NOTES
1722
Vol. 67
former case the transmitted beam is effectively diffused but, with water present, the beam remains collimated, though somewhat fuzzy. I n the case of the semioctagonal cell, the expected decrease is observed for -90”. The ( Z - ~ ~ / 1 ~ ~ ) / ( Z e / ~6 )~ ) ~ s i n ratios without Mylar film confirm the fact that for geometrical reasons there is no effective reflection of light scattered in the 4-45 and +135’ directions in this cell.
TABLE I REFLECTION EFFECTS FOR VARIOUS SCATTERIXG CELLSa Cell e Ratiob Square, 30 X 30 mm., clear glass -90” 1.043 Cylindrical, 26 mm. i.d., flat en-90” 1.045 trance and exit windows, inside -45” 1.038 0 to 180’ surface frosted - 135” 1.047 Semioctagonal, 40 X 40 mm., -90” 1.046 clear glass -45O 1.043c Fig. 1.-Percentage decrease in conductance produced by p-135” I.048c nitroaniline. Solid curve, ButNBr a t c = 9.70 X variable Black Mylar film, dull surface facing center of ceII, placed PYA. Numbered points described in text. inside of cell covering +90° face for square and semioctagonal cell and 0 to 180’ surface for cylindrical cell. Ratio of scattering ratios without and with Mylar film in place. (1.-$0/1,~)/ the acetonitrile molecules which by hypothesis are sol(Io/Iw)(sine) without Mylar film. vating the bromide ions, and therefore slow the latter Q
The results summarized in Table I provide experimental verification for the assumptions made in deriving the equations presented to account for reflection effects in square, sernioctagonal, and cylindrical calls.
ELECTROLYTE-SOLVENT IKTERACTION. X. DIPOLE SOLVATION BY ALESSAXDRO D’APRAKO~ A K D RAYRIOND RI. Fuoss Contribution No. 1751 from the Sterlzng Chemastry Laboratoi y, Yale Unzvereity, iVew Hacen, Connecticut Recezzed February 26, 1966
Solvents of high dielectric constant obviously are composed of polar molecules. When an electrolyte is dissolved in such a solvent, the solvent dipoles in the immediate vicinity of the ions must be oriented by the ionic fields. h choice between two extremes may be made in the model used to describe the system: (1) treat the solvent as a continuum and consider volume polarization or (2) treat solvent molecules which are nearest neighbors to ions as individuals and use the continuum for more distant solvent. We present herewith experiments which show that the second model is more realistic, in that it accounts for a variety of experimental detail which cannot easily be explained on the basis of a continuum. Consider acetonitrile (D = 36.0) as solvent; the molecules are fairly small and have a dipole momentZof 3.51. If we locate the dipole as a point dipole at the nitrogen atom, and estimate distances using Hirschfelder models, the potential energy of an acetonitrile molecule in contact with a bromide ion is 1.5-2.0 times k T . This is almost enough energy to stabilize an aggregate Br-.CH3CN; let us make the working hypothesis that, due to electrostatic attraction, one acetonitrile molecule on a time average stays with the bromide ion (“solvates” it). Experiments on the two-component system Bu4NBr in acetonitrile cannot test this hypothesis. But suppose we nom add a much stronger dipole, such as p-nitroaniline (PKA) whose moment3 is 6.32. We would expect that the PNA would displace (1) On leave of absence from the Universlty of Palermo. Grateful aoknowledgment 18 made for 8, Fulbright Travel Grant and for a DuPont Postdoctoral Research Fellowshlp. (2) G. I,. Lewis and C . P. Smyth, J . Cfzern Phgs., 7 , 1085 (1939). (31 C. G. LeFdvre and R. J. W. LeFBvre, J. Cham. Soc., 1130 (1936).
down, because PK‘A is much more bulky than RileCPu’. The prediction was therefore made that addition of PNA to a dilute solution of Bu4NBr in MeCN would decrease the conductance, to an extent proportional to its own concentration. The data of Table I verify the prediction; herec’is the concentration of PNA (moles/l.), TABLE I EFFECT OF PNA ox COXDUCTAXE OF BudNBr IX MeCX c (Bu&Br) = 0.9704 X 10-3 10%‘
AP
00
150.29
1 091
150.07
2 208
149.83
4.351
149 35
8 617
148.44
- &A/Ac’
202 208 216 215
Ap is 1000~(obsd.)/c, and AA/Ac’ is the chord slope from the origin to the corresponding data point. The total effect (1.25%) is far too large to ascribe to any changes in bulk properties of the solvent caused by addition of PYA: the dielectric constant of a solution of PXA a t c’ = 8.813 X was 35.95 f 0.05 us. Do= 36.00 and the viscosity was 3.448 X 10-3 us. 3.449 X The specific conductance of this solution was 1.63 X low7 ( K ~= 1.3 X which mas a magnitude smaller than 1% of the specific conductance (1.4584 X of the Bu&Br solution. A sniall correction was made for the density changes; at c’ = 0 (Table I), p = 0.77695, and at c’ = 8.617 X lou3,p = 0.77768. Further experiments were then made, with the results sho\Tn in Fig. 1, where lOO(A - &)/A is plotted against c’. Assume that a displacement occurs
RTeCN.Br’
+ PSA
PKA.Br’
+ MeCN
(1)
where the corresponding mass action equation is [PKA.Br’]/ [IUeCN.Br’][PYA] = K
(2)
(due to the enormous excess of solvent, its concentration has been absorbed in the constant K ) . Abbreviate by setting [PXA-Br’] = 2 ; then [RIeCN.Br’] = (c - z), where c is the stoichiometric concentration of
NOTES
