Effective Microporosity for Enhanced Adsorption Capacity of Cr (VI) from Dilute Aqueous Solution: Isotherm and Kinetics

The adsorbent pore structure significant to enhanced adsorption capacity of Cr (VI) from dilute aqueous solution is evaluated. As reference, low-cost micro-mesoporous activated carbon (AC) of high basicity, mesoporosity centred about 2.4 nm, and effective microporosity centred about 0.9 nm was tested for removal of Cr (VI) from dilute aqueous solution in batch mode. At pH 2 the low-cost AC exhibited highly improved Langmuir Cr (VI) capacity of 115 mg/g which was competitive to high performance commercial AC. A Comparison with treated characterization results of literature adsorbents/ACs showed that moderate to high effective micropore volume of average pore-size Original Research Article Mukosha et al.; CSIJ, 19(4): 1-12, 2017; Article no.CSIJ.34082 2 about 0.9 ± 0.1 nm is critical for increased adsorption capacity of Cr (VI) from dilute aqueous solutions. The mesostructure of the tested low-cost AC was associated with rapid kinetics that was fitted by the Pseudo-second kinetics model. While Biot numbers suggested slight significant contribution of intraparticle diffusion. It is hoped that this study may be a useful contribution to development of effective adsorbents for the efficient abatement of toxic Cr (VI) from wastewater and water.


INTRODUCTION
The necessity for removal of highly toxic Cr (VI) from wastewaters and the highly feasible use of the economical and efficient adsorption technology have been adequately discussed [1][2][3]. It is at low concentration of Cr (VI) in water bodies that is significant to environmental protection as reflected in stringent Cr (VI) contaminant limits of 0.05 mg/L in drinking water and 0.1 mg/L for wastewater discharge to surface waters [4]. For solution Cr (VI) concentration < 1000 mg/L, the predominant species are hydrogen chromate oxyanion (HCrO 4 -) in pH 1 -6.5 and chromate oxyanion (CrO 4 2-) in pH 6.5 -10 [2]. With reference to diameter of CrO 4 2of ca. ≈ 0.50 nm [5] and its spatial arrangement, it could be assumed that the diameter of showed that adsorbent specific surface functionality (acidic or basic) would enhance affinity for HCrO 4 either by ion-exchange interaction [6] or electrostatic attraction [7,8]. It is evident from X-ray Photoelectron Spectroscopy analysis that HCrO 4 -/biosorbent interaction could plausibly proceed through adsorption-coupled reduction and chemisorption or complexation of resultant Cr 3+ dependent on amount of acidic surface groups [8][9][10].
At present, however, the outstanding fact about Cr (VI) adsorption is the lack of conclusive empirical evidence on the relevant pore-size distribution (PSD) for enhanced adsorption capacity from dilute industrial wastewaters [typically < 400 ppm] significant to environmental protection. Referenced to silica nanoparticles of mean adsorption pore size about 7.0 nm, the researchers [11] concluded that adsorbent broad PSD, not surface area or average pore size, is important for enhanced removal of Cr (VI) from wastewater. In another study [12], ordered mesoporous carbon (OMC) of PSD centered about 22 nm was reported to have very high capacity for Cr (VI) than micro-mesoporous activated carbon (AC) of wide PSD centered about 3.2 nm. Contrary to above both reports, it is known that the adsorption process would follow a sequential occupancy of adsorption sites based on level of adsorption potential [13][14][15]. In this sense, for adsorption from dilute solutions, the adsorption potential would be highest in effective micropores with monolayer or primary volume filling capacity due to strong overlapping of adsorption potential from opposite walls, as opposed to surface coverage in wider pores. This means that enhancement of adsorption potential in effective micropores depends on the ratio of micropore size to adsorbate size. In related study, the high butane adsorption capacity from dilute solution was reported to occur in effective micropores with primary volume filling [16]. This should be contrasted with adsorption from concentrated solutions when capacity could be a function of total micropore volume.
The contribution of knowledge of the relevant PSD for enhanced Cr (VI) capacity from dilute solutions would be significant for optimal design of future adsorbents. Interestingly, many studies have explored the potential application of abundantly available biomass wastes for development of low-cost adsorbents/ACs for abatement of Cr (VI) from wastewater [1,2,17]. The low-cost adsorbents/ACs were developed using the backward approach of first developing the adsorbent and then testing for quality in adsorption of Cr (VI). However, most of developed low-cost adsorbents/ACs have showed low Cr (VI) capacities from dilute aqueous solutions. In practical application, low Cr (VI) capacities on low-cost adsorbents would translate into usage of large quantities of adsorbent and design of large sized adsorption units. The handling and disposal of large quantities of spent adsorbent could also be an environmental problem. Therefore, there is still need to develop new low-cost adsorbents of high efficient removal of Cr (VI) from dilute aqueous solutions.
In this study, attempt is made to evaluate the effective microporosity for enhanced Cr (VI) capacity from dilute aqueous solution and, thereby, promote the forward approach of incorporating relevant adsorbent properties at development stage. Low-cost sawdust AC (denoted L-AC) developed at our previously determined optimum conditions [16] was submitted for removal of Cr (VI) from dilute aqueous media. The L-AC was characterized for relevant adsorptive properties and batch adsorption studies to evaluate effect of pH, equilibrium capacity and kinetics were conducted. Importantly, the pore structure the L-AC is discussed in relation to adsorption potentials for Cr (VI) from dilute aqueous media. The equilibrium capacity was compared with commercial AC. Thereafter, using our L-AC as reference, literature adsorbent/AC characterization results were treated and their relevance to results of comparative analysis was made to validate the effective micropore average size available for adsorption for enhanced Cr (VI) capacity from dilute solutions.

