- Research Article
- Open Access
Ligand exchange method for determination of mole ratios of relatively weak metal complexes: a comparative study
© The Author(s) 2018
- Received: 9 May 2018
- Accepted: 4 December 2018
- Published: 20 December 2018
- Ligand exchange method
- Mole ratio method
- Job’s method
- Relatively weak complexes
The mole ratio is the proportion of number of moles of any two chemical entities involved in a compound or a chemical reaction. Studying the mole ratio is important to calculate the reaction yield, determine the stoichiometry and monitor the reaction kinetics. Several spectrophotometric methods were developed for the determination of the molar ratio of metal complexes. The first method goes back to the contributions of Ostromisslensky  and Job , and was widely known as Job’s method of continuous variations. In this method, a series of solutions are prepared by mixing varying proportions of the metal and ligand, keeping the sum of the total molar concentrations constant. The absorbance of each solution is then plotted against the mole fraction of either the ligand or metal. The position of the maximum in the resulting curve, or minimum in some cases , gives the mole fraction. The simplicity of the method made it widely applied for the study of various metals and association complexes [4–9], in spite of its limitations. For instance, strong complexes give triangular plots from which the position of the maximum is easily determined, while the plots of weak complexes are highly curved leading to unreliable results. Normalized absorbance plots (A/Amax vs. mole fraction) gave sharper plots at the maxima and allowed for better location of the mole ratio , but for weak complexes, these normalized Job plots were still highly curved.
Besides the method of continuous variations, the mole ratio method has been used frequently since its introduction by Yoe and Jones . In this method, a series of solutions are prepared by varying the amount of ligand in each solution while the amount of metal is kept constant. If a stable complex is formed, a plot of absorbance versus mole ratio of ligand to metal (L/M) gives a straight line that rises until it reaches the point corresponding to the mole ratio (L/M), then it breaks to a differently sloped line. For moderately stable complex, the mole ratio corresponds to the point of intersection of the tangents of straight-line portions of the plot. However, if a weak complex is formed, a very curved plot is obtained, making the identification of the molar ratio of these complexes uncertain. As a result, several chemical  and mathematical modifications [13–15] have been made to the basic mole ratio method so that it can reliably be applied to study the composition of weak complexes. However, these modifications make the method relatively more complicated and are only applicable when the ligand has significant absorbance which is not always the case.
Equation 3 is a straight line equation (y = a ± bx) with an intercept equals εMX·CMX and a slope equals −n·εMX. If A was plotted against CL, a straight line with a negative slope will be obtained as shown in Fig. 1. The mole ratio can be determined graphically from the overlay of the two calibration curves as follows:
Jenway 3510 (Jenway, UK) and Biochrom libra S80 (Biochrom, Cambridge, UK) were employed in all pH and absorbance measurements, respectively.
Alendronate sodium trihydrate, etidronate disodium, and ibandronate sodium monohydrate of pharmaceutical grade were kindly provided by Sigma Pharmaceutical Industries (Quesna, Menofyia, Egypt). All other chemicals and solvents used were of analytical ACS grade, purchased from Fisher Scientific (Fair Lawn, NJ, USA) and Sigma-Aldrich (St. Louis, MO, USA).
Fe(III)-salicylate solution was prepared at 10 mM in water/methanol (50:50, pH 3.2) and was proved to be stable for months when kept refrigerated. Fe(III) chloride stock solution (for the mole ratio and Job’s methods) was prepared at 10 mM in 2 M HClO4. Etidronate disodium stock solution was prepared at 10 mM in two different diluents: 2 M HClO4 for both the mole ratio and Job’s methods and water/methanol (50:50, pH 3.2) for the ligand exchange method. Similarly, stock solutions of alendronate sodium and ibandronate sodium were prepared.
Ferric salicylate complex calibration curve
A series of standard solutions of ferric salicylate in the range of 0.1–0.6 mM were prepared by accurately transferring appropriate aliquots of ferric salicylate stock solution (10 mM) into a series of 10 mL calibrated volumetric flasks, then completed to the mark with water/methanol (50:50, pH 3.2) (Ionic strength was adjusted with 0.5 M NaCl). Absorbance at 535 nm was measured and plotted against ferric salicylate concentration.
