2.1 Material and methods

The experimental details have been reported before (Aghaie et al., 2011).

2.2 Apparatus

A metrohome pH/mV meter, an Ag/AgCl/ KCl(sat) electrode in conjunction with the respective standard calomel electrode (SCE) and a Hooke model FK2 circulation water bath at 25.0 ± 0.1 °C were used to carry out the respective experiments.

2.3 Membrane preparation prepared

The composition of the used membrane was 66.7% w/w TBP, 30.0% w/w PVC, 1.3% w/w oleic acid and 2.0 w/w DBO as ionophore. It should be noted that the presence of lipophilic and immobilized ionic additive or salt of two lipophilic ions could diminish the membrane resistance and eliminate the diffusion potential (Mousavi et al., 2001; Thomas and Underhill, 1972).

2.4 Emf measurements

All the electromotive force (emf) measurements were carried out with following assembly:

Ag/AgCl/internal solution (1.0 × 10⁻³M Al(NO₃)₃, pH = 5)/PVC membrane/test solution/KCl (satd)/Hg₂Cl₂/Hg. A metrohom pH meter was used for the potential measurements in the temperature range of 20–50 °C.

3.1 The effect of pH in aqueous medium

The influence of pH of the test solution on the potential response of the aluminum sensor was studied as previously for concentration of Al⁺³ (1.0 × 10⁻³M) over the pH range of 1.0–80. The pH of solutions was adjusted with HCl or NaOH solutions. As the results show (Fig. 1) the suitable pH range is 3.2–7.8. Within this working pH range, the predominant species is Al³⁺. At lower pH (pH < 3.2), the proposed sensor responds to H⁺ ions and a decrease in potential at higher pH may be due to the formation of some of aluminum hydroxide species. In order to reach a higher stable response a buffer solution of CH₃COO⁻–CH₃COONa (pH = 5) was recommended for test samples.

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Figure 1 The effect of pH on the potential response.

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3.2 The effect of temperature

The electrode potentials were measured in aqueous medium at different temperatures in the concentration range of 1.0 × 10⁻⁶–1.0 × 10⁻¹ M. The electrode shows a good Nernstian response at the temperature range of 20–50 °C. The plots of the E_cell versus pAl³⁺ were obtained at 20, 25, 30, 35, 40, 45 and 50 °C. The results show that the electrode exhibits a good Nernstian slope at the considered temperatures. The slopes and intercepts of the plots have been summarized in Table 2.

3.3 Determination of $E_{\mathit{cell}}^0$ and $E_{\mathit{elec}}^0$

The intercept of the plot of E_cell versus pAl³⁺ at each temperature represents the $E_{\mathit{cell}}^{°}$ of related temperature (Caulton and Cotton, 1971; Macca, 2003). The standard potentials of calomel electrode, SCE, at different temperatures may be estimated by using the following equation:

3.4 Thermodynamic properties

The following equation is used for temperature dependent of $E_{\mathit{cell}}^{°}$ : (Bühlmann et al., 1998; Bakker et al., 1997)

The plot, of $E_{\mathit{cell}}^{°}$ and $E_{\mathit{elec}}^{°}$ versus θ = (t °C −25) gave two straight lines (Fig. 2(a) and (b)) with the slopes of 9.99 × 10⁻⁴ V/°C and 3.93 × 10⁻⁴ V/°C respectively.

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Figure 2 The variation of standard potential of the electrode (a) and the cell (b) with θ = (t°C – 25).