Materials
The low-cost AC (L-AC) was developed from Pine tree (Pinus patula) sawdust obtained locally (Singisi Sawmill, KwaZulu Natal, South Africa). The commercial AC (Norit RO 0.8), vendor specified as suitable for wastewater treatment was purchased from Sigma, USA and used for comparison. Potassium dichromate (K 2 Cr 2 O 7 , 99+ %) powder was purchased from Sigma, USA. Hydrochloric acid (HCl, 32%) Sodium Chloride standard solution (NaCl, 99.5%) and Sodium Hydroxide pellets (NaOH, ≥ 95%) were purchased from SMM, South Africa. Stock solutions were prepared using deionised water. All chemicals used were of analytical reagent grade.

Development and Characterization of Activated Carbon
The carbonization and activation of carbon samples were performed in a stainless steel vertical fixed-bed tubular reactor. Equipments and details of preliminary optimization of carbonization/activation processes have been previously reported [18]. Briefly, the P. patula sawdust was carbonized in continuous N 2 flow (570 mL/min) at 10 K/min to 800°C and 2 hrs, and the char cooled to ambient temperature in N 2 flow. To develop L-AC, the prepared char was heated in continuous preheated N 2 flow (180°C, 570 mL/min) at 10 K/min to 800°C and superheated steam (180°C, 1.6 bar, and 780 mL/min) activated for 1.5 hrs, and cooled to ambient temperature in N 2 flow and stored in a desiccator. The during activation or in-situ modification of surface groups occurred at the activation temperature in flowing N 2 -steam mixture.
The outgassed L-AC sample was analyzed for textural properties using 77K N 2 -adsorption (TriStar II 2030, Micromeritics) and 273K CO 2adsorption (ASAP 2020, Micromeritics), and surface morphology using scanning electron microscope (SEM, Cambridge Instrument 360). While the total acidity and basicity were determined by the standardized Boehm titration method and the pH point of zero charge (pH PZC ) from proton binding isotherm obtained by the manual potentiometric titration method. Details of instruments and procedures were previously reported [16]. The bulk density was determined using the graduated cylinder method. The average pore size (L AVE , nm) of micropores available for adsorption was calculated from the geometrical relation [19]: where, V MIC (cm 3 /g) and S MIC (m 2 /g) are t-plot (analogue of α-plot [13]) micropore volume and surface area respectively.

Batch Equilibrium
Equilibrium adsorption studies were conducted in sample bottles with 0.8 g/L-AC in solutions of known Cr (VI) concentrations shaken in a thermostated water shaker (Labcom, Maraisburg) at 200 rpm and 25°C for 24 hrs equilibration, paper filtration and the filtrates Cr (VI) concentrations determined by the EPA recommended 1, 5-Diphenylcarbazide method using UV-Vis spectrophotometer (Libra S12, UK) at 543 nm. The effect of pH was studied using triplicate samples. Solutions pH was adjusted using HCl or NaOH solutions, and using precalibrated pH meter (Orion 4 star, USA). Subsequent to determining the adsorption optimum pH all other adsorption tests were carried out at that optimum pH. The uptake q e (mg/g) and percentage removal φ (%) were calculated according to equations (2) and (3) respectively.

