Langmuir Isotherm Essay

Improved Essays
Langmuir isotherm
The Langmuir adsorption model is established on the following hypotheses: (1) uniformly energetic adsorption sites, (2) monolayer coverage, and (3) no lateral interaction between adsorbed molecules [26]. A mathematical expression of the Langmuir isotherm is given by the following equation:
Where qe (mg/g) is the amount of dye adsorbed on the solid adsorbent at equilibrium, qm (mg/g) is the maximum adsorption capacity, KL (L/mg) is the Langmuir equilibrium constant, and Ce (mg/L) is the EBT dye concentration at equilibrium. The essential characteristic of the Langmuir isotherm can be expressed by the dimensionless constant called equilibrium parameter, RL, defined by:
Where C0 is the initial EBT
…show more content…
Figure 8 shows the plot of Freundlich isotherm for EBT dye onto P – PAN and C – PAN adsorbents showing an acceptable linearity straight line. Values of n parameter are 1.7 for P – PAN and 2.22 for C – PAN suggesting values of 1/n comprised between 0 and 1 indicating a favorable adsorption of EBT dye onto both dyes.
Tempkin isotherm
Tempkin considered the effects of some indirect adsorbate/adsorbate interactions on adsorption isotherms and suggested that because of these interactions the heat of adsorption of all the molecules in the layer would decrease linearly with coverage. The Tempkin equation is given as described in the reference [28].
Where:
A plot of qe versus Ln (Ce) enables the determination of the isotherm constants BT and KT from the slope and the intercept, respectively. KT is the equilibrium binding constant (L/mol) corresponding to the maximum binding energy and constant BT is related to the heat of adsorption.
The isotherm constants of each model were calculated and presented in Table 2. Examination of the linear isotherm parameters show that the correlation coefficients (R2) obtained from the Freundlich isotherm model were higher in comparison with the others
…show more content…
The parameter KC can be calculated using the following equation as described in the reference [29]:
Where Ce is the equilibrium EBT dye concentration on the adsorbent (mg/L) and qe is the solid phase concentration (mg/g).
The values of ΔH0 and ΔS0 were calculated from the slope of the linear plot of Ln (KC) versus 1/T (see Figure 9) and the free energy change ΔG0 was calculated at different temperatures and are given in Table 3.
We consider firstly the adsorption of EBT dye onto P – PAN adsorbent, the negative values of ΔG0 has decreased from - 2.72 to -7.48 kJ/mol with an increase in temperature from 298 K to 328 K. This behavior indicated that the spontaneous nature of adsorption and favorable at higher temperatures. In the other hand, the positive value of ΔH0 (44.514 kJ/mol) suggest that the process was endothermic nature. While the positive value of ΔS0 (158.51 J/mol K) indicating the entropy of the system increased during the

Related Documents

  • Improved Essays

    Tempkin Isotherm Essay

    • 982 Words
    • 4 Pages

    Tempkin isotherm contains a factor that explicitly takes into account adsorbing species-adsorbate interactions . This isotherm assumes that the heat of adsorption of all molecules in the layer decreases linearly with coverage due to adsorbate-adsorbate interaction and adsorption was characterized by a uniform distribution of binding energies, up to some maximum binding energy. Tempkin isotherm has generally been used in the linearized and rearranged form as following: Q_e⁡〖=β lnK_T+ β ln⁡〖C_e 〗 〗.............................6 where, KT is an equilibrium constant of binding corresponding to the maximum energy of binding (mg L-1) and the β is related to the heat of adsorption. Figure 9. shows a plot of Qe versus…

    • 982 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    The Freundlich model can be expressed as [8]: .................................................................................................... (6) where qe mass of adsorbate is adsorbed per unit mass of adsorbent (mg/g), Ce is the equilibrium concentration of adsorbate (mg/l), Kf indicates adsorption capacity and n an intensity factor of the adsorption process , which varies with the heterogeneity of the adsorbent. The adsorption is better favorability when 1/n is to be grater. The fractional values of 1/n ranged between 0 and 1. The constants Kf and 1/n were calculated from the intercept and slope of the plot of ln qe versus ln Ce. Fig.10 shows the linear plot of Freundlich isotherm for adsorption of CV and MB onto fennel seeds.…

