Introduction

Environmental contaminations by toxic wastes pose a serious problem worldwide due to their incremental accumulation in the food chain and continued persistence in the ecosystem. The residual dyes from different sources such as: textile, paper and pulp, dye and dye intermediates, pharmaceutical, tannery, and kraft bleaching industries are considered as organic colored pollutants (Rajgopalan 1995; Routh 1998; Kolpin et al. 1999; Ali and Sreekrishnan 2001). These industries utilize large quantities of a number of dyes which residues lead to large amount of colored wastewaters, toxic and even carcinogenic, posing serious hazard to aquatic living organisms. Most dyes used in industries are stable to light, heat, and oxidation, they are not biologically degradable and are also resistant to aerobic digestion and even when they does, they produce toxic and hazardous products (Sun and Yang 2003; Shawabkeh and Tutunji 2003). Alizarin Red S (ARS) an anthraquinone dye is available as sodium salt of 1,2-dihydroxy-9,10-anthraquinonesulfonic acid (Fig. 1), it is referred to as Mordant Red 3, C.I. No. 58005. Alizarin a natural dye obtained from madder (Rubia tinctorum, L. Rubiaceae) by sulphonation, is a water-soluble, widely used anthraquinone dye in textile and as a stain in clinical study of synovial fluid to assess basic calcium phosphate crystals (Zucca et al. 2008). ARS is a durable pollutant when released to aquatic ecosystems. It cannot be completely degraded by general physicochemical and biological processes because of the complex structures of the aromatic rings that afford high physicochemical, thermal, and optical stability (Carneiro et al. 2005; Panizza et al. 2001). Therefore, most treatments for such dye-laden effluents are largely inadequate; however, removal of this dye from industrial wastewaters is a crucial process, from both economic and environmental points of view (Panizza et al. 2001).

Fig. 1
figure 1

Structure of Alizarin Red S (ARS)

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Convectional technologies, such as ion exchange, chemical precipitation, oxidation reduction, filtration, electrochemical techniques, and other sophisticated separation processes using membranes, are often ineffective and/or expensive. Furthermore, most of these techniques are based on physical displacement or chemical replacement, generating yet another problem in the form of toxic sludge, the disposal of which adds further burden on the techno-economic feasibility of the treatment process. Recently, calcium phosphates, and particularly calcium hydroxyapatite (Ca-HA), attracted much interest because of their high potential application for the remediation of toxic materials in liquid wastes coupled with their biocompatibility and low cost. For example, hydroxyapatites have been employed as inorganic cation exchangers, for removal of lead, cadmium, and nickel ion from aqueous solution (Suzuki et al. 1984; Miyake et al. 1990; Ma et al. 1994; Nzihou and Sharrock 2010; Nzihou and Sharrock 2010; Minh et al. 2012, 2014; Mobasherpour et al. 2012). Nano crystalline hydroxyapatite also served as adsorbents for the adsorption and separation of biomolecules (Wei et al. 2009; Takagi et al. 2004) and removal of dye molecules from aqueous solution (El Boujaady et al. 2014).

In this study, a one-step approach was adopted for the preparation of calcium phosphate (Ca-P)-based materials starting from calcium carbonate and orthophosphoric acid for the removal of alizarin dye from aqueous solution. The material was characterized by scanning electron microscopy (SEM), Fourier transform infrared (FTIR), and X-ray diffraction (XRD). A series of adsorption experiments on the removal of the dye from aqueous solution were investigated in a batch system. The effect of solution pH, initial contaminants concentrations, and contact time were also studied.

Materials and methods

Synthesis of calcium phosphate

All the chemicals used in this study were analytical grade which includes CaCO3, H3PO5, NH4OH, HCl, NaOH, and ARS. Hydroxyapatite Calcium Phosphate was synthesized in a three necked flask. Slurry of 150 mL of 0.1 M CaCO3 in was made quantitatively in the flask and stirred to make a uniform disperse. Then, 150 mL of 0.6 M H3PO5 was added slowly for 4 h with constant stirring while the temperature was maintained at 80 °C. The pH was maintained at 9.5 with 25 % NH4OH. The stirring was continued for 24 h after which the mixture is allowed to age for another 24 h after, when it was filtered off and dry at 106 °C.

