SOLVOLYSIS OF L-BUTYL CHLORIDE
Nov. 20, 195i
and a t the University of Michigan. h stimulating discussion with Dr. Noyes on the kinetic and mechanistic aspects of ( S ) is gratefully acknowl-
[CONTRIBUTION FROM THE
5937
edged. The financial assistance of the Research Corporation is sincerely appreciated. CHICAGO 16, ILLINOIS
DEPARTMENT O F CHEMISTRY,
UNIVERSITY O F CALIFORNIA AT LOS ANGELES]
Correlation of Solvolysis Rates. 1V.l Solvent Effects on Enthalpy and Entropy of Activation for Solvolysis of &Butyl Chloride2 BY S. WINSTEINAND ARNOLDH. FAINBERC RECEIVED M A Y 13, 1957 In probing t h e basis of the success and limitations of linear free energy correlations of rates of solvolysis, the behavior of A H + and A S * for solvolysis of t-butyl chloride toward solvent variation has been explored. The variation of AH* and AS* with solvent has been scrutinized in the large variety of solvents reported on previously. In five of six pure solvents, A S * for solvolysis of t-butyl chloride is relatively constant a t ca. -3 e.u. On the other hand, water is uniquely set apart from the other solvents, A S * now being 15 e.u. higher. A similarly anomalous position is occupied by the solvent water in solvolysis of other materials. With the aid of Henry's law constants for t-butyl chloride, the AA F* due t o a solvent change can be dissected into separate effects on the ground state and transition state, namely, A A P v and AAF*s, respectively. Henry's law constants a t several temperatures make possible the analogous dissection of the AAH* and A A S * terms. For changes of medium from one pure solvent t o another in the case of t-butyl chloride solvolysis, AAF*g tends to be of major importance. However, for the MeOH + HOH or EtOH + HOH solvent changes, AAFO,, related to the ground state, is of major importance. For solvolysis of t-butyl chloride in binary solvent mixtures, t h e behavior of AH* and AS* toward
solvent composition tends to be complex. I n this respect, the EtOH-HOH system is the most complex. For the various binary solvent systems, a linear relation between AS* and AH* is the exception rather than the rule. An ABC classification system can be set up for characterizing the AS*, AH* behavior in solvolysis, and the symbolic terminology has been employed in summarizing and comparing the behavior of t-butyl chloride and a number of other substrates. As anticipated, the AS*, AH* behavior in t-butyl chloride solvolysis in binary solvent mixtures is poorly accounted for by a simple electrostatic treatment. Examination of Henry's law constants for t-butyl chloride in MeOH-HOH mixtures show t h a t both ground state and transition state contributions t o the AAH* and AAS* values are important. Comparing the AS*, AH* behavior for t-butyl chloride with t h a t for other substrates, it is evident t h a t the various substances do not obey generalizations based solely on the nature of the solvent systems. Instead, as can be anticipated, the AS*, AII* behavior depends on substrate structure as well as on the nature of the solvent system. The pattern of behavior of AH* and AS* for solvolysis of a substrate molecule determines the effect of temperature variation on the precision of the mY correlation of the rates of solvolysis of that substrate molecule. This matter is treated analytically.
The thermodynamic quantities of activation, AH+ and AS*, for the solvolysis of the key substance, t-butyl ~ h l o r i d e are , ~ of interest in probing the basis of the success and limitations of the linear free energy relationships3 1, 2 and 3. In relationship 1, (k/Ko)~xis the ratio of first-order solvolysis rate constants of RX in a solvent and in a standard solvent, respectively, while ( k / k o ) ~ yis the analogous ratio for the substance RY. Relationship 3 makes use of a set of Y values for sol-
sible utility in diagnosis of mechanism.5 However, before any safe generalizations can be drawn regarding the connection between mechanism and AS*, for example, the dependence of A S * on solvent composition for known mechanisms needs to be explored. The variation of AH* and A S * with solvent for the solvolysis of t-butyl chloride has been scrutinized in the large variety of solvents reported on in a previous paper.3c These results are reported and discussed in the present article.
