Analysis of Thermodynamics, Kinetics and Equilibrium Isotherm on Fe/Fe Adsorption onto Palm Kernel Shell Activated Carbon (PKSAC): A Low-cost Adsorbent

Adsorption of Fe 3+ /Fe 2+ from a polluted shallow well water onto a palm kernel shell activated carbon (PKSAC) has been studied. Batch experiment was adopted to study the Removal efficiency of Fe 3+ /Fe 2+ on varying contact time, temperature, adsorbent loading and concentrations. Equilibrium isotherm and kinetic were also studied. Removal efficiency progressed with contact time till the peak adsorption time of 100 minutes when the efficiency remained at equilibrium. Also, removal efficiency got to equilibrium at the peak values of 80oC, 4.8g and 12.5mg/l for temperature, adsorbent loading and concentration variations respectively. The adsorption isotherm models fitted the isotherm data got at 25oC, 40oC and 80oC in this order; Langmuir > Temkin>Freunlich. The dimensionless separation factor of 0.012, 0.017 and 0.015 for 25oC, 40oC and 80oC respectively confirmed favorable adsorption of Fe 3+ /Fe 2+ on the PKSAC adsorbent. Langmuir adsorption capacity increased from 203.9mg Fe 3+ /Fe 2+/ g to 389.3 mg Fe 3+ /Fe 2+/ g when the temperature increased from 25oC to 40oC but decreased to 308.1 mg Fe 3+ /Fe 2+/ g at Original Research Article American Chemical Science Journal, 4(3): 298-325, 2014 299 temperature of 80oC. The kinetic models described the kinetic study data got at 25oC, 40oC and 80oC as follows; power-function>second-order>Elovick>intra-diffusion>first-order kinetics. Mass transfer through liquid film diffusion controlled the adsorption of Fe 3+ /Fe 2+ onto PKSAC. Negative values of the Thermodynamic parameters (∆ , ∆ and ∆ ) got at various temperature values showed favorability of adsorption of Fe 3+/ Fe 2+ onto PKSAC. It is therefore concluded that PKSAC removed Fe 3+/ Fe 2+ from aqueous solution.

/Fe 2+ from a polluted shallow well water onto a palm kernel shell activated carbon (PKSAC) has been studied. Batch experiment was adopted to study the Removal efficiency of Fe 3+ /Fe 2+ on varying contact time, temperature, adsorbent loading and concentrations. Equilibrium isotherm and kinetic were also studied. Removal efficiency progressed with contact time till the peak adsorption time of 100 minutes when the efficiency remained at equilibrium. Also, removal efficiency got to equilibrium at the peak values of 80ºC, 4.8g and 12.5mg/l for temperature, adsorbent loading and concentration variations respectively. The adsorption isotherm models fitted the isotherm data got at 25ºC, 40ºC and 80ºC in this order; Langmuir > Temkin>Freunlich. The dimensionless separation factor of 0.012, 0.017 and 0. 015

INTRODUCTION
Iron is a major constituent of the earthcrust [1]. 5% of average crustal abundance is iron. Depending on the sediment transport, the geochemical history and rock from which the soil was formed, the iron content is of the range of between 0.5% and 5% [2]. The iron mainly occurs in natural form as iron minerals which include; siderite, hematite, goethite and magnetite. The weathering releases the iron in the water. That is the natural pathway. Iron can as well find its way into the water through anthropogenic means. The most common means are through industrial effluent, acid-mining drainage, sewage and landfill leachate [3]. There are two forms of iron in water; ferric ion (Fe 3+ ) and ferrous iron (Fe 2+ ). In surface water the ferrous iron dominates due to it soluble nature while in ground water, the fate of iron depends on the prevailing conditions. Under the condition of reduction reaction, ferrous iron is prevalent while ferric iron dominates under oxidation condition [4]. The transition from ferrous to ferric iron in the presence of oxygen explains why ground water sufficiently polluted by ferrous iron gradually turns brownish on exposure to atmosphere. The ferrous iron is oxidized to ferric iron by the atmospheric oxygen. The insolubility tendency of ferric iron, couple with its ability to form complexes makes it susceptible to precipitation hence the reddish brown sediment. The reaction is as follows: 4Fe + 3O 2 + 6H 2 O -> 4Fe 3+ + 12OH --> 4Fe(OH) 3

