273
NOTES
time. l1-I5 Shereshefsky’s equation is similar in form to the latest of these equations, Eberhart’s,16 which Schmidt‘G has shown is a first-order approximation of all the earlier equations and which Ramalirishna and Suri” have extensively analyzed. Shereshefsky has utilized the same assumptions and approximations as Eberhart, but his equation generates more detailed information about surface region structure than Eberhart’s equation from the same surface tension data. (11) B. V. Srykowslti, 2’. Phys. C’hem. (Leiprig), 64, 385 (1908). (12) J. W. Belton and M. G. Evans, Trans. Faraday Soc., 41, 1 (1945). (13) E. A. Guggenheim, “Mixtures,” Oxford University Press, London, 1952. (14) 3. H. Hildebrand and R. L. Scott, “Solubility of Wonelectrolytes,” Dover Publications Inc., New York, N. Y., 1964. (15) J. G. Ebsrhart, J. Phw,a. Chem., 70, 1183 (1966). (16) R. L. Schmidt, ibzd., 71, 1152 (1967). (17) V. Ramaltrishna and S. K. Suri, Indian J . Cliem., 5, 310 (1967).
Calculation of the Wavelength Maxima for Some Triphenylmethane Dye Carbonium Ions by Edward 0. Holmes, Jr. Hughes Eesearch Laboratories, Ilrlalibu, California 90366 (RPceined June 1’7, 1968)
In a former publication* the author pointed out some interesting relations between the frequencies of the peak values),,A,( of the absorption bands of the three triphenylmethane carbonium ions (crystal violet (CV+), malachite green (JIG+), and sunset orange (SO+)) as related to the structure of these ions. Since then the author has extended the investigation to include several more carbonium ions of this type and has found the ratios to be quite general and consistent, so much so that they are used as a guide in arriving at an empirical equation by which, , ,A can be calculated with a fair degree of accuracy for most of the bands. Table I shows the frequency ratios of the ions considered. The dyes are divided into three groups: (a) synimetrical, those in which all three nitrogens in the para position are bonded to hydrogen atoms or the same group : p-roseaniline2 (RO +), crystal violet (CV+), ethyl violet (EV+),and hexahydroxyethyl violet (HHEV+); (b) semisymmetrical, those having one phenyl group containing no amino group : Dobner’x violet (DV+), malachite green (MG +), brilliant green (BGf), and his [p-(diphenylamino) phenyl lphenylmethyl carbonium ion (2DPP+); and (c) unsymmetrical, sunset orangel (SO+). All solutions were in absolute ethyl alcohol. The ions were obtained from the leucocarbinols or ethers by adding a trace of acid or from the leucocyanides by photolysis with minimum exposure.
Table I : Frequency Ratios of the Absorption Maxima for the Carbonium Ion Dyes Ratios of
vmlLX--------
_ I ~ -
Ions
g:x
h:g
ET:+ HHEV+
1.89 1.93 1.92 1.93
1.21 1.21 1.21
DV + MG + BG + 2DPP +
RO +
cv
so
+
n:y
y:x
g:y
1.85 1.93 1.96 2.07
..* ...
...
1.27 1.26
1.81 1.82
...
1.41 1.45 1.45 1.44
1.31 1.35 1.36 1.42
...
1.31
1.81
, . .
1.35
+
...
A large number of expressions for the calculation of the Amax of the various bands were tried but none gave results as good as the relative!y simple formula stated below which we converted to a form that would yield results in wavelengths (in millimicrons) rather than frequencies. A,,
=
l.lN(A,
of the g band, in mp)
The g band is chosen for reference as it is common to all ions and can be measured with a fair degree of accuracy on a Gary spectrophotometer. N , the exponent of 1.1,is designated as the band number. The base 1.1 is used because when raised to the appropriate power it reproduces so many of the band ratios such as 1.21, 1.47, and 1.95, for example. Tables I1 and IT1 show our results.
Discussion The band number N is assigned the values of 7, 3, 0,
-2, and -3 for the bands x, y, g, h, and n, respectively.
