Medical, Pharma, Engineering, Science, Technology and Business

^{1}Department of Chemical Engineering, Bapatla Engineering College, Guntur, India

^{2}Department of Chemical Engineering, S.V. University, Tirupati, India

- Corresponding Author:
- Srinivasa Rao J

Department of Chemical Engineering

Bapatla Engineering College

Guntur, India

**E-mail:**[email protected]

**Received** January 28, 2013; **Accepted** February 06, 2013; **Published** February 08, 2013

**Citation:** Srinivasa Rao J, Kesava Rao C, Prabhakar G (2013) Optimization of
Biosorption Performance of *Casuarina* Leaf Powder for the Removal of Lead Using
Central Composite Design. J Environ Anal Toxicol 3: 166. doi: 10.4172/2161-0525.1000166

**Copyright:** © 2013 Srinivasa Rao J, et al. This is an open-access article distributed
under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the
original author and source are credited.

**Visit for more related articles at** Journal of Environmental & Analytical Toxicology

Rapid industrialization, urbanization and increase in population have led to increasing the pollution levels. Heavy metal pollution of water is of major concern now-a-days as water is the basic need for mankind. The present investigation is removal of lead from aqueous solutions using a new biosorbent Casuarina leaf powder. The cumulative effects of operating parameters such as initial metal ion concentration, pH of the aqueous solution, biosorbent dosage and temperature on the lead biosorption were analyzed using Response Surface Methodology (RSM). For obtaining the mutual interaction between the variables and optimizing these variables, a 24 full factorial central composite design was employed. According to ANOVA results, the proposed quadratic model for CCD fitted very well to the experimental data. The optimal set of conditions for maximum percentage biosorption of lead is found to be pH=4.988, biosorption dosage (w) =35.37 g/L, initial lead concentration (Co)=18.0555 mg/L and temperature=306.47 K and the % of biosorption calculated at these values found to be 95.73%. The Langmuir isotherm fitted well with a correlation factor of 0.9944, followed by Freundlich and Temkin. The entire biosorption process followed pseudo second order kinetics. By applying the Van’t Hoff equation the thermodynamic parameters such as enthalpy (ΔH°), entropy (ΔS°) and free energy (ΔG°) were evaluated which described the biosorption process as spontaneous, irreversible and endothermic in nature. The optimized values obtained through central composite design and one factor at a time process is in good agreement.

Biosorption; *Casuarina* leaf powder; Central composite
design; Isotherms; Kinetics

Water is no alien to all the living beings upon earth. It has no barrier
or bars over constituencies or continents, as it leaves only 1/4^{th} of the
land of whole ecosystem. The contaminated water may cause anemia,
headache, chills, diarrhea and reduction in hemoglobin formation
[1]. The influence of pollution on the global environment, through
activities such as rapid industrialization, urbanization and mining
operations often lead to an increase in the discharge of toxic metals,
such as lead, nickel, chromium, cobalt, copper, cadmium etc., into the
environment, which results in a contamination of water. These heavy
metal contaminants are hazardous to the environment, because they do
not naturally degrade [2]. Beyond certain limits, heavy metals are toxic
to living organisms and may cause serious hazard to public health [3].
Environmental engineers and scientists are faced with the challenging
task to develop appropriate low cost technologies for effluent treatment
[4].

Traditional methods for removal of lead ions from solution include chemical precipitation, ion exchange, electrodialysis and membrane separations. All these methods have various disadvantages, specifically, high capital investment and operating cost, incomplete removal, low selectivity and high energy consumption. Therefore, there is a need for a cost effective treatment method that is capable of removing low concentrations of lead from solution For the last decades, biosorption or sorption of contaminants by sorbents of natural origin has gained important credibility due to the good performance and low cost of these complexing materials [5-10]. A multitude of biomass types comprising fungal biomass, bacterial biomass, algae, peat etc., have been studied for their biosorption of metals [11-14]. Agricultural wastes such as tree bark, peanut skin, hull, tobacco, tomato root tissues and plants waste have been used to remove heavy metals from water [15-17].

