Adsorption of New Azo Dyes Derived From 4-Aminoantipyrine from Aqueous solution by A New Type of Activated Carbon: Equilibrium and Kinetic Studies

 

Khalid A.O. AL-Memary¹, Emad A.S. Al-Hyali², Homam T. S. AL-Sayd Toohi³

^1,2,3Department of chemistry/ college of Education of pure Sciences/ University of Mosul, Iraq.

 

ABSTRACT:

This study is aimed to the synthesis of new azo dyes starting with 4-Aminoantipyrine. The thermodynamic behavior of the dyes adsorption on a new kind of activated carbon prepared from (Asphalt : Polymer) mixtures are studied. The research involved the selection of the optimum conditions for the adsorption process by studying the factors affecting it such as the effect of adsorbent dose, contact time, initial concentration and temperature, the work also included the fitting of two models of isotherm equations (Freundlich, Langmuir isotherms) on experimental data of adsorption models under consideration. This study was carried at different temperature and at range of concentrations. The constants of these isotherms were used to describe the nature of the studied systems and the type of interaction between dye and carbon surface. Depending on the results obtained from adsorption study at different temperature, the values of thermodynamic functions of adsorption were calculated at different concentration, using the equilibrium constant which obtained from the ratio between the concentration of the adsorbed and the free dye in solution. The above results showed that, the adsorption of these dyes are of physical nature and the experiential data were better obeyed Langmuir isotherm. The study also involved employing four kinetic models on the experimental data; pseudo first order, pseudo second order, Elovich and intraparticle diffusion equations. The results of this study showed that, the adsorption system under investigation obeyed the Pseudo second order model and the intraparticle diffusion is not the only mechanism controlling the adsorption systems under study.

 

 

 

1. INTRODUCTION:

The development of the lifestyles and the need to provide specific requirement especially in the field of textile, food, leather, and cosmetics led to deployment of such industries[1].

 

The availability of raw materials for such industries especially in the third world countries facilitated the prevalence of such industries and became very common[2].

 

 

Water lately subjected to a great deterioration as a results of the large amounts of chemical compounds ejected to the water resources[3].

 

The huge industrial evolution increased the proportion of pollutants in the environment especially in water sources and soil, which has increased the danger of pollution and its impact on human, plant, and animals[2].  The need for prior treatment and proper recycling technique of the waste water before ejecting to the environment.       

 

Dyes are dangerous organic pollutive to water resources since they are widely used in various industries in many fields such as in woolens and leather dyeing and as supplements in oil industries etc. So these dyes may be the main cause of pollution, which is the reason of maladies spread everywhere today.

 

Table (1): The properties of prepared activated carbon which obtained by using microwave technique at power(720watt).

 

Researchers were become more interested to find ways to lower the effect of these pollutants and managing to remove these organic pollutant found in waste water. The adsorption technique is the most useful technique which is characterized in terms of its efficiency, simple use, cost and availability using the prepared activated carbon.

 

AL-Hyali [4] and his group were studied the adsorption of  Di- Azo dyes on commercial activated carbon and high lighting the effect of structures by the central parts, which are either ortho, meta or para phenylene diamine on the adsorption efficiency.

 

Robert[5] proved that, the use of activated carbon as adsorbent to remove the pollutive material from water was highly effective due to the high porosity nature of activated carbon.

 

FIL and Ozmetin[6] were studied adsorption of cationic dye from aqueous solution by clay as an adsorbent.

Also (AL-Taai) [7] managed to prepare new types of activated carbon and tested their efficiencies by adsorbing some dyes on it. His study also involved the application of number of adsorption isotherms besides the application of four kinetic models on the experimental data of adsorption.  The results showed that, the adsorption was of physical nature and the system (Dye-Activated carbon) obeyed the pseudo-second order model.

 

Muslim [8] and his group were studied the possibility of producing activated carbon from natural asphalt. The resulted activated carbon then mixed with waste condensation potymers(phenol formaldehyde).

