Analytical Chem istry - DePauw University

Chapter 10 Spectroscopic Methods589method of continuous variations, also called Job’s method, is the mostpopular. In this method a series of solutions is prepared such that the totalmoles of metal and ligand, n total , in each solution is the same. If (n M ) i and(n L ) i are, respectively, the moles of metal and ligand in solution i, thenn = ( n ) + ( n )total M i L iThe relative amount of ligand and metal in each solution is expressed as themole fraction of ligand, (X L ) i , and the mole fraction of metal, (X M ) i ,( X )Mi( X )Li( n )L i=ntotal( n ) ( n )L i M i= 1− =n ntotaltotalThe concentration of the metal–ligand complex in any solution is determinedby the limiting reagent, with the greatest concentration occurringwhen the metal and the ligand are mixed stoichiometrically. If we monitorthe complexation reaction at a wavelength where only the metal–ligandcomplex absorbs, a graph of absorbance versus the mole fraction of ligandwill have two linear branches—one when the ligand is the limiting reagentand a second when the metal is the limiting reagent. The intersection ofthese two branches represents a stoichiometric mixing of the metal and theligand. We can use the mole fraction of ligand at the intersection to determinethe value of y for the metal–ligand complex ML y .Example 10.8ny = X XLn= LX= L1 − XMTo determine the formula for the complex between Fe 2+ and o-phenanthroline,a series of solutions is prepared in which the total concentrationof metal and ligand is held constant at 3.15 10 –4 M. The absorbance ofeach solution is measured at a wavelength of 510 nm. Using the followingdata, determine the formula for the complex.X L absorbance X L absorbance0.000 0.000 0.600 0.6930.100 0.116 0.700 0.8090.200 0.231 0.800 0.6930.300 0.347 0.900 0.3470.400 0.462 1.000 0.0000.500 0.578MLYou also can plot the data as absorbanceversus the mole fraction of metal. In thiscase, y is equal to (1–X M )/X M .To prepare the solutions for this exampleI first prepared a solution of 3.15 10 -4M Fe 2+ and a solution of 3.15 10 -4M o-phenanthroline. Because the twostock solutions are of equal concentration,diluting a portion of one solutionwith the other solution gives a mixturein which the combined concentration ofo-phenanthroline and Fe 2+ is 3.15 10 -4M. If each solution has the same volume,then each solution contains the same totalmoles of metal and ligand.