June 20, 1958
COMMUNICATIONS TO THE EDITOR
3163
are used until the one is found which linearizes the y-x plot. The slope gives K A ; then from y ( 0 ) FUNDAMEXTAL RESEARCH GLENE. ARTH = ( J - KAA~),J and hence a are evaluated. If JOHN FRIED KA is known (e.g., by extrapolation of log KA vs. MERCKSHARP& DOHME LABORATORIES DIVISION DAVIDB. R. JOHNSTON l/D), define AJ = (A,' K~cyofZA,,). A plot of DALER. HOFF AJ against cy0 is linear with slope and intercept MERCK& Co., INC. RAHWAY, NEW JERSEY LEWISH. SARETT ROBERTH. SILBER equal to J and Ao, respectively. Alternatively, if (A,,' - Jc-yo). Then a MERCKINSTITUTE FOR HERBERT C. STOERK a is known, define AK THERAPEUTIC RESEARCH CHARLES A . WINTER plot of Ax against cy@A,, determines AO and KA. RECEIVED MAY12, 1958 Equation 4 applied to the Mcrcier and Kraus5 data for BudNBr in dioxane-water lead to a-values 4.8 _< a _< 5.4. The spread is much less than that CONDUCTANCE OR IONOPHORES reported before; we therefore believe the present Sir : equations represent a better approximation. Deequations were presented which tails will be presented later. permit calculation of conductance for 1-1 electro( 5 ) P. Mercier and C. A. Kraus, Proc. Nul. A c a d Sci., 41, 1033 lytes in terms of three arbitrary parameters: (1955). Bo, the limiting equivalent conductance, a, the INSTITUTO DI CHIMICA-PISICA center-to-center distance a t contact of cation and UNIVERSITA RAYMOND M. FIJOSS DEGLI STUDIDI ROMA anion and K-4, the association constant. These ROME,ITALY RECEIVED MAY1, 1958 equations have since been revised; the final results, given below, are much more convenient for practical computations. The algebraic form of RETARDATION OF EXCHANGE PROCESSES BY the equations has been rearranged. The dilemma MOLECULAR ASSOCIATION : METHYL ALCOHOL regarding the Stokes radius in the velocity term of Sir: the relaxation field has been resolved. A virtual I n high resolution nuclear magnetic resonance force arising from asymmetry of osmotic pressure has been included. When association is slight, the studies of liquids, exchange processes frequently preclude the observation of spin-spin multiplets. cs/2 terms are negligible for Ka < 0.2; when association is not negligible, the c'/' term in ac- I n specific cases one can reduce the rate of exIn tivity completely swamps the J Z term; hence the change by carefully purifying the latter has been dropped. I n order to save space, all some instances, however, an alternative procedure symbols not explicitly defined here will have the can be employed which provides information concerning exchange processes and molecular commeanings given in refs. 1-3. Define A, = (1 Fc) where Fc = 5$/2. This plexes in liquid systems. This is achieved by addis the observed conductance, corrected for volume ing to the sample a complexing agent which prefviscosity (see first column, p. 330g3). This be- erentially forms a stable molecular complex with comes the dependent variable if viscosity data are the sample under study and, consequently, deavailable; if not, the viscosity effect is approxi- creases the rate of exchange. As an example, consider the proton magnetic mated by moving (- FAoc) to the right as before. Then for negligible association, A, = (A0 - Scl/' resonance spectrum of methyl alcohol. The spinEc log c Jc), where J = (VI A. a)replaces spin multiplets which should be observable in the spectrum of this molecule have long eluded detecthe former J1. Here tion, presumably because of exchange effects. On U , = (KzUzb2/12C)[h(b) + 0.9074 111 ( K U / C ' / * ) ] ( 1 ) the other hand, in solutions containing sufficient uz = a4 + (ll~KU/12C'/Z)- (~abB/8C'/2)[1.0170f quantities of acetone, hydrogen bonding increases In ( K b / C % ) ] (2) the lifetime of -OH group protons in enough moleh ( b ) = (2b2 2b - l)/bJ. cules to reveal the fine structure. Figure 1 shows (3) Define A,' = (A, Scl/z - Ec log c). For the the spectrum of methyl alcohol as observed a t 40 Owen and Zeldes4data on potassium halides a t 25", Mc. in a solution of acetone containing 25% CHSOH a plot of A,,' against c is accurately linear. The in- by volume. The theoretical spectrum for the tercept a t c = 0 evaluates A0 and the slope gives J . special case of J / S = 0.21 is added for comparison. The 8. - values found are: KCl, 3.07; KBr, The experimental trace gives J = 4.8 see.-' and 6 3.26; KI, 3.50. These values agree well with the = 22.8 sec.-l. It should be noted that two of the lines in the observed -OH multiplet are not presums of the corresponding crystallographic radii. When association is not negligible, 70 is com- dicted theoretically. One of these has been shown Sc'/z to be water; the other is attributed to an additional puted as before. Then A,,' becomes (A,, impurity. y ~ - ' /~ Ec yo log c yo) where Supplementary experiments with methanol and At, = Ao - Sc'/2yo1/~ Ecyo log C Y O + J ~ y oother molecules have shown that (a) by varying &CYrif'& (4) the acetone concentration the internal chemical The quantities AA, y and x are redefined as follows: shift can be changed and the concomitant alteraAA = (A,,' - A,) = ( J c y ? - KACY@A,>;y = tions in fine structure observed and compared AA/cyo and x = ?A,,. Again trial values of A0 (1) R. S. Gutowsky, D. W. McCall and C. P. Slichter, J. Chum. Elmer Alpert in coordinating the clinical investigations.
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(1) R. M. Fuoss and L. Onsager, J. Phys. Chcm., 61, 668 (1957).
(2) R.M. Fuoss, THISJOURNAL, 79, 3301 (1957). (3) R. M. Fuoss and C. A. Kraus, ibid., 79,3304 (1957). (4) B.B. Owen and H. Zeldes. J . Chcm. Phys., 18, 1083 (1950).
Phys., 21, 279 (1953). (2) R.A. Ogg, ibid., 22, 560 (1954). (3) I. Weinberg and J. R. Zimmerman, ibid.. 23, 748 (1955). (4) J. T. Arnold, Phys. Reo., 108,.136 (1956).