In view of the above, the authors tried to use a novel biosorbent *Casuarina* leaf powder to remove lead from aqueous solutions and
report the application of Response Surface Methodology using Central
Composite Design to develop a mathematical model and predict the
response and check the adequacy of the model. The objectives of the
present study include identifying the maximum lead uptake capacity
of the *Casuarina* leaves powder with respect to various governing
parameters. In addition, biosorption isotherms were described by
using Langmuir, Freundlich and Temkin models and the kinetic
experimental data were correlated by the pseudo first and second order
kinetic models. Thermodynamics for biosorption of lead on *Casuarina*
leaves powder is also studied and fitted in to Van’t Hoff equation.

**Biosorbent**

*Casuarina* leaves were collected from the surroundings of Bapatla,
Guntur. The *Casuarina* leaves were washed thrice with tap water and
once with distilled water in order to remove adhering surface impurities.
The leaves were dried in sunlight until all the moisture was evaporated.
The crispy *Casuarina* leaves were then grinded in a ball mill to powder,
separated using British Standard Sieves (BSS) and stored in dry air tight
packs to prevent moisture penetration and readily used as biosorbent.

**Preparation of metal solutions**

Test solutions containing lead ions were prepared from Pb (NO_{3}
)_{2} at
different concentrations ranging from 25, 50, 100, 150, 200, 250 mg/L. The
pH of each test solution was adjusted to the appropriate value by using 0.1
N HNO_{3} or 0.1 N NaOH solutions. All the chemicals used in preparing the
stocks are of analytical grade and the water used is double distilled water
prepared from Millipore ELIX-10 unit.

**Batch sorption studies**

The biosorption was carried out in a batch process by contacting
a pre-weighed amount of the *Casuarina* leaves powder with a known
volume of aqueous solution. Experiments were conducted in 250 ml
Erlenmayer flasks containing 50 ml of 20 mg/L metal solution using
single step optimization procedure. The flasks containing aqueous
solution and biosorbent were agitated on an orbital shaker at 180 rpm
and samples were taken at predetermined time intervals (1, 3, 5, 10,
15, 20, 25, 30, 40, 50, 60, 90, 120, 150 and 180 min) and centrifuged
at 14000 rpm and the supernatant liquid was analyzed in Atomic
Absorption Spectrophotometer (AAS) - Shimadzu make AA-6300
for final concentrations. Similarly the other variables were varied for
a wide range: Biosorbent Size (63, 75 and 105 μm), pH of the aqueous
solution (2, 3, 4, 5, 6, 7 and 8), Initial concentration of lead solution (20,
50, 80, 120 and 150 mg/L), Biosorbent dosage (5, 10, 15, 20, 25, 30, 35,
40 and 50 g/L) and Temperature (283, 293, 303, 313 and 323 K).

**Process optimization**

Final experimental runs for optimization were obtained through
Response Surface Methodology using Central Composite Design
with 2^{4} factorial runs, 6-central points and 8-axial points. Design
of Experiments (DoE) obtained based on the above optimization
technique using STATISTICA software. The extent of biosorption
of lead calculated at the preliminary optimum conditions is verified
with the final runs for the optimum conditions. For the optimization
of biosorption, the regression equation is written in terms of %
biosorption of lead (Y) as function of the parameters having greater
influence over the response i.e. pH (X_{1}), Co (X_{2}), w (X_{3}), and T (X_{4}).
Based on experimental runs and predicted values proposed by CCD
design, the following equation represents multiple regression analysis
of the experimental data for the biosorption of lead:

Y = b_{0}
+ b_{1} X_{1} +b_{2}X_{2} + b_{3}X_{3}+ b_{4}X_{4} + b_{11}X_{1}^{2}+b_{22}X_{2}^{2}+ b_{33}X_{3}^{2} + b_{12} X_{1}X_{2}+ b_{13}
X_{1}X_{3}+ b_{23} X_{2}X_{3}+ b_{44} X_{42}+ b_{14 }X_{1}X_{4} + b_{24} X_{2}X_{4}+ b_{34} X_{3}X_{4}