Analytical procedure

The dried material was characterized by different physico-chemical techniques. XRD data were collected using a PAN Analytical X’Pert PRO X-ray diffractometer with Cu Kα radiation (λ = 1.5418 Å). FTIR spectra were recorded from 400 to 4000 cm−1 in TENSOR 27 spectrometer (Bruker, Germany) using KBr pellet technique. Surface morphology of the material was analysed using SEM [VEGA3 TESCAN]. The concentrations of the dye in the solutions were estimated using spectrophotometer (UV–VIS–NIR VARIAN 500 Scan CARY). Non-linear regression analysis method using a program written on Micro Math Scientist software (Salt Lake City, Utah) was used to obtain the least square fit for all the models.

Equilibrium studies

The effects of adsorbent dosage, initial dye concentration, pH, and temperature on the adsorption removal of ARS were studied. Sample solutions were withdrawn at intervals to determine the residual dye concentration by using UV–VIS–NIR spectrophotometer. The amount of dye removed at equilibrium, Q e (mg g−1), was calculated using Eq. (1) below:

$$Q_{\text{e}} = \frac{{(C_{\text{o}} - C_{\text{e}} )V}}{W},$$
(1)

where C o (mg L−1) is the initial concentration and C e (mg L−1) is the concentration of the dye at equilibrium in the liquid-phase. V is the volume of the solution (L) while W is the mass of the adsorbent. The percentage dye removal as color removal is also estimated as

$$\%\; {\text{Color removal}} = \frac{{({\text{Abs}}_{\text{o}} - {\text{Abs}}_{\text{e}} ) \times 100}}{{{\text{Abs}}_{0} }},$$
(2)

where Abso, is the blank absorbance and Abse is the absorbance at equilibrium.

Effect of adsorbent dosage

The study of effect of adsorbent dosages for removal of ARS from aqueous solution was carried out at different adsorbent doses ranging between 0.1 and 1.0 g using 50.0 mg L−1 of the dye solution. The Erlenmeyer flasks containing the dye solutions of the same initial concentration but different adsorbent masses were placed on orbital shaker at 200 rpm. After some time, the samples were filtered off and the dye solution was analyzed for the residual dye content using UV visible spectrophotometer.

Effects of initial dye concentration and contact time

The effects of initial dye concentration and contact time on adsorption were investigated with 100 mL dye solution of initial concentrations between 25 and 150 mg L−1 in series of Erlenmeyer flasks with fixed amount of adsorbent (0.1 g) on orbital shaker at 200 rpm. Samples were withdrawn and analyzed for the residual dye from the aqueous at preset time intervals.

Effect of pH on adsorption process

pH plays an important role on adsorption process of dye by influencing the chemistry of the adsorbent, dye molecule and that of adsorption process in the solution. To investigate the effect pH, on the removal of ARS, a series of experiments were carried out on solutions with initial pH varied between 3 and 11. The pH was adjusted with 0.1 M NaOH or 0.1 M HCl and measured using pH meter. The concentrations of the solutions, adsorbent dosage, and temperature were held constant at 50 mg L−1, 0.1 g and 30 °C, respectively.

Adsorption isotherms

The equilibrium data from this study were described with the six adsorption isotherm models. These are models by Langmuir (1918), Freudlinch (1906), Tempkin and Pyzhev (1940), Dubinin and Radushkevich (1947), Sips (1948) and Redlich and Peterson (1959). The acceptability and suitability of the isotherm equation to the equilibrium data were based on the values of the correlation coefficients, R 2 estimated from linear regression of the least square fit statistic on Micro Math Scientist software.

Langmuir isotherms

The Langmuir isotherm equation is based on the following assumptions: (1) that the entire surface for the adsorption has the same activity for adsorption, (2) that there is no interaction between adsorbed molecules and (3) that all the adsorption occurs by the same mechanism and the extent of adsorption is less than one complete monomolecular layer on the surface. The Langmuir equation is given by Eq. (3) (Langmuir 1918):

$$Q_{\text{eq}} = \frac{{Q_{\text{o}} bC_{\text{e}} }}{{1 + bC_{\text{e}} }},$$
(3)

