(a) Prove mathematically that the peak in a continuous-variations plot occurs ata

Chapter 14, Problem 14-24

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(a) Prove mathematically that the peak in a continuous-variations plot occurs ata combining ratio that gives the complcx composition.(b) Show that the overall formation constant for the complex MI." iswhere A is the experimental absorbance at a given value on the x-axis in acontinuous-variations plot, A"" is the absorbance determined from theextrapolated lines corresponding to the same point on the x-axis, eM is themolar analytical concentration of the metal, cL is the molar analytical concentrationof the ligand, and n is the ligand-to-metal ratio in the complex.'"Under what assumptions is the equation valid?What is c?Discuss the implications of the occurrence of the maximum in a continuousvariationsplot at a value of less than OSCalabrese and Khan 35 characterized the complex formed between [, and [-using the method of continuous variations. They combined 2.60 X 10-4 Msolutions of [, and 1- in the usual way to obtain the following data set. Usethe data to find the composition of the [,11- complex.g) The continuous-variations plot appears to be asymmetrical. Consult thepaper by Calabrese and Khan and explain this asymmetry.(h) Use the equation in part (a) to determine the formation constant of the complexfor each of the three central points on the continuous-variations plot.