or 4Fe(OH) + 4 H 2 O
Iron is a dietary need either in binary or tertiary form for both micro and macro organisms. Iron is essential for nitrogen binding and nitrate reduction processes, which when in scarce can limit growths of phytoplankton growth. Soil types containing high or low concentration of water soluble iron portends growth problems to plants [5]. In human being, iron forms chelation complexes which encourage production of hemoglobin and in turn binds and releases oxygen during breathing [6]. When in deficits iron could lead to anemia, causing tiredness, headaches and loss of concentration [7]. Presence of iron in drinking water at low concentration is not considered a health problem. Small iron concentration is essential for human health but over dosage of iron gives drinking water unpleasant taste. It also makes vegetables cooked with iron-contaminated water appear unappetizing with dark appearance [8]. Iron bacteria, does not pose much health problem but leave behind reddish-brown slime clogs to plumbing materials as they live in the iron just to survive. This equally causes an offensive odor. Presence of These bacteria is also obvious in the slimy coating of the pipe, staining of lundary materials and toilet tanks [7]. To human being, iron concentration in drinking water beyond world health organization (WHO) recommended limit of 0.3mg/l or at unbearably high level could lead to adverse health effects which include; conjunctivitis, siderosis etc [6]. With these seeming environmental problems, researchers have adopted traditional methods to remove iron from drinking water. These methods comprise; the reverse osmosis, water softener(ion exchange).aeration, oxidizing filter, chlorination and filter, Fenton etc [9,10,11,12,13,14,15]. Adsorption techniques using synthetic adsorbents have yielded significant results [16,17]. Some of these methods are no doubt efficient but expensive with adverse after effects [18]. Chlorination has yielded appreciable result in iron removal, but could be harmful to health due to poor handling. Several researchers have equally explored various adsorption techniques on iron and heavy metal removal in drinking water using adsorbent materials. [19] Used zoelite, kaolinite and bentonite for such treatment. Although, it has been proven that the high cost of these adsorbents has being a challenge. In the light of this, researchers made use of agricultural waste and other available low cost adsorbent materials for remediation. This yielded good results. For example, [20,21,22,23] have shown the effectiveness of agricultural waste and other organic solid waste adsorbents in removing varying concentrations of heavy metals, dye and organic pollutants. Low cost adsorbents have successfully removed types of dye species [22]. [24,25,26,27] substantially reduced high concentrations of Hazardous brilliant blue dye, Azo dye(Metani Yellow), crystal violet dye and Reactofix golden yellow 3-RFN in drinking water using bottom ash and de-oiled soya, wheat-husk,. Similarly, [28] explored biosorption technique to treat nickel contaminated drinking water using algae (oedogonium hatei) as adsorbent. Palm kernel shell activated carbon which is available and affordable has in resent time been used by several researchers to remove varying concentration degrees of heavy metal in drinking water. Emmanuel et al. [29]  . Other researchers have stressed on the availability , affordability and effectiveness of palm kernel activated shell to remove metal pollutant from drinking water [21,18,6,9], but on study has robustly treated remediation of Iron pollution in drinking water using palm kernel shell activated carbon. This study investigated the effectiveness of palm kernel shell activated carbon in removing iron ion form drinking water . The study also measured the adsorption isotherms and kinetics models of the work. To assess the fitness of the data to various isotherm and kinetic models.

Preparation of Activation Carbon Fiber and Fiber Characterization
The palm kernel shell of the lignocellulosic material fiber was used to produce high quality activated carbon for this study. The palm kernel shell was obtained from an palm oil processing mill at Umuagwo-Ohaji Owerri Imo state south-Easther Nigeria. The material was carbonized and activated in a furnace of temperatures of 600ºC and 800ºC respectively. [31,32,33] published in details the preparation, carbonization and activation procedures of the material.

Characterization of Palm Kernel Shell Activated Carbon (PKSAC)
A sample of the PKSAC was used to measure the following properties; Conductivity, Ph, Percentage yield, Bulk density, Ash content, Moisture content , Carbon hardness and Porosity. Ph and moisture content values of the activated carbon were determined using standard test methods of ASTM D 3838-80 (ASTM 1996) and ASTM D 2867-91 (ASTM 1991) respectively. Tampering procedure as proposed by [34] was adopted to find out the bulk density. Percentage yield, ash content, conductivity, and carbon hardness were determined according to procedures described by [35,36,37,38] respectively.

