A New Method for the Determination of Equilibrium Constant and Molar Extinction Coefficient of 1 : 1 Type Complex

Abstract

Job’s method of continuous variation has been reinvestigated with respect to the formation of 1 : 1 type complex from the view point of (i) geometrical significance of the Job curve, (ii) developing a method for determining the equilibrium constant and molar extinction coefficient of the complex. A mathematical analysis of the method of continuous variation as applied to the formation of strictly 1 : 1 type complex shows that the Job curve is a hyperbola obeying the equation\frac(d–β)2a2−\frac(CM°⁄λ–1⁄2)2b2=1where d is the corrected optical density, CM° is the initial concentration of the metal ion in solution, λ is a constant equal to the sum of the concentrations of the metal and the ligand in solution, β is the ordinate of the local origin of the hyperbola referred to the conventional framework of the Job curve, a and b represent respectively the semi-major and semi-minor axes of the hyperbola. The equation has been recast into the form x=A3d2+A2d+A1, where x=(CM°/λ–1⁄2)2 and A3, A2, and A1 are the appropriate coefficients. A parabolic fit of this equation between x and d by the least square deviation method using the computer B-6800 system enables one to find the coefficients A3, A2, and A1 from which K and ε are evaluated. This equation has been tested with literature data on a variety of 1 : 1 type metal complexes whose formation constants and extinction coefficients as calculated by the present method agree closely with those determined by other methods. The promising features of the equation have been discussed.