Lagergren Pseudo-First Order Kinetic Model

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4.1 Lagergren Pseudo – first order kinetic model: The rate constant of adsorption was determined from Lagergren (1998) Pseudo – first order equation which is generally expressed as
Log⁡(q_(e )– q_(t ) )=logq_e- (k_ad/2.303) ×t Eq. (3)
Here qt&qe (both in mg/g) are the amount of nickel adsorbed at time t (min) and at equilibrium respectively. A straight line plot of log(qe-qt) against time(min)
4.2 Ho Pseudo second order kinetic model: The linear form of Ho and McKay, (1999) pseudo –second order kinetic model is expressed as dqt/(dt ) = k_(2 ) (q_e- q_(t ) )² Eq. (4)
For the boundary conditions t = 0 to t = t and qt = 0 to qt = qt, the integrated formof Eq. (4) becomes: t/(qt )= 1/k_(2q_e² ) +(1/q_e )t
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The adsorption data used for Langmuir isotherms are given in (Table No. 1). Langmuir adsorption isotherm is plotted by taking Ce versus Ceq/qeq. Ceq and qeq are the equilibrium adsorbate concentrations in the aqueous and solidphases, respectively and b is the equilibrium constant related to the energy of adsorption.
The Langmuir isotherms for manganese are shown in (Fig. 4). The values of correlation coefficient R2 were 0.997 which were high and indicated a monolayer adsorption manganese ions onto the biosorbent.The important characteristics of the Langmuir isotherm can be described by a separation factor also called as dimensionless equilibrium parameter, R2. The magnitude of R2 obtained for T. cordifoliawas 0.977 as the values lie between 0 to1, theadsorption process for manganeseseems to be favorable.
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The FTIR spectra of the prepared adsorbents before and after treatment were presented in (Fig. 6). FTIR spectrum of prepared bioadsorbent coming from T. cordifolia (constituted by carbohydrates, proteins, lipids, and fibers) was recorded to identify functional groups responsible for the metal ion coordination. The FTIR spectra of the biosorbent and metal ion loaded biosorbent were compared to determine which functional groups (Table No. 3)are responsible for the manganese biosorption.When compare the two spectra before and after adsorption, as shown in the (Fig. 5) spectra from before metal adsorption, the spectra display a number of absorption peaks, indicating the nature of the biomass of T.cordifolia. The bands observed at 3419.73 cm-1 and 2922 cm-1 bonded –OH group and aliphatic -C-H group. The peak around 1637.15 cm-1 corresponds to the –C=O group. The peak observed at 1515.53 cm-1, 1431.56 cm-1could beassigned to aromatic -C=C- weak bands, the another peak 1235.23 cm-1 and 1074.93 cm-1shows the strong peak of presence of acid and alcohol

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