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Iodine complexes in inert solvents
JOURNAL
OF
MOLECULAR
Iodine Part
8, 373-382 (1962)
SPECTROSCOPY
Complexes
XIII. The System:
P. A. II. DE MAINE Department
in Inert Solvents
of Chemistry,
Iodine-Benzene-CC& AND M. M. DE Mach-E
University
of Mississippi,
University,
Mississippi
AND CHARLOTTE Department
of Mathematics,
7’niversity
FROESE
of British
Columbia,
Vancouver,
B.
C.,
Canada
Equilibrium constants, heat of formation, and molar extinction coefficients for the benzene-iodine complex, together with molar extinction coefficients for uncomplexed iodine and benzene have been calculated by means of an electronic computer from spectrophotometric data at fifteen wavelengths between 2700 A and 3500 A for the benzene-iodine-carbon tetrachloride system at 15” and 45” C. Deviat,ions at high benzene concentrations can be qualitatively explained by the additional reactions: benzene
+
benzene
(complex)l
+
-
IS A
K, Kg
(complex)l (complex)z
with K1 small. INTRODUCTION
Since publication of the Benesi-Hildebrand equation (1) in 1949, several workers (2-5) have used modified forms of this equation t’o calculate formation constants and molar extinction curves for one-to-one complexes from spectrophotometric data. To solve the Beneei-Hildebrand equation and its modified forms, it is necessary to assume t#hat t,he molar ext’indion curves for each of the uncomplexed components do not change in the presence of each other. Orgel and Mulliken (6) suggest, in their contact charge-t#ransfer theory that this assumption is not valid for iodine solut#ions. They attribute the contradictions of Mulliken’s charge-transfer theory (7), observed for iodine complexes (8) to changes in t,he molar extinction curves for the separate components in the presence of each other. Spectrophot,ometric data for iodine-n-heptane-perfluoro373
X-4
1lE MAINE
IlE MAINE,
ASI> FROESE
hcptane solutions collected by Evans (9) were cited as supporting evidence (fj). McGlynn (10) has thoroughly reviewed these theories. Scott (.$) has stated that analysis of spectrophotometBric data w&h the HencsiHildebrand equation, or its modified forms does not yield consistent results. He also emphasized t,he role played by the activity coefficient’ for each of th(b species presem at equilibrium. Shinoda and Hildebrand (11) have published thermodynamic data for the iodine-benzene system whirh was interprct,rd as supporting the Orgel-Mulliken hypothesis (6). dc Maine (12) has shown t,hat for systems with reversible one-t’o-one complcses, formation constants and molar extjinction curves for each species present (‘a11be c*alrulated from spectrophotometric data without’ assumpt~ions about the molar extinction curves for each separate species. Here WC report a t,cst of the Orgel1Iulliken hypothesis wit,h spectrophotonx+ric data for t)he henzenr-iodinrcarbon tetraehloride system. II. KSPERIMENTAI, Rlallinckrodt reagent grade benzene, Fisher spectrograde carbon tetrachloridc and n-heptane were purged wit’h dry nitrogen (dew point -40°C) befort> use. Fisher certified reagent grade iodine (resrtblimrd) was used wit,hout further purification. Solut,ions cont,aining iodine dissolved in pure benzene, or in henzcnc~ plus carbon trtrachloride were made in a dry nitjrogen atmosphere (13) For earh solution, there was prepared a reference sohuion in n-hept,ane whicah contained the sam(a amount, of carbon tet’raehloridc and no iodine or benzene. In wpuratc~ rsperiment.s, and in published work (9,Z,$), it has been shown that rr-heptam~ does not, absorb light in the spectral region studied (2700A ---f 4000 .I), All measurements were made with t,wo calibrated Reckman DI- Spwtrophotometers, equipped with photomultiplier t’ubcs, tempcrat,urr c~mtrol a~‘cessories and four matched one wntimet,er glass-stoppercd quartz snmplc (*ells in a dry nitrogen at,mosphere 11.5). Optical densities at 15 and 45°C’ for c~a& iodilic-bellzene-carboil t,etrachloride solut’ion were measured at 50.1iritcrvals I,f~twfw~ 2700 A and 3700 A, with the cwrrcsponding ;rz-heptanc-carbon t,etrachloride solution as reference. Opt’ical densities between 0.060and 1.000 \vcr(l reproducible to within 0.002 unit. Spectra of t’wo hundred solutions with twenty different benzene concrnt rations (mole fractions bet’ween 0.048.i and 1.OOO) (and ten differem iodine c*onc*ciltrations between 8.04 X lo-’ and 4.01 X IO-%I were measured at 1.5nttd4.5”(1. Spectral data were ohtjaincd for t’wenty iodine-caarbon trtrachloridc and t jvc’ttt,v bcnzenewrhon tetrachloride solutions. III. METHOI)
I’or thr
reversible
equilibrium
OF C.4LCI:I,ATIOS
reaction :
C6H6 + I2 A
Complex,
375
IODINE-BENZENE-CC&
with [GH,]
))) [IZ], the concentration
of the complex
c, = KC,Ce/(
(C,) is given by the equation
1 + KC,) )
(1)
with ( CI - C,) and (C, - C, = C,) the concentrations of uncomplexed iodine and benzene, respectively. According to Beer’s Law, the measured optical density D, at a given wavelength is related to the molar extinction coefficients and concentrations of bhe components by the equat’ion D = c,(C, Substituting
-
Cc) + E&‘B + EJ’~
for C, from Eq. (1)) this equation EI +
D= Kow define D = D -
&
CB
I+
becomes
CI +
(2)
EB CB .
cBCB ; t,hen from Eq. (2)) D = fICI + KqJIBC,
- KC,ii.