Results I n Table I are summarized the first-order rate constants a t 0" or 50" for solvolysis of t-butyl chloride in the various pure and mixed solvents. Most vents equal to log (klko) a t 25" for the standardsub- of the rate constants are new, a few representing stance, t-butyl chloride. Thus, the Y values, or duplication as indicated in the footnotes. In virtumeasures of solvent ionizing power, are based on a ally all cases, the solvent mixtures were from the blend of specific and general solvent influences3z4 same batches as those employed to obtain the rates appropriate to t-butyl chloride solvolysis. a t 25.0" reported p r e v i o ~ s l y . ~ ~ A further interest in the thermodynamic quantiAlso listed in the table are the values of G I * and ties of activation of solvolysis is based on their pos- A S * calculated from the present and previous3~ data. Based on the estimated probable error of the (1) Presented before the Division of Physical a n d Inorganic ChemisAH* is considered accurate to rate try of the American Chemical Society, Minneapolis, Minn., Sept. 16, 1955; page 52R of Abstracts. h0.15 kcal./mole, and A S * to hO.5 e.u. (3) Research sponsored by t h e Office of Ordnance Research, U. S. Some further comment on the present AH* values Army. is in order because reactions involving increase of (3) (a) E. Grunwald and S. Winstein, THISJ O U R N A L , 70, 846 charge, and therefore increased solvation, during (1948); (b) S. Winstein, E. Grunwald and H. W. Jones, ibid., 73, 2700 (1931); (c) A. H. Fainberg and S. Winstein, ibid., 78, 2770 (1956). passage into the transition state, commonly dis(4) E. Gelles, E. D. Hughes and C. K. Ingold. J . Cizem. Soc., 2918 (1954).
(5) E . g . , S. Winstein and R. Heck, Tms
JOURNAL,
78, 4801 (1950).
TABLE I
Ihim
OF
Solveiit, vol. Lj/b
SOLVOLYSIS OF t-Bvrsr, CIILORIDE~
*
AfI kcal. mole (2.50
0.00 :: L I e t h o t i C 0.02"
AS*, e.u. (2.5")
IitOH-HzO
x
98
x x
x
8.3!1'. 1G 8k
s s S I1 13
47 5 ;,8,0 72 7
s
!JO
S
80 70
X X H X
23.58
-8.3 -8.7 - fj . GQ
40
22.72
20
s
22.34Q 21.90 21.G7 21.G3" 21 , 0 a
20.32 20.24 20.20
20.57 21.20 22.01 22.61 23.25
23.48 23.22
-5.4
-3.7 -1.4IA --?.I -3.3 -3.0 -2.5
-0.1 i2.9
fG.3 +8.9 f11.7 +12.8 t12.2
H H
H 11
I1 1r
2.10 10.81 44.9
140 0,249 ,922
24.88 23.33
-4.0
22.40
-4.7
,)21.9 21.G3 21.64 21.45 21.33 21.81 22.79
,932 2.00 7.09 10.3 2li.5 ,I.-! 0
" 3 , OR
-3.1
-4
-2.2 -2.1
%U
(X2/a X3'/9 11.29
-O.G
Y .
x
48.1k
13.8
X
X X
0 . GO9 2.90 1nR
25,80 24.52
23.14 22.13
-2.5 -3.G -4.7 -3.8 -3.1
0.908
21.89
x x
3.731 4.97 6.89 7.74
21.01 20.78 20.87 20,23 20.44 90.82 21,no
-1 7' -1.9
X X
S
25.13 23.91 23.14
-3.7 -6.3 -5.8
22.41
-5.5
21.53 21.24
-4.8
10.29 30.3 .i in
-2.4
-3.1
-1.7 +1.8 -t-I.O
AcOH-H20 0 . 8 0 AI H2O 2 . 0 0 M H20 4 . 0 0 3f H z 0 8.00M HzO 1 0 . 0 0 34 HzO 00
80
.+n 2 ,j 10
X
1.OG1
S
3.12
8.11 29.2
X
161 X
x Ii X
s
1.10 2.73 G.54 21.1 18,O
21.30
21.21 21 , 5 5
-3.4 -1.2 +0.2 +3 7
GO .70 40
30 20
In
2l.J
21.85 22.01
21.1e
-16.8 -1li -10.0
20.78
-5.4
20.41
-1.7
32.63
+!I.l
0.1190 .4.2'.1 417.1
24.17 23.07 22.24 21.7
-11.0 -7.3
74.G
22.36 21.83
-3.8 -1.9
0.58
-5.1 -3
Forrnaniiile-€120
s
100 80
x
0.70
