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7,5, , TIIE DRAGO-WAYLAND EQUATION, 15, , In )965 Drago and Wayland introduced an empirical four-parameter equation to describe, and predict the enthalpy change accompanying the reaction of weak neutral acids with, weak neutral bases in poorly solvating solvents or in the gas phase. This equation takes, the form, , -AH= E,,.E,; + C1.Cs, , 1, •, , (7.75), , where E,,. and C,,. are parameters for the acid (arbitrarily set as E,,. = 0.50 and c,,. = 2.00, for Ii) and where Es and Cs are parameters for the base. It is felt that the E1.Es term, reflects the electrostatic part of the ·acid-base interaction and that the C,,.Cs term reflects, the covalent part. The equation is similar in form to a number .of other equations in the, literature, but differs in that the others correlate independently observable quantiti~ such, as stability constants with the Bnisnsted acidity and oxidative coupling constants. The, beauty of the Drago-Wayland equation lies in its minimum of constraints, which in turn, allows the best possible fitting _of the enthalpy data by an equation of its form . Accordingly, it can perform equally the task of fitting a given set of data as an equation of similar, form that uses observable properties as parameters. It ·thus sets a limit to the degree to, which any equation of its form can fit a set of data. With the constants listed in Table 7.6, we can predict the enthalpy-change for 900, acid-base reactions'. If an interchange reaction between two acid-base adducts is considered, we can predict approximately one million such enthalpies by the equation, , where the A terms are all consistent (either all A and ·B subscripted 1 subtracted from, those subscripted 2, or vice versa). We can use such ~ata to construct affinity diagrams,, and it can be shown that a consistent ordering of hardness or softness cannot be achieved, with the set of,acids and bases for which we have E and C parameters. · ·, Along with predicting enthalpy data, the Drago-Wayland equation can be used to select solvents that have·nearly the same extent of acid-base interactions ~ith solutes matching the E and C parameters. Thus dimethyl sulfoxide (dmso) and dtmethylformamide, (dmf) would show similar acid-base behavior toward solutes, since they have almost identical E and C values. ·, 15, , R. S. Drago and B. B. Wayland, J. Am. Chem . Soc . 1965, 87, 3_571.

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,>', , ', , ', , (, , ,· II, , 344, , PART 111, , I II, , Table 7.6, , 11, , I, , Chemical Heactiona, , E and C parameters (Equation (7. 78)) for eo.m e acids Bild, , Acid, , I i-J, , l2, H20, H2S, HF, HCI, HCN, CHJOH, C2H5QH, CH50H, .(CH3)3COH, HCCb, HCFJ, CH3C02H, B(OCHJ)J, B(C2H5)3, PF3, Asf3, S02, , b111e 8--., , A~, 0.50, 1.54, 0.77, 2.03, 3.69, 1.77, 1.25, 1.34, 2.27, 1.36, 1.49, 1.32, 1.72, 0.54, 1.70, 0.61, 1.48, 0.56, , 2.00, 0.13, 0.20, 1.46, 0.56, 0.30, 0.47, 0.74, 0.55, 0.50, 0.54, 0.75, 0.39, 0.69, 0.41, 1.07, 0.39, 0.51, 0.48, 0.46, 0.45, 0.91, 0,27, 0.86, 0.63, 1.22, 0.84, 2.71, · 0.61, 0.36, 0.87, 1.14, 0.78, 1.52, 0.8_6, , ff+, u+, K+, , NHt, (CH3)2NH{, (CH3)3Nff+, (Cff:J)4N+, C5H5Nff+, H3Q+, (H20)2H+, (H20)3H+, CH;-, , E.,,, 45.()(), 11.12, 3.78, .4.31, 3.21, 2.60, 1.96, 1.81, 13.27, 11.39, , l 1.21, 10.68, 19.70, , 13.03, l,45, 0.10, 4.31, 0.10, l,33, 2.36, 1.33, 7.89, 6.03, 4.66, 4.11, 12.61, , IJo.ll, 24.lJ, 20.)9, 18.Jl, 20.Jl, 15,95, , 8.JJ, 21.Ji, 20 01, 7,)6, 2.34, , -3.25, , 55,IYJ, , 7.4: Would pyridine (C5H5N)' be. closest. in acid-base behavior toward solutes to a primary, secondary, or tertiary ·alkyl amine?, ·, ,, ·, , EXAMPLE, , Solution:, , The E and C values for pyridine fall between those for CH 3 NH 2 and (CH 3)2NH, so, pyridine ,should be intermedia~e in acid-base behavior between prim_ary and secondary amines., , r, , A modification o_f Equation (7. 