(Z3)
Equations ( 1) -( 3) were used to determine EB, tI , cc , and K. The data collected at a given wavelength, temperature and benzene concentration range (low benzene concentrations 0.043.5 to 0.2352 mole fraction units: high benzene concentrations 0.4815 to 1.000 mole fraction units) were arranged in matrix form, with columns and rows representing fixed iodine and benzene concentrations, respectively. The procedure was then as follows: Step 1. For each row, (CB = constant) eBCB was determined by fitting a straight line to t’he data with use of the least squares approximation. According to Eq. (2)) +CB is the intercept of the line at CI = 0. Step 2. The D mat,rix was computed as 15 = D - cBCB . TABLE
I
VALUEB FOR h-,eC,AND q DETERMINED WITH DATA COLLECTED AT 15°C BY THE PROCEDURE DESCRIBED IN STEPS 1-4 (A) AND IN STEP 5 (B), RESPECTIVELY. K IS IN MOLE FRACTION UNITS. Wave length m/J 280 285 290 295 300 305 310 315 320
s A 1.64 1.68 1.45 1.32 1.31 1.29 1.16 1.04 0.87
tc
B 1.67 1.56 1.57 1.45 1.42 1.32 0.97 0.98 0.57
A 13,000 14,700 17,500 18,900 17,900 15,900 14)300 12,200 10) 700
t1
B 12,800 15,400 16,500 17,600 16,800 15,600 12,800 10,700
A
B
86 83 104 109 75 51 33 32 19
109 89 79 77 55 53 ci2 38 19
2
^.
0.080 -0.015
0.099 0.005
0.114 0.002
0.127 -0.003
0.131 0.003
0.140 -0.004
0.1294
0.1507
0.1720
0.1931
0.2142
0.2352
0.065 0.002
0.0866
0.065 -0.002
0.049 0.002
0,065l
0.1081
0.035 0.001
0.0435
Iodine
0.382
Fr.
Benzene
Mole
0.275 -0.006
0.250 -0.006
0.244 -0.003
0.217 -0.002
0.194 0.005
0.189 0.014
0.139 0.001
0.115 -0.008
0.091 -0.002
0.062 -0.003
0.765
0.420 0.005
0.396 0.018
0.364 0.002
0.315 -0.011
0.275 -0.011
0.274 0.016
0.210 0.002
0.180 0.000
0.135 -0.002
0.092 -0.004
1.147
0.556 0.005
0.508 -0.001
0.472 -0.009
0.430 0.000
0.384 0.006
0.334 -0.010
0.296 0.018
0.235 -0.004
0.186 0.004
0.002
0.129
1.530
_
ior
5).
0.818 -0.009
0.772 0.013
0.709 -0.004
0.641 -0.001
0.579 0.012
0.510 0.001
0.420 -0.002
0.353 -0.002
0.275 0.003
0.185 -0.004
2.295
Iodine
is 3000
fractiuii
FC
= 16,839;
0.956 -0.007
0.892 0.005
0.820 -0.011
0.745 -0.003
0.670 0.008
0.590 -0.003
0.501 0.009
0.410 -0.004
0.320 0.004
0.215 -0.004
2.677
Concentration
Wavelength
K is in mule
1.090 -0.010
1.015 0.000
0.844 -0.012
0.759 0.001
0.670 -0.007
0.580 0.018
0.471 -0.001
0.361 -0.001
0.246 -0.004
3.060
Times
A.
umts.
cl=
10,000
(moles/liter)
11.6
1.236 0.002
1.159 0.022
1.050 -0.014
0.950 -0.011
0.860 0.008
0.760 0.001
0.640 0.005
0.525 -0.005
0.409 0.003
0.276 -0.005
3.442
13~~10~
iii the test.
iodiiie-benzcne-
defined
the indicated
K, EC and eI are
(AD)
AD value.
K= 1.1299;
0.686 -0.003
0.641 0.008
0.599 0.004
0.530 -0.007
0.470 -0.004
0.413 -0.015
0.360 0.010
0.295 -0.002
0.229 0.002
0.115 -0.003
1.912
the corresponding
(moles/liter)
eB CB,
II
(as per step
at 45°C.
rlot been recycled
10,000
TABLE (I,) aiid deviations
solutions
densities
is given
have
Times
D value
each
Concentration
data
tctrachloride
oplical
These
carbon
Measured
1.365 -0.007
1.280 0.014
1.175 -0.004
1.060 -0.006
0.954 0.007
0.840 -0.002
0.720 0.015
0.579 -0.010
0.454 0.003
-0.003
0.309
3.825
0.007
0.002
0.013
0.007
0.002
0.011
0.005
0.005
0.003
0.003
‘^BCB
IIa
0.484 -0.008
0.415 0.002 0.429 -0.003 0.440 -0.011
0.311 0.002 0.324 0.003 0.329 0.001 0.346 0.000 0.397 0.011 0.372 -0.009
0.261 0.005 0.263 0.002 0.270 0.002 0.271 -0.004 0.332 0.013 0.306 -0.006
0.200 0.003 0.209 0.004 0.210 0.003 0.210 -0.002 0.205 -0.009 0.234 -0.006
0.140 0.000
0.139 -0.001
0.146 0.002
0.155 0.002
0.147 -0.005
0.166 -0.004
0.083 0.000
0.081 -0.001
0.085 0.002
0.095 0.004
0.082 -0.004
0.101 -0.001
0.718
0.775
0.832
0.889
0.945
1.000
K = 0.659
0.470 -0.002
0.407 0.008
0.300 0.008
0.245 0.008
0.188 0.006
0.125 0.000
0.076 0.003
0.392 0.008
0.376 0.007
0.355 0.009
0.339 0.005
0.277 -0.001
0.231 0.002
0.185 0.006
0.117 -0.004
0.078 0.004
0.601
0.320 0.000
0.260 -0.006
0.230 0.007
0.165 -0.003
0.111 -0.006
0.070 0.000
0.542
eC
= -2,980
0.509 -0.012
0.452 0.001
0.440 0.003
0.425 0.003
0.410 0.010
0.388 0.004
0.365 -0.003
0.340 -0.014
0.297 -0.010
0.247 -0.011
0.202 -0.009
0.067 -0.002
0.482
5.419
Iodine Concentration
0.161 -0.004
(moles /liter)
0.110 -0.006
100,000 4.646
x 3.871
1.548
of Benzene
0.774
3.097
Iodine Concentration
0.580 -0.013
0.560 -0.005
0.534 -0.003
0.523 0.005
0.510 0.009
0.500 0.013
0.460 0.008
0.436 0.001
0.416 -0.002
0.371 -0.026
(moles,/liter) 6.968
EI = 5210
0.650 -0.014
0.630 -0.005
0.620 0.006
0.594 0.010
0.570 0.009
0.552 0.011
0.552 0.012
0.496 0.006
0.463 -0.004
0.433 -0.016
Below
100,000
6.194
x
These data have not been recycled (as per step 5). K is in mole fraction units. each D value is given the corresponding AD value. Wavelength is 3000 A.
