299
Anal. Chem. 1904, 56,299-300
If [A] is eliminated between eq 1 and 4, one obtains an expression for the fraction x of [A], complexed
which is equivalent to eq 3 of ref 1. I have here introduced the symbols A = 6 - 6~ and Ac = 6c - bA to represent displacements of chemical shifts relative to that of pure A. Now if the reactants are present in equimolar quantities, [A], = [B],, [A] = [B] and when eq 5 is substituted into eq 3, there results
which is eq 6 also in ref 1. Horman and Dreux (1)gather lH NMR data from two sets of solutions containing equimolar quantities of A (s-trinitrobenzene) and B (hexamethylbenzene) and plot one of these sets in their Figure 1. They observe that the product KAc is constant in the two experiments and also when the data are analyzed by two other methods. I will comment first on the ramifications of this constancy. The source of this behavior stems from the (1 - x ) fador ~ in eq 6 and it is important to examine the three terms which comprise its quadratic expansion (1- 2x x 2 ) . For the experimental data graphed in Figure 1 of ref 1, it appears that the solution having the largest fraction complexed has a chemical shift near 739 Hz. Species A has an intrinsic chemical shift 6A of about 746 Hz and the intrinsic shift 6c of the complex is apparently near 665 Hz so that the fraction x in this solution is 0.0864. The three terms in the quadratic factor, hence, are in the ratios of 1:0.17:0.0075. Because this solution contains the largest x , the relative magnitudes of the three terms corresponding to other solutions are even greater. Thus the x 2 term is rather negligible in the sum and a reasonable approximation results when (1 - 2%)replaces (1 - x ) in~ eq 6. Now substitution of A/Ac for x in this approximation yields
+
K(Ac - 2A)
A/[A]o
(7)
which, parenthetically, is algebraically equivalent to eq 7 and 8 of ref 1. Furthermore, in this experiment that term 2A is small relative to Ac. It varies from a maximum of 17% of AC down to nearly zero in the most dilute solutions and this accounts for the constancy of KAc. If for all solutions 2A