**Effect of agitation time**

Duration of equilibrium biosorption is defined as the time
required for heavy metal concentration to reach a constant value
during biosorption. The equilibrium agitation time is determined by
plotting the % biosorption of lead against agitation time as shown in
**figure 1** for the interaction time intervals between 1 to 180 min. For
63 μm size of 10 g/L biosorbent dosage mixed in 50 mL of aqueous
solution (C_{o}=20 mg/L), 50.4% of lead is biosorbed in the first one
minute and reached to 55.7% after 5 minutes of biosorption. The %
biosorption is increased briskly up to 60 min reaching 86.5%. Beyond
60 min, the % of biosorption is constant indicating the attainment of
equilibrium conditions. The maximum biosorption of 86.5% is attained
for 60 min of agitation time. The rate of biosorption is fast in the initial
stages because adequate surface area of the biosorbent is available for
the biosorption of lead. As time increases, more amount of lead gets biosorbed onto the surface of the biosorbent due to Vanderwaal’s
forces of attraction and resulted in decrease of available surface area.
The biosorbate, normally, forms a thin one molecule thick layer over
the surface. When this monomolecular layer covers the surface, the
biosorbent capacity is exhausted. Therefore, all other experiments are
conducted at this agitation time.

**Effect of biosorbent size**

The variations in % biosorption of lead from the aqueous solution
with biosorbent size are drawn in **figure 2** with percentage biosorption
of lead as a function of biosorbent size. The percentage of biosorption
is decreased from 86.9% to 80.2% as the biosorbent size increases from
63 to 105 μm. This phenomenon is expected, as the size of the particle
decreases, surface area of the biosorbent increases; thereby the number
of active sites on the biosorbent also increases.

**Effect of pH**

Biosorption is controlled by pH by the influence of surface charge
of the biosorbent, the degree of ionization and the species of biosorbate.
In the present investigation, effect of pH on lead biosorption is obtained
in the pH range of 2 to 8 of the aqueous solution (C_{o} =20 mg/L) using
10 g/L of 63 μm size biosorbent. The effect of pH of aqueous solution
on % biosorption of lead is shown in **figure 3**. The % biosorption of
lead is increased from 64.6% to 91.4% as pH is increased from 2 to 5
and decreased beyond the pH value of 6. Percentage of biosorption is
decreased to 62.1% from 84.3% for pH variation of 6 to 8. Since the pH of
aqueous solution influences the solution chemistry of the heavy metals,
the binding of metal ions by surface functional groups is strongly pH
dependent. The increase in % removal when pH increases from 2 to 5
could be due to decrease in competition between hydrogen ions and
metal species for appropriate sites on the biosorbent surface and also by
the decrease in positive surface charge on the adsorbent. However, with
increasing pH above 5 lead tends to hydrolyze and precipitate instead
of adsorption and adsorbent was deteriorated with accumulation of
metal ions, making the true adsorption studies unpredictable.

**Effect of initial concentration of lead**

The effect of % biosorption on initial concentration of lead in the
aqueous solution is shown in **figure 4**. The percentage biosorption of
lead is increased from 73.3% to 90.1% with decrease in C_{o} from 150
mg/L to 20 mg/L. Such behavior can be attributed to the increase in
the amount of biosorbate to the unchanging number of available active
sites on the biosorbent.

**Effect of biosorbent dosage**

The percentage biosorption of lead is drawn against biosorbent
dosage for 63 μm size biosorbent in **figure 5**. The biosorption of lead
increased from 87.2% to 93.4% with an increase in biosorbent dosage
from 5 to 35 g/L. Such behavior is obvious because with an increase
in biosorbent dosage, the number of active sites available for lead
biosorption would be more. The change in percentage biosorption of
lead is marginal from 93.4% to 93.8% when ‘w’ is increased from 35 to
50 g/L. Hence all other experiments are conducted at 35 g/L dosage.