2.323
Mole Fraction
TABLE
Measured optical densities (D) and deviations (AD) for the indicated iodine-benzenecarbon tetrachloride solutions at 45°C. eBCB, K, EC and cI are defined in the text.
0.720 -0.016
0.700 -0.004
0.670 0.000
0.650 0.007
0.611 0.001
0.590 0.002
0.590 0.020
0.551 0.008
0.510 -0.006
0.480 -0.017
7.742
0.029
0.023
0.022
0.020
0.025
0.027
0.017
0.020
0.020
0.021
‘BCB
2
.. ?Y
0.710 0.700
0.560 0.546
0.540 0.530
0.1931
0.2142
0.2352
0.061 0.064
0.061 0.066
0.074 0.076
0.064 0.064
0.056 0.062
0.560 0.570
0.570 0.580
0.060 0.060
0.600 0.581
0.1720
0.1507
0.1294
0.059 0.072
0.055 0.061
0.580 0.590
0.0866
0.710 0.720
0.060 0.061
0.610 0.590
0.0651
0.1081
0.060 0.066
0.730 0.610
0.0435
15°C
2800
2750
BUI2eIle
Mole Fr.
) at the
0.017 0.022
0.017 0.022
0.023 0.023
0.017 0.017
0.019 0.018
0.012 0.014
0.026 0.009
0.010 0.017
0.016 0.013
2850
1.11
1.08
1.15
1.14
1.13
2750
0.117 0.121
0.117 0.119
0.122 0.126
0.120 0.120
0.115 0.138
0.116 0.120
0.111 0.114
0.117 0.130
0.121 0.127
0.120 0.130
2800
45°C
) is
indicated
Coefflcwnts
Of each number pair (6:
iodine (cB
Molar Extinction
0.023 0.029
0.024 0.028
0.030 0.030
0.024 0.025
0.019 0.028
0.019 0.024
0.012 0.020
0.022 0.033
0.023 0.031
0.025 0.032
2850
1.000
0.945
0.034 0.034
0.035 0.034
0.037 0.035
0.889
0.0119 0.0121
0.0109 0.0107
0.0111 0.0109
0.0124 0.0118
0.0125 0.0128
0.044 0.044
0.715
0.043 0.041
0.0131 0.0150
0.047 0.049
0.718
0.832
0.0124 0.0129
0.0119 0.0114
0.0151 0.0148
0.0134 0.0134
2850
0.053 0.053
0.049 0.048
0.059 0.059
0.056 0.055
2800
15°C
0.660
0.601
0.542
0.482
BlXYZeIle
Mole Fr.
and temperahue.
) and in Ccl, plus
value.
wavelengths
in CCI, (ci
the upper and (eB ) the lower
benzene concentrations,
for benzene dissolved
TABLE III
2900
0.0074 0.0074
0.0061 0.0066
0.0060 0.0065
0.0065 0.0070
0.0064 0.0069
0.0074 0.0082
0.0062 0.0070
0.0061 0.0059
0.0081 0.0078
0.0071 0.0069
0.059 0.059
0.062 0.061
0.06’7 0.066
0.074 0.072
0.079 0.077
0.083 0.084
0.085 0.085
0.090 0.088
0.087 0.092
0.101 0.099
2800
2900
0.0120 0.0127
0.0118 0.0124
0.0127 0.0130
0.0133 0.0133
0.0145 0.0150
0.0164 0.0178
0.0061 0.0062
0.0053 0.0065
0.0056 0.0068
0.0060 0.0068
0.0067 0.0076
0.0077 0.0084
0.005 7 0.0072
0.0071 0.0073
0.0150 0.0158 0.0159 0.0157
0.0074 0.0069
0.0092 0.0092 0.0165 0.0164
0.0187
0.0189
2850
45°C
379
IODINE-BEXZENE-CCL,
Step 3. The constants K, Q , and Edwere obtained by performing a regression analysis on D with C, , C,C, , and CnD independent variables, as indicated by Eq. (3). Step 4. The deviation matrix (AD = D - eICI - K+2,C’, + KC’,o,) was computed for each D matrix : AD is the difference between t,he actually measured value and that predicted by Eq. (3) with the constants taken to be those determined in Step 3. Step 5. Elements in the D matrix with corresponding large deviations were discarded and Steps 14 repeated. On the whole this did not reduce significantly the scatter in the results but did provide an estimate of the sensitivity of the results on the data. This point is illust,rated in Table I. All calculations were performed on the ALWAC III-E computer at the University of British Columbia. Typical D (measured optical density) and AD (deviations) matrices, together with values of +,Cg , K, rI , and cc are shown in Tables II and IIa. IV. RESULTS
K, cc , es , and eI have been determined by the method just described at wavelengths between 2700 A and 3500 A from data for iodine-benzene-carbon tetrachloride solutions measured at 15°C and 45°C. These solutions contained either high (0.4815 -+ 1 .OOO)or low (0.0435 to 0.2352) mole fractions of benzene. The molar extinction coefficients for benzene (E=) and molecular iodine (Ed) were also determined at the same wavelengths and temperatures with separate carbon tetrachloride solutions. Molar extinction coeficients for benzene dissolved in carbon t,etrachloride ( cBS) and in carbon tetrachloride plus iodine (Ed) are given in Table III. Molar TABLE
IV
FORMATION CONSTANTS AND MOLAR EXTINCTION COMPLEX
COEFFICIENTS FOR BOTH THE
(CBHB.IL) AND MOLECIJLAR IODINE DETEFMINED
BENZENE-IODINE-CARBON
WITH
TETRACHLORIDE SOLUTIONS AT 15°C
DATA
FOR
AND 45°C.