= ( − ) /
(2) where, C O is the solute initial concentration (mg/L), C e is the equilibrium solute concentration in solution (mg/L), V S is the solution volume (L), and m is mass of AC (g).
The isotherm parameters were evaluated using the isotherm models of the Langmuir (equation 4) and Freundlich (equation 5) [20]. The agreement of model to data was validated by nonlinear regression of minimizing the Chi-squared (χ2) function per equation 6 [20], with solutions generated using Microsoft Excel 2010, Add-in solver.
where, Q max is the monolayer adsorption capacity (mg/g), and K L is the Langmuir constant (L/mg). K F is Freundlich constant related to the adsorption capacity (mg/g) and Fr is the heterogeneous factor.

Batch Kinetics
Batch adsorption kinetics tests were conducted for the evaluation of the rate constants and diffusion parameters. A laboratory batch stirred tank with 600 mL solution of 50 mg/L Cr (VI) and stirring speed of 400 rpm was used by the method detailed in [21]. Syringe filters (0.2 µm) were used to withdraw 5 mL aliquot samples at predetermined time intervals. The variable studied was initial concentration. The uptake with time t (min), q(t) (mg/g) was calculated by: where, C(t) is solute concentration in (mg/L) at time, t.
The kinetics rate constants were evaluated using the adsorption surface reaction models of the pseudo first-order (equation 8) and the pseudo second-order (equation 9) [8,22], with conformity of model to data assessed through minimum Chisquared function, equation 6 = ( − )/ (15) = 4 / (16) where, q 1 and q 2 are adsorbed quantities (mg/g), k 1 and k 2 are rate constants, h is initial sorption rate (min), q O adsorbed quantity (mg/g) in equilibrium with C O , d p is particle diameter (cm), ρ p is particle density (g/cm 3 ) estimated by equation 11 [23], ρ b is bulk density (g/cm 3 ), ɛ b is bed porosity of typically about 0.4 for AC [25], U(t) is the fractional attainment to equilibrium; w is the equilibrium partition ratio (0 < w < 1 indicates finite solution case i.e. concentration of adsorptive in solution continuously changes from initial to equilibrium, and w > 1 indicates infinite solution case i.e. concentration of adsorptive remains constant in solution), τ is dimensionless time constant and, the ϴ and β terms are the negative and positive roots respectively, of equation (17). The high N 2 adsorption start point in Fig. 1 suggested N 2 molecule diffusional restrictions in narrow micropore (< 0.5 nm) at 77K 0.06 in our short experiment time of 8 hrs [15] and, therefore, narrow microporosity was evaluated from CO 2 -adsorption isotherm data at 273K and P/P O < 0.04 and 8 hrs [insert in Fig. 1]. The mesopore PSD was determined by the Pierce method [13] and results shown in Fig 3, where it was confirmed that the L uniform mesopores in the narrow range 2.0 nm pore diameter centred at about 2.5 nm pore diameter. From CO 2 -adsorption data, the instrument software calculated narrow microporosity distribution (Horvath method) is shown as insert in Fig. 2. It was observed that the narrow microporosity was mostly 0.4 nm in diameter. However, the adsorption start point in Fig. 1 molecule diffusional restrictions in narrow micropore (< 0.5 nm) at 77K and P/P O < 0.06 in our short experiment time of 8 hrs [15] and, therefore, narrow microporosity was adsorption isotherm data at < 0.04 and 8 hrs [insert in Fig. 1].

adsorption/desorption AC [Insert: 273K CO 2 -♦) of L-AC]
AC. Particle 1000 +850 µm; Mag.: 500 x 10µm The mesopore PSD was determined by the Pierce method [13] and results shown in Fig 3, the L-AC had uniform mesopores in the narrow range 2.0 -8.0 nm pore diameter centred at about 2.5 nm pore adsorption data, the instrument software calculated narrow microporosity distribution (Horvath-Kawazoe in Fig. 2. It was observed that the narrow microporosity was mostly 0.4 nm in diameter. However, the measured high N 2 -BET surface area (S Table 1 indicated presence of wide micropore (0.5 -2.0 nm). Using equation (1), the calculated average pore width (L AVE ) of wide micropores available for adsorption was 0.9 nm.

