*2.7.2. Effect of contact time on sorption*

The effect of contact time on sorption of lead (II), cadmium (II) and copper (II) by modified and unmodified algae was done by taking a sample, 0.2 g of the sorbent (modified and unmodified algae) into the plastic bottles and 50 ml of the adsorbate of concentration 10 ppm added. The mixture was buffered to the optimum pH value for each metal and agitated at predetermined time intervals of 2–150 min. The samples were then removed from the shaker and the solutions filtered, and the metal ion concentration in the filtrate was determined.

### *2.7.3. Effect of initial metal ion concentration on sorption*

The extent to which metal ions are adsorbed as a function of the initial ion concentration was investigated by mixing 0.2 g of finely ground modified and unmodified algae separately with 50 ml of varying concentrations of the test solutions, buffered at the optimal pH value for each respective metal. The respective mixtures were allowed to equilibrate for a sufficient duration and then filtered and the concentration of the metal ions in the filtrate was determined.

### *2.7.4. Effect of sorbent dose on percentage metal removal*

The effect of sorbent dose was investigated by agitating 50 ml (10 μg ml−1) of the adsorbate solutions of lead (II), cadmium (II) and copper (II) with various dosages of the sorbents. 0.1, 0.5, 1.0, 1.5 and 2.0 g of modified and unmodified algae were used. The solutions of the adsorbate were buffered to the optimum pH of each respective metal ion under investigation. The solutions were for 2 h with the temperature set at 25°C. The resulting mixtures were filtered and the concentration of the residual metal ions determined.

### *2.7.5. Determination of adsorption capacity of modified and unmodified algae*

The adsorption capacity was determined by mixing 0.2 g of finely ground sorbent material with 50 ml of varying concentrations of the test metal solution (concentrations 10–250 ppm) buffered at the optimum pH for each respective metal. The mixtures were agitated for 30 min and then filtered, and the concentrations of metal ions were determined.

### *2.7.6. Adsorption models*

The experimental data on metal sorption were also analyzed using adsorption models so as to establish the sorption kinetics and mechanism.

### *2.7.7. The kinetics of adsorption*

To determine the necessary time, different solutions of for adsorption lead (II), cadmium (II) and copper (II) 20 ml containing 10 μg ml−1 of the adsorbate were introduced in different sets of plastic bottles containing 0.2 g of the adsorbent, and the pH sets an optimal value for each metal. The mixtures were then introduced in the shaker temperature of 25°C and equilibrated at different time intervals of 2, 5, 10, 20, 30, 60, 90 and 120 min. They were then filtered, and the filtrate was analyzed for adsorbate concentration. The data obtained was treated with Lagergren's [17] pseudo-first-order and Ho et al.'s [18] pseudo-second-order equations to determine molecularity of the adsorption.

The Lagergren first-order and Ho's second-order kinetic models are expressed as shown in equations 5.1 and 5.2, respectively:

$$\ln(C\_o - C\_t) = Kt + A \tag{1}$$

$$\frac{1}{q\_{\epsilon}} = Kt + A\tag{2}$$

where *Co* is the adsorption per unit mass of adsorbent at equilibrium, *K* is the adsorption rate constant, *A* is intercept and *Ct* is the concentration at time *t*.

### *2.7.8. Adsorption isotherms*

The experimental data for the effect of metal ion concentration obtained was treated with the Freundlich and Langmuir isotherm models to obtain the adsorption mechanism.