AH Is THE HEAT OF FORMATION OF THE COMPLEX CALCULATED WITH VAN’T
HOFF’S
t1
EQUATION. k’ (mole fraction units)
CC
Wave length (A)
15°C
45°C
2900
79
2950
77
3000
55
3050 3100
15°C
45°C
58
16,500
31
17,600
12
53 62
AH Kcal/Mole
15°C
45°C
17,200
1.57
1.19
17,000
1.45
1.21
1.04
16,800
16,800
1.42
1.13
1.34
16
15,600
16,300
1.32
0.99
1.70
32
14) 300
15,000
0.97
0.75
1.52
Average
1.45 (~kO.24)
1.63
380
I>E MAINE
I)E MAINE,
ANI_, FROESE
extinction coefficients for molecular iodine (Q) and for the complex (cc) determined from data for the benzene-iodine-carbon tetrachloride solutions, are given in Table IV. Formation constants (K) and values for the heat, of formation computed with van’t Hoff’s equilibrium constant1 equation are given in Table IV. V. J)IHCUSSION nlolar caxt#inctioncoefficients for molecular benzene dissolved in carbon t&rachloride, and for benzene dissolved in carbon tetrachloride plus iodine appear to be identical at each benzene concentration, temperature, and wavelength. This means that’ the assumptions made by Ham et al. i 26) in their study of the spectrum of the benzene-iodine complex at wavelengths hrt,ween 2300 A and 2800 A are justified in part. The endot,hermic dependence on t,emperat’ure of t,he benzene molar ext’inct ion coefficients (Table III) can be at,tributed to the “hot-band” (17) i and the cxothermic dependence of t’he calculated molar extinction coefficients ( tI) of mole+ ular iodine (Table IV) can easily he attributed to reversible formation of J4 (18-21). Comparison of these cI values with corresponding molar extinction cocfTicient,s for iodine dissolved in carbon tetrachloride (18-21) reveals t,hat# enhancement occurs only at the low temperat’ure. At wavelengt,hs betSwren 2750 A and 3200 A, t,he inrrease is less than 100%. However, t’he calculations show t,hat, even for the solutions with highest iodine concentrat,ions (3.442 X 10P4 moles per liter), the actual increase in absorption is less than one-half of one percent of the measured optical density. Thus these data do not, support, the cont,ac:t charge-transfer hypot,hesis (6) . The new absorption maximum (near 2900 A at, 45°C) observed for iodine dissolved in benzene-carbon t,et,rachloridc> solutions is near that for the I2 - I+ + 1.- transition reported by l’ric(l (22). HOWPVW,t’he comparatively low molar extinction cocfficient,s (Table IV) indicat,r t,hat the concentration of ion-pairs, if present,, is low in t,he mixed solutions (23) .I Clalculated molar extinction coefficients for the benzene iodine complex (tc , Table IV) appear to he t,emperature-independent. This was also concluded by Ham (9,G) from liquid-nit’rogen temperature studies of the benzenc-iodine complex. The new results agree with published values obtained by older methods ( 1, 3) for t’he iodine-benzene complex dissolved in carbon trtrachloride ( 1, ,%-,27) and paraffins (1, 98). Thus, the Orgel-Mulliken (6) contact chargetransfer hypothesis, which predicts the endotharmic dependence of cc , is drfinitely cont,radicted. Formation constants for the complex (Table IV) do show a small significant, decrease at, increased wavelengths. However, values for K (mole fraction units) at, the ahsorption maximum (2900 A) and average AH values for the complex
1The large formation const,ant (900 liters/mole at 35°C) and molar extinction (about 40,000 at 2900A) found for the tri-iodide ion in water support this view.
coefficients
IODINE-BENZENE-CC14
381
in close agreement with corresponding values (25-28) calculated with the Ketelaar, or Benesi-Hildebrand methods. Thus, Scott’s (4) assertions that his modification of the Benesi-Hildebrand equation yielded K and ec values different from those obtained by other methods (1, 25-27)) is not supported by the new data for the weak benzene-iodine complex. Attempts to calculate K, cc,and or from data for mixed solutions with high benzene concentrations (mole fraction 0.4815 to 1.000) yielded negative values for Emand/or eI (Table IIa) . However plots of cB calculated by the method described in Ref. 12, versus the benzene concentration yielded straight lines with positive slope at each wavelength and temperature studied. It can be shown that this linear relation arises because of partial reversible dimerization of the benzene (18-21). Thus, the decrease in K values with increased wavelength may well be due to two additional reactions: are
C&H, + C&H6&
( complex 11,
+ Iz &
(complex)z .
(conlplex)1
This would also explain the constant AH values (Table IV) and negative values for cc and or obtained for the high benzene concentration. However, quantitative calculations cannot be completed without further information about Kl and Kz . ACKNOWLEDGMENTS P. A. D. de Maine gratefully acknowledges financial support of this work by the American Chemical Society-Petroleum Research Fund. Table IIa has been inserted at the suggestion of the referee. RECEIVED:
September
18, 1961 REFERENCES
1. H. A. BENESI AND J. H. HILDEBRAND, J. Am. Chem. sot. 71,2703 (1949). R. L. J. ANDREWS AND R. M. KEEFER, J. Sm. Chen~. Sot. 73,4169 (1951). 8. J. A. A. KETELAAR, C. VAN DE STOLPE, A. GOUDSMIT, AND W. DZCUBAS, IZec. trav. chim. 71, 1104 (1952). 4. R. L. SCOTT, Rec. trav. chim. 76, 787 (1956). 5. P.A.D. DE MAINE, J. Chem. Phys. 26, 1042 (1957). 6. L. E. ORGEL AND R. S. MULLIKEN, J. Am. Chem. Sot. 79,4839 (1957). 7. R. S. MULLIKEN, J. Phys. Chem. 66, 801 (1952). 8. P. A. D. DE MAINE, J. Chem. Phys. 26, 1199 (1957). 9. D. F. EVANS, J. Chem. Phys. 23, 1424 (1955). 10. S. P. MCGLYNN, Chem. Rev., 68, 1113 (1958). 11. K. SHINODA AND J. H. HILDEBRAND, J. Phys. Chem. 62,295 (1958). 12. P. A. D. DE MAINE, Spectrochim Acta 16, 1051 (1960). lb. P. A. D. DE MAINE, J. Chem. Phys. 26, 1192 (1957). 14. W. F. POTTS, J. Chews. Phys. 20, 809 (1952). 15. P. A. D. DE MAINE AND J. PEONE, JR., J. Mol. Spectroscopy, 4, 262 (1960). 16. J. 8. HAM, J. R. PLATT, AND H. MCCONNELL, J. Chem. Phys. 19,130l (1951).