 

This research included the synthesis of new azo dyes. These dyes were examined by their adsorption on a new type of activated carbon prepared in our laboratory from mixing asphalt with reclaimed tires rubber and Polymethyl methacrylate. These material form a part of pollution sources, which are constituting a major burden on the environment. These pollutants have been converted into a useful materials by using it the preparation of an effective substance used to control pollution as well as could be a source of national income of the country.

 

The optimal conditions were characterized, such as contact time, dose, initial concentration and effect of temperature.       

 

2. MATERIALS AND METHODS:

2.1 Adsorbents:

The adsorbent used in this study was an activated carbon prepared from AL-Qayarah asphalt with a mixture of reclaim tires rubber and Polymethyl methacrylate in ratio (1:1) (polymer : polymer) with excess of KOH with a ratio of (2:1) using thermal fusion carbonization at 350ºC for three hours. The temperature was raised gradually to 700 ºC within two hours to complete carbonization process. The reason for using the gradual heating was to make KOH reaching its melting point and to be completely mixed with other materials.

 

Thermal activation is then carried out by employing microwave technique at power 720 watt for 30minutes. Table (1) shows the properties of the activated carbon prepared by thermal activation using microwave technique at power 720 watt and compared with the commercial model.

 

2.2 Synthesis of dyes:

Three azo dyes derived from 4-Aminoantipyrine are selected for achieving this investigation. They were prepared as the follow:

 

1. Preparation of diazonium salt[9-11]:

A solution consists of (0.01 mol) of  4-Aminoantipyrine dissolved in (3ml) of concentrated HCl and 2ml distilled water shacked well and kept cold in ice bath at (0-5 ºC). Then a solution of (0.015mol) NaNO₂ in 5ml distilled water was added slowly with keeping the temperature lower than (5 ºC) at each addition.

 

2. Phenol solution Preparation:

9 mL solution of 10% NaOH was put in an ice bath 0.015 mol of phenol is added with keeping temperature in the range of (0-5 ºC). The solution prepared in the first step is then added to the solution prepared in second step slowly with continuous shaking till the crystals of the desired material is formed. The mixture was put in an ice bath for 30 min then it was filtered and washed with distilled water and dried. Other dyes investigated in this study shown in Table (2) were prepared in the same way.

 

2.3 The diagnosis of the Synthesized dyes:

The Synthesized dyes were diagnosed using IR technique following the values of the stretch band of azo group (-N=N-) which formed at frequencies range (1488-1544 cm^-1), UV-visible spectra (the highest absorbance values  (), melting points and colors. Table (2) presented some of these physical properties.

Table(2): Names, Structures and some physical properties of the studied dyes.

 

2.4 Preparation of stock solution:

A stock solution of the dye was Prepared with a concentration of (4×10^-4M) in a mixture of ethanol : water 50% (v:v) as a solvent by dissolving a certain weight of dye in 50ml ethanol after that diluted with distilled water to 100ml. This solution was used to prepare  other solutions with lesser concentration by dilution. The wavelength of the maximum absorption () of the dye is measured  using a mixture of the same ratio of (ethanol : water) as blank.

 

2.5 Adsorption process:

Batch method is used to undergo this study. The amount of adsorbed dye is estimated in terms of the adsorption efficiency and capacity. The concentration of the adsorbed dye is calculated by employing a calibration curve for each dye achieved at the value of () of each dye within the detection limit of the dye according to Beer^'s law.

 

The adsorption efficiency is expressed in terms of adsorption ratio and is calculated using equation (1), while adsorption capacity q_e (mg/g) is measured by equation (2).

 

% Adsorption =    

 

 

q_e =

 

where:

C_i: The initial concentration of the dye (mg/L).

C_e: The concentration of the dye in the solution at the equilibrium.

m: The weight of the adsorbent (activated carbon)(g).

V: The solution volume used in the adsorption process(L).

2.5.1 Determination of adsorbent dose

Three different weight of activated carbon were taken at initial concentration(4×10^-4 M) at 20 ºC and shacked for 70 min at natural pH.