where Q o is the maximum amount of the dye molecule per unit weight of the coagulant to form a complete monolayer on the surface C e (mg g−1) is the concentration of the dye remaining in solution at equilibrium and b is equilibrium constant (L mg−1). The shape of Langmuir Isotherm can be used to predict whether a process is favorable or unfavorable in a batch adsorption process. The essential features of the Langmuir isotherm can be expressed in terms of a dimensionless constant separation factor (R L) that can be defined by the following relationship (Aniruldhan and Radhakrishnan 2008):

$$R_{\text{L}} = \frac{1}{{1 + bC_{0} }},$$
(4)

where C o is the initial concentration (mg L−1) and b is the Langmuir equilibrium constant (L mg−1). The value of separation parameter R L provides important information about the nature of adsorption. The value of RL indicated the type of Langmuir isotherm to be irreversible if R L = 0, favorable when 0 < R L < 1, linear when R L = 1 and unfavorable when R L > 1. However, it can be explained apparently that when b > 0, sorption system is favorable (Aniruldhan and Radhakrishnan 2008).

Freundlich isotherm

The Freundlich isotherm is an empirical equation based on sorption on a heterogeneous surface. It is commonly presented as

$$Q_{\text{eq}} = K_{\text{F}} C_{\text{e}}^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-0pt} \!\lower0.7ex\hbox{$n$}}}} ,$$
(5)

where K F and n are the Freundlich constants related to the adsorption capacity and intensity of the sorbent, respectively (Bello et al. 2008; Adeogun et al. 2012).

Redlich–Peterson isotherm

A three parameters Redlich–Peterson equation has been proposed to improve the fit by the Langmuir or Freundlich equation and is given by Eq. (6).

$$Q_{\text{eq}} = \frac{{Q_{\text{o}} C_{\text{e}} }}{{1 + K_{\text{R}} C_{\text{e}}^{\beta } }},$$
(6)

where K R and β are the Redlich–Peterson parameters, β lies between 0 and 1 and for β = 1, Eq. (6) converts to the Langmuir form.

Tempkin isotherm model

Temkin isotherm model was also used to fit the experimental data. Unlike the Langmuir and Freundlich equations, the Temkin isotherm takes into account the interaction between sorbent and adsorbent. It is based on the assumption that the free energy of sorption is a function of the surface coverage (Adeogun et al. 2012). The Tempkin isotherm is represented as in Eq. (7):

$$Q_{\text{e}} = \frac{RT}{{b_{T} }}\ln a_{T} C_{\text{e}} ,$$
(7)

where C e is concentration of dye in solution at equilibrium (mg L−1), Q e is the amount of dye molecule coagulated at equilibrium(mg g−1), T is the temperature (K), and R is the ideal gas constant (8.314 J mol−1 K−1) and ‘a T’ and ‘b T’, are constants relating to binding constant (L mg−1) equilibrium corresponding to the maximum bonding energy and the heat of adsorption, respectively.

The Dubinin–Radushkevich isotherm

The Dubinin–Radushkevich model (Dubinin and Radushkevich 1947) was chosen to estimate the heterogeneity of the surface energies and also to determine the nature of adsorption processes as physical or chemical. The D–R sorption isotherm is more general than the Langmuir isotherm as its derivation is based on ideal assumptions such as equipotent of the sorption sites, absence of stoic hindrance between sorbed and incoming particles and surface homogeneity on microscopic level (Weber and Morris 1963; Malik 2004). D–R isotherm is represented by Eq. (8) below:

$$Q_{\text{e}} = Q_{\text{m}} e^{{ - \beta \varepsilon^{2} }} ,$$
(8)

where Q m is the theoretical saturation capacity (mol g−1), β is a constant related to the mean free energy of adsorption per mole of the adsorbate (mol2 J−2), and ε is the Polanyi potential given by the relation; \(\varepsilon = \ln \left( {1 + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {C{}_{\text{e}}}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${C{}_{\text{e}}}$}}} \right)\). C e is the equilibrium concentration of dye in solution (mg L−1), R (J mol−1 K−1) is the gas constant and T (K) is the absolute temperature. The constant β gives an idea about the mean free energy E (kJ mol−1) of adsorption per molecule of the adsorbate when it is transferred to the surface of the solid from relationship (Malik 2004).

$$E = (2\beta )^{ - 0.5} .$$
(9)

If the magnitude of E is between 8 and 16 kJ mol−1, the process is chemisorption, while for values of E < 8 kJ mol−1 suggests a physical process.

