGS.

Figure 9a Pseudo first order kinetics for adsorption on BGSL.

Figure 9b Pseudo second order kinetics for adsorption on BGSL.

Figure 9c Intra-particle diffusion kinetics for adsorption on BGSL.

Figures 7a–9c shows the linear plots used to evaluate pseudo-first-order kinetic rate constant, pseudo second order kinetic constant, intra-particle diffusion kinetic constant and equilibrium adsorption capacities for the simultaneous adsorption of Pb, Ni and Cd ions onto RBGS, CBGS and BGSL bio - adsorbents. The coefficient of determination, R2 values for Pb, Ni and Cd ions were obtained from the plots (Table 4). Similarly, a comparison of the linear regression equations with equation (8), showed pseudo first-order rate constant (k2), pseudo-second order kinetic constant (k2), intra-particle diffusion kinetic constant (kd) for Pb, Ni and Cd ions and the adsorption capacity at equilibrium (Qe) for Pb, Ni and Cd ions for all the bio – adsorbents were predicted and represented in Table 5. Adsorption kinetic analysis helps to establish the mechanism and rate that control step of an adsorption process. The linear lines for the intra-particle diffusion kinetic model do not cross the origin of the graphs. This implied that intra-particle diffusion alone does not control the adsorption of the metals onto the adsorbents, but diffusion and chemisorption both controlled the process12; 39-41.

Parameters

RBGS

CBGS

BGSL

Pb

Ni

Cd

Pb

Ni

Cd

Pb

Ni

Cd

Pseudo first order kinetic

K1 (min-1)

0.0091

0.0094

0.0153

0.0105

0.0105

0.0196

0.0125

0.0119

0.0295

R2

0.8388

0.9264

0.926

0.8495

0.9218

0.9522

0.8657

0.9381

0.9894

Pseudo second order

K2 (mg/g min)

0.3638

0.2441

0.3283

0.3708

0.2523

0.3344

0.3771

0.2601

0.3402

R2

0.9983

0.9985

0.9989

0.9985

0.9988

0.999

0.9986

0.9989

0.9991

Intra-particle diffusion

Kd

0.0087

0.0095

0.009

0.0087

0.0095

0.009

0.0087

0.0095

0.009

R2

0.8486

0.9311

0.8836

0.8482

0.931

0.8833

0..8486

0.931

0.8836

Table 4 Summary of kinetic constant

Time (min)

Predicted Qt (mg/g)

Predicted Ct (mg/l)

Pb

Ni

Cd

Pb

Ni

Cd

0

0

0

0

1.27

1.06

1.14

30

0.17274

0.12071

0.16424

0.34872

0.41621

0.26405

60

0.19988

0.15016

0.19275

0.20397

0.25915

0.112

90

0.21093

0.16345

0.20459

0.14504

0.18827

0.04885

120

0.21692

0.17102

0.21108

0.11309

0.14789

0.01424

150

0.22069

0.17591

0.21217

0.09299

0.12181

0.00843

180

0.22327

0.17932

0.2129

0.07923

0.10363

0.00453

210

0.22515

0.18184

0.21308

0.0692

0.09019

0.00357

240

0.22658

0.18378

0.21311

0.06157

0.07984

0.00341

270

0.22771

0.18532

0.2133

0.05555

0.07163

0.0024

300

0.22862

0.18657

0.2135

0.05069

0.06496

0.00133

1000

0.23452

0.19484

0.2136

0.01923

0.02085

0.0008

Table 5 Predicted concentration of heavy metals

In comparison, the second-order pseudo kinetics provided a better fit to the experimental data obtained from the adsorption of lead, nickel, and cadmium onto RBGS, CBGS, and BGL adsorbents than the pseudo-first-order kinetics and intra-particle diffusion model as shown in Table 4. Additionally, the pseudo-second-order was better at predicting the adsorption capacity at equilibrium. The R2 values obtained from the analysis of the pseudo-second-order kinetic constant were consistently higher than those obtained from the pseudo-first-order kinetic rate constant. As a result, the adsorption of Pb, Ni, and Cd ions by RBGS, CBGS, and BGL was more explained using the pseudo second-order kinetic model. These results are in line with previous studies on adsorption heavy metal using bio-adsorbents.2,24,4244 Although,45 had reported a better experimental fit with pseudo first-order kinetics compared to pseudo second-order for adsorption of Cd onto coconut shell.

The amounts of lead, nickel and cadmium ions in the treated wastewater after 120 minutes (2 hours) of contact time with RBGS, CBGS and BGSL bio – adsorbents were above limits given by WHO for good water quality. Therefore, the kinetic models were used to estimate the time for which the concentration of metals had reduced below WHO minimum limits.46 In achieving this, the predicted second-order rate constants and equilibrium adsorption capacity were substituted into pseudo second order kinetic model. This kinetic rate model was chosen because it performed better than the other models. Figure 10 demonstrated the capability of the model in predicting the concentration of lead, nickel and cadmium ions in the treated wastewater for BGSL bio – adsorbent at contact time up to 1000 minutes (16.67 hours).

Figure 10 Prediction of heavy metal reduction with time.

The predicted concentration of heavy metals adsorbed onto the bio-adsorbent and concentration in wastewater at any given time, up to 1000 minutes (16.67 hours), are presented in Table 5.

The amounts of Pb, Ni, and Cd ions predicted for BGSL by the pseudo-second-order model were comparable to values obtained from the experiment. However, the results predicted (Table 5) after a contact time up to 1000 minutes (16.67 hours) did not show reduction in the levels of the heavy metals below the standard limit (WHO limits) except Cd, which occurred after 270 – 1000 minutes (4.5 – 16.67 hours). This inability of the adsorbents to remove more of the metal from the wastewater, even up to 1000 minutes of contact time, could be attributed to over saturation of the adsorbents.47–53 Thus, the dosage of 0.8g used may not be enough to completely or reduce the concentration of lead, nickel and cadmium ions to level below the permissible limits. Therefore, increasing the adsorbent dosage further may remove concentration of heavy metals in the wastewater to levels below WHO recommended standards.

Conclusion and future work

The performance of the different formulations of Bambara groundnut shells as bio-adsorbents for the treatment of wastewater from a petrochemical plant was studied, based on the results, the following conclusions have been drawn:              

  1. The smoother surfaces of RBGS, CBGS and BGSL after the adsorption process, as revealed by SEM analysis, is an indication that the pore spaces or vacant site were occupied by the lead, nickel and cadmium ions, thereby reducing their concentration in the wastewater.
  2. The amount of lead, nickel and cadmium remaining in the wastewater after adsorption process by the RBGS, CBGS and BGSL adsorbents for 120 minutes contact time were above the maximum specified standard limits for good water quality. Also, the predicted values of Pb and Ni ions after 1000 minutes (16.67 hours) contact time were above the maximum specified limits.
  3. Therefore, increasing the adsorbent dosage might completely remove or reduce the concentration of Lead, Nickel and Cadmium to the level below the permissible limits. In addition, a minimum of 120 minutes contact time should be maintained with the water pH adjusted to about 7.
  4. Based on the findings, it is therefore recommended that further modification of the formulated RBGS, CBGS and BGSL as bio-adsorbents should be carried out to enhance more removal of these heavy metal ions from contaminated industrial effluent below the acceptable limits recommended by World Health Organization.

Acknowledgments

None.

Conflicts of interest

The authors declare that they have no competing interests.

Funding

None.

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