 

2.5.2 Effect of concentration

The effect of concentration was studied as the following:

20mL of five different concentrations of the dye in the range (2×10^-4-6×10^-4M) were shacked with 0.01g of activated carbon for (70 min) at a velocity of (100cpm), then filtered and the adsorption efficiency and capacity were determined.

 

2.5.3 Effect of temperature

The study was carried out as follows:

Five solutions of the same concentration of dye and similar amount of activated carbon were shacked for (70) min at various temperatures in the range (20-60 ºC). The solutions were filtered and the adsorption efficiency and capacity were evaluated.

 

2.6 Determination of the thermodynamic functions

The values of adsorption equilibrium constant (K) were calculated at different temperatures at equilibrium from the ratio between the concentration of adsorbed and the left dye in solution. The adsorption enthalpy is calculated by applying Vant Hoff equation which represent the relation between the equilibrium constant and temperature.

                                  (3)

 

where:

∆H: Variation in adsorption enthalpy.

K: adsorption equilibrium constant .

K_o: constant value.

By drawing the relation between (lnK) versus (1/T) the value of ∆H is calculated from the slope.

Other thermodynamic functions (∆Sº, ∆Gº) can be estimated from the following equations:

 

3. RESULTS AND DISCUSSION:

3.1 Analytical method:

This method includes the construction of a calibration curve at the maximum wavelength () of each dye within the range of concentration (1×10^-4ــــ1×10^-5 M) which is compatible to the color intensity of every dye.

The calibration curve was estimated depending on Beer^'s Lambert law[12] which can be expressed as the following equation:

 

  where:-

A: the adsorption of the dye.

: the molar absorbance (liter.mol^-1.cm^-1).

b: the length of the light bath (b=1cm).

C: the molar concentration (mol/L) .

 

In this study, the solvent used is a mixture of (ethanol/water)50% (v:v). Figure (1) shows the calibration curves of the studied dyes.

 

Fig (1): Calibration curves of the studied dyes.

 

Figure 2: Relation between adsorption capacity (mg/g), adsorption efficiency and adsorbent dose(mg/g) of the dyes under investigation.

 

3.2 Effect of adsorbent dose

Three dyes (H₁,H₂,H₃) were chosen for this study. Their initial concentration is (4×10^-4 M). The study was carried out at different doses of adsorbent (0.5,1,1.5 g/L) of dye solution at(20ºC) and natural pH. The got results are shown in Figure (2).   

 

From Figure 2, It can be noticed that, the adsorption capacity decrease with the increase of the amount of adsorbent at a fixed concentration with increasing in adsorption efficiency. This phenomena could be attributed to the increase of the active sites on the solid surface with the increase in activated carbon amount[13].

 

The amount of (0.5g/L) of activated carbon was the optimum dose to be used in further studies.

 

3.3 Effect of initial concentration.

The effect of initial concentration was tested in a range of (2×10^-4ــــ 6×10^-4M) at constant temperature, pH and by using (0.5 g/L) of activated carbon. The obtained results are listed in Table(3).

 

 

The results obtained from this study show the following:-

 

The adsorption efficiency is decreased with the increase of concentration while adsorption capacity is increased with the increase of concentration.

 

 

Table(3): The effect of the initial concentration on the adsorption capacity and adsorption efficiency at (20ºC) of dyes under investigation.

 

Table (4): The effect of contact time on the adsorption capacity and adsorption efficiency at different temperatures of dye under investigation.

Fig. 3. Variation of adsorption efficiency with time for the studied dyes.

 

This is because at the beginning of adsorption the increase in concentration will increase the number of the available molecules for adsorption, in addition the qualified locations of adsorption on the solid surface are available. By time passing, the competition among dye molecules to be connected to the rest of the active location on the surface of the activated carbon is increased. The increase in concentration lead to leave more quantity of dye in solution after equilibrium. This will lower the adsorption efficiency when it calculated from the ratio between the quantity of the adsorbed dye and the quantity left in solution at equilibrium according to equations (5) and (6) [14].