Fig. 3. The mesopore-size distribution ( L-AC [Insert: The narrow micropore distribution (■) of L-AC]
From Table 1, the L-AC showed high 1079 m 2 /g with wide micropore surface area (S MIC ) at ca. 54%, and total pore volume ( 0.71 cm 3 /g with moderate wide micropore volume (V MIC ) of 0.25 cm 3 /g. The high proportion of mesoporosity (V T -V MIC ) at ca. 65% was important for reduced diffusion limitation of HCrO 4 oxyanion to interior wide micropores that would be sites of high adsorption potential [13][14][15]. Reported theoretical calculations have indicated that the important parameter for enhanced adsorption potential in effective micropores is the ratio of micropore size to adsorbate size, with upper ratio limit for primary volume filling in the range 1.5on actual shape (slit-like or cylindrical) pores [13]. With reference to approximate size of HCrO 4 -(≈ 0.50 nm), narrow micropores (< 0.5 nm) would be closed due to size exclusion effect. Also, the adsorption capacity would be reduced in micropores of same size as HCrO kinetic limitations. Thus, considering the theoretical upper ratio limit of effective micropore size for primary filling at 2.0, it could be assumed that for enhanced adsorption capacity of HCrO from dilute solutions the effective wide micropore PSD would be in the range 0.50the evaluated PSD of L-AC of moderate wide micropore volume of average pore widt 0.9 nm) and high proportion of narrow mesoporosity was promising for enhanced capacity and fast kinetics of Cr (VI) oxyanion, subject to enhanced affinity of HCrO situ created surface groups.
; Article no. CSIJ.34082 BET surface area (S BET ) in Table 1 indicated presence of wide micropore 2.0 nm). Using equation (1), the calculated ) of wide micropores available for adsorption was 0.9 nm.

size distribution (•) of The narrow micropore-size AC]
AC showed high S BET of micropore surface area ) at ca. 54%, and total pore volume (V T ) of /g with moderate wide micropore /g. The high proportion ) at ca. 65% was important for reduced diffusion limitation of oxyanion to interior wide micropores that would be sites of high adsorption potential 15]. Reported theoretical calculations have indicated that the important parameter for enhanced adsorption potential in effective ropore size to adsorbate size, with upper ratio limit for primary 2.0 dependent like or cylindrical) pores [13]. With reference to approximate size of ≈ 0.50 nm), narrow micropores (< 0.5 would be closed due to size exclusion effect. Also, the adsorption capacity would be reduced in micropores of same size as HCrO 4 due to kinetic limitations. Thus, considering the theoretical upper ratio limit of effective micropore g at 2.0, it could be assumed that for enhanced adsorption capacity of HCrO 4 from dilute solutions the effective wide micropore -1.0 nm. Thus, AC of moderate wide micropore volume of average pore width (L AVE = 0.9 nm) and high proportion of narrow mesoporosity was promising for enhanced capacity and fast kinetics of Cr (VI) oxyanion, subject to enhanced affinity of HCrO 4 for the in-  Fig. 4 shows that the L-AC was highly basic with pH PZC about 10, consistent with the Boehm titration calculations of high total basicity (940 µmol/g) against total acidity (71 µmol/g). The high activation temperature (800°C) basicity of L-AC could be due to presence of thermally stable surface oxygen basic groups (pyrone and chromene) and delocalized ᴨ-electrons system on basal graphene layers [26].

