Analytical Chem istry - DePauw University

592 Analytical Chemistry 2.0from conditions in which there is a linear relationship between absorbanceand the relative amounts of metal and ligand. If a metal–ligand complex isvery weak, a plot of absorbance versus X L or n L /n M may be so curved that itis impossible to determine the stoichiometry by extrapolation. In this casethe slope-ratio may be used.In the slope-ratio method two sets of solutions are prepared. The firstset of solutions contains a constant amount of metal and a variable amountof ligand, chosen such that the total concentration of metal, C M , is muchlarger than the total concentration of ligand, C L . Under these conditionswe may assume that essentially all the ligand reacts in forming the metal–ligand complex. The concentration of the complex, which has the generalform M x L y , isC[ ML]=x yyLIf we monitor the absorbance at a wavelength where only M x L y absorbs,thenεbCA= εb[ ML]=x yyand a plot of absorbance versus C L is linear with a slope, s L , ofbs = εLyA second set of solutions is prepared with a fixed concentration of ligandthat is much greater than a variable concentration of metal; thusC[ ML]=x yxMεbCA= εb[ ML]=x yxbs = εMxA ratio of the slopes provides the relative values of x and y.ssMLεb/x= =εb/yAn important assumption in the slope-ratio method is that the complexationreaction continues to completion in the presence of a sufficientlylarge excess of metal or ligand. The slope-ratio method also is limited toyxLM