Cyanex 272 (Cytec Canada Inc.) was purified by the micro-emulsion formation method [31] to 99% BTMPPA (potentiometric titration), and characterized by its density (0.9152 g/mL at 298 K) and viscosity (120 mN/m at 298 K) [32]. Aliphatic colorless kerosene distilling over 200˚C - 260˚C was used as diluent. NiSO₄·6H₂O (Fluka, >99%) was used as a source of Ni²⁺. Other chemicals were of reagent grade and used as received.

The [Ni²⁺] in the aqueous phase was determined by the bromine-dimethylglyoxime method [33] at 445 nm using a WPA S104 Spectrophotometer and occasionally by the AAS method using a Shimadzu AA-6800 Spectrophotometer, especially when its concentration was low. The stock solution of Ni²⁺ was prepared by dissolving 22.39 g NiSO₄∙6H₂O in water to make 1 L solution and standardized by EDTA-titration. The solution was found to contain 4.99 g/L Ni²⁺. The acidity of the aqueous solutions was measured by a Mettler Toledo MP 220 pH meter on calibration by double buffers of pH 4 and 7.

The construction of single drop apparatus is described elsewhere [34]. Its schematic diagram is in Figure 1. A falling drop apparatus was used. In the experiment, the continuum was the organic phase and drops of aqueous solution were allowed to fall through the continuum and collected continuously from the bottom of the column, leaving a pool of ca 2 - 3 drops of aqueous phase to avoid entrainment. For each experiment, the volume of 100 collected drops was estimated by the density-mass method; so that the volume of a single drop could be calculated. In the actual experiments, an uncounted

number of aqueous drops (internally circulating and slightly oscillating) of diameter (1.81 ± 0.03) mm were allowed to fall, collected in a previously weighed dry beaker and the volume of the collected aqueous phase (ca 2.5 mL) was determined by the density-mass method. The [Ni²⁺] in the collected mass was then estimated. On knowing the volume of a drop (determined previously), the number of drops in actual experiment could be determined. The cumulative time for 10 separate drops falling one after another was determined to get the average drop fall time, which was mostly dependent of column height and only slightly dependent on the composition of phases.

At a particular temperature, (F) of Ni²⁺ transfer can be represented as [35]:

The quantity, F, at a constant temperature is related to the concentration terms as:

where, the unit of (k_f) depends on the values of a, b, c, d and e. Equation (2) can be rewritten as:

Equation (3) states that if pH, [H₂A₂], and [Ac⁻] are kept constant at pH, [H₂A₂], and [Ac⁻], respectively; and (F)-values are determined for various concentrations of [Ni²⁺], then the plot of log(F) vs log [Ni²⁺] will be a straight line with s = 1 and

.

From I-value, (k_f) can be calculated after determining the values of b, c, d and e. Similarly, the values of b, c, d and e together with four sets of (k_f)-values can be determined from the log(F) vs pH, log(F) vs log[H₂A₂]_(o), log(F) vs log and log(F) vs log[Ac^‒] plots, respectively. The temperature dependence data can be treated by Arrhenius equation and Activated complex theory [36].

The plot of from a drop vs t (obtained by using different C.H) [37] is a straight line which cuts the time axis at −0.5 s (Dt = 0.5 s). This time is designated as end correction term (attributed to time for drop formation and coalescence). In F-calculation, Dt term must be added to t; otherwise, error appears as demonstrated below:

When and F_f are calculated by neglecting and considering Dt value, respectively, then it is seen that log is decreased, whilst log F_f remains unchanged with increasing C.H and at any C.H, [37]. It is concluded that F will be independent of C.H if Dt is added to t; and any C.H. can be used if F_f (not) is calculated.

The log(F_f, kmol/m²∙s) vs log([Ni²⁺], kmol/m³) plots are displayed in Figure 2. In all cases, straight lines are obtained with s = (1.01 ± 0.03) and I as typed on the body of figure. The unity s indicates that the rate of forward extraction of Ni²⁺ by Cyanex 272 is directly proportional to initial [Ni²⁺]. In other words, the reaction order wrt [Ni²⁺]_(ini) is unity (i.e., a = 1).