Characterization of the Shallow Well Water (SWW)
Random sampling method was adopted in the collection of SWW samples from seven shallow wells within Buguma city, Rivers state Nigeria. Each sample was analyzed for ph, phosphate(p), lead (pb), total dissolved solids(TDS), Conductivity(µs), Biological oxygen demand(BOD),Ph and iron ion . All the analysis were carried out using standard methods. The results of all the samples were averaged and presented in the table.

Adsorption Equilibrium Fe 3+ /Fe 2+
To estimate the adsorption capacity of the adsorbent (PKSAC) through equilibrium time study, a batch adsorption equilibrium experiment was carried out. In this experiment, 500ml round bottom flask was used into which a solution of 100mg/l concentration of 200mg/l formed with 2.1g of the adsorbent was introduced. Also introduced was a 150ml of well water with an Fe 3+ /Fe 2+ concentration of 10mg/l. The PKSAC/SWW system was shaken at 260RPM at room temperature of 25ºC until adsorption equilibrium time was established. At this period, an aliquot from the flask was removed. The left-over PKSAC particles in the aliquot were filtered off using 0.43µm filter before it was analyzed for Fe The experimental data were fitted into the classical Fraundlich, Langmuire amd Temkin adsorption models expressed in equations 2, 3 and 4 respectively.

Freundlich model
Freundlich model describes the multilayer adsorption process of adsorbate and affinity over a heterogeneous adsorbent surface. The adsorbent surface has adsorption sites onto which adsorbates are held by binding energies. Those with stronger binding energies are occupied first with an exponential decrease in the energy as adsorption completes. Freunlich model is expressed as follows: 2a The nonlinearized form of equation 2a is converted into a linearized equation by taking natural log of both sides of equation 2a and it is given as follows: Where qe represents the adsorbate adsorbed at equilibrium, K F is the Freunlich constant, 1/n is the heterogeneity factor. n measures the deviation from linearity of adsorption . n can still be described as a measure of adsorption intensity or surface heterogeneity. Adsorption surface becomes more heterogeneous as n value tends to zero [39]. Therefore various values of n describe the form the adsorption takes. n is measured in the range between 0 and 1. Adsorption is said to be linear if n=1. Adsorption is chemical if n<1 and physical if n>1

Langumir Model
Langumir model quantifies adsorption capacity of adsorbents of a homogeneous surface.
Langumuir describes an adsorption process on a fixed or definite site which provides no lateral interaction between adsorbed molecules [40]. Langumir model described and adsorption surface with the following qualities (1) The adsorption surface must be homogeneous in nature.
(2) each adsorption molecule must have equal Enthalpy and activation energies. (3) all the adsorption sites possess the same attraction to the adsorbing substance adsorption of substance onto such surface presupposes that the movement of adsorbed molecule from one site to another may be impossible [41,42,43]. With all these assumptions, langumir proposed the following model to predict the adsorption of aqueous substance in a monolayer pattern onto a solid surface.
The non-linear form of the model is as = .
. 3a The linearized form is expressed as = + 3b Where and remain as defined above while and are defined as the maximum adsorption and Langmuir constant respectively. Also, a dimensionless constant popularly know as separation factor R L proposed by Webber and Chakkravorti, [43] further describes the adsorption capacity of the adsorbent. Webber and Chakkravorti, [43] mathematically expressed R L as = 3c Where K L is as defined above and Co refers to as the initial concentration of the adsorbate. Values of R L provides important information about the nature of adsorption and that is expressed as follows; RL < 1 means favourable adsorption, R L > 1 refers to unfavourable adsorption, R L = 1 suggests linear adsorption and R L =0 confirms an irreversible adsorption. Adsorption is more favourable as R L tends to lower value.

Temkin model
Temkin isotherm model describes the adsorbate-adsorbent interaction and uniform distribution of binding energies between the adsorbing molecules and the surface adsorbent during adsorption processes. The model also assumes the heat of adsorption which is a function of temperature varying linearly with coverage rather than logarithmically. Temkin model is mathematically expressed in non-linear and linear form as shown in equations 4a and 4b respectively = 4a = + 4b Where and are described as maximum binding energy and heat of biosorption respectively. Heat of biosorption suggests adsorption potentials or intensity of adsorption of the adsorbent.