 

From the above, the concentration of (3×10^-4M) is chosen for achieving the next studies since it represents an intermediate case in its effect on the adsorption efficiency and capacity and keep the color in an acceptable range.   

 

3.4 Effect of contact time:

The effect of contact time was studied at a constant initial concentration(3×10^-4M), natural pH. (20ml) of dye solution  was shaken using (0.01g) prepared activated carbon at different temperature for (10-70 minutes) with a speed (100 cpm).

 

The results obtained were listed in Table (4) and shown in Figure (3).

 

The variation in the values of adsorption efficiency which appear in Figure (3) shows that, the adsorption process occurred in two steps; initial rapid step represented by the first 10 minutes which it was so fast where at this step 70-80% of dyes were adsorbed by prepared activated carbon. After these 10 minutes, the second step began which was slower and the adsorption rate was gradually decreased with time and reach equilibrium in (60-70 minutes). The time chose for further studies was (70 min).

 

The results in Figure 3 indicated that, the adsorption process was so fast in first 20 minutes then began gradually to slow till reaching equilibrium.  When  the rate of the adsorption process(the adsorbate bounded to the adsorbent surface) become equal to the rate of desorption of another molecules from adsorbents surface to the solution this situation is called equilibrium[15]. The dye under investigation reached the equilibrium in time periods (60-70)min, so the time (70) min is chosen to be used in further studies.

 

3.5 Effect of Temperature on Adsorption:

This study has carried out at initial concentrations (3×10^-4ــــ 6×10^-4M) and temperature range of (20-60 ºC) at natural pH and by shaking (20 ml) of dye solution using (0.5 g/L) of the activated carbon. The solutions were shaken for 70min in a velocity of (100 cpm). The obtained results listed in Table (5).

 

Table (5): The effect of temperature on the adsorption efficiency of dyes under investigation.

 

The results in the table above show the following:-

1. In general, at a constant concentrations it is observed that the increase in the temperature of the adsorption medium from(20-60 ºC) will lead to decrease of the adsorption efficiency and capacity due to the effect of high temperature which cause the dye molecules to leave the adsorbent surface and return to the solution (desorption) [16]. This phenomena is due the weakness in the binding force between dye molecules and adsorbent surface. This an indication of the physical nature of adsorption process which is an exothermic process[17].

 

2. At constant temperature, increasing in concentration reducing the adsorption efficiency and increasing adsorption capacity as mentioned in Table(3).

 

The effect of temperature was studied at different concentrations in order to calculate thermodynamic functions and to apply the equilibrium data on some adsorption isotherms. Depending on adsorption isotherms constants an attempt could be carried out to find the changes in the driving force of adsorption process as will be explained later.

 

3.6 Calculation of Thermodynamic Functions for Adsorption  Process

The thermodynamic functions are considered as important variables which could gives significant explanations about the adsorption systems. Those functions describing the nature of studied system, the type of the driving forces controlling the adsorption process, besides they can providing conceptions about the kinds of molecular intersections those could happen during the adsorption process which act an important role in the determination of its efficiency. The value of adsorption enthalpy(H) is considered as a direct measure to the type of the intermolecular forces between the adsorbate molecules and the adsorbent surface.

 

It is important to understand the role of such parameter in order to control the condition of system under investigation to duiding the reaction to the desirable direction which gives the highest qualification and lowest cost.

 

The thermodynamic study was done depending on the variation in adsorption capacity with temperature. The values of adsorption thermodynamic functions were calculated at equilibrium for dye under investigation. The value of equilibrium constant (K) is calculated from the ratio of the concentration of adsorbed dye to the residual dye concentration in solution at equilibrium in a range of temperature (293-333)K,  initial concentration (3×10^-4)M and at natural pH using (0.5g/L) of the prepared activated carbon and shaken for 70min with a velocity of 100cpm.