August, 1963 BurNBr. The equivalent conductances Ap of Table I were computed as 103~/c,where K is the observed specific conductance a t a given value of c’, with c fixed a t 0.9704 X 10-3. Letting XI, XZ, and A3 represent the conductances of the ions Bu4N +, MeCN Br ’, and PNA. Br’, respectively Ap
Xi
4- (1 - z/c)X~ 1- XAB/C
A - (x/c)(X, -
X3)
(3) (4)
(5) where AX is the difference in conductance of bromide ion solvated by acetonitrile and by PNA, and (2) has been substituted in (4) to get (5). Then y, the ordinate in Fig. 1,is given by
1723
able. Consider a solution containing N 1 large cations, Zl small anions, Z z dipoles stronger than solvent (e.g., PKA in the above example), and Z3 anion-dipole complexes in a total volume 8. Ad$ 6 2 more dipoles; consider them as point dipoles whme potential energy is zero unless they strike a target vc+$ume Y which represents the volume of an anion plus dipole; in Y, let the potential energy be plcT where p ‘ i s a pure number. Then
- 6Z1 = 6Z3 = ZlveP6.Z
A -. AX K[PNA]
2, =
lOOK(Ah/A)[PNA]
(6)
i.e., linearity in Pn’A as observed. Point 1 of Fig. 1 corresponds to c = 1.156 X BurNBr; a t e’ = A = 156.56. The value of y is a little 8.63 X smaller than a t c = 9.70 X over half of this difference is due to the larger A a t the lower concentration of salt. As eq. 6 predicts, y is primarily determined by the concentration of PNA, independent of salt concentration, because the ratio x/c appears in (2) and (4). If the model is correct, larger ions should show a smaller effect. Point 2 shows the effect of PNA a t c’ = 8.65 X 10-30nBu4N.BPh4at c = 1.018 X The total effect is only 0.4%; if we split it equally between the two ions (which are nearly the same size), then the effect on bromide ion is 1.070, or five times as great. Point 3 corresponds to tetrabutylammonium picrate, c = 10.13 XlO-4 and c’ = 8.82 X 10-3; again, with both ions large, the decrease in conductance is small. On the other hand, if we go to the bromide of a smaller cation, the total effect should increase. Point 4 for and MerNBr at c = 9.87 X PKA at c’ = 9.15 X 10-4 a t first glance appears to contradict the whole argument. But in acetonitrile, with D = 36, salts with both ions small show some association to pairs: for example14for Me4N.NO3 in acetonitrile, the association if we assume about constant K A is 23. At c = the same association constant for Me4NBr, the conductance would have about 2.5% ion pairs. Addition of PXA, by association with bromide ions, would by mass action increase the dissociation of ion pairs, increasing the conductance and opposing the solvation effect; the net effect would therefore be a smaller decrease in conductance. The final experiment, shown as point 5, was therefore made. It corresponds to c’ = about a and Me4NBrat c = 1.163 X 8.47 X tenth the concentration of point 4 and where association effects are nearly negligible. Now the effect for MelNBr a t a given PXA concentration is greater than for BurNBr, as it should be. We therefore believe that our experiments demonstrate that ions and dipoles can associate under the influence of electrostatic forces. Incidentally, these experiments also confirm the triple ion hypothesis6 according to which an ion pair, acting as a dipole, can associate with a single ion under the action of mutual Coulomb forces. A simple calculation shows that the order of magnitude of the observed change in conductance is reason(4) D.
S. Berns and R. M. Fuoss, J . Am. Chem. Boc., 83, 1321 (1961).
(5) R. M. Fuoss and C . A . Kraus, ibzd., 68, 2387 (1933).
(7)
and
6Z? = (V
- ZlV) 62 = v 62
(8) byuse of Boltzmann’s methods.6 Dividing (7) by (8) and integrating 2 1
-- Nl exp (- &YeP/ V )
(9)
The exponent is small compared to unity; heme approximately
Z 3 = NlvePZ2/V (10) and converting to moles/l. (L is Avogadro’s number) and using our earlier symbols for concentrations of the various species
x/c [PNA]
=
LveP/lOOO
(11)
or
K = LveP/lOOO = 2.52 X 10-3i3eP
(12) if we represent the volume v as a sphere of radius i (in Angstrom units). From the slope of the y - c’ line of Fig. 1, ( K AX/A) = 1.4. Suppose we estimate AX/h as and i as 4. This leads to p = 3, i e . , a n energy of association of about 3kT between a bromide ion and a molecule of p-nitroaniline. (6) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Inc., 1959, Chapters 16 and 18.
T H E IONIZATION CONSTANTS OF 0-NITROPHENOL AND 4-NITRO-m-CRESOL FROM 5 TO 60’ BY R. A. ROBIMON AND ADAMPEIPERL Solutaon Chemastry Sectzon, National Bureau of Standards, Washangton, D. C.
Receaved February 18, 1965
There is some evidence1 that, for a series of substituted anilinium ions, the enthalpy change on ionization is a linear function of the change in free energy on ioniza,tion. It would follow that, if two acids of like structure have similar pK values, their enthalpy changes on ionization should also be similar. The ionization constant of p-nitrophenol has already been measured? over a temperature range; in order to test this postulate, sjmilar measurements have now been made with o-nitrophenol and 4-nitro-m-cresol in aqueous solution. o-Nitrophenol (Eastman) was recrystallized once from methanol (m.p. 45.0’) : 4-nitro-nz-cresol (Calbiochem) was recrystallized twice from water (m.p. J. Chem floc., 2572 (1981). (2) G. F. Allen, R. A. Robinson, and V. E. Boner, J . Phys. Chem., 66, 171 (1962). (1) A . I. Biqgs,