Effect of pH
The pH influences the ionization of AC surface groups and Cr (VI) in water and, therefore, the evolution of uptake with pH could be used to elucidate the type of surface interactions e.g. complexation or ion exchange or electrostatic attraction or combinations. Fig. 5 shows the effect of pH (2 -12) on percentage removal of Cr (VI) on L-AC.  AC was highly basic with about 10, consistent with the Boehm titration calculations of high total basicity (940 µmol/g) against total acidity (71 µmol/g). The C) basicity of AC could be due to presence of thermally c groups (pyrone and electrons system Proton binding isotherm for L-AC. The pH influences the ionization of AC surface and, therefore, the evolution of uptake with pH could be used to elucidate the type of surface interactions e.g. complexation or ion exchange or electrostatic attraction or combinations. Fig. 5 shows the 12) on percentage removal of Cr

Effect of pH on sorption of Cr (VI) on 425 + 106 μm: Equilibrium pH (X)
The results in Fig. 5 showed that percentage removal was high at pH 2 (ca. 98 ± 1.6%) and minimal for pH > 2. A similar trend has been reported [27,28]. On the other hand, the equilibrium pH slightly increased for initial pH (2 -8), and was similar to initial pH for pH (10 12). An only slight increase in equilibrium pH at initial pH 2 suggested that the sol reduction of Cr (VI) to Cr (III), catalyzed by surface acidic electron-donor groups and complexation of Cr (III) as suggested in [8,29] may not be the main mechanism of Cr (VI) adsorption. Otherwise, the equilibrium pH would have substantially increased due to consumption of large quantities of solution protons in the reduction process as per equation (18) [17]. The negligible direct reduction of Cr (VI) at pH has been similarly reported [6,8,17]. For 100 mg/L, the predominant species pH 1 -6.5 [2] and L-AC surface is protonated as shown in Fig. 4. The observed slight increase in equilibrium pH for initial pH < 10 in Fig. 4 may be explained by surface protonation. Significant ion exchange of surface protons for HCrO as per equation (19) proposed in [6] may also not be the main mechanism, because the L highly basic with low concentration of acidic groups that would be main sites of ion exchange to account for the measured high ca. 98 ± 1.6% removal for C O = 100 mg/L at pH 2. Therefore, the high adsorption at pH 2 was suggestive of primary physical non interactions of electrostatic attraction between HCrO 4 and protonated surface groups e.g. equation (20). Since the level of acidic groups was low on L-AC, it would be expected that only part of surface bound HCrO 4 was reduced and complexed. In this study, experiments not shown, the adsorption-coupled reduction and complexation of part of surface bound HCrO could be supported by loss of Cr (VI) adsorption capacity at ca. 52% on reusability of column regenerated Cr (VI) saturated L-3M NaOH eluent. The observed low adsorption ; Article no.CSIJ.34082 The results in Fig. 5 showed that percentage removal was high at pH 2 (ca. 98 ± 1.6%) and 2. A similar trend has been reported [27,28]. On the other hand, the equilibrium pH slightly increased for initial pH (2 8), and was similar to initial pH for pH (10 -12). An only slight increase in equilibrium pH at initial pH 2 suggested that the solution direct reduction of Cr (VI) to Cr (III), catalyzed by donor groups and complexation of Cr (III) as suggested in [8,29] may not be the main mechanism of Cr (VI) adsorption. Otherwise, the equilibrium pH would increased due to consumption of large quantities of solution protons in the reduction process as per equation (18) [17]. The negligible direct reduction of Cr (VI) at pH ≥ 2 has been similarly reported [6,8,17]. For C O = 100 mg/L, the predominant species is HCrO 4 in AC surface is protonated as shown in Fig. 4. The observed slight increase in equilibrium pH for initial pH < 10 in Fig. 4 may be explained by surface protonation. Significant ion exchange of surface protons for HCrO 4 at pH 2 as per equation (19) proposed in [6] may also not be the main mechanism, because the L-AC was highly basic with low concentration of acidic groups that would be main sites of ion exchange to account for the measured high ca. 98 ± 1.6% = 100 mg/L at pH 2.
Therefore, the high adsorption at pH 2 was suggestive of primary physical non-specific interactions of electrostatic attraction between and protonated surface groups e.g. equation (20). Since the level of acidic groups AC, it would be expected that only was reduced and , experiments not coupled reduction and complexation of part of surface bound HCrO 4 could be supported by loss of Cr (VI) adsorption capacity at ca. 52% on reusability of column -AC bed using 3M NaOH eluent. The observed low adsorption of chromium oxyanions in pH (2was attributed to very low level of surface protonation as seen in Fig. 4. While for pH > 10 the L-AC surface was deprotonation and repulsion of chromium oxyanions occurred. Further adsorption tests in this study were conducted at pH 2.