Adsorption kinetic Studies
To study the equilibrium time and kinetics of adsorption of Fe 3+ /Fe 2+ onto PKSAC, batch process similar to that adopted in the equilibrium study was employed. For the kinetic study, adsorption of Fe 3+ /Fe 2+ was studied at interval of 10 minutes up to 120 minutes. Adsorption kinetic studies were also carried out at varying temperature values of 25ºC, 40ºC and 60ºC, different initial SWW concentrations of 2.8mg/l, 5.8mg/l and 10.92mg/l and different adsorbent weight of 2.1g, 3.5g and 5.1g. The study at interval of 10 minutes implies that samples were collected from the supernatant at the end of every 10 minutes of adsorption process for Fe  To interpret the time dependent experimental data the following kinetic models were considered and were mathematically expressed as follows;

Psuedo-first order equation
After separating the variables and integration, equation 6a is gives and have been defined above. represents the Psuedo-first order reaction constant while t is the time of adsorption

Second order kinetic
is simplified by separating the variables, integrating and applying the boundary conditions; α' represents initial adsorption rate (mg/g min) while β is the desorption constant (g/mg). Also [46] reported that β is related to the extent of coverage of the adsorbate onto the adsorbent.

Intra-particle diffusion
Adsorption process takes place in two major stages; external mass transfer and intra-particle diffusion. The intra-particle diffusion is expressed by this model; (10a) Where K t decides the adsorption capacity of the adsorbent. K t is expressed as follows; suggesting that K t increases with increasing adsorption equilibrium and the intra-particle diffusion D. K t also finds out the adsorption capacity. Equations 10 a and b are applied when intra-particle diffusion controls the adsorption.
For the external mass transfer stage (that is the migration of solute molecule from the liquid phase up to the solid phase) a model referred to as liquid diffusion model is employed and is expressed as Where is the fractional attainment to equilibrium (FATE). FATE is expressed as = ∞ . M t represents the concentration of iron ion at time t, while ∞ is the concentration of iron ion at infinity or equilibrium. High values of suggests quick attainment of adsorption process to equilibrium. If the plot of ( − ) gives a linear curve with out passing through the origin, it is sufficient to conclude that the diffusion of iron ion under study gets to the adsorbent (PKSAC) through the liquid film boundary surrounding the adsorbent. This implies that the external particle diffusion mechanism predominates. It further suggests that the iron ion particle diffused the PKSAC through the liquid film before the intra-particle diffusion stage takes place.

Thermodynamic Process
The study was carried out to determine the following thermodynamic changes; activation energy, changes in Gibb-free energy(∆Go), Enthalpy(∆H) and Entropy (∆S).

The activation energy was studied at different temperature values using the arrhenius model
While A is the Arrhenius constant, Ea is referred to as activation energy of adsorption (KJmol   -1 ) . Ea is the minimum energy value required to initiate chemical adsorption. R and T are the gas constant (8.314 J/mol/K) and absolute temperature (k) respectively, is adsorption rate constant.
Natural log was taken on both sides of 11a to form a straight line equation expressed as

Gibb-free Energy of Adsorption (∆G) was expressed as follows
Gibbs free energy is an available useful energy that can do useful work in an adsorption process [39]. Gibb free energy determines levels of adsorption processes. For instance, negative values of ∆G show the feasibility of adsorption [47]. Spontaneity of adsorption decides between ∆G and temperature. In that light, decrease in the values of ∆G with increasing temperature marks the spontaneity of adsorption at higher temperature [48].

Characterization of Adsorbent
The results of the Textural characteristics of the adsorbent, PKSAC were shown in Table 1. The values of the analysis were virtually in line with the results obtained by other researchers. There were slight differences between values of bulk density (0.8332 g/cm3) and % as h(6.435) content obtained by Ademiluyi and David-West [30] from the present study. The disparity in values could be attributed to difference in species of the palm fruits.

Characteristics of the Well Water
The results of the physic-chemical properties of the water sample were show on Table 2. The results indicated that the sample values were within WHO drinking water standards except the iron concentration and conductivity which exceeded the standard. Concentration of iron was high while that of conductivity exceeded WHO standard slightly. The high iron content of the water sample is a source of concern to the users of this water. With the value of iron at 10.92 mg/l the water sample exceeded the WHO standard of 0.3 mg/l hence the need for its removal. The slight increase in the conductivity value could be as a result of high iron content of the water sample [49].