Initial concentration of 0.02-0.04 111 when dcvclopnient JI when acidonictric :mnlysis was employed. X vol. c/o A - B means x volumes of X plus 100 - x volumes of €3, each a t 25.0" beforc mixing. H = acidometric analysis; X = halide analysis. ri The average deviation of all of the new rates herein reported that are constant is zkl.Oyo of k ; the probable error r in log k is estimated to be 0.005. e Interpolation a t 50.0' of data reported3" a t other temperatures in EtOH containing several concentrations of KOAc, with simultaneous linear extrapolation to zero salt concentration, gives 0.278. j Calculation from data previously reported* gives &ET* 25.53, A S * -4.9. 0 Recalculation of data previously reported gives for 106k at 50.0": 18.4,e 18.2,' 16.7,s 18.59; AH*: 22.37,6 22.G0,' 21.80,* 22.599; A S + : -G.5,6 -5.8,' -8.6,5 -5.8.9 h Recalculation of data previously repnrteds gives for 106k a t O 0 , 1.05; AH* 22.35; A S * f0.6. Initial rates; upward drift in the course of the runs; see Esperimental section of the previous p a p ~ r . 3 ~j Calculatcd from data of Hughes6 a t other temperatures. k Tcmpernture 75.0Oo. Estrapolated from data in t h e aqueous formic acid mixtures. nf lialitle inn was followed; 0.001-0.005
play10-12 appreciable negative temperature coef In the case of t-butyl chloride itEtOH-H20, Shorter and Hinshelreported a change of activation energy of solvolysis with temperature. Also, Tommila'2 has reported, in a paper which became available t o us since the present work was first presented,' a value of ca. - 60 cal. per mole per degree for AC*, in the most highly aqueous acetone solvents. In the present work, the thermodynamic quantities of activation are calculated, for the most part, from data a t 25 and 50" in the low water regions and at 0 and 25" in the high water regions. Thus, most of the AH* values correspond to a11average temperature of either 37.5 or 12.5". This switch from 37.5 t o 12.5" has a perturbing effect on the plots of AH or AS* 11s.mole fraction solvent coniposition, but i t does not affect the broad conclusions regarding complex behavior of AH* and A S * toward solvent .r.ariation. The most coniplex behavior is observed in the highly aqueous solvents, while the 37.,5 to 12.5" temperature switch is made earlier. AS*, A H * Relations.-In order to obtain a point of departure in discussing the relative he-
*
(6) 13. D . H u g h e s , -7. C h r : n . .Sot., 2 3 5 (1985). (7) E;.A . Cooper,E.D.Hnghes, C. E;. Ingold, G. A. Afaw and B. J.
Dioxane-HzO
00 80 70
0.237 3.G87
+0.0 +4.2 f8.7 +IO 7
HCOOH-Hz0 100 95 90
1.90'
3.50
(IcoII-IIcooII
50 2 .i
IT
s X
\IeOH-I120
100 90 75
10
X
.,
H H I1
GO GO 50 -10 30 20 10
H
F0
', -
€I H I€
70
30
0.58 10.00 43.6
80
5.84 5.76
25 20
100
S
-3.2J -7.2
- . I d
s
5.08 11.10 18.5 25.0 31.0 39.7
I120
s
j0
2 G . 13l 24.4G
1.353''
I1 H U I1
5
2.9Zk
70
0 . 27Ze 0,50!l 1.125 18.5" ii8 , !I 226
40 37.5 35 30
16 10
X
80
I )ioxane-HCOOH
100
9.5 yo 80 70 00 50 45 40
M eaCO-HzO 90
s X X X H
FI H
TI TI
0.156i 2.61i 18.28 83
0.748 2.90 9.10 21.7 $3.3
21.55 22.03
22.01 21.3 21.08 21.0"
21.21 21 88 22.4s
-18.5 -11.6 -7.7 -7 -4.G -2.1 +0.8 4-6.0 "8.6
hfcNulty, ibid.,2040 (1048). (8) V , J . S h i n e r , TiiIs J O r R N A r . , 7 6 , lFOX (1D54). (9) H . C.Brown and H.L. Berneis, ibid , 7 5 , 10 (1963). (10)B . Bensley a n d G . Kohnstani, J . Chrm. SOL.,287 (103G). (11) (a) J . B. Hyne a n d R . E. Robertson, Can. J . Chpm., 33, 1544 (19.55);( h ) R.E.Robertson, J . Cizem. Phy.c., 25, 375 (1956). (12) Ti. Tommila, 31. Tiilikninen a n d A . Voipio, Annalrs 4 r d . S c i . F e : i : ? i c a c , 65, 1 (3933). (13) J . Shurlcr xnrl C . Ilinshelivooii, J . C h m ? . S c r . , 2.112 (1940).