Adsorption Isotherm and Comparative Cr (VI) Capacities
The equilibrium isotherm data was treated to evaluate the maximum adsorption capacity of L AC for Cr (VI) from dilute aqueous solution.
Generally, for economical and efficient operation of adsorption units, the AC must have high capacity for the solute so that relatively small quantities can be used to effect a given wastewater treatment. Fig. 6 compares the isotherm curves of Cr (VI) on L commercial AC (Norit RO 0.8). Both ACs exhibited L-type isotherms indicative of weak competition between Cr (VI) and water for active adsorption sites [30]. The isotherm parameters were calculated using the Langmuir (equation (14)) and Freundlich (equation (15)) models and results presented in Table 2.

Adsorption Isotherm and Comparative
The equilibrium isotherm data was treated to evaluate the maximum adsorption capacity of L-AC for Cr (VI) from dilute aqueous solution. Generally, for economical and efficient operation of adsorption units, the AC must have high for the solute so that relatively small quantities can be used to effect a given wastewater treatment. Fig. 6 compares the isotherm curves of Cr (VI) on L-AC and commercial AC (Norit RO 0.8). Both ACs type isotherms indicative of weak ion between Cr (VI) and water for active adsorption sites [30]. The isotherm parameters were calculated using the Langmuir (equation (14)) and Freundlich (equation (15)) models and According to Table 2, the isotherm data of both ACs were well fitted by the Langmuir model (lowest χ2) that underpins monolayer coverage, suggesting uniform distribution of active adsorption sites [20]. However, L-AC showed high monolayer capacity for Cr (VI) than Norit AC (RO 0.8). A further comparison of Cr (VI) capacities from dilute solutions (< 400 mg/L) in ure sawdust low-cost adsorbents/ACs and commercial ACs was summarized in Table 3. It was noticed in Table 3 that the Cr (VI) capacity on sawdust low of this study was on the higher side of sawdust low-cost adsorbents/ACs, and competitive with high performance commercial ACs. Due to low cost, the high Cr (VI) capacity on L translate into high adsorption capacity per cost of adsorbent compared with expensive commercial ACs [40], and can be used on a once basis without considerations for the costly regeneration [32]. This result qualified the L to be very economical and efficient for abatement of Cr (VI) from wastewater, even at large scale. The spent AC would be safely disposed off through a strict toxic sludge containment protocol, otherwise use of the common spent AC incineration method would have a major problem of Cr (VI) thermal decomposition at about 196 to highly thermal stable and carcinogenic chromium (III) oxide [41].
In majority of studies on adsorption of Cr (VI) on AC the pore structure was not fully characterized. Nevertheless, for dilute solutions, the results in Table 3 indicate that Cr (VI) capacity is not influenced by surface area. Analysis of surface functionality show that low and high Cr (VI) capacities have been obtained on either acidic or basic ACs, suggesting that pore-size distribution (PSD) strongly influences HCrO 4 AC. For assumed spherical HCrO (size ≈ 0.5 nm); we calculated the monolayer equivalent surface area (S EQ ) of adsor HCrO 4 on L-AC and compared it with the measured wide micropore surface area ( L-AC. It was found that S EQ was less than With reference to the average wide micropore size available for adsorption (L AVE = 0.9 nm) of L AC, and the assumed range 0.5 (section 3.1) of effective micropore PSD for HCrO 4 primary volume filling, the calculated < S MIC showed that only effective micropores with monolayer filling were involved in the adsorption from dilute solution. To support this finding, we treated literature AC characterization results and compared with L-AC. For adequately characterized ACs in Table 3, It was found that always S EQ < S