### *2.7.8.1. Langmuir isotherm*

The solutions were for 2 h with the temperature set at 25°C. The resulting mixtures were filtered

The adsorption capacity was determined by mixing 0.2 g of finely ground sorbent material with 50 ml of varying concentrations of the test metal solution (concentrations 10–250 ppm) buffered at the optimum pH for each respective metal. The mixtures were agitated for 30 min

The experimental data on metal sorption were also analyzed using adsorption models so as to

To determine the necessary time, different solutions of for adsorption lead (II), cadmium (II) and copper (II) 20 ml containing 10 μg ml−1 of the adsorbate were introduced in different sets of plastic bottles containing 0.2 g of the adsorbent, and the pH sets an optimal value for each metal. The mixtures were then introduced in the shaker temperature of 25°C and equilibrated at different time intervals of 2, 5, 10, 20, 30, 60, 90 and 120 min. They were then filtered, and the filtrate was analyzed for adsorbate concentration. The data obtained was treated with Lagergren's [17] pseudo-first-order and Ho et al.'s [18] pseudo-second-order equations to

The Lagergren first-order and Ho's second-order kinetic models are expressed as shown in

*Kt A*

where *Co* is the adsorption per unit mass of adsorbent at equilibrium, *K* is the adsorption rate

The experimental data for the effect of metal ion concentration obtained was treated with the

Freundlich and Langmuir isotherm models to obtain the adsorption mechanism.

is the concentration at time *t*.

1 *e*

*q*

ln( ) *C C Kt A o t* - =+ (1)

= + (2)

and the concentration of the residual metal ions determined.

*2.7.6. Adsorption models*

250 Water Quality

*2.7.7. The kinetics of adsorption*

establish the sorption kinetics and mechanism.

determine molecularity of the adsorption.

equations 5.1 and 5.2, respectively:

constant, *A* is intercept and *Ct*

*2.7.8. Adsorption isotherms*

*2.7.5. Determination of adsorption capacity of modified and unmodified algae*

and then filtered, and the concentrations of metal ions were determined.

For molecules in contact with a solid surface at a fixed temperature, the Langmuir isotherm, developed by Irving Langmuir in 1918, describes the partitioning between gas phase and adsorbed species as a function of applied pressure [19]. Langmuir adsorption isotherm is the widely used isotherm for modeling of adsorption data [20]. Langmuir considered adsorption of an ideal gas on an ideal surface. It is based on the assumption that adsorption can only occur at fixed sites and only hold on one adsorbate molecule (monolayer). All sites are equivalent with no interaction between adsorbed molecules, and the sites are independent as reported by Langmuir [19]. The Langmuir equation was derived from Gibbs approach which takes the form shown in equation 5.3 [19, 21]:

$$q\_e = \frac{K\_L C\_e}{1 + a\_L C\_s} \tag{3}$$

where *Ce* is the equilibrium concentration, *KL* is the equilibrium constant, *qe* is the metal concentration on the sorbent phase at equilibrium in mg g−1 and *aL* is a Langmuir constant. Eq. (3) can be linearized and often referred to as linearized Langmuir equation as shown in equation 5.4:

$$\frac{C\_e}{q\_e} = \frac{1}{K\_L} + \frac{a\_L C\_e}{K\_L} \tag{4}$$

The experimental data was applied on the equation above, and a plot of against *Ce* gave a linear regression. This indicates that the adsorption prescribes to the Langmuir model, where the gradient is the theoretical saturation capacity (units in mg g−1) and the intercept is 1 [19, 22, 23].

### *2.7.8.2. Freundlich isotherm*

Freundlich isotherm is an empirical equation based on heterogeneous surface [23]. This is a multi-site adsorption isotherm for heterogeneous surfaces and has a general form as shown in Eq. (5):

$$q\_e = K\_F C\_e^{h^F} \tag{5}$$

The equation was linearized by taking logarithms and then applied to determine if the systems are heterogeneous with highly interactive species [24]:

$$
\ln q\_e = \ln K\_F + b\_F \ln C\_e \tag{6}
$$

where *qe* and *Ce* have the same meaning as in Eq. (3); the numerical value of *KF* presents adsorption capacity, and *bF* indicates the energetic heterogeneity of adsorption sites [24]. From the data, if a plot of **ln** *qe*versus **ln** *Ce* gave a straight line, it indicates that the adsorption prescribes to the Freundlich model.