382
I)b; MAINE
22. 23. 24. 25. $6. 27. 28.
MAINE,
ANI)
FROESE
B. KISTIAKOWSKY AND A.K. SOLOMON,./. C'hena. Phys. 6,609 (1937). 1’. A. I). DE MAINE, ./. C’hm. Phys., 24, 1091 (1956). R. M. REEFER AND T. L. AI,I,EN, .I. Chem. Phys., 26, 1059 (1956). P. A. 11. DE MAUVE, ('an. J. ('hem. 36, 573 (1957). M. M. DE MAINE, P. A. I). 1)~ MAINE, ANI) (;. 11:. MC-ALOXIE, J. ~Wol. Spertrrwopy 4, ‘Jil (1960). W. C. 1'R1m (private conmuniration). il. L). AWTREY AND It. E. CONNICK, J. do. Chem. SW. 73, 18-C (1951). J. H. ITAM, J. Am. Chem. Sot. 76, 3875 (195-1). L. J. ANDREWS AND R. M. REEFER, .J. ilm. (Them. SW. 74, -1500 (1952). M. TAMRES, I). R. VIRZI, AND 8. SEARLES, 1. d-lv~. C’h.enr. Sot. 76, 4358 (1953). 1,. J. ANDREWS AND R. M. KEEFJSR, J. Am. (Them. SW. 77, 2164 (1955). c. VAN DE STOLPE, thesis, “7L o 1vatie van Jodium in Organ&he Oplosmiddelen,” Amstrrdam, 1953.
fY. G.
18. 19. 90. 21.
DE
OF
MOLECULAR
Iodine Part
8, 373-382 (1962)
SPECTROSCOPY
Complexes
XIII. The System:
P. A. II. DE MAINE Department
in Inert Solvents
of Chemistry,
Iodine-Benzene-CC& AND M. M. DE Mach-E
University
of Mississippi,
University,
Mississippi
AND CHARLOTTE Department
of Mathematics,
7’niversity
FROESE
of British
Columbia,
Vancouver,
B.
C.,
Canada
Equilibrium constants, heat of formation, and molar extinction coefficients for the benzene-iodine complex, together with molar extinction coefficients for uncomplexed iodine and benzene have been calculated by means of an electronic computer from spectrophotometric data at fifteen wavelengths between 2700 A and 3500 A for the benzene-iodine-carbon tetrachloride system at 15” and 45” C. Deviat,ions at high benzene concentrations can be qualitatively explained by the additional reactions: benzene
+
benzene
(complex)l
+
-
IS A
K, Kg
(complex)l (complex)z
with K1 small. INTRODUCTION
Since publication of the Benesi-Hildebrand equation (1) in 1949, several workers (2-5) have used modified forms of this equation t’o calculate formation constants and molar extinction curves for one-to-one complexes from spectrophotometric data. To solve the Beneei-Hildebrand equation and its modified forms, it is necessary to assume t#hat t,he molar ext’indion curves for each of the uncomplexed components do not change in the presence of each other. Orgel and Mulliken (6) suggest, in their contact charge-t#ransfer theory that this assumption is not valid for iodine solut#ions. They attribute the contradictions of Mulliken’s charge-transfer theory (7), observed for iodine complexes (8) to changes in t,he molar extinction curves for the separate components in the presence of each other. Spectrophot,ometric data for iodine-n-heptane-perfluoro373
X-4
1lE MAINE
IlE MAINE,
ASI> FROESE
hcptane solutions collected by Evans (9) were cited as supporting evidence (fj). McGlynn (10) has thoroughly reviewed these theories. Scott (.$) has stated that analysis of spectrophotometBric data w&h the HencsiHildebrand equation, or its modified forms does not yield consistent results. He also emphasized t,he role played by the activity coefficient’ for each of th(b species presem at equilibrium. Shinoda and Hildebrand (11) have published thermodynamic data for the iodine-benzene system whirh was interprct,rd as supporting the Orgel-Mulliken hypothesis (6). dc Maine (12) has shown t,hat for systems with reversible one-t’o-one complcses, formation constants and molar extjinction curves for each species present (‘a11be c*alrulated from spectrophotometric data without’ assumpt~ions about the molar extinction curves for each separate species. Here WC report a t,cst of the Orgel1Iulliken hypothesis wit,h spectrophotonx+ric data for t)he henzenr-iodinrcarbon tetraehloride system. II. KSPERIMENTAI, Rlallinckrodt reagent grade benzene, Fisher spectrograde carbon tetrachloridc and n-heptane were purged wit’h dry nitrogen (dew point -40°C) befort> use. Fisher certified reagent grade iodine (resrtblimrd) was used wit,hout further purification. Solut,ions cont,aining iodine dissolved in pure benzene, or in henzcnc~ plus carbon trtrachloride were made in a dry nitjrogen atmosphere (13) For earh solution, there was prepared a reference sohuion in n-hept,ane whicah contained the sam(a amount, of carbon tet’raehloridc and no iodine or benzene. In wpuratc~ rsperiment.s, and in published work (9,Z,$), it has been shown that rr-heptam~ does not, absorb light in the spectral region studied (2700A ---f 4000 .I), All measurements were made with t,wo calibrated Reckman DI- Spwtrophotometers, equipped with photomultiplier t’ubcs, tempcrat,urr c~mtrol a~‘cessories and four matched one wntimet,er glass-stoppercd quartz snmplc (*ells in a dry nitrogen at,mosphere 11.5). Optical densities at 15 and 45°C’ for c~a& iodilic-bellzene-carboil t,etrachloride solut’ion were measured at 50.1iritcrvals I,f~twfw~ 2700 A and 3700 A, with the cwrrcsponding ;rz-heptanc-carbon t,etrachloride solution as reference. Opt’ical densities between 0.060and 1.000 \vcr(l reproducible to within 0.002 unit. Spectra of t’wo hundred solutions with twenty different benzene concrnt rations (mole fractions bet’ween 0.048.i and 1.OOO) (and ten differem iodine c*onc*ciltrations between 8.04 X lo-’ and 4.01 X IO-%I were measured at 1.5nttd4.5”(1. Spectral data were ohtjaincd for t’wenty iodine-caarbon trtrachloridc and t jvc’ttt,v bcnzenewrhon tetrachloride solutions. III. METHOI)
I’or thr
reversible
equilibrium
OF C.4LCI:I,ATIOS
reaction :
C6H6 + I2 A
Complex,
375
IODINE-BENZENE-CC&
with [GH,]
))) [IZ], the concentration
of the complex
c, = KC,Ce/(
(C,) is given by the equation
1 + KC,) )
(1)
with ( CI - C,) and (C, - C, = C,) the concentrations of uncomplexed iodine and benzene, respectively. According to Beer’s Law, the measured optical density D, at a given wavelength is related to the molar extinction coefficients and concentrations of bhe components by the equat’ion D = c,(C, Substituting
-
Cc) + E&‘B + EJ’~
for C, from Eq. (1)) this equation EI +
D= Kow define D = D -
&
CB
I+
becomes
CI +
(2)
EB CB .