Effects of contact time
The time effects of percentage removal of Fe 3+ /Fe 2+ were evaluated at varying periods and the trend of variation was illustrated in Fig. 1. The efficiency varied directly with time until at a point when removal became constant with time in all the study conditions. It was observed from the result that the rate of removal was generally rapid at the time lag of 0-80 minutes and thereafter became constant as the time progressed . This could be attributed to the fact that the adsorption sites of the adsorbents were saturated with the adsorbates at adsorption periods beyond 80 minutes. Oladoja et al. [50] achieved saturation of methelene blue dye adsorption on ground palm kernel coat adsorbent at 68  on the palm kernel shell activated carbon also corroborated this work.

2 Effects of Temperature
Temperature is an important parameter in adsorption process. In this study, there was apparent variation in temperature with percentage removal of Fe 3+ /Fe 2+ . The variation assumed direct proportionality where temperature values increased as percentage removal also increased. As shown in Fig. 2, percentage removal increased linearly with temperature until at the temperature of 80ºC where the removal reached the plateau and remain constant. Temperature affects adsorption process in many ways. For instance increase in temperature increases the active sites of the adsorbents making the sites available for effective adsorption with concomitant removal of the adsorbate [44]. The same reason could be attributable to the pattern of adsorption observed in this study where adsorption of Fe 3+ /Fe 2+ from the well water sample onto PKSAC got to its saturated limit at 80ºC. Again  adsorption with temperature, could be attributed to the direct temperature effect with the mobility of adsorbate. In the light of this, temperature enhances the mobility of adsorbate from bulk solution towards the adsorbent surface [53,20]. Also, the point of equilibrium and possible adsorption decrease observed after 80ºC could suggest seeming solubility of Fe 3+ /Fe 2+ in the bulk solution [46]. Further temperature increase could lead to increase in oscillation energy of Fe 3+ /Fe 2+ resulting to Fe 3+ /Fe 2+ desorption from the adsorbent surface into the bulk solution [47]. This was equally substantiated by the observation that solubility of pollutants in bulk fluid determines its hydrophocity, implying that a highly hydrophobic substance, that is, a substance sparingly soluble shows greater affinity towards the adsorbate [48].

Effects of adsorbent loading
This work also studied the effects of adsorbent loading in relation to percentage removal. The study revealed that percentage removal increased with increasing adsorbent loading at the initial time but got to its equilibrium point as the process progressed. The results obtained from this study was shown in Fig. 3 the figure showed that percentage removal of Fe 3+ /Fe 2+ got to its equilibrium level at adsorbent loading of 4.8g. The initial trend of increase in percentage removal with increase in adsorbent loading could be attributed to provision of more surface areas as more adsorbent was loaded [49]. The prevailing condition resulted to more adsorption capacity of the adsorbent [54]. On the other hand, the percentage removal experienced an equilibrium state despite increase in adsorbent load. This condition could be attributed to large number of adsorbent sites having definite concentration of adsorbate [54,27]. The resultant effect is apparent reduction in Fe 3+ /Fe 2+ uptake and consequent decrease in percentage removal from the bulk solution [47]. Also, [55] corroborated the reason for the percentage removal equilibrium condition observed in this study to mean saturation of adsorption sites by Fe

Effects of initial concentrations
Initial concentration of the polluted well water was varied to study its effects on the percentage removal of Fe

Adsorption Equilibrium Experiments
The data obtained from equilibrium experiment were calibrated using the following classical isotherm models; Langmuir, Fraunlich and Temkin .  onto PKSAC experienced a decline with possible desorption as temperature increase progressed [60]. This trend confirms the exothermic nature of the adsorption [61]. It could also be attributed to oscillation energy increase and insolubility of Fe

Separation factor
Favorability of Langmuir isotherm to equilibrium data was further investigated using a dimensionless constant popularly known as separation factor (RL) proposed by Webber and Chakkravorti 1974 [43] and mathematically expressed as shown in equation 3c. In this study, R L was calculated with the Fe 3+ /Fe 2+ concentration of the well water (C o ) to be 10.92mg/l. R L was calculated for various temperature values and the results were shown on Table 3. The result showed that RL values were less than 1 but greater than zero (0<RL<1) , indicating that the adsorption of Fe 3+ /Fe 2+ onto the PKSAC was a favorable process and also confirm the suitability of Langmuir model to describe the equilibrium data.