**Effect of temperature**

The effect of temperature on the equilibrium metal uptake was
significant. The effect of changes in the temperature on the lead uptake
is shown in **figure 6**. Lead uptake marginally increased from 92.2 to
94.6% with increasing temperature from 283 K to 323 K indicating that
the biosorption of lead on to *Casuarina* leaf powder is endothermic
process. Adsorption processes are normally exothermic and as the
temperature increases the % adsorption decreases in accordance with
Le Chatelier principle. The reverse phenomena could be activation of
non living biomass under moderate temperatures and Increasing the
temperature is known to increase the rate of diffusion of the adsorbate
molecules across the external boundary layer and in the internal pores
of the adsorbent particles, owing to decrease in the viscosity of the
solution.

**Isotherms**

**Langmuir isotherm:** Irving Langmuir developed an isotherm named Langmuir isotherm. It is the most widely used simple twoparameter
equation. The Langmuir relationship is hyperbolic and the
equation is:

q_{e}/q_{m} = bC_{e}/ (1+bC_{e}) (1)

Equation (5.1) can be rearranged as

(C_{e}/q_{e}) = 1/(bq_{m}) + C_{e}/q_{m} (2)

From the plots between (C_{e}/q_{e}) and C_{e}, the slope {1/ (bq_{m})} and the
intercept (1/b) are calculated. Further analysis of Langmuir equation is
made on the basis of separation factor, (RL) defined as RL = 1/ (1+bC_{e}).

0<R_{L}<1 indicates favorable adsorption

R_{L}>1 indicates unfavorable adsorption

R_{L} = 1 indicates linear adsorption

R_{L} = 0 indicates irrepressible adsorption

Langmuir isotherm is drawn for the present data and shown in
**figure 7**. The equation obtained is C_{e}/q_{e} = 0.0663142C_{e} + 1.0222246
with a good linearity (correlation coefficient, R^{2}~0.9944) indicating
strong binding of lead ions to the surface of *Casuarina* leaf powder.
The maximum metal uptake of (q_{m}) 15.0797 mg/g is observed and
the separation factor obtained (R_{L}) is 0.88617, indicating favorable
biosorption.

**Freundlich isotherm:** Freundlich presented an empirical
biosorption isotherm equation that can be applied in case of low and
intermediate concentration ranges. It is easier to handle mathematically
in more complex calculations.

The Freundlich isotherm is given by

q_{e} = K_{f} C_{e} n (3)

Where, K_{f} (mg) represents the biosorption capacity when metal
equilibrium concentration and n represents the degree of dependence
of biosorption with equilibrium concentration. The above equation is
represented as

ln q_{e} = ln K_{f}+ n ln C_{e} (4)

Freundlich isotherm is drawn between lnC_{e}and lnq_{e} (**Figure 8**). The obtained equation is lnq_{e} = 0.600397 lnC_{e} + 0.274637; for the present
data. The resulting equation has a correlation coefficient of 0.9832. The
‘n’ value (0.600397) in the above equations satisfies the condition of
0<n<1 indicating favorable biosorption. The K_{f} obtained was 1.882075.

**Temkin isotherm**: Temkin and Pyzhev isotherm equation describes
the behavior of many biosorption systems on the heterogeneous surface
and it is based on the following equation

q_{e}= RT ln(A_{T}C_{e})/b_{T} (5)

The linear form of Temkin isotherm can be expressed as

q_{e}= (RT/ b_{T} ) ln(A_{T}) + (RT/b_{T}) ln(C_{e}) (6)

The present data are analysed according to the linear form of
Temkin isotherm and the linear plot is shown in **figure 9**. The equation
obtained for lead biosorption is: q_{e} = 3.07614 lnC_{e} – 0.7570 with a correlation coefficient 0.9817. The best fit model is determined based
on the linear regression correlation coefficient (R^{2}). From the **figure
7-9**, it is found that biosorption data are well represented by Langmuir
isotherm with higher correlation coefficient of 0.9944, followed by
and Freundlich and Temkin isotherms with correlation coefficients
of 0.9832 and 0.9817 respectively. The validity of Langmuir model
suggests the adsorption process is monolayer and adsorption of each
molecule has equal activation energy. The isotherm constants are given
in **table 1**.