The Sips isotherm

The Sips isotherm model is a combined form of the Langmuir and Freundlich expressions deduced for predicting the heterogeneous adsorption systems and circumventing the limitation of the rising adsorbate concentration associated with the Freundlich isotherm model (Sips 1948). At high adsorbate concentration, it predicts monolayer adsorption characteristics of Langmuir isotherm, while at low adsorbate concentration, it reduces to Freundlich isotherm. The Sips model is expressed as Eq. (10) below:

$$Q_{\text{eq}} = \frac{{Q_{\text{o}} (k_{\text{s}} C_{\text{e}} )^{{m_{\text{s}} }} }}{{1 + (k_{\text{s}} C_{\text{e}} )^{{m_{\text{s}} }} }},$$
(10)

where k s is the Sips isotherm model constant and m s is the Sips isotherm model exponent.

Adsorption kinetics studies

The procedures for the kinetics studies were basically identical to those of equilibrium tests. The aqueous solutions of known dye concentration with a predetermined amount of adsorbent were placed in Erlenmeyer flasks in an orbital shaker, samples were taken at preset time intervals, and the concentrations of the dye were similarly determined. The amount of dye removed at time t, Q t (mg g−1), was calculated using Eq. (11):

$$Q_{t} = \frac{{(C_{\text{o}} - C_{t} )V}}{W},$$
(11)

where C o (mg L−1) is the initial concentration and C t (mg L−1) is the concentration of the dye at time t in the liquid-phase. V is the volume of the solution (L), and W is the mass of adsorbent. In order to investigate the mechanisms of the adsorption process, pseudo-first order, pseudo-second-order, Avrami, and Elovich models, respectively, were applied to describe the kinetics of adsorption of ARS to calcium phosphate. A model is adjudged best-fit and selected based on statistical parameters.

The pseudo-first order kinetics model

A simple kinetics analysis of the process under the pseudo-first order assumption is given by Eq. (12) below (Lin and Brusick 1992; Kundu and Gupta 2006):

$$\frac{{{\text{d}}Q}}{{{\text{d}}t}} = k_{1} (Q_{\text{e}} - Q_{t} ),$$
(12)

where Q e and Q t are the dye concentrations (mg g−1) at equilibrium and at time t (min), respectively, and k 1 the adsorption rate constant (min−1), and t is the contact time (min). The integration of Eq. (16) with initial concentrations, Q t = 0 at t = 0, and Q t = Q t at t = t, yields Eq. (13) below:

$$\ln (Q_{\text{e}} - Q_{t} ) = \ln Q_{\text{e}} - k_{1} t.$$
(13)

Upon rearrangement, Eq. (13) becomes:

$$Q_{t} = Q_{\text{e}} (1 - e^{{ - k_{1} t}} ).$$
(14)

The values of Q e and k 1 were calculated from the least square fit of Q t versus t at different dye concentrations.

The pseudo-second order kinetics model

A pseudo-second order kinetics model is based on equilibrium adsorption (Bello et al. 2008; Kundu and Gupta 2006) and it is expressed as shown Eq. (15) below:

$${\raise0.7ex\hbox{$t$} \!\mathord{\left/ {\vphantom {t {Q_{t} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Q_{t} }$}} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {k_{2} Q_{\text{e}}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k_{2} Q_{\text{e}}^{2} }$}} + ({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {Q_{t} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Q_{t} }$}})t.$$
(15)

The expression above can also be rearranged to give Eq. (16) below:

$$Q_{t} = \frac{{k_{2} Q_{\text{e}}^{2} t}}{{1 + k_{2} Q_{e} t}},$$
(16)

where k 2 (g mg−1 min−1) is the rates constant of pseudo-second order adsorption, The values of Q e and k 2 were calculated from the least square fit of Q t versus t at different dye concentrations.

Elovich model

Elovich model is a kinetic equation describing a chemisorption process (Chien and Clayton 1980), it describes the rate of adsorption which decreases exponentially with an increase in the adsorbed. It is generally expressed as shown by Eq. (17) (Chien and Clayton 1980):

$$Q_{t} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \beta }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\beta $}}\ln (\alpha \beta *t),$$
(17)

where α is the initial adsorption rate (mg g−1 min−1), β is the desorption constant (g mg−1). The value of reciprocal of β reflects the number of sites available for adsorption, whereas the value of adsorbed quantity when t is equal to zero is given by \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \beta }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\beta $}}\ln (\alpha \beta )\).