cBCB ; t,hen from Eq. (2)) D = fICI + KqJIBC,
- KC,ii.
(Z3)
Equations ( 1) -( 3) were used to determine EB, tI , cc , and K. The data collected at a given wavelength, temperature and benzene concentration range (low benzene concentrations 0.043.5 to 0.2352 mole fraction units: high benzene concentrations 0.4815 to 1.000 mole fraction units) were arranged in matrix form, with columns and rows representing fixed iodine and benzene concentrations, respectively. The procedure was then as follows: Step 1. For each row, (CB = constant) eBCB was determined by fitting a straight line to t’he data with use of the least squares approximation. According to Eq. (2)) +CB is the intercept of the line at CI = 0. Step 2. The D mat,rix was computed as 15 = D - cBCB . TABLE
I
VALUEB FOR h-,eC,AND q DETERMINED WITH DATA COLLECTED AT 15°C BY THE PROCEDURE DESCRIBED IN STEPS 1-4 (A) AND IN STEP 5 (B), RESPECTIVELY. K IS IN MOLE FRACTION UNITS. Wave length m/J 280 285 290 295 300 305 310 315 320
s A 1.64 1.68 1.45 1.32 1.31 1.29 1.16 1.04 0.87
tc
B 1.67 1.56 1.57 1.45 1.42 1.32 0.97 0.98 0.57
A 13,000 14,700 17,500 18,900 17,900 15,900 14)300 12,200 10) 700
t1
B 12,800 15,400 16,500 17,600 16,800 15,600 12,800 10,700
A
B
86 83 104 109 75 51 33 32 19
109 89 79 77 55 53 ci2 38 19
2
^.
0.080 -0.015
0.099 0.005
0.114 0.002
0.127 -0.003
0.131 0.003
0.140 -0.004
0.1294
0.1507
0.1720
0.1931
0.2142
0.2352
0.065 0.002
0.0866
0.065 -0.002
0.049 0.002
0,065l
0.1081
0.035 0.001
0.0435
Iodine
0.382
Fr.
Benzene
Mole
0.275 -0.006
0.250 -0.006
0.244 -0.003
0.217 -0.002
0.194 0.005
0.189 0.014
0.139 0.001
0.115 -0.008
0.091 -0.002
0.062 -0.003
0.765
0.420 0.005
0.396 0.018
0.364 0.002
0.315 -0.011
0.275 -0.011
0.274 0.016
0.210 0.002
0.180 0.000
0.135 -0.002
0.092 -0.004
1.147
0.556 0.005
0.508 -0.001
0.472 -0.009
0.430 0.000
0.384 0.006
0.334 -0.010
0.296 0.018
0.235 -0.004
0.186 0.004
0.002
0.129
1.530
_
ior
5).
0.818 -0.009
0.772 0.013
0.709 -0.004
0.641 -0.001
0.579 0.012
0.510 0.001
0.420 -0.002
0.353 -0.002
0.275 0.003
0.185 -0.004
2.295
Iodine
is 3000
fractiuii
FC
= 16,839;
0.956 -0.007
0.892 0.005
0.820 -0.011
0.745 -0.003
0.670 0.008
0.590 -0.003
0.501 0.009
0.410 -0.004
0.320 0.004
0.215 -0.004
2.677
Concentration
Wavelength
K is in mule
1.090 -0.010
1.015 0.000
0.844 -0.012
0.759 0.001
0.670 -0.007
0.580 0.018
0.471 -0.001
0.361 -0.001
0.246 -0.004
3.060
Times
A.
umts.
cl=
10,000
(moles/liter)
11.6
1.236 0.002
1.159 0.022
1.050 -0.014
0.950 -0.011
0.860 0.008
0.760 0.001
0.640 0.005
0.525 -0.005
0.409 0.003
0.276 -0.005
3.442
13~~10~
iii the test.
iodiiie-benzcne-
defined
the indicated
K, EC and eI are
(AD)
AD value.
K= 1.1299;
0.686 -0.003
0.641 0.008
0.599 0.004
0.530 -0.007
0.470 -0.004
0.413 -0.015
0.360 0.010
0.295 -0.002
0.229 0.002
0.115 -0.003
1.912
the corresponding
(moles/liter)
eB CB,
II
(as per step
at 45°C.