Langmuir | Freundlich | Temkin |
---|---|---|

q_{m} = 15.0797 |
k_{f}= 1.882075 |
A_{T} = 0.781859 |

b = 0.06487 | n = 0.600397 | b_{T} = 818.9295 |

R^{2} =0.9944 |
R^{2} =0.9832 |
R^{2} =0.9817 |

**Table 1:** Isotherms constants.

**Kinetics**

The order of biosorbate – biosorbent interactions have been described using kinetic model. Traditionally, the first order model of Lagergren finds wide application. In the case of biosorption preceded by diffusion through a boundary, the kinetics in most cases follows the first order rate equation of Lagergren:

(dq_{t}/dt)= K_{ad} (q_{e} – q_{t}) (7)

Where, qe and qt are the amounts adsorbed at t, min and equilibrium time and Kad is the rate constant of the lagergren first order biosorption.

The above equation can be presented as

∫ (dq_{t}/ (q_{e} – q_{t})) = ∫ K_{ad}dt (8)

Applying the initial condition q_{t} = 0 at t = 0, we get

log (q_{e} – q_{t}) = log q_{e}– (K_{ad}/2.303) t (9)

Plot of log (q_{e}–q_{t}) versus‘t’ gives a straight line for first order
kinetics, facilitating the computation of adsorption rate constant (K_{ad}).

The pseudo second order kinetic equation given below:

(dq_{t}/dt) = K (q_{e} – q_{t})2 (10)

Where, ‘K’ is the second order rate constant.

Substituting these values in above equation, we obtain:

1/ (q_{e} – q_{t}) = Kt + (1/q_{e}) (11)

Rearranging the terms, we get the linear form as:

(t/q_{t}) = (1/ Kq_{e}^{2} ) + (1/q_{e} ) t (12)

The pseudo second order model based on above equation,
considers the rate -limiting step as the formation of chemisorptive bond
involving sharing or exchange of electrons between the biosorbate and
biosorbent. If the pseudo second order kinetics is applicable, the plot
of (t/q_{t}) versus‘t’ gives a linear relationship that allows computation
of q_{e} and K. The first order and the second order kinetics plots are
given in **figures 10** and **11** respectively. The rate equations obtained
and comparative lead uptake capacities are given in **table 2** and **table 3** respectively. The correlation coefficients indicate that the system under
consideration is more appropriately described by pseudo-second order
model. The regression coefficient of 0.9897 shows that that the model
can be applied for the entire adsorption process. The confirmation of
pseudo second order kinetics indicates that in the adsorption process,
concentrations of both adsorbent and adsorbate are involved in rate
determining step. In the range of studied parameters, the metal uptake
is very good for *Casuarina* leaf powder.

Order | Equation | K, min^{-1} |
R^{2} |
---|---|---|---|

First order | log (q_{e}-q_{t})=–0.019698 t–0.073348 |
0.04513 | 0.9507 |

Second order | t/q_{t}=0.5935 t + 1.85514 |
0.18987 | 0.9897 |

**Table 2:** Rate Equations and coefficients for biosorption of lead on Casuarina leaf
powder.

Authors | Biosorbent | qt, mg/g |
---|---|---|

S.A. Abo-El-Enein [18] | rice husk ash | 158 |

Erdal Kenduzler [19] | Amberlyst 36 | 88 |

Vijayaraghavan [20] | Sargassum | 20.2 |

Fuat Guzel [21] | black carrot | 5.003 |

Mustafa Tuzen [22] | Pseudomonas aeruginosa | 5.83 |

Present investigation |
Casuarina leaf powder |
15.0797 |

**Table 3:** Lead uptake capacities for different biosorbents.

**Thermodynamics of biosorption**

Biosorption is temperature dependant. In general, the temperature dependence is associated with three thermodynamic parameters namely change in enthalpy of biosorption (ΔH), change in entropy of biosorption (ΔS) and change in Gibbs free energy (ΔG). Enthalpy is the most commonly used thermodynamic function due to its practical significance. The negative value of ΔH will indicate the exothermic/ endothermic nature of biosorption and the physical/chemical in nature of sorption. It can be easily reversed by supplying the heat equal to calculated ΔH.