Statistical test for the kinetics data

The acceptability and hence the best fit of the kinetic data were based on the square of the correlation coefficients R 2 and the percentage error function which measures the differences (% SSE) in the amount of the dye concentration coagulated at equilibrium predicted by the models, (Q cal) and the actual, (i.e., Q exp) measured experimentally. The validity of each model was determined by the sum of error squares (SSE, %) given by:

$$\%\; SSE = \sqrt {\frac{{\left( {{{(Q_{(\exp )} - Q_{{({\text{cal)}}}} )} \mathord{\left/ {\vphantom {{(Q_{(\exp )} - Q_{{({\text{cal)}}}} )} {Q_{\exp } }}} \right. \kern-0pt} {Q_{\exp } }}} \right)^{2} }}{N - 1} \times 100} .$$
(18)

N is the number of data points. The higher is the value of R 2 and the lower the value of SSE; the better fitted the data.

Intra-particulate diffusion model

Due to the fact that the diffusion mechanism cannot be obtained from the kinetics model, the intraparticlate diffusion model (Wu et al. 2009) was also tested. The initial rate of the intraparticle diffusion is given by the following expression:

$$Q_{t} = K_{\text{id}} t^{0.5} + C_{i} ,$$
(19)

where K id is the intraparticle diffusion rate constant (mg g−1 min−0.5) and C i is intercept and a measure of surface thickness.

Thermodynamics of adsorption process

The thermodynamics parameters i.e., ∆G°, ∆H°, and ∆S° were estimated using the following relation (Lyubchik et al. 2011):

$$\varDelta G^\circ = - RT\ln K_{\text{d}} ,$$
(20)
$$\ln K_{\text{d}} = \frac{\varDelta S^\circ }{R} - \frac{\varDelta H^\circ }{RT}.$$
(21)

The equilibrium constant, K d, is obtained from the value of Q e/C e at different temperature equilibrium studies. Van’t Hoff plot of ln K d against the reciprocal of temperature (1/T), should give a straight line with intercept as \(\frac{\varDelta S^\circ }{R}\) and slope as \(\frac{\varDelta H^\circ }{R}\).

Result and discussion

Synthesis and characterization of calcium phosphate

The XRD pattern for the synthesized Ca-Hap powder is shown in Fig. 2. All reflections can be accounted for using the reference spectra for HA, β-TCP, and α-TCP, with no other significant phases present. The major peaks in are from hydroxyapatite which contains sharp and strong peaks due to the high degree of crystallinity of the powder. The three highest peaks of appears at 2θ = 11.79, 21.08, and 29.42. The phase composition indicates that the majority of the material remains as HA, with the remainder composed of TCP phases. SEM micrograph of the synthesized calcium phosphate (Fig. 3) showed that the powder layer exhibited a porous microstructure with micropores which were relatively well separated and homogeneously distributed over the surface. The FTIR spectra of the synthesized Ca-Hap powder are shown in Fig. 4. Typical absorption bands at 884.81, 567.38, 601.97, and 1036.19 cm−1 related to the nodes of phosphate and the broad band at 3444.7 and 3670.8 cm−1 are assigned to the hydroxyl while those at 1711.34, 1631.60, and 1418.32 cm−1 can be attributed to the water molecule present in the powder. Upon the adsorption of the dye molecule, the spectra changed drastically as shown in (b) the band at 884.81 cm−1 disappeared, while others undergo a reduction in intensity and little shifts. It is worth noting that the OH− is still retained although the intensity is reduced which may be as a result of H-bonding interactions with the dye molecule.