MIC , confirming that only an effective microporosity was involved in adsorption from dilute solution, in agreement with results in related study [16]. The high Cr (VI) capacity on the L-AC of this study could be related to presence of large volume of effective micropores with primary filling capacity. It could be argued that the same reason may explain t reported high Cr (VI) capacity on mesoporous silica nanoparticles (SNP) having broad PSD [11]. While the minimal capacity for AC with ; Article no.CSIJ.34082 that the Cr (VI) capacity on sawdust low-cost AC of this study was on the higher side of sawdust cost adsorbents/ACs, and competitive with performance commercial ACs. Due to lowcost, the high Cr (VI) capacity on L-AC would translate into high adsorption capacity per cost of adsorbent compared with expensive commercial ACs [40], and can be used on a once-through or the costly regeneration [32]. This result qualified the L-AC to be very economical and efficient for abatement of Cr (VI) from wastewater, even at large scale. The spent AC would be safely disposed off through a strict toxic sludge containment otherwise use of the common spent AC incineration method would have a major problem of Cr (VI) thermal decomposition at about 196°C to highly thermal stable and carcinogenic In majority of studies on adsorption of Cr (VI) on AC the pore structure was not fully characterized. Nevertheless, for dilute solutions, the results in Table 3 indicate that Cr (VI) capacity is not influenced by surface area. Analysis of surface functionality show that low and high Cr (VI) been obtained on either acidic or size distribution 4 capacity on AC. For assumed spherical HCrO 4 oxyanions ≈ 0.5 nm); we calculated the monolayer ) of adsorbed AC and compared it with the measured wide micropore surface area (S MIC ) of was less than S MIC . With reference to the average wide micropore = 0.9 nm) of Lange 0.5 -1.0 nm (section 3.1) of effective micropore PSD for primary volume filling, the calculated S EQ showed that only effective micropores with monolayer filling were involved in the adsorption from dilute solution. To support this ing, we treated literature AC characterization AC. For adequately characterized ACs in Table 3, It was found that , confirming that only an effective microporosity was involved in , in agreement with results in related study [16]. The high Cr (VI) AC of this study could be related to presence of large volume of effective micropores with primary filling capacity. It could be argued that the same reason may explain the reported high Cr (VI) capacity on mesoporous silica nanoparticles (SNP) having broad PSD [11]. While the minimal capacity for AC with L AVE = 0.6 nm (Table 3) could be attributed to almost absence of effective microporosity as confirmed by very large difference between S EQ and S MIC , suggesting that this AC had majority of micropores below 0.6 nm and size exclusion effects could have dominated. On the other hand, for moderate to high V MIC of ACs, the results in Table 3 seem to indicate gradual decrease of capacity with monotonic increase of L AVE above 0.9 nm. The decrease of capacity could be attributed to progressive loss of effective micropores with increase in L AVE > 0.9 nm. The exceptional very low capacity at L AVE = 1.0 nm (Table 3) could be explained in terms of very low V MIC . Interestingly, for ordered mesoporous carbon (OMC) it was observed that S EQ > S MIC : The very high Cr (VI) capacity on OMC of large sized pores may be explained in terms of bilayer or secondary volume filling considering the estimated average pore size available for adsorption (L AVE = 1.7 nm), and high C O upto 3000 mg/L used in the equilibrium adsorption experiments. The treated results in Table 3 confirm the suggestion that an effective micropore PSD is significant for enhanced sorption capacity of Cr (VI) from dilute aqueous solutions.