The ΔH is related to ΔG and ΔS as

ΔG = ΔH – T ΔS (13)

ΔS < 1 indicates that biosorption is impossible whereas ΔS > 1 indicates that the biosorption is possible. ΔG < 1 indicates the feasibility of sorption.

The Vant Hoff’s equation is

log (q_{e} /C_{e}) = ΔH/(2.303 RT) + (ΔS/2.303 R) (14)

log (q_{e} /C_{e}) = – 0.40566 (1 / T) + 1.029489 (15)

Where, (q_{e}/C_{e}) is called the biosorption affinity.

If the value of ΔS is less than zero, it indicates that the process
is highly reversible. If ΔS is more than or equal to zero, it indicates
the reversibility of process. The negative value for ΔG indicates the
spontaneity of biosorption, whereas the positive value indicates non
spontaneity of sorption. Experiments are conducted to understand the
biosorption behavior varying the temperature from 283 to 323 K. The
Van’t Hoff’s plot for the biosorption data obtained is shown in **figure
12**. From the plot the equation obtained is log (q_{e} /C_{e}) = – 0.40566
(1 / T) + 1.029489. The values obtained from the equation are ΔG =
-5964.899, ΔH = 7.7672 and ΔS = 19.71177. ΔH is positive indicating
that the biosorption is endothermic. The negative value of ΔG indicates the spontaneity of biosorption. As ΔS is more than zero, it indicates the
irreversibility of biosorption.

**Optimization using Response Surface Methodology (RSM)**

In order to determine an optimum condition for Pb ions
removal, the parameters having greater influence over the response
is to be identified. In the present study, the relationship between four
independent variables and percent of Pb ions biosorption fitted well
with the quadratic model. Levels of different process variables in coded
and un-coded form (**Table 4**), Results from CCD (**Table 5**), Analysis
of variance (ANOVA) (**Table 6**), Estimated regression coefficients
(**Table 7**) and Comparison of optimum values obtained from CCD
and experimentation (**Table 8**) for biosorption of lead using *Casuarina*
leaf powder are presented below. For the optimization of biosorption
the regression equation: % biosorption of lead (Y) is function of the pH (X_{1}), Co (X_{2}), w (X_{3}), and T (X_{4}). Based on experimental runs and
predicted values proposed by CCD design.

Variable |
Name |
Range and levels |
||||
---|---|---|---|---|---|---|

-2 |
-1 |
0 |
1 |
2 |
||

X_{1} |
Biosorbent dosage, w, g/L | 25 | 30 | 35 | 40 | 45 |

X_{2} |
Initial concentration, C_{o}, mg/L |
10 | 15 | 20 | 25 | 30 |

X_{3} |
pH of aqueous solution | 3 | 4 | 5 | 6 | 7 |

X_{4} |
Temperature, T, K | 283 | 293 | 303 | 313 | 323 |

Run no. | X_{1}(w) |
X_{2}(C_{o}) |
X_{3}(pH) |
X_{4}(T) |
% biosorption of cobalt | |
---|---|---|---|---|---|---|