Ligand exchange method
Aliquots in the range 0.2–1.8 µmol of etidronate disodium were accurately transferred into a series of 10 mL volumetric flasks containing 3 µmol ferric salicylate, then completed to the mark with water/methanol (50:50, pH 3.2) (Ionic strength was adjusted with 0.5 M NaCl). Absorbance at 535 nm was measured and plotted against concentration. A similar procedure was applied to determine the mole ratio of Fe(III)-alendronate and Fe(III)-ibandronate.
Standard nine mixtures of ferric chloride (in 2 M HClO4) and etidronate (in 2 M HClO4) were prepared by adding aliquots of Fe(III) equivalent to 1 − 9 µmol into a series of 10 mL volumetric flasks containing aliquots of etidronate equivalent to 9 − 1 µmol so that each flask contains a total number of 10 µmol. Each flask is completed to the mark using HClO4 (2 M). Job’s graph is obtained by plotting absorbance at 300 nm against the mole fraction of Fe(III) ion. The same procedure was repeated with ibandronate and alendronate.
Mole ratio method
Standard mixtures of ferric chloride (in 2 M HClO4) and etidronate (in 2 M HClO4) were prepared by adding aliquots of Fe(III) equivalent to 0.4–30 µmol into a series of 10 mL volumetric flasks containing 5 µmol of etidronate. Each flask is completed to the mark using HClO4 (2 M). The mole ratio graph is obtained by plotting absorbance at 300 nm against the mole ratio (Fe(III)/etidronate). The same procedure was applied to study the stoichiometry of Fe(III)-ibandronate and Fe(III)-alendronate.
Ligand exchange method using Fe(III)-salicylate
According to a previously published work that studied the effect of pH and ionic strength on the absorbance of Fe(III)-salicylate complex , the absorbance of the complex was found constant over a pH range of (2.5–3.5). After trying several solvents, a 50% methanol at pH 3.2 was chosen owing to the high Fe(III)-salicylate absorbance and reasonable plateau that ensures the robustness of the method against small changes in pH. A solution of 0.5 M NaCl was used to adjust the ionic strength and keep it constant over all the following procedures.
Comparison to other mole ratio methods
Compared to the Job and mole ratio methods, the ligand exchange method offers several advantages: (i) it enables the study of the composition of colorless metal complexes using a colorimetric technique and the green LED lamp that is commercially available in most colorimeters (ii) it requires fewer steps than Job’s and the mole ratio methods because fewer number of points can be adequate to plot a straight line and several ligands can be studied against a single calibration curve of the initial complex, (iii) the ligand exchange method is more accurate and more precise than Job’s and the mole ratio methods for determination of weak and relatively weak complexes; determining the mole ratio using these methods in this case is subjective due to the curved lines. As shown in Additional file 2: Fig. S1, different tangents can be drawn for the same group of points, which may lead to false conclusions while in the ligand exchange method, there is no need to draw tangents which obviates bias and decreases the risk of error. (iv) The ligand exchange method could be used for metals other than ferric, such as Cu(II), and for determination of mole ratios other than 1:1  which indicates the generality of the method and (v) neither Job’s nor the mole ratio methods can be used unless one of the studied reactants or the formed complex are absorbing. In this case, the ligand exchange will be the method of choice.
The ligand exchange method can reliably be used as an alternative to Job’s and mole ratio methods for the determination of formula of complexes with the aid of a simple colorimeter, and could be superior in determining the composition of weak and relatively weak complexes. The method has successfully been applied to the study of the composition of ferric ion complexes with the non-chromophoric bisphosphonates: alendronate, etidronate and ibandronate. The ligand exchange method gives straight lines from which the exact mole ratio can be determined. The method does not require tangent drawing which can be subjective and may lead to inaccurate conclusions especially when weak complexes are studied. The ligand exchange method could also be preferable for determining the composition of high ratio complexes and that will be the focus of our future research.
MM participated in the study design and the results discussion and revised the manuscript. SFH participated in the study design and the results discussion and revised the manuscript. MAA conducted the practical work, participated in the results discussion and the preparation and writing of the manuscript. FRM proposed the study design, participated in the results discussion, literature review, manuscript preparation and revision. All authors read and approved the final manuscript.
The author declares that they have no competing interests.
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