The logF_f vs pH_(ini) plots are shown in Figure 3 The experimental points for a particular system fall on a curve having higher slope in lpHr and lower slope in hpHr. The experimental points for a particular set of parameters fall on curve represented by:

where, constant = −6.382 (for 0.025 mol/L [H₂A₂]_(o,ini) system), −6.062 (for 0.10 mol/L [H₂A₂]_(o,ini) system) or,

−5.80 (for 0.30 mol/L [H₂A₂]_(o,ini) system) and 10^6.32 is a proportionality constant resulting from non-linear curve fitting. Its unit is L/mol. I-values of the asymptotic lines are embodied in figure. It is concluded that the rate of Ni²⁺ extraction is independent of [H⁺] in lpHr; whereas, inversely proportional to [H⁺] in hpHr. In other words, the reaction order wrt [H⁺] is −1 (b = 1) and 0 (b = 0) in lpHr and hpHr, respectively.

Figure 4 displays logF_f vs log[H₂A₂]_(o,ini) plots. For each pH system, the plot is a straight line whose s and I are given. The s-values indicate that the rate of forward extraction is directly proportional to the square root of the extractant concentration (i.e., c = 0.5).

The nature and extent of variations of F_f with are displayed in Figure 5. The experimental points for a particular set of parameters fall on a curve represented by:

where, constant = −6.4 (for pH_(ini)= 6.70, [H₂A₂]_(o,ini) = 0.025 mol/L system) or, −5.95 (for pH_(ini) = 6.40, [H₂A₂]_(o,ini) = 0.30 mol/L system); and 6.30 is a proportionality constant resulted fromnon-linear curve-fitting and its unit is considered as L/mol. The intercepts of the asymptotic lines are given in figure. The rate of Ni²⁺ transfer is therefore inversely proportional to the term. This means that d is 0 at lcr of and −1 at hcr of.

The log(F_f, kmol/m² s) vs log[Ac⁻], mol/L) plot for pH_(ini) = 6.60 and [H₂A₂]_(o,ini) = 0.025 mol/L is represented in Figure 6. Experimental points fall on a curve represented by:

where, 0.55 L/mol is proportionality constant whose value is originated from non-linear regression analysis. I-values of the asymptotic lines are quoted. The rate of Ni²⁺ transfer is therefore inversely proportional to the term (1 + 0.55 [Ac⁻]). In other words, e = 0 at lcr of [Ac⁻] and e = −1 at hcr of [Ac⁻].

The logF_f vs 1/T (Arrhenius) plots for 5-sets of experimental parameters are depicted in Figure 7. From top

to bottom, 1^st, 4^th and 5^th systems yield straight lines and s of these lines give E_a values of 19, 56 and 17 kJ/mol, respectively. On the other hand, for the 2^nd and 3^rd systems, curves are obtained. From limiting s of the curves, E_a values of 25.5 kJ/mol and 57.5 kJ/mol are obtained at htr and ltr, respectively for the 3^rd system; whereas, 27.5 kJ/mol and 62.0 kJ/mol are obtained at htr and ltr respectively, for the 2^nd system.

The temperature dependence rate data have also been treated by the Activated Complex Theory to estimate the DH^± and DS^±. The plots of log (F_fh/kT) vs (1/T) are given in Figure 8. Natures of plots are similar to those of Arrhenius plots. The “s”, “I”, DH^± and DS^± values are embodied in the figure. In calculating DS^± values, logf(R)- values are needed which are calculated using the relation:

The calculated DH^± value varies within 17 - 65 kJ/mol; whereas, DS^± values are always negative.

From “I” of the straight lines or the asymptotic lines in Figures 2-6, the average value of logk_f at 303 K in presence of 3% (v/v) octan-1-ol in the organic phase has been evaluated to be −3.742, with stand. dev. of 0.04. The

value of logk_f has also been obtained graphically. As the flux equation can be represented as: logF_f = logk_f + logf(R), the plot of logF_f vs logf(R) should be a straight line with s = 1 and I equaling to the value of logk_f. The plot is given in Figure 9. A good fit Least Squares straight line is obtained with s = 1.0288 (should be 1) and I = −3.6781. The latter value corresponding to log k_f is comparable to that obtained above. Hereafter, k_f = 10^−3.7 m^5/2/kmol^1/2∙s will be considered in discussion.