Experimental | Predicted | |||||

1 | -1.0000 | -1.0000 | -1.0000 | -1.0000 | 93.18 | 93.21 |

2 | -1.0000 | -1.0000 | -1.0000 | 1.0000 | 93.67 | 93.65 |

3 | -1.0000 | -1.0000 | 1.0000 | -1.0000 | 93.19 | 93.18 |

4 | -1.0000 | -1.0000 | 1.0000 | 1.0000 | 93.59 | 93.60 |

5 | -1.0000 | 1.0000 | -1.0000 | -1.0000 | 92.2 | 92.21 |

6 | -1.0000 | 1.0000 | -1.0000 | 1.0000 | 92.79 | 92.82 |

7 | -1.0000 | 1.0000 | 1.0000 | -1.0000 | 92.89 | 92.91 |

8 | -1.0000 | 1.0000 | 1.0000 | 1.0000 | 93.51 | 93.50 |

9 | 1.0000 | -1.0000 | -1.0000 | -1.0000 | 93.8 | 93.78 |

10 | 1.0000 | -1.0000 | -1.0000 | 1.0000 | 94.17 | 94.20 |

11 | 1.0000 | -1.0000 | 1.0000 | -1.0000 | 93.29 | 93.31 |

12 | 1.0000 | -1.0000 | 1.0000 | 1.0000 | 93.74 | 93.71 |

13 | 1.0000 | 1.0000 | -1.0000 | -1.0000 | 91.98 | 92.01 |

14 | 1.0000 | 1.0000 | -1.0000 | 1.0000 | 92.62 | 92.60 |

15 | 1.0000 | 1.0000 | 1.0000 | -1.0000 | 92.28 | 92.27 |

16 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 92.83 | 92.84 |

17 | -2.0000 | 0.0000 | 0.0000 | 0.0000 | 94.34 | 94.30 |

18 | 2.0000 | 0.0000 | 0.0000 | 0.0000 | 94.21 | 94.20 |

19 | 0.0000 | -2.0000 | 0.0000 | 0.0000 | 94.13 | 94.12 |

20 | 0.0000 | 2.0000 | 0.0000 | 0.0000 | 92.28 | 92.25 |

21 | 0.0000 | 0.0000 | -2.0000 | 0.0000 | 90.71 | 90.67 |

22 | 0.0000 | 0.0000 | 2.0000 | 0.0000 | 90.89 | 90.88 |

23 | 0.0000 | 0.0000 | 0.0000 | -2.0000 | 93.77 | 93.73 |

24 | 0.0000 | 0.0000 | 0.0000 | 2.0000 | 94.75 | 94.74 |

25 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

26 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

27 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

28 | 0.00000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

29 | 0.00000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

30 | 0.00000 | 0.0000 | 0.0000 | 0.0000 | 95.6 | 95.60 |

Experimental conditions [Coded Values] and observed response values of central
composite design with 2^{4} factorial runs, 6- central points and 8- axial points.
Agitation time fixed at 60 min and biosorbent size at 63 μm

**Table 5:** Results from CCD for cobalt biosorption by *Casuarina* leaf powder.

Source of variation | SS | df | Mean square(MS) | F-value | P> F |
---|---|---|---|---|---|

Model | 53.85109 | 14 | 3.8465 | 4649.27 | 0.0000 |

Error | 0.01241 | 15 | 0.0008273 | ||

Total | 53.8635 |

df, degree of freedom; SS, sum of squares; F, factor F; P, probability.
R^{2}=0.99977; R^{2} (adj): 0.99955

**Table 6:** Analysis of variance (ANOVA) of lead biosorption for entire quadratic model.

Terms | Regression coefficient | Standard error of the coefficient | t-value | P-value |
---|---|---|---|---|