 

This experiment is repeated several times at same conditions using different initial concentration in a range of (4×10^-4- 6×10^-4M). The obtained results (K, ΔG°, ΔH, ΔS°, ΔS)  were listed in Table (6-8). Figure 4 shows the linear relationships obtained from plotting ln K versus (1/T ) by the application of Vant Hoff equation (Eq.7).

 

 

 

Figure 4: The relationship between ln K versus (1/T ) to calculate the values of adsorption enthalpies of dyes under investigation .

Table(6):The values of the equilibrium constants and the thermodynamic functions at adsorption equilibrium of the dye (H1) on prepared activated carbon at various concentrations (3×10^-4- 5×10^-4 M)  and temperature range (293-333K) .

 

Table(7): The values of the equilibrium constants and the thermodynamic functions at adsorption equilibrium of the dye (H2) on prepared activated carbon at various concentrations (3×10^-4- 5×10^-4M)  and temperature range (293-333K) .

Table(8):The values of the equilibrium constants and the thermodynamic functions at adsorption equilibrium of the dye (H3) on prepared activated carbon at various concentration (3×10^-4- 5×10^-4M)  and temperature range (293-333K) .

 

The results in Table(6-8) show that, the adsorption systems under consideration are exothermic and the driving force controlling the adsorption systems and representing the binding forces connecting dyes to the activated carbon surface are of physical nature and of type of Van Der Waals forced. This is indicated by the values and sign of ∆H.

 

The adsorption process occurs spontaneously in the direction of adsorption which indicated by the negative sign of (ΔG^º) this will lead to lowering the randomness of the system indicated by (ΔS) values.

 

3.7 Adsorption isotherms:

3.7.1 Freundlich  isotherm[18,19]

Freundlich isotherm was applied on the experimental data of the studied dye according to Eq(8). Plotting the relation between Logq_e versus LogC_e, the values of Freundlich constants (K_f , n) were calculated from the slope and the intercept respectively. The obtained results are listed in Table (12).

 

                       (8)

 

3.7.2 Langmuir isotherm[20].

Langmuir isotherm is significant in the description and the study of the mono-layer adsorption. It suggests that, the energy is distributed in a homogenous manner on the adsorbent surface at constant temperature. It gives information about the adsorption system represented by the theoretical maximum capacity of adsorption (Q_max) [21,22].

 

The linear form of Langmuir equation is given as[23]:-

 

                  (9)

 

Drawing of the relation between C_e/q_e versus C_e a straight-line is obtained with slope (1/ Q_max) and intercept (1/b Q_max) from which the constants b, Q_max could be calculated

where:-

b: is a constant related to the connection force between the dye and the adsorbent surface.

q_e: the adsorption capacity at equilibrium representing the amount of adsorbed dye (mg) per (g) of adsorbent .

C_e: is the equilibrium dye concentration in solution(mg/L).

Q_max: is the theoretical maximum adsorbent capacity(mg/g).

The obtained results were listed in Table (9),

 

 

Table(9): Results of the fitting of Freundlich and Langmuir isotherm on the adsorption data on activated carbon.

 

The gotten results indicated the following:

1.      The experimental data obeyed Freundlich isotherm. This is indicated by values of correlation coefficient close to unity lying  in the range of (0.952-0.999). The values of (n) were from (1-10) which refer to favorite physical adsorption while the values of K_f decrease with temperature increase.

2.      The values of Langmuir constants (b)  are found to decrease with increasing temperature so this will support the physical nature of the studied systems which is conformed with previous studies[15,24,25]. The values of Q_max were remained constant and not affected within the studied range of temperatures.

 

Langmuir isotherm has a special character known as Dimensionless constant separation factor (R_L) which can be expressed as in the following equation [24-26]

 

                             (10)

 

Ci : initial concentration of adsorbate(mg/L).

the obtained results were listed in Table (10).

 

 

 

 

 

 

 

 

 

 

 

Table(10): The values of R_L of Langmuir isotherm for the adsorption of all dyes at different concentrations and temperatures.