75) by Drago et al. 16 adds a term, W, a constant contri_bution to the enthalpies of-reaction fot a p~ti~ular acid (or ba:se) that is independent of the, bases (or acid,s) -r eacting., (7.77), , The term Wis usually zero for neutra_J acids reacting ·_with neutral ~ases. As an exce~tion., this term would be the enthalpy required for the dissociation of a dimeric acid pnor to, combination with a base., ., . ·c, For reactions of a cationic acid with a neutral base, a neutral acid with an amtd, base, or a-cationic acid ,with an anionic acid base, the amount of charge transfer invodv~y, requires an equation of the form of Equation (7. 77). Reactions of ions can be ha nd ie d Ts, replacement of W with two additional parameters: R,.. for the acid as the receptor an, for the base as the transmitter. Values for R,.. and Ts are given in Table 7.6., (/,78), , 16, , R. S. Drago, N. Wong, C. Bilgrien, and G. C. Vogel, lnorg. Chem. 1987, 26, 9., , J, , I

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345, , 1, , .. Acid• and 8a1t•, c~apttr '·, , ,bl 7,6 EandCparameten(Equation(7,78)], e e acid11 and ba11e11- (Continued), for 80111, Base, Ta, Ca, Ea, , 1, , [JaSt, , 2.31, 2.16, 1.80, 1.21, 2.35, 0.80, 1.78, 1.64, , Nlh, , CH]OH, C2H50H, C6"6, H2S ·, HCN, HiO, , 0.56, 0.59, 0.64, 0.75, .0.54, 0.83, 0.73, 0.83, , 2.04, 3.12, 4.21, 5.61, 3.30, 6.72, 3.54, 0.71, , Ea, , Ca, , 1.80, 1.85, 0.70, 0.04, 1.19, 2.28, , 0.65, 1.09, 0.45, 1.56, 0.10, 0.10, , r., 0.70, 0.70, , 0.81, c1M.JH2, 1.13, (Cff3)zNH, o'. 90, (CHJhN, 0.43, c2H,NH2 ., HC(C2ff4)3N, 37.40, 4.28, C,H,N, p9.73, 12.30, 3.76, · CHJCN, 7.50, .c1'I, 5.86, 3.21, HC(O)N(<;:ff3)2, 6.74, Br0.74, 1.31, 2.19, 6.26, (dmO, 2.97, 5.48, 10.76, 1.63, I.SO, 9.20, (C2H,)z0, 6.52, 7.23, 0.71, 1.29, ., 1.86, 50.73, 4',60, O(C2RihO, 10.43, ow, 33.77, (CH3)2SO, 4.42 ', 10.03, 0.65, 1.47, CH)o2.40, (dmso), 0.73, I.SO, 1.68, (CH3)zO, 1.07, -3_75, (, ., 0.25, (CH3)zS, I (),9() ., ,,, 3.44, 1.46, ' (CHJhP, " •Data reproduced with permission from R. S. Drago, D. C. Ferris, and N. Wong, J; Am. Chem. Soc. 1990,, JIZ. 8953 and R. S. Drago, N. Wong, and D. C. Ferris, J. Am. Chem. Soc. ·1991, HJ, 1970., bThese parameters yield enthalpy values in kcal/mot adduct., ' The original sources give parameters for additional-acids and bases_and give limitations of dat~ for some, , cw, , values., •l, , Gas-phase acid-base reactions of ions involve very :large charge transfer. Note the, very-large change in parameters for W compared to,ttie_W(H20)n species given in Table, 7.,6. These effects show that proton affinities are_-~ot good guides to the interpretation of, ,, , acid-base reactions in solution., 1, , EXAMPLE, , 7.5: Calculate -t:.H for t~e c~~bination ·of W ;with 'H20 successively to produce, , , HJo+, W(H20h, W(H20h, and W(H2~)4 . Compar~ the resul!5 ., . Solution: For W + H 0, H30+, .-tiff ;::: (45.00)(2.28) + (13.03)(0. IO) +, 2, (130.21)(0.43) = 159.89, kcal/mol (669 kJ/rriol) Experiment~ value: -!:.ff = 166.5 kcal/mol., For Hlo+ + H20 ' -, , W(H20h,, , ., , -Ml = 39.65 kcal/mol (166 kJ/mol), r, , For H+(H 20h + H~O, For W(H 20)3 + H20, , •, , •, , ., ,1, , W(H20)3,, ', ,, -t:.H = 29.7 kcal/mol (124 kJ/mol), -, , W(H20).,, -t:.H = 27.0 kcal/mol (113 ~Jim?)), , Obvi;usly the enthalpy ~ban~~ is very large for formation of }{30+' with smaller enthalpy, changes for each additional H20,