Batch Kinetics and Intraparticle Mass Transfer
Besides high adsorption capacity for Cr (VI), the Cr (VI) uptake rate on L-AC is integral to optimal design of adsorption units for it would affect the throughput. Fig. 7 shows the effect of initial concentration and contact time on sorption of Cr (VI) on L-AC. The L-AC exhibited fast adsorption kinetics that could be associated with the mesostructure that offered reduced diffusion resistance for HCrO 4 oxyanions to interior wide micropores the sites of high adsorption energy. The applicable rate constant was determined from fitting the pseudo-first order (equation 4.5) and pseudo-second order (equation 4.7) to kinetics data, and results presented in Table 4. The kinetics rate constant is an essential parameter for optimal design of batch adsorption units by use of the contact time model [42]. The results in Table 4 indicated that the pseudo second order model adequately described the kinetics data (lowest χ2), as confirmed in Fig. 7.
The Pseudo-second model is formulated on chemisorption kinetics [43] and, therefore, its agreement with kinetic data suggested involvement of chemical adsorption, further support of occurrence of some coupled adsorption-reduction of Cr (VI). The analysis of second-order kinetic parameters revealed that the initial adsorption rate, h, increased with an increase in C O , consistent with results in Fig. 7.
On the other hand, the adsorption rate constant, k 2 , decreased with an increase in variation of k 2 with C O was reported for sorption of Cr (VI) on sawdust [17]. The increase of an increase in C O was attributed to high concentration gradients at high initial concentration causing fast diffusion of HCrO oxyanion to the AC surface. As would be expected of equilibrium uptake, the increased with an increase in C attributed to large number of HCrO available for adsorption and hence long equilibrium times as C O increased. 9 The applicable rate constant was determined first order (equation 4.5) second order (equation 4.7) to ed in Table 4. The kinetics rate constant is an essential parameter for optimal design of batch adsorption units by use of the contact time model [42]. The results in Table 4 indicated that the pseudosecond order model adequately described the ), as confirmed in Fig. 7. second model is formulated on chemisorption kinetics [43] and, therefore, its agreement with kinetic data suggested involvement of chemical adsorption, further support of occurrence of some coupled reduction of Cr (VI). The analysis of order kinetic parameters revealed that , increased with an , consistent with results in Fig. 7. On the other hand, the adsorption rate constant, an increase in C O . Similar was reported for sorption of Cr (VI) on sawdust [17]. The increase of h with was attributed to high concentration gradients at high initial concentration causing fast diffusion of HCrO 4 oxyanion to the AC surface. As would be expected of equilibrium uptake, the q 2 values  25]. The knowledge of diffusion limiting stage would allow for proper design of process conditions to enhance Cr (VI) uptake. To determine the effective intraparticle diffusion coefficient (D eff ), the Patterson model (equations 13 -17) was fitted to kinetics data and the model performance shown in Fig. 8. While Fig. 9 shows the fitting of the M&W (LDF) rate law (equations 4. 12 -4.14) to kinetic data at = 50 mg/L Cr (VI) in the initial adsorption time < 5 min for determination of the [batch] liquid mass transfer coefficient (k fb ).  ), the Patterson model 17) was fitted to kinetics data and the model performance shown in Fig. 8. While f the M&W (LDF) rate 4.14) to kinetic data at C O = 50 mg/L Cr (VI) in the initial adsorption time < 5 min for determination of the [batch] liquid-film Patterson model fit to kinetics data was excellent, with an average error between experimental and model values of ca. ≤ 8% for all concentrations studied. Equally, the M&W (LDF) fit to kinetic data was excellent with > 0.98 for all concentrations studied. The estimated values of are summarized in Table 5. The Patterson model is applicable to intraparticle diffusion control and finite solution case, with  (17) of 0 < w < 1 for all initial concentrations studied. The magnitudes of estimated D eff (10-8 cm 2 /s) and k fb (10-3 cm/s) are typical of metal ions diffusion into AC porous structure reported in literature [23,24] and, therefore, further validating the applicability of the Patterson model and M&W (LDF) rate law to kinetic data. The k fb values were similar at C O (10 and 30 mg/l), but decreased at C O = 50 mg/L. Choy et al. [24] have reported a similar trend for sorption of Zn (II) on bone char. The D eff values decreased with an increase in C O , indicative of increasing intraparticle resistance presumably due to HCrO 4 anions crowding of the adsorbent surface and, therefore, anions competition for adsorbent pores. Consequently, the Bi increased with increase in C O . Intraparticle diffusion sorely controls the adsorption process for Bi > 30, while film diffusion controls the adsorption for Bi < 0.5 [23]. Therefore, the calculated (Bi) values indicated that intraparticle diffusion resistance was relatively significant for C O ≥ 20 mg/L.

CONCLUSION
Optimally developed low-cost adsorbent/ activated carbon (AC) of tailored microporosity distribution would provide a sustainable alternative for economical and efficient removal of Cr (VI) from dilute wastewaters. The results of this study showed that adsorbent effective microporosity strongly influences the sorption capacity of Cr (VI) from dilute solutions significant to environmental protection. Consequently, the optimum design of low-cost adsorbent/AC should factor moderate to high micropore volume and effective microporosity of average pore size about 0.9 ± 0.1 nm. Also, a high proportion of mesoporosity is desirable for reduced diffusion limitations to interior effective micropores. The results of this study show that the forward approach of tailoring relevant adsorptive properties at adsorbent preparation stage is important than the backward approach of developing the adsorbent first and then testing for quality. The determining of adsorbent/AC micropore volume and an average effective micropore size from N 2 adsorption isotherm data would be simple routine quality control procedure to ensure quality of developed adsorbent/AC.