For the symmetrical ions which have x, g, and h bands only 7, 0, and -2 are used. With one exception the agreement between the measured value and the calculated is fairly good. However, when the band numbers are applied to the semisymmetrical and unsymmetrical ions, the agreement is not as good. (By deviating from the above sequence of band numbers and using 6.5 instead of 7 for the x band of DV+, - 1in place of - 2 for the h band of HHEVf, etc., the agreement is very much closer.) At present we cannot explain the significance of the band numbers chosen. On calculating the ratios of the frequencies of the y :x bands of six other carbonium ions from the work of Tolbert and others4in which the phenyl group was substituted progressively for the methyl groups in malachite green, we find the ratios to be remarkably con(1) E. 0. Holmes, Jr., J. Phys. Chem., 70, 1037 (1966). (2) fIighly purified, supplied by Dr. John Vandenbelt of the Parke
Davis Co. (3) E. 0. Holmes, Jr., J . Phys. Chem., 62, 884 (1958). (4) B. M. Tolbert, G. E. K. Branch, and B. E. Berlenback, J . Amer. Chem. Soc., 67, 890 (1945). Volume ‘79, Number 1
January 1969
274
NOTES
Table 11: Wavelengths for Amax for the Bands of the Carbonium Ions Calculated by the Empirical Formuia for Symmetrical Ions" Xmax
7--
Dye ion
RO +
Band
mfi
X
547 290 240
g
h
cv+b
X
g h
EV+
X
g
h
H€IEV+
x g
h
(obsd)--------, eV
,__--
XmiLr !calcd)-------
-----Difference----mfi
N
mfi
OV
2.28 4.28 5.17
7 0 -2
566 290 238
2.19 4.28 5.21
19
0.07
2
0.04
589 305 252
2.10 4.06 4.92
7 0 -2
586 305 251
2.12 4.06 4.94
3
0.01
1
0.02
592 -306 254
2.09 4.05 4.88
7 0 -2
593 306 253
2.09 4.05 4.90
1
0.00
1
0.02
590 308 280
2.10 4.03 4.43
7
601 308 254
2.06 4.03 4.88
11
0.04
26
0.45
' This group contains no y and n bands.
0 -2
eV
* Reference 1.
Table 111: Calculated Wavelengths for Semisymmetrical and Unsymmetrical Carbonium Ions from Formula Dye ion
DV+ a
Band X
Y g h n
MG+
X
Y g
h n
BG +
X
Y g
h n 2DPP+
X
Y g
h n
SO+b
eV
N
____ mfi
2.20 3.11 4.07
7 3
595 405
2.08 3.06
31 6
0.12 0.05
622 428 318 257 236
1.99 2.90 3.90 4.94 5.25
CI
3 0 -2 -3
620 423 318 262 239
2.00 2.93 3.90 4.73 5.19
2 5
0.01 0.03
11 3
0.21 0.06
627 427 317 282 235
1.98 2.90 3.91 4.92 5.28
7 3 0 -2 -3
620 422 317 262 238
2.00 2.94 3.91 4.73 5.21
7 0
0.02 0.04
10 3
0.19 0.07
680 470 330 ? ?
1.82 2.64 3.76
7 3 0
644 439 330
1.92 2.83 3.76
36 31
0.10 0.19
2.68 3.59 4.70 4.86
3 0 -2 -3
459 345 287 259
2.70 3.59 4.31 4.79
4
0.02
23 4
0.39 0.07
564 399 305
... 463 345 264 255
eV
-----Difference----mfi
eV
0
R. Meyer and 0. Fischer, Ber. Bunsenges Phys. Chem., 46, 70 (1913).
stant, namely, 1.44 (=kO.O1), and consistent with our values. This ratio is affected very little by the nature of the groups attacked to the nitrogen atoms. Unfortunately, Tolbert did not determine the h and n bands for the dye ions. The g:x ratios are the next most constant but tend to increase with some property of the groups attached to the nitrogen atoms. This extension of the author's earlier work' strengthens the previous assignment of the various induced The J o v n a l of Physical Chemistry
Xmax (ca1cd)-
?
Y h n
Amax (obsd)--------.
9
X
g
a
---_-
Reference 1.
Reference 3.
dipoles to the structure of the ions. Note that the two longest ultraviolet bands of aniline and dimethylaniline are in the ratio 1.21, which corresponds to the h : g frequency ratio in the ions RO+, DV+, and EV+. The corresponding bands ratios of BG+ and MG t are 1.26 and 1.27, respectively, arid that in SOT is 1.31, undoubtedly due to the fact that these ions contain phcnyl groups without a substituted amino group in the p a r a position.