rlot been recycled
10,000
TABLE (I,) aiid deviations
solutions
densities
is given
have
Times
D value
each
Concentration
data
tctrachloride
oplical
These
carbon
Measured
1.365 -0.007
1.280 0.014
1.175 -0.004
1.060 -0.006
0.954 0.007
0.840 -0.002
0.720 0.015
0.579 -0.010
0.454 0.003
-0.003
0.309
3.825
0.007
0.002
0.013
0.007
0.002
0.011
0.005
0.005
0.003
0.003
‘^BCB
IIa
0.484 -0.008
0.415 0.002 0.429 -0.003 0.440 -0.011
0.311 0.002 0.324 0.003 0.329 0.001 0.346 0.000 0.397 0.011 0.372 -0.009
0.261 0.005 0.263 0.002 0.270 0.002 0.271 -0.004 0.332 0.013 0.306 -0.006
0.200 0.003 0.209 0.004 0.210 0.003 0.210 -0.002 0.205 -0.009 0.234 -0.006
0.140 0.000
0.139 -0.001
0.146 0.002
0.155 0.002
0.147 -0.005
0.166 -0.004
0.083 0.000
0.081 -0.001
0.085 0.002
0.095 0.004
0.082 -0.004
0.101 -0.001
0.718
0.775
0.832
0.889
0.945
1.000
K = 0.659
0.470 -0.002
0.407 0.008
0.300 0.008
0.245 0.008
0.188 0.006
0.125 0.000
0.076 0.003
0.392 0.008
0.376 0.007
0.355 0.009
0.339 0.005
0.277 -0.001
0.231 0.002
0.185 0.006
0.117 -0.004
0.078 0.004
0.601
0.320 0.000
0.260 -0.006
0.230 0.007
0.165 -0.003
0.111 -0.006
0.070 0.000
0.542
eC
= -2,980
0.509 -0.012
0.452 0.001
0.440 0.003
0.425 0.003
0.410 0.010
0.388 0.004
0.365 -0.003
0.340 -0.014
0.297 -0.010
0.247 -0.011
0.202 -0.009
0.067 -0.002
0.482
5.419
Iodine Concentration
0.161 -0.004
(moles /liter)
0.110 -0.006
100,000 4.646
x 3.871
1.548
of Benzene
0.774
3.097
Iodine Concentration
0.580 -0.013
0.560 -0.005
0.534 -0.003
0.523 0.005
0.510 0.009
0.500 0.013
0.460 0.008
0.436 0.001
0.416 -0.002
0.371 -0.026
(moles,/liter) 6.968
EI = 5210
0.650 -0.014
0.630 -0.005
0.620 0.006
0.594 0.010
0.570 0.009
0.552 0.011
0.552 0.012
0.496 0.006
0.463 -0.004
0.433 -0.016
Below
100,000
6.194
x
These data have not been recycled (as per step 5). K is in mole fraction units. each D value is given the corresponding AD value. Wavelength is 3000 A.
2.323
Mole Fraction
TABLE
Measured optical densities (D) and deviations (AD) for the indicated iodine-benzenecarbon tetrachloride solutions at 45°C. eBCB, K, EC and cI are defined in the text.
0.720 -0.016
0.700 -0.004
0.670 0.000
0.650 0.007
0.611 0.001
0.590 0.002
0.590 0.020
0.551 0.008
0.510 -0.006
0.480 -0.017
7.742
0.029
0.023
0.022
0.020
0.025
0.027
0.017
0.020
0.020
0.021
‘BCB
2
.. ?Y
0.710 0.700
0.560 0.546
0.540 0.530
0.1931
0.2142
0.2352
0.061 0.064
0.061 0.066
0.074 0.076
0.064 0.064
0.056 0.062
0.560 0.570
0.570 0.580
0.060 0.060
0.600 0.581
0.1720
0.1507
0.1294
0.059 0.072
0.055 0.061
0.580 0.590
0.0866
0.710 0.720
0.060 0.061
0.610 0.590
0.0651
0.1081
0.060 0.066
0.730 0.610
0.0435
15°C
2800
2750
BUI2eIle
Mole Fr.
) at the
0.017 0.022
0.017 0.022
0.023 0.023
0.017 0.017
0.019 0.018
0.012 0.014
0.026 0.009
0.010 0.017
0.016 0.013
2850
1.11
1.08
1.15
1.14
1.13
2750
0.117 0.121
0.117 0.119
0.122 0.126
0.120 0.120
0.115 0.138
0.116 0.120
0.111 0.114
0.117 0.130
0.121 0.127
0.120 0.130
2800
45°C
) is
indicated
Coefflcwnts
Of each number pair (6:
iodine (cB
Molar Extinction
0.023 0.029
0.024 0.028
0.030 0.030
0.024 0.025
0.019 0.028
0.019 0.024
0.012 0.020
0.022 0.033
0.023 0.031
0.025 0.032
2850
1.000
0.945
0.034 0.034
0.035 0.034
0.037 0.035
0.889
0.0119 0.0121
0.0109 0.0107
0.0111 0.0109
0.0124 0.0118
0.0125 0.0128
0.044 0.044
0.715
0.043 0.041
0.0131 0.0150
0.047 0.049
0.718
0.832
0.0124 0.0129
0.0119 0.0114
0.0151 0.0148
0.0134 0.0134
2850
0.053 0.053
0.049 0.048
0.059 0.059
0.056 0.055
2800
15°C
0.660
0.601
0.542
0.482
BlXYZeIle
Mole Fr.
and temperahue.
) and in Ccl, plus
value.
wavelengths
in CCI, (ci
the upper and (eB ) the lower
benzene concentrations,
for benzene dissolved
TABLE III
2900
0.0074 0.0074
0.0061 0.0066
0.0060 0.0065
0.0065 0.0070
0.0064 0.0069
0.0074 0.0082
0.0062 0.0070
0.0061 0.0059
0.0081 0.0078
0.0071 0.0069
0.059 0.059
0.062 0.061
0.06’7 0.066
0.074 0.072
0.079 0.077
0.083 0.084
0.085 0.085
0.090 0.088
0.087 0.092
0.101 0.099
2800
2900
0.0120 0.0127
0.0118 0.0124
0.0127 0.0130
0.0133 0.0133
0.0145 0.0150
0.0164 0.0178
0.0061 0.0062
0.0053 0.0065
0.0056 0.0068
0.0060 0.0068
0.0067 0.0076
0.0077 0.0084
0.005 7 0.0072
0.0071 0.0073
0.0150 0.0158 0.0159 0.0157
0.0074 0.0069
0.0092 0.0092 0.0165 0.0164
0.0187
0.0189
2850
45°C
379
IODINE-BEXZENE-CCL,
Step 3. The constants K, Q , and Edwere obtained by performing a regression analysis on D with C, , C,C, , and CnD independent variables, as indicated by Eq. (3). Step 4. The deviation matrix (AD = D - eICI - K+2,C’, + KC’,o,) was computed for each D matrix : AD is the difference between t,he actually measured value and that predicted by Eq. (3) with the constants taken to be those determined in Step 3. Step 5. Elements in the D matrix with corresponding large deviations were discarded and Steps 14 repeated. On the whole this did not reduce significantly the scatter in the results but did provide an estimate of the sensitivity of the results on the data. This point is illust,rated in Table I. All calculations were performed on the ALWAC III-E computer at the University of British Columbia. Typical D (measured optical density) and AD (deviations) matrices, together with values of +,Cg , K, rI , and cc are shown in Tables II and IIa. IV. RESULTS
K, cc , es , and eI have been determined by the method just described at wavelengths between 2700 A and 3500 A from data for iodine-benzene-carbon tetrachloride solutions measured at 15°C and 45°C. These solutions contained either high (0.4815 -+ 1 .OOO)or low (0.0435 to 0.2352) mole fractions of benzene. The molar extinction coefficients for benzene (E=) and molecular iodine (Ed) were also determined at the same wavelengths and temperatures with separate carbon tetrachloride solutions. Molar extinction coeficients for benzene dissolved in carbon t,etrachloride ( cBS) and in carbon tetrachloride plus iodine (Ed) are given in Table III. Molar TABLE
IV
FORMATION CONSTANTS AND MOLAR EXTINCTION COMPLEX
COEFFICIENTS FOR BOTH THE
(CBHB.IL) AND MOLECIJLAR IODINE DETEFMINED
BENZENE-IODINE-CARBON
WITH
TETRACHLORIDE SOLUTIONS AT 15°C
DATA
FOR
AND 45°C.