Fig. 2
figure 2

XRD patterns of the synthesized powders

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Fig. 3
figure 3

Scanning electron micrograph of the synthesized powders

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Fig. 4
figure 4

FTIR spectrum: a Ca-Hap before adsorption, b after adsorption, and c Alizarin S dye

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Batch equilibrium studies

Effect of pH on adsorption process

One of the major factors affecting the adsorption of a dye on an adsorbent is the pH of the adsorbate solution (Royer et al. 2009). It affects the chemistry of both the adsorbent and the dye in the solution. The percentages color removal and adsorption capacity variation with pH is shown in Fig. 5. At pH lower than 5, the adsorbent (Ca-P) dissolved in the solution and as such limited the study to pH 5 and above. The color removal efficiency and adsorption capacity are optimum at the at pH range of 7.0 and 8.0 with about 95 % color removal efficiency. This observation is due to the fact that at higher pH, the OH− predominates the surface of the adsorbent and the interaction is solely between the negatively charged dye molecules and Ca2+ presents at the adsorbent surface (Mobasherpour et al. 2012).

Fig. 5
figure 5

Effect of pH on the adsorption process

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Effect of adsorbent dosage

The effect of adsorbent dosage on the efficiency of color removal by Calcium Phosphate during the adsorption process was investigated using various amount of the CaP. Figure 6 shows the plot of adsorbent dosage versus the percentage color removal and Q e (mg g−1) during the adsorption process. From the figure, it is glaring that as the adsorbent dosage is increased the percentage color removal increases from 9.3 to about 84.0 %, this is attributed to increase in the adsorption sites as the adsorbent dosage increases. On the contrary, the adsorption capacity decrease with increase dosage is mainly due to the increase of free adsorption sites as the dosage increases.

Fig. 6
figure 6

Effect Adsorbent dosage on the adsorption process

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Effect of initial dye concentrations and contact time

The effect of initial dye concentration on the adsorption removal of ARS is shown in Fig. 7 for dye concentrations increasing from 25 to 150 mg L−1. The process showed rapid removal in the first 30 min for all the concentrations studied. The efficiency of the process increases from 11.72 to 67.76 mg g−1 as the initial concentration increase from 25 to 150 mg L−1. As there is no significant difference in the amount adsorbed after 60 min of the process, a steady-state approximation was assumed and a quasi-equilibrium situation was reached. The adsorption curves were single, smooth, and continuous, leading to saturation. This is an indication of possible monolayer coverage on the surface of the adsorbent. Also at low concentration of the dye molecule, there is a significant increase in dye adsorption capacity as a result of considerable amount of active site on adsorbent’s surface was occupied by small amount of dye, making the adsorption capacities to become slower due to the saturation of active sites and hence longer time for equilibrium (Table 1).

Fig. 7
figure 7

Effect of initial dye concentration on the adsorption process

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Table 1 Properties of Alizarin Red S (ARS)
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Adsorption study

Adsorption isotherms

The adsorption data obtained at different initial dye concentrations were fitted into six different isotherm models as shown in Fig. 8. Table 2 showed the values of maximum adsorption capacities (Q m), correlation coefficients (R 2), and other constant parameters for the six isotherm models equations for the adsorption process at 30 °C. For the Langmuir isotherm, the Q m value of 100.36 mg g−1 was obtained and the value of R 2 of 0.988 shows good fitting of this isotherm to the experimental data (Table 5). The separation factor (R L), an important parameter of the Langmuir isotherm was 0.035 (average of six concentrations) indicate favorable adsorption of the ARS onto Ca-P. The decrease in R L with an increase in the initial concentration indicates that the adsorption is more favorable at high concentrations (figure not shown). Freundlich isotherm’s constant, K F is 30.32 mg g−1 (mg L−1)−1/n (R 2 = 0.976) and the value of n (1.96) obtained in this study is an indication of favorable physical process and the normal Langmuir isotherm. For Redlich–Peterson isotherm parameters, Q o values of 117.68 mg g−1 (R 2 = 0.980) is also close to the Langmuir maximum adsorption, 0.56 obtained the value of β show a favorable fit (0 < β < 1). Temkin isotherm constant b T, which is related to the heat of adsorption obtained for this study is 102.76 (R 2 = 0.991) and its positive value indicates an endothermic process. The Dubinin–Radushkevich model and Sip isotherm parameters are also shown in Table 2. From the analysis of all the isotherms and the knowledge of the most their important parameters, the isotherms can be arranged according to their capacity to predict or their efficiency in predicting the experimental behavior of the ARS adsorption on Ca-P. With respect to Q m (in descending order): Redlich–Peterson > Langmuir > Dubinin–Radushkevich > Sip. However, when R 2 is considered, the order is (in descending order): Sips > Dubinin–Radushkevich > Redlich–Peterson > Tempkin > Langmuir > Freundlich. The value of E obtained in D–R isotherm was found to be 1.32 kJ mol−1 and since E < 8 kJ mol−1, it suggests that the adsorption mechanism is physical in nature (Helfferich 1962).

