Mole ratio method

Both the method of continuous variations and the mole-ratio method rely on an extrapolation of absorbance data collected under conditions in which a linear relationship exists between absorbance and the relative amounts of metal and ligand. When a metal-ligand complex is very weak, a plot of absorbance versus Ay or n-J m may be curved, making it impossible to determine the stoichiometry by extrapolation. In this case the slope ratio may be used. 

This experiment describes the use of FIA for determining the stoichiometry of the Fe +-o-phenanthroline complex using the method of continuous variations and the mole-ratio method. Directions are also provided for determining the stoichiometry of the oxidation of ascorbic acid by dichromate and for determining the rate constant for the reaction at different pH levels and different concentration ratios of the reactants. 

Yang et al. [12] determined the ionization constants of primaquine by a titrimetric method and studied its coordination ratio with vitamin C. The ionization constants of primaquine in 50% (v/v) ethanol in water determined at 25 °C in the ionic strength range of 5 x 10 to 5 x 10-2 mol/L are given. The coordination ratio of primaquine to vitamin C is determined by continuous variation and mole ratio methods based on pH and conductance measurements to be 1 1, indicating that the coordination compound formed in the solution is mainly a 1 1 compound. 

Vives, M., Gargallo, R., and Tauler, R., Study of the intercalation equilibrium between the polynucleotide poly(adenylic)-poly(uridylic) acid and the ethidium bromide dye by means of multivariate curve resolution and the multivariate extension of the continuous variation and mole ratio methods, Anal. Chem., 71, 4328 1-337, 1999. 

Having established the composition of the complex, the stability constant of the complex was determined by (i) mole ratio method and (ii) continuous variations method. In the former method, the equilibrium considered is... 

In the mole-ratio method a series of solutions is prepared in which the concentration of one reactant (usually the metal ion) is held constant while the other reactant (usually the ligand) is varied. In the discussion that follows it is assumed that the ligand concentration is varied. 

The three most common techniques used for complex-ion studies are (1) the method of continuous variations, (2) the mole-ratio method, and (3) the slope-ratio method. 

In the mole-ratio method, a series of solutions is prepared in which the analytical concentration of one reactant (usually the cation) is held constant while that of the other is varied. A plot of absorbance versus mole ratio of the reactants is then made. If the formation constant is reasonably favorable, we obtain two straight lines of different slopes that intersect at a mole ratio corresponding to the combining ratio in the complex. Typical mole-ratio plots are shown in Figure 26-15. Notice that the ligand of the 1 2 complex absorbs at the wavelength selected so that the slope beyond the equivalence point is greater than zero. We deduce that the uncomplexed... 

There are different methods to determine the stoichiometry, e.g. Continuous Variation Methods [6], the Slope Ratio Method [7], the Mole Ratio Method [8], and others. Because the Continuous Variation Method is the most popular among these, this method is adopted here to determine the stoichiometry. 

Method of Continuous Variations (Job s Method). In this method, a series of solutions are prepared in which, to take metal eomplexation formation as an example, the sum of the concentrations of the metal and ligand is held constant, as the mole ratio of M to L is varied from 0.0 to 1.0 in steps of 0.1 (or smaller). As with the mole ratio method, the data is seen to form two linear segments which intersect at a point that reveals the composition of the complex. For ML, this point is at mole ratio 0.5 for ML2, the lines intersect at 0.33[M] [L], etc. The differences in absorbance between the values on the hypothetical extrapolated lines and the experimental values provide the basis of calculating the P value. A comparison of Figures 19.3 and 19.4 show that Job s method gives clearer definition of complex composition when p values are small. 

Solving mass-mass stoichiometry problems requires all the steps of the mole-ratio method. The mass of starting substance is converted to moles. The mole ratio is then used to determine moles of desired substance, which, in turn, is converted to mass. 

Stoichiometric problems involving gas volumes can be solved by the general mole-ratio method outlined in Chapter 9. The factors 1 mol/22.4 L and 22.4 L/1 mol are used for converting volume to moles and moles to volume, respectively. (See Figure 12.16.) These conversion factors are used under the assumption that the gases are at STP and that they behave as ideal gases. In actual practice, gases are measured at other than STP conditions, and the volumes are converted to STP for stoichiometric calculations. 

The mole ratio method is a means of performing stoichiometric calculations based upon the constant ratios of the numbers of moles of various reactants and products, regardless of the overall quantity of reaction taking place. 

The mole ratio method greatly simplifies stoichiometric calculations. It can even be used to relate relative quantities of reaction participants in a series of reactions. For example, if a particular quantity of reactant is involved in a reaction followed by one or more additional reactions, the amount of a product in the final reaction is readily calculated by the mole ratio method. 

To illustrate the mole ratio method, consider a typical reaction, namely, that of hydrogen gas and carbon monoxide gas to produce methane ... 

Several problems will be presented that illustrate the mole ratio method. First, however, it will be helpful to learn the following steps used in solving a stoichiometric problem by this method ... 

As another example of a stoichiometric calculation by the mole ratio method, consider the reaction of iron(III) sulfate, Fe(S04)3, with calcium hydroxide, Ca(OH>2. This reaction is used in water treatment processes for the preparation of gelatinous iron(III) hydroxide, Fe(OH)3, which settles in the water, carrying solid particles with it. The iron(III) hydroxide acts to remove suspended matter (turbidity) from water. The Ca(OH)2 (slaked lime) is added as a base (source of OH ion) to react with iron(III) sulfate. The reaction is... 

Briefly define and explain the mole ratio method of stoichiometric calculations. 

What is the first step required to solve a problem by the mole ratio method ... 

In general, it is advisable to use a combination of the methods listed above to determine the stoichiometry. The mole ratio method (No. 2 above) is very straightforward as it usually involves inspecting the titration isotherm obtained upon titration of a guest into a host solution. The apparent linear portions of the beginning and end of the titration curve are extrapolated. The point where these two lines intersect usually corresponds to the main inflection point on the binding isotherm and the corresponding [G]o/[H]o... 

Different methods can be used to determine the guest-to-host ratio, or stoichiometry, of a host-guest system. Among them, the continuous variations, also called Job s method [50], and the mole ratio method [51], are certainly the easiest and most common techniques. 

In the mole ratio method, the concentration of the [host] is kept constant while the concentration of [pyrene] is varied, and the absorbance of the system versus the molar ratio [pyrene]/[host] is plotted. An abrupt change in the slope will correspond to the stoichiometric ratio. With this method, the absorption of the complex is proportional to its concentration (Beer-Lambert law) thus, selecting the value of absorbance at offers the highest precision, although... 

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