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According to the thermodynamic equation, $\mathrm{\Delta }{G}^{°}=-{\mathit{nFE}}^{°}$ , we can estimate the standard Gibbs free energy change, $\mathrm{\Delta }{G}^{°}$ , related to $E_{\mathit{cell}}^{°}$ and $E_{\mathit{elec}}^{°}$ (n = 1 and F is the Faraday constant). $$\mathrm{\Delta }{G}_{298\text{,}\mathit{cell}}^{°}=-7496.9\text{J}{\text{mol}}^{-1}$$ $$\mathrm{\Delta }{G}_{298\text{,}\mathit{elec}}^{°}=-31068.3\text{J}{\text{mol}}^{-1}$$ The corresponding standard entropy change, $\mathrm{\Delta }{S}^{°}$ , is: $\mathrm{\Delta }{S}^{°}=\mathit{nF}\frac{{\mathit{dE}}^{°}}{\mathit{dT}}$ . So, $$\mathrm{\Delta }{S}_{\mathit{cell}}^{°}=96.39\text{J}{\text{K}}^{-1}{\text{mol}}^{-1}\text{and}\mathrm{\Delta }{S}_{\mathit{elec}}^{°}=37.92\text{J}{\text{K}}^{-1}{\text{mol}}^{-1}$$ In turn, the corresponding standard enthalpy change, $\mathrm{\Delta }{H}^{°}$ is: $\mathrm{\Delta }{H}^{°}=\mathrm{\Delta }{G}^{°}+T\mathrm{\Delta }{S}^{°}$ . So $$\mathrm{\Delta }{H}_{\mathit{cell}}^{°}=28622\text{J}{\text{mol}}^{-1}\text{and}\mathrm{\Delta }{H}_{\mathit{elec}}^{°}=-19768\text{J}{\text{mol}}^{-1}(\text{at}298\text{K})$$

3.5 The effect of mixed solvent

The behavior of the mentioned electrode was studied in the mixed solvents such as water–ethanol and water–dioxane at 25 °C and in various percentages of the component. The volume percents were varied for ethanol and dioxane. The results are shown in Table 4. As we can see the results show that electrode gives a good Nernstian response in the mixed solvents from 0 to 15% V/V of ethanol and 0 to 5% V/V of dioxane.

3.6 Determination of the formation constant (K_f)

The emf values were determined over a concentration range of Al⁺³ ion (1.0 × 10⁻⁶ to 1.0 × 10⁻¹ M) in the water–dioxane solutions (3% V/V of dioxane). As the results show (Fig. 3), the selective electrode exhibits linear response to the activity of Al³⁺ ions. The Nernstian slope is 18.8 mV/decade.

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Figure 3 The potential response of the electrode to the solutions of Al³⁺ ion in the “water–dioxane” system at 25°C.

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According to this behavior of the proposed electrode and by using the present methods (Bakker et al., 1999; Baghdar et al., 2010; Linder, 1988) the K_f was determined as follows:

1. 10 mL of Al³⁺ ion solution (1.0 × 10⁻⁴ M) was tested by the cell assembly. The potential response was 63 mV which can be indicated by E.

2. 0.1 mL of the ionophore (5.0 × 10⁻³ M) was added to the previous solution.

   • The cell voltage reached 68.6 mV, which can be indicated by E_1. The concentration of species involved in the equilibrium reaction of complex formation was determined by using the amounts of E, E₁ and the following equations:

     (4)

     $${[{\text{Al}}^{3+}]}_{\mathit{free}}=9.9\times {10}^{-5}\times {10}^{\frac{E-E_1}{D}}$$

     (5)

     $$[{\text{AlL}}^{3+}]=9.9\times {10}^{-5}-{[{\text{Al}}^{3+}]}_{\mathit{free}}$$

     (6)

     $${[\text{L}]}_{\mathit{free}}=4.95\times {10}^{-5}-[{\text{AlL}}^{3+}]$$ where L stands for DBO.

3. Then we can calculate the formation constant (the K_f) for ionophore – Al(III) complex by exerting the concentration of species in the following equations:

   (7)
   $${\text{Al}}^{3+}+\text{L}\leftrightarrows {\text{AIL}}^{3+}{K}_f=\frac{{\text{AlL}}^{3+}}{{[{\text{Al}}^{3+}]}_{\mathit{free}}{[\text{L}]}_{\mathit{free}}}$$ The experiments were performed for four times and the results have been shown in Table 5.