Based on the results obtained, F in this system at 303 K can be expressed as:

Equation (8) is a too much complicated equation. It can be changed to a number of simplified flux equations depending on the concentration regions of H⁺, and Ac⁻. Here, following two extreme cases will be considered for discussion:

1) At hcr of H⁺, but lcr of and Ac^‒

where, 10^‒10.02 = 10^‒3.7 ´ 10^‒6.32; and 2) At lcr of H⁺ but hcr of and Ac^‒

where, 10^‒4.24 = 10^‒3.7/6.3 ´ 0.55.

In the present case, as the reaction order wrt extractant concentration is a one-half, the monomeric model of extractant will be applicable [35]. The monomeric model of H₂A₂ is:

Combination of Equation (9) with Equation (11) yields the flux equation as:

Equation (12) gives the slow reaction step occurring in the bulk aqueous phase as:

In this experimental parametric condition, Ni²⁺ extraction by Cyanex 272 is therefore chemically controlled and this statement is supported by high E_a (56 kJ/mol) obtained at the investigated hcr of H⁺ (pH = 5) and lcr of (0.05 mol/L) and Ac^‒ (0.25 mol/L).

The chemically controlled rate-determining step: may occur either by an S_N1 or S_N2 mechanism [38]. For S_N2 mechanism, the bimolecular reaction step may be shown as:

with the rate expression :

Equation (15) is identical to Equation (12). Consequently in an S_N2 mechanism, the attachment of an additional ligand (A^‒) to the restricted co-ordination sphere of Ni²⁺ acts as the rate determining step. The other is the S_N1 mechanism which a unimolecular process as follows:

The steady state approximation results the rate expression for the S_N1 mechanism as:

and if, then the Equation (17) takes form of Equation (15); whereby (k₁k₃/k₂) will represent k_f.

Thus, it is possible to explain the same rate data by both S_N1 and S_N2 mechanisms; and as a result, it is difficult to decide whether the reaction proceeds via Equation (14) or (16). But this difficulty may effectively be overcome by the use of the thermodynamic data of the activated state, especially the (DS^±) data for the system.

The solution effect dominates the entropy of activation where charged ions are involved. If the solvent molecules are tightly attached around Ni²⁺ ions, their entropy is lost i.e. DS^± becomes negative. On the other hand, if the solvent molecules dissociate from the metal ions, their entropy is increased; and so, DS^± becomes positive. Thus for an S_N2 mechanism, where the ligand (A^‒) co-ordinates to the metal ion, [Ni(H₂O)_x]²⁺ to form the higher co-ordinated activated complex, [Ni(H₂O)_x∙A]⁺, the value of DS^± would be expected to be more negative than the ground state. But for the S_N1 mechanism, where the formation of lower co-ordinated activated complex, [Ni(H₂O)_x‒1]²⁺ takes place, DS^± should be positive. In the present case, DS^± at all experimental parameters are highly negative; and so the rate controlling chemical reaction step represented by Equation (13) occurs via an S_N2 mechanism.

On the other hand, at lcr of H⁺ but hcr of and Ac^‒, the existing Ni²⁺ species may be considered as [Ni(OH)(SO₄)(Ac^‒)]^2‒. So Equation (10) takes the form:

And with the help of b₁ and b₂, Equation (18) takes the form:

Monomeric model of H₂A_2(o) i.e. Equation (11) transforms Equation (19) to

This equation suggests the rate controlling extraction reaction step given in Equation (13) is also the rate determining chemical reaction step in the latter set of condition. But E_a of 17 kJ/mol obtained at lcr of [H⁺] (i.e. high pH: 6.7) and hcr of (1 mol/L) and Ac^‒ (2 mol/L) suggests that the diffusion of a reactant to the reaction site or the product from the reaction site to the bulk organic phase is slower than the reaction step given in Equation (13).

Thus depending on the extraction condition, the Ni²⁺ extraction in the present system by Cyanex 272 may be either 1) pure chemical controlled (at low pH, and [Ac^‒]) or 2) pure diffusion controlled (at high pH, and [Ac^‒]) or 3) mixed (intermediate) controlled. In most of the cases (moderate pH and/or, and/or [Ac^‒]) at 303 K, the process is mixed controlled which may be chemically controlled at ltr and diffusion controlled at htr.