Freundlich model
Freunlich model, as mathematically expressed in equations 2a and 2b, was also applied to analyze the equilibrium data. This was carried out by plotting a linear relationship of and . The Freundlich constants, and n values were obtained from the intercept and slope of the curve respectively. From The linear plot, presented in Fig. 6. R 2 , K F and n values at various temperature values were determined and shown on Table 3. With the R 2 value of 0.96, Freunlich model described the equilibrium adsorption data better at 40ºC . Values of n for all the temperature values under study were within the range of between 0 and 1 suggesting heterogeneity of PKSAC surface. The least n value recorded at temperature value of 40ºC indicated adsorption favorability [18,42] and also implied that PKSAC surface was more heterogeneous at that temperature. This observation buttressed the axiom that adsorption surfaces become more heterogeneous as n value tends to zero [62]. On the nature of adsorption, Freunlich model confirmed the adsorption of Fe 3+ /Fe 2+ onto PKSAC chemisorptions as n values were less than unity [63].

Temkin model
To further evaluate the adsorption potentials of PKSAC for Fe 3+ /Fe 2+ , Temkin adsorption isotherm models shown in equations 4a and 4b were adopted. The temkin isotherm plot made by Vs for the three temperature values under study were presented in Fig. 7 and the isotherm parameters, and calculated from the slope and intercept of the plot respectively were shown on Table 3. The Temkin constants and showed apparent variations with temperature.
which gives impression of heat of sorption and binding energy increased from 6.08x10 -4 at temperature of 25ºC to 0.001 at 40ºC but decreased to 5.22x10 temperature increase [64]. A T values assumed the same trend of temperature variation with that of , buttressing the fact that adsorption capacity of the adsorbent was higher at 40ºC than at 80ºC. With the prevailing condition, the possibility was that the adsorbent-adsorbate interaction related to Temkin model must be low at 80ºC [65] leading to low adsorption potential. Also, Correlation coefficient, R 2 varies with temperature as represented in Table 3. The correlation coefficients were reasonably high but recorded the highest value at 40⁰C.

Adsorption Kinetic Study
To understand the interaction of Fe 3+ /Fe 2+ with PKSAC and to predict their fate with time, the following adsorption kinetic models were adopted; pseudo-first, second order kinetics, power-function, Elovick and intra-diffusion equation.

Pseudo-first order equation
Plots of ( − ) shown in Fig. 8 for various temperature values under study gave linear curves. The relationship between the plotted variables was generally not strong as all the R 2 values were below 0.9. From the results on Table 4, R   2 varied with temperature, the correlation value (R 2 ) was highest at temperature value of 40ºC followed by that of 25ºC and the least value was observed at 80ºC. Low value of R 2 recorded at the highest temperature of 80ºC showed that the first order kinetic equation does not provide a good model for the adsorption of Fe 3+ /Fe 2+ onto PKSAC at that temperature. K 1 equally varied linearly with temperature.
The highest K 1 value observed at 80ºC indicated a low uptake of Fe

Second order kinetic
The Second order kinetic as presented in equations 7a and 7b was also adopted for the kinetic study. A plot of Vs presented a linear curve shown on Fig. 9, with substantially high R 2 values for all the temperature values, suggested that the adsorption of Fe 3+ /Fe 2+ was better represented by the second-order kinetic model than the first-order model.. The rate constant of second -order adsorption (k 2 ) was found to be lower than that obtained for the pseudo-first order model. This observation showed faster uptake of Fe 3+ /Fe 2+ onto the PKSAC and favorable as described by the model [67]. The R 2 values at various temperature ranges were shown on Table 4 -2

Power function
Power function model was adopted to describe the adsorption kinetic data of this study. The model is as expressed in equations 8a and 8b. To test the suitability of the model to the data, a plot of Vs was made and presented in Fig. 10. The plots made at various temperature values of 25ºC, 40ºC and 80ºC produced linear curves with a and b as the power function constants. Values of correlation coefficients (R 2 ) and the power function constants for the three temperature values were shown on Table 4. These values showed some variations with temperature. At temperature of 80ºC which seemed to be the temperature of least adsorption value (as observed previously), power function constant ''a'', has the least value compared with that of other temperature values. As power constant ''a'' indicates the adsorption and or desorption rate of the pollutants [68,69], it was then implied that the rate of adsorption was minimal at temperature of 80ºC and highest at 40ºC. Regarding the fitness of the kinetic data the correlation coefficient recorded 0.97,0.99 and 0.95 for 25ºC, 40ºC and 80ºC respectively indicated that power function described the data better than described by pseudo-first order and second-order models.