AH Is THE HEAT OF FORMATION OF THE COMPLEX CALCULATED WITH VAN’T
HOFF’S
t1
EQUATION. k’ (mole fraction units)
CC
Wave length (A)
15°C
45°C
2900
79
2950
77
3000
55
3050 3100
15°C
45°C
58
16,500
31
17,600
12
53 62
AH Kcal/Mole
15°C
45°C
17,200
1.57
1.19
17,000
1.45
1.21
1.04
16,800
16,800
1.42
1.13
1.34
16
15,600
16,300
1.32
0.99
1.70
32
14) 300
15,000
0.97
0.75
1.52
Average
1.45 (~kO.24)
1.63
380
I>E MAINE
I)E MAINE,
ANI_, FROESE
extinction coefficients for molecular iodine (Q) and for the complex (cc) determined from data for the benzene-iodine-carbon tetrachloride solutions, are given in Table IV. Formation constants (K) and values for the heat, of formation computed with van’t Hoff’s equilibrium constant1 equation are given in Table IV. V. J)IHCUSSION nlolar caxt#inctioncoefficients for molecular benzene dissolved in carbon t&rachloride, and for benzene dissolved in carbon tetrachloride plus iodine appear to be identical at each benzene concentration, temperature, and wavelength. This means that’ the assumptions made by Ham et al. i 26) in their study of the spectrum of the benzene-iodine complex at wavelengths hrt,ween 2300 A and 2800 A are justified in part. The endot,hermic dependence on t,emperat’ure of t,he benzene molar ext’inct ion coefficients (Table III) can be at,tributed to the “hot-band” (17) i and the cxothermic dependence of t’he calculated molar extinction coefficients ( tI) of mole+ ular iodine (Table IV) can easily he attributed to reversible formation of J4 (18-21). Comparison of these cI values with corresponding molar extinction cocfTicient,s for iodine dissolved in carbon tetrachloride (18-21) reveals t,hat# enhancement occurs only at the low temperat’ure. At wavelengt,hs betSwren 2750 A and 3200 A, t,he inrrease is less than 100%. However, t’he calculations show t,hat, even for the solutions with highest iodine concentrat,ions (3.442 X 10P4 moles per liter), the actual increase in absorption is less than one-half of one percent of the measured optical density. Thus these data do not, support, the cont,ac:t charge-transfer hypot,hesis (6) . The new absorption maximum (near 2900 A at, 45°C) observed for iodine dissolved in benzene-carbon t,et,rachloridc> solutions is near that for the I2 - I+ + 1.- transition reported by l’ric(l (22). HOWPVW,t’he comparatively low molar extinction cocfficient,s (Table IV) indicat,r t,hat the concentration of ion-pairs, if present,, is low in t,he mixed solutions (23) .I Clalculated molar extinction coefficients for the benzene iodine complex (tc , Table IV) appear to he t,emperature-independent. This was also concluded by Ham (9,G) from liquid-nit’rogen temperature studies of the benzenc-iodine complex. The new results agree with published values obtained by older methods ( 1, 3) for t’he iodine-benzene complex dissolved in carbon trtrachloride ( 1, ,%-,27) and paraffins (1, 98). Thus, the Orgel-Mulliken (6) contact chargetransfer hypothesis, which predicts the endotharmic dependence of cc , is drfinitely cont,radicted. Formation constants for the complex (Table IV) do show a small significant, decrease at, increased wavelengths. However, values for K (mole fraction units) at, the ahsorption maximum (2900 A) and average AH values for the complex
1The large formation const,ant (900 liters/mole at 35°C) and molar extinction (about 40,000 at 2900A) found for the tri-iodide ion in water support this view.
coefficients
IODINE-BENZENE-CC14
381
in close agreement with corresponding values (25-28) calculated with the Ketelaar, or Benesi-Hildebrand methods. Thus, Scott’s (4) assertions that his modification of the Benesi-Hildebrand equation yielded K and ec values different from those obtained by other methods (1, 25-27)) is not supported by the new data for the weak benzene-iodine complex. Attempts to calculate K, cc,and or from data for mixed solutions with high benzene concentrations (mole fraction 0.4815 to 1.000) yielded negative values for Emand/or eI (Table IIa) . However plots of cB calculated by the method described in Ref. 12, versus the benzene concentration yielded straight lines with positive slope at each wavelength and temperature studied. It can be shown that this linear relation arises because of partial reversible dimerization of the benzene (18-21). Thus, the decrease in K values with increased wavelength may well be due to two additional reactions: are
C&H, + C&H6&
( complex 11,
+ Iz &
(complex)z .
(conlplex)1
This would also explain the constant AH values (Table IV) and negative values for cc and or obtained for the high benzene concentration. However, quantitative calculations cannot be completed without further information about Kl and Kz . ACKNOWLEDGMENTS P. A. D. de Maine gratefully acknowledges financial support of this work by the American Chemical Society-Petroleum Research Fund. Table IIa has been inserted at the suggestion of the referee. RECEIVED:
September
18, 1961 REFERENCES
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382
I)b; MAINE
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ANI)
FROESE
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fY. G.
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DE