    • 1209 Words
    • 5 Pages
    Improved Essays
  • Improved Essays

    [53]. The direct band gap energy (Eg) of Tb3+: SA crystals grown by SEST and SR methods are found to be 4.20 eV, 4.10 eV respectively, which is in good accordance with the reported values [54]. The value of band gap of Sulfamic acid was found to decrease with increase in impurity concentration and it is found between 4 and 5 [54, 55]. Fig(7). Plot of α vs. photon energy.…

    • 1875 Words
    • 8 Pages
    Improved Essays
  • Improved Essays

    10(B) shows the calibration curve of the reduction peak currents vs. the concentration of H2O2. As shown, it presents the linear response region of MWCNTs-PB (Fig. 10(B) (a)) and MWCNTs@PpPD-PB (Fig. 10(B) (b)). The result of MWCNTs-PB modified GCE is similar to that of a previously reported study [67].…

    • 1355 Words
    • 5 Pages
    Improved Essays
  • Great Essays

    Thin Layer Chromatography

    • 1134 Words
    • 5 Pages

    Using the equations and the numbers on Table 1 found in the data section, the Rf value for the isolated biphenyl was 0.66, the weight was 0.107 g, and recovery percentage was 35.7%. The pH level of the aqueous solvent was then manipulated from a base (sodium benzoate) back into an acid (benzoic acid), by adding HCl. The Rf value for benzoic acid was 0.115, the weight was 0.092 g and the recovery percentage was 30.7%. Using the equation shown in the data section, the total recovery weight came out to be 0.199 and the total recovery percentage was calculated to be…

    • 1134 Words
    • 5 Pages
    Great Essays
  • Improved Essays

    1. 1. Effect of [Ag] The effect of AgNPs/f-silica samples prepared at various AgNO3 concentrations on the adsorption rate of the IC was examined (Fig. 4A and Table 1). The adsorption efficiency reached a maximum at ca 0.03 M (sample S3) and after that, it decreases.…

    • 1062 Words
    • 5 Pages
    Improved Essays
  • Superior Essays

    Al, Alloy 1 And Elece

    • 1504 Words
    • 7 Pages

    Afterwards AlCl3 dissolves as [AlCl4]- ions at around the pitting potential [23, 24]. In case of Alloy 2, the quick rise in current density in the anodic branch suggested that the pitting potential, Ep, was near-by Ecorr indicating the higher activity of the Alloy 2 compared to Alloy 1 and Al. The important point is that the addition of Ga and Pb to Alloy 2 shifts the polarization…

    • 1504 Words
    • 7 Pages
    Superior Essays
  • Improved Essays

    Sodium thiosulphate and hydrochloric acid were added aswell. Product collected by vacuum filtration and recrystallized from 96% ethanol. IR- and H- NMR-spectrum were taken to determine the location of the I+. I had a yield of 0,7 g (2,66mmol, 18,2%). The iodide’s position is opposite of the –OH group.…

    • 960 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    The kinetics model is able to predict the rate of each of the reactions and the temperature variations along the length of the gasifier. (Wang and Kinoshita) modelled the biomass gasification considering kinetics of the surface reactions and assumed the initial concentrations of before char reduction to be equal to zero. The gasifier was divided into Flaming Pyrolysis, Char Reduction and inert char zones. In the Char reduction zone the reaction rate is much greater than in the flaming pyrolysis zone. The temperature of the reduction zone is around and hence no equilibrium is achieved in the reduction zone.…

    • 905 Words
    • 4 Pages
    Improved Essays
  • Great Essays

    This downward trend is represented in the formula y= -0.001x+0.0045 with an R2 value of 0.6154. The correlation shown is negative. Glycine is the data represented in the furthest left data grouping, then alanine, followed by valine, leucine, and then finally isoleucine. Figure 3: The figure above shows the configuration of each of the amino acids that were analyzed for solubility and hydrophobicity. Column 1 Column 2 Column 1 1 Column 2 -0.76384 1 Table 1: The table above represents the correlation of the amount of moles of amino acids dissolved in relation to Engleman’s measurements.…

    • 1026 Words
    • 5 Pages
    Great Essays