Elovich kinetic model
Kinetic study of adsorption of Fe 3+ /Fe 2+ onto PKSAC was further carried out using Elovich kinetic model and was presented in Fig. 11. The results of the study for the study temperature values indicated that the plots of Vs were linear over the whole time range. The Elovick constants, α and β which characterize the adsorption and desorption rates of process respectively were calculated and presented on  [70]. The low uptake rate at high temperature was further substantiated by increase in value of β at high temperature which indicated high rate of desorption due to rise in temperature [42]. Correlation coefficients were also deduced from observed, Elovick model reasonably described the adsorption data but not as sufficient as described by the power function and second-order model.

Intra diffusion kinetic model
In order to determine the adsorption steps of this study, intra-particle diffusion(diffusion of solute molecules into the interior of the pores) as presented in equations 10a and 10b was used. A plot of Vs . produced a linear curve shown in Fig. 12 where was calculated from the slope and its values for various temperature values shown on Table 4. The correlation coefficients (R 2 ) were equally presented on the table. Temperature variation has pronounced effects on values. The intra-diffusion constant, increased with temperature but reduced at temperature of 80ºC. This observation suggested that the adsorption capacity of PKSAC was low at that temperature. The linear plot not passing through the origin confirmed the possibility of less influence of intra-particle diffusion of Fe 3+ /Fe 2+ into the pores of the adsorbent, PKSAC at the initial stage of the adsorption process. From equation 10b, varies directly with equilibrium concentration, and square root of the diffusion coefficient, D. Although intra-particle diffusion not wield much influence on this adsorption process, the prevailing condition implies that determined the diffusion of Fe  To further decide the rate controlling step, liquid diffusion model expressed in equation 10c was employed where ( − ) Vs t was ploted and the plot yielded a linear curve without passing through the origin,(see Fig. 13). This signified that the mass transfer of Fe 3+ /Fe 2+ through the liquid film onto the PKSAC took place before the intra-particle diffusions of the pollutant molecules. Several researchers observed similar trend in their various studies [38,44,71].

Activation energy of adsorption
The average rate constants of adsorption(Kad) was determined at each temperature values of 25ºC, 40ºC, and 80ºC by computing the quotient of the amount of Fe 3+ /Fe 2+ adsorbed at various time of adsorption. With the Arrhenius model, a plot of was made. From the slope and the intercept of the linear curve presented in Fig. 14  in the bulk solution leading to high adsorption with its attendant increase in binding strength of the adsorbate to the adsorption sites [69]. Also, the steady and definite arrangement of the adsorbate / adsorbent interface occasioned by decrease in adsorption Enthropy, provided straight course for Fe 3+ /Fe 2+ towards adsorption. With this axiom it therefore implied that the affinity of Fe 3+ /Fe 2+ to PKSAC was high and was higher at higher negative values of Enthalpy of adsorption as shown on Table  5.

CONCLUSIONS
Fe 3+ /Fe 2+ adsorption of a shallow well water, onto palm kernel shell activated carbon (PKSAC) adsorbent was studied in batch experiment. Percentage removal increased with increased adsorbent loading, temperature and Fe 3+ /Fe 2+ concentration decrease. Removal efficiency got to equilibrium at optimal temperature of 80ºC. Also, removal efficiency increased progressively with contact time till the optimum time of 100 minutes.
The adsorption isotherm models was adopted to test the relevance of these models to the equilibrium experimental data. The models fitted the data in this order; Langmuir > Temkin>Freunlich. The kinetic of adsorption study with First-order, Second-order, Power-function, Elovick and Intra-diffusion models showed that the models reasonably described the data. Variations were observed on the extent at which the kinetic models described the data and that was ranked in this order; power-function>second-order>Elovick>intra-diffusion>first-order kinetics. For the rate controlling step of the adsorption, mass transfer predominated the adsorption as Fe 3+ /Fe 2+ transferred through the liquid film diffusion onto PKSAC before the intra-particle diffusion.