 

From results in Table (10) it can be observed:

1-     All the calculated values of R_L at all initial concentrations and at temperature range (20-60) ºC were within the range of (0 < R_L < 1 ) which means that, the adsorption was favorable within the tested range .

2-     The values of R_L were decreased with the increase of initial concentration, while their effect by temperature is seems to be wavy. Under these two condition the R_L values are moved toward the undesirable shape. By increasing temperature, the connection forces between dye ad the activated carbon surface are weakened. The adsorption is occurred as a results and leading to the increase of the R_L value. This gives an indication to the physical nature of the adsorption system. While with the increase of the concentration, the values of R_L are decreased and the system approaching from the irreversible process. The results so far give an indication that, the systems under investigation is highly efficient at low concentration.     

 

3.8 Adsorption Kinetics.

The kinetic of adsorption data was processed to provide a valuable insight into the adsorption pathways and the attachment mechanism between dyes and activated carbon, which involve mass transfer and chemical reaction which are necessary for determining the adsorption efficiency.

 

Four kinetic models were applied on the adsorption kinetic data aiming for studying the behavior of azo dyes during the adsorption process onto activated carbon, these models are: Pseudo first order, Pseudo second order, Elovich and intraparticle diffusion models.

 

3.8.1 Pseudo first-order Kinetic Model

The rate constant of adsorption is determined from the first order rate expression suggested by Lagergren and Svenska[27]. Which can be expressed as in equation:

 

 

where q_e and q_t are the adsorption capaceties (mg/g) at equilibrium and at any time t,k₁ is the rate constant (min^-1). The relationship between ln(q_e-q_t) versus t gives a straight line. The rate constant k₁ is obtained from the slope of the straight lines. The k₁ values, and the correlation coefficients, R², are listed in Table (11). From this Table, it has been seen that the Pseudo first-order Kinetic Model does not fit, the adsorption system under consideration indicated by the low value of R² (0.6131< R²<0.9742) and the inconsistency between the calculated ad experimental values of q_e.

 

3.8.2 Pseudo second order Kinetic Model

The Pseudo second order kinetic model can be expressed as in equation[28,29].

      

Where K₂ is the rate constant of Pseudo second order equation (g.mol^-1.min^-1( and h=k₂qe² is initial adsorption rate (mol.g^-1.min^-1). The Pseudo second order kinetics is applicable, when the plot of t/qt versus t is a linear relationship and there a consutency between the calculated and the experimental values of q_e. Values of k₂ and q_e were calculated from the intercept and slope of the straight line.  The linear relationship are presented in Figure (7) and the results obtained are listed in Table(11).

 

The results in Table (11) showed that, this model is fitted well to  the adsorption data for the whole range of contact time. Excellent linear relationship obtained Figure 5 noticed by the values of correlation coefficient which found to be in the range of (0.991-0.9998) for all dyes and at all temperature. Also the values of calculated q_e(q_{e calc}.) reconcile very well with the experimental q_e data. Those parameters suggest that the adsorption of the studied dyes on activated carbon obeys the Pseudo second order kinetic model which suggest that the rate-limiting step may be physisorptions [30,31].

 

This prove that the adsorption of dyes occurred probably via surface exchange reactions until the active sites on surface were fully filled then dye molecules diffused into the intra porous structure of activated carbon.

 

Figure 5: Second-order kinetic equation for adsorption of (H1) on activated carbon at different temperature.

 

Table(11): The approchement of the Elovich, first-order, second-order constant and correlation coefficients at different temperatures.