constant | -280.353 | 5.533036 | -50.669 | 0.000000 |

X_{1} |
1.233 | 0.047130 | 26.151 | 0.000000 |

X_{2} |
-0.013 | 0.000220 | -61.134 | 0.000000 |

X_{3} |
0.694 | 0.046155 | 15.036 | 0.000000 |

X_{4} |
-0.024 | 0.000220 | -109.843 | 0.000000 |

X_{1}*X_{1} |
12.272 | 0.232115 | 52.871 | 0.000000 |

X_{2}*X_{2} |
-1.204 | 0.005492 | -219.326 | 0.000000 |

X_{3}*X_{3} |
2.071 | 0.033977 | 60.965 | 0.000000 |

X_{4}*X_{4} |
-0.003 | 0.000055 | -61.816 | 0.000000 |

X_{1}*X_{2} |
-0.008 | 0.000288 | -26.511 | 0.000000 |

X_{1}*X_{3} |
-0.022 | 0.001438 | -15.385 | 0.000000 |

X_{1}*X_{4} |
-0.000 | 0.000144 | -0.782 | 0.446215^{a} |

X_{2}*X_{3} |
0.037 | 0.001438 | 25.468 | 0.000000 |

X_{2}*X_{4} |
0.001 | 0.000144 | 5.998 | 0.000024 |

X_{3}*X_{4} |
-0.000 | 0.000719 | -0.608 | 0.551990^{a} |

**Table 7:** Estimated regression coefficients for the lead biosorption onto Casuarina leaf powder.

Variable | CCD | Experimental value |
---|---|---|

pH of aqueous solution | 4.9884 | 5.0 |

Biosorption dosage, w, g/L | 35.3702 | 35 |

Initial cobalt concentration, mg/L | 18.0555 | 20 |

Temperature, K | 306.4727 | 303 |

% biosorption | 95.7337 | 93.9 |

**Table 8:** Comparison of optimum values obtained from CCD and experimentation.

Y = –280.353 + 1.233 X_{1} + 0.694 X_{2} + 12.272 X_{3} + 2.071 X_{4} – 0.013
X_{1}^{2} – 0.024 X_{2}^{2}– 1.204 X_{3}^{2}– 0.003 X_{4}^{2}– 0.008 X_{1}X_{2} + 0.022 X_{1}X_{3} + 0.000 X_{1}X_{4} + 0.037 X_{2}X_{3} + 0.001 X_{2}X_{4} +
0.000 X_{3}X_{4} (16)

From the Central Composite Design, the Pareto Chart (**Figure 13**),
Observed Vs Predicted values plot (**Figure 14**) and Surface contour plot
(**Figures 15 a-f**) for biosorption of lead on to *Casuarina* leaf powder
are presented below. The optimal set of conditions for maximum
percentage biosorption of lead is pH= 4.9884 biosorption dosage (w)
=35.3702 g/L, initial lead concentration (Co) =18.0555 mg/L and
temperature=306.4727 K and the % of biosorption calculated at these
values found to be 95.73%.

The analysis of the experimental and theoretical data resulted that
the equilibrium agitation time for lead biosorption is 60 minutes. The
% removal of lead from an aqueous solution increases with a decrease
in the particle size of the biosorbent and increases with increase in
biosorbent dosage. With an increase in the initial concentration of lead in the aqueous solution, the percentage removal of lead from the
aqueous solution is decreased. Percentage removal of lead from the
aqueous solution increases significantly with increase in pH from 2
to 5, thereafter percentage removal decreases for further increase in
pH. In the range of variables studied, percentage removal is increased
from 50.44% to 93.9%. The maximum uptake capacity of 15.0797
mg/g is obtained at temperature 303 K. The kinetic studies show that
the biosorption of lead is better described by pseudo second order
kinetics It is also found that the data are well represented by Langmuir
isotherm with higher correlation coefficient of 0.9944, followed by
Freundlich and Temkin isotherms. The biosorption of lead on to
*Casuarina* leaf powder is irreversible, spontaneous and endothermic
in nature. The present study involves the use of statistical experimental
design to optimize process conditions for maximal biosorption of lead
from aqueous solution using CCD involving RSM. The maximum
biosorption of lead (95.73%) onto *Casuarina* leaf powder is observed
when the processing parameters are set as follows: pH = 4.988, w =
35.37 g/L, Co =18.0555 mg/L and T=306.47 K. Therefore the above
said *Casuarina* leaf powder is effective and efficient biosorbent and is
capable of removing lead.

The authors wholeheartedly thank the Bapatla Engineering College and TEQIP-World Bank for supporting the authors and sparing the equipment for Research Purpose.

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