Fig. 8
figure 8

Least square plots of the a Langmuir, b Freundlich, c Redlich–Peterson, d Temkin, e Dubinin–Radushkevich, and f Sips isotherm for the adsorption of ARS on Ca-P

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Table 2 Isotherm values for the adsorption of ARS on Ca-P
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Adsorption kinetics

The plots of four different kinetic models used to explain the adsorption data are shown in Fig. 9. Pseudo-second-order kinetic models fit well with experimental data when compared with other models (Table 3). The rate constant from all the models showed an initial increase with increasing initial dye concentration, however, there is no significant increase as the concentration is increased up to 100 mg L−1. This shows that at higher initial concentration the electrostatic interaction decreases at the site, thereby lowering the adsorption rate. The behavior of Elovich constant shows that the process of adsorption is more than one mechanism.

Fig. 9
figure 9

Least square plots of a pseudo-first-order, b pseudo-second-order, c Avramin, and d Elovich kinetic models for the adsorption of ARS on Ca-P

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Table 3 Kinetic parameters for the adsorption of ARS on Ca-P
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Adsorption mechanism

The mechanism of adsorption was investigated by subjecting the data to intraparticulate diffusion model. The plots are shown in Fig. 10. The linearity of the plot is not over the whole time range rather they exhibit multi-linearity revealing the existence of three successive adsorption steps. The first stage is faster than the second, and it is attributed to the external surface adsorption referred to as the boundary layer diffusion. Thereafter, the second linear part is attributed to the intraparticle diffusion stage; this stage is the rate-controlling step. Table 3 shows the intraparticle model constants for the adsorption removal of ARS dye by Ca-P. The K di values were found to be decreasing from first stage of adsorption toward the second stage. The increase in dye concentration results in an increase collision of dye molecules thereby affecting the dye diffusion rate.

Fig. 10
figure 10

Intraparticulate diffusion model plots for the adsorption of ARS on Ca-P

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Thermodynamic parameters

The free energy change, ΔG is obtained from Eqs. (20 and 21) according to the van’t Hoff linear plots of ln K d versus 1/T plot in Fig. 11. The thermodynamic parameters are presented in Table 4. From the Table, it is found that the negative value of ΔG as the temperature increases indicates the spontaneous nature of adsorption. Positive value of enthalpy change indicates that the adsorption process is endothermic in nature, and the negative value of change in internal energy (ΔG) show the spontaneous adsorption of ARS on to Ca-P. Positive values of entropy change show the increased randomness of the solution interface during the adsorption process (Table 5).

Fig. 11
figure 11

Plot of ln K d and 1/T for the for the adsorption of ARS on Ca-P

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Table 4 Intraparticulate diffusion parameters
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Table 5 Thermodynamic parameters for the adsorption of ARS on Ca-P
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Conclusion

Calcium phosphate was prepared from CaCO3 and HPO5 and the physico-chemically characterized with XRD, SEM, and FTIR. Ca-P removed ARS from aqueous solution via adsorption process which depends on factors such as: adsorbent dosage, solution pH, temperature, initial dye concentration, and contact time. The percentage removal of the dye increased with pH up to 7, also contact time and current density increase influence the removal positively. Equilibrium data fitted very well with the isotherm equation in the order of Sips > Dubinin–Radushkevich > Redlich–Peterson > Tempkin > Langmuir > Freundlich. Langmuir adsorption isotherm confirmed the monolayer adsorption with capacity of 100.36 mg g−1 at 303 K. The kinetics of the process is best explained using a pseudo-second order kinetics model, with higher R 2 (Table 5). Intra-particle diffusion was not the sole rate-controlling factor. The thermodynamics parameters obtained indicate that the process is spontaneous endothermic nature of the process. In conclusion, Ca-P prepared from a cheap source has demonstrated the capability as a cheap adsorbent for remediation of dye-contaminated water.