Dyes	Temperature (ºK)	Kinetic Models
		Pseudo-first-order				Pseudo-second-order					The Elovich Equation
		k1 (min‾¹)	qe(Calc) mg/g	qe(exp) mg/g	R2	k2   (g.mg‾¹.min‾¹)	qe(Calc) mg/g	qe(exp) mg/g	h (mg.g‾¹min‾¹)	R2	Α(mg.g‾¹. min‾¹)	β (g.mg‾¹)	R2
H1	293	0.1027	313.56	175.94	0.6257	0.0006	196.08	175.94	23.585	0.9983	86.03	0.028	0.9549
	303	0.104	341.96	175.82	0.6131	0.0005	200.00	175.82	21.786	0.9980	70.06	0.027	0.9553
	313	0.076	208.74	175.52	0.9158	0.0005	200.00	175.52	20.284	0.9981	59.99	0.026	0.9649
	323	0.077	227.97	175.17	0.9025	0.0004	204.08	175.17	18.182	0.9960	47.43	0.024	0.9502
	333	0.078	258.06	174.80	0.8836	0.0005	200.00	174.80	19.268	0.9987	44.51	0.024	0.9539
H2	293	0.0694	142.17	181.40	0.8874	0.0008	196.08	181.40	32.258	0.9960	808.31	0.043	0.9339
	303	0.069	148.98	178.85	0.8649	0.0008	192.31	178.85	29.851	0.9938	688.61	0.043	0.9059
	313	0.068	128.06	172.61	0.8836	0.0009	185.19	172.61	31.25	0.9958	945.81	0.047	0.9649
	323	0.068	141.85	171.60	0.8391	0.0008	185.19	171.59	28.409	0.9939	29.05	0.045	0.9113
	333	0.070	169.32	170.82	0.8281	0.0007	188.68	170.82	24.096	0.9910	319.55	0.041	0.9067
H3	293	0.052	29.62	141.91	0.9742	0.0031	147.06	141.91	68.027	0.9998	7291.67	0.109	0.9872
	303	0.061	64.64	141.52	0.9390	0.0016	149.25	141.52	35.211	0.9984	3255.65	0.068	0.9308
	313	0.065	95.84	141.48	0.9235	0.0011	153.85	141.48	25.907	0.9967	553.30	0.054	0.9279
	323	0.068	115.32	140.75	0.8538	0.0009	153.85	140.75	23.364	0.9960	7277.60	0.047	0.9631
	333	0.069	139.65	140.01	0.8930	0.0008	156.25	140.01	18.416	0.9947	123.81	0.042	0.9683

 

 

 

 

3.8.3 The Elovich Equation

The Elovich model could be written as the following equation:

   

 

 

To simplify the Elovich³², by assuming and by applying the boundary conditions q_t=0 at t=0 and q_t=q_t t=t, Eq(2) will be written as: 

 

The relationship between q_t  versus ln t should give a linear relationship with a slope β/1 and an intercept of β/1 ln(αβ). The α initial adsorption rate (mol.g^-1.min^-1), β the adsorption constant (g.mol^-1) values, and R²(correlation coefficients), were listed in Table (11). From these mechanisms, it was obvious that the Elovich Kinetic model was not satisfactorily fit the experimental values(0.9059<R²<0.9683).

 

3.8.4  Intra-particle Diffusion Model:

The Intra-particle diffusion model suggested by Furusawa and Smith[32] is employed to study the adsorption process, which is written as:

 

                     (15)

 

Where, K_diff mg/g.min is the diffusion rate constant and C (mol /g) is a value proportional to boundary layer thickness. C is the intercept(mol/g) and it gives information about the boundary layer thickness where as the larger the intercept the greater is the effect of boundary layer [33]. The values of k_diff are found from the slopes of q_t versus t^1/2 plots. The applicability of intra particle diffusion model prove that it is the rate determining step, but in this study, the application of  this model application gave a linear relationship but did not pass through the origin this meant  that the intra particle diffusion is not the only mechanism controlling the adsorption process of the studied systems.

 

 

 

 

 

 

 

Table (12): The values of intra - particle diffusion constants and correlation coefficient which gut by its application on experimental data of adsorption at initial concentration (3×10^-4M) and dose (0.01g) at different temperatures.  

 

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Received on 22.11.2018         Modified on 13.01.2019

Accepted on 18.01.2019      © RJPT All right reserved