Nov. 20, 195’7
havior of AS* and AH* toward solvent variation i t is useful t o inquire what relation would be required between A S * and AH* t o have the linear free energy relationship 3 obeyed strictly, not only a t one temperature, but a t other temperatures as well. I n relation 3, Y is treated as temperatureinvariant, Y values a t 25” being e m p l ~ y e d . Re~ ferring to eq. 3 and dissecting A F * into the component AH* and - TAS* parts, one may express m as in eq. 4. For eq. 3 to be obeyed strictly a t all
temperatures, m must be a constant, independent of Y, a t each temperature. For this to be true, both (bAH*/bY) and (bAS*/bY) must be constant. I n other words, AH* and A S * must be linear functions of Y. As a consequence, any pair of the quantities, AH+,AS*, A F * and Y are linearly related.14 Linear relations between A S * and AH* have long been discussed. Such linearity was anticipated by Evans and Polanyi16aon the basis of similar linear relations between entropy and enthalpy of solution for both ground and transition states. Such linearity may also be anticipated on the basis of electrostatic considerations, as will be brought out later in the manuscript. An excellent review of the success of such linear AS*, AH* relations through 1953 has been furnished recently by Leffler.17 His review contains several examples of solvolysis with linear relations between AS* and AH* as solvent is varied. A considerable body of pertinent solvolysis data has become available since 1953, and some of it is referred to in the present paper. Tt is convenient to set up the set of linear relations between AH*,A S * and A F * by starting with eq. 5 . This expresses AH* as linear in AF*, the
+d = (q) AF* + d/T
AH* = a ( A F * ) As*
5939
SOLVOLYSIS OF L-BUTYL CHLORIDF:
(5) (6)
(7)
the other hand, water as solvent is uniquely set apart from the others, AS* being some 15 e.u. higher. For the 5 solvents with relatively constant AS*, AH* is obviously fairly linear in AF* with an a value in eq. 5 near unity. ,4 least squares line with a equal to 0.96 reproduces the AH* values with a probable error of 0.17 kcal./mole. TABLE I1 THERMODYNAMIC QUANTITIESO F ACTIVATION FOR SOLVOIAYSIS OF &BUTYLCHLORIDE I N PURE SOLVENTS
+,
*,
Solvent
AH kcal./mnlc
AS e.u.
HOH HCOOH HCONHz MeOH AcOH EtOH
23.22 21.0 22.3G 24.88 25.80 26.13
+12.2 -1.7 -3.8 -3.1 -2.6 -3.2
-2.9
* 0.6
As brought out in Table 111, a similar anomalous position is occupied by the solvent water in solvolysis of various materials, whether or not solvolysis mechanism resembles that for t-butyl chloride. I n the case of methyl p-toluenesulfonate, Hyne and Robertson1*measured rates in water and in a series of nine alcohols. For the alcohols, a plot of A S * vs. AH* is quite linear. The point for water, however, falls far off the line. Solvation of Ground and Transition States.It is generally understood that the energy of activation for ionization of a substance such as tbutyl chloride is reduced to accessible values by solvation of the polar transition state. This is shown schematically as
7
AP” AF*
6
RX(S)-+R e -
6 ------. - - X ~ ( S )+ R6(s) + 1;3(s) A
slope being a. On this basis, the slopes of the A S * vs. A F * and A S * vs. AH* plots are (a- l ) / T a n d (a - l ) / a T , respectively, as expressed in eq. 6 and
7. Pure Solvents.-Examination of the thermodynamic quantities of activation for the six pure solvents in which data are available is summarized in Table 11. It is immediately obvious that A S * is relatively constant a t the level of ca. - 3 e.u., ac0.6 e.u., for five of the solvents. On tually -2.9
*
(14) It is important t o note t h a t t h e above conclusions are valid for any measure of solvolyzing power with which t h e logarithms of t h e rate constants are t o be linearly correlated, whether this measure be Y, some function of t h e dielectric constant, or another “Y” based o n some compound other t h a n t-butyl chloride. T h e conclusions drawn apply t o other linear free energy relationships employing a parameter invariant with temperature. An example of such a parameter is o in Hammett’s p u treatrnent.16 (15) (a) L. P. H a m m e t t , “Physical Organic Chemistry,” McGrawHill Book Co., Inc., Xew York. X. Y.,1940; (b) H. H. Jaff‘C, Chem. Revs., SS, 191 (1953); (c) J. E Leffler, J . Chem. Phys., 23, 2199 (1955). (16) (a) A. G . Evans and M. Polanyi, T r a n s . F a r a d a y S O C .32, , 1333 (1936); (b) R. P. Bell, ibid., 33, 496 (1937); (c) I M Barclay and J. A. Butler, i b i d . , S 4 , 1445 (1938). (17) J. E. Leffler, J . 0,g. Chem., 20, 1202 (1955).
I
L-AP
AI
[the symbols (g) and (s) refer to gas and solution phases, respectively]. On this basis, A F * for ionization in solution differs from AF*g, the free energy of activation in the gas phase, by the sum of AF*,, the large negative standard free energy of solution of the polar transition state, and AFnv, the molar standard free energy of vaporization of R X from the appropriate solvent. On the microscopic level, the AF*’, and AFav quantities are determined by interactions of solvent molecules with: (i) the transition state, (ii) the ground state and (iii) other solvent molecules. The above analysis of A F * is expressed in eq. S. If one is interested in a solvent change, the A A F * associated with the solvent change may be expressed as in eq. 9 as the difference between the effects of the solvent change on the free energies of transition and ground states, respectively, namely, (18) J. B. Hyne a n d R. E . Robertson, C a n . J . Chem., 3 4 , 803,931 (1956).
S . L~INSTEIN .WD ARNOLDH.FAINRERG
5940
VOl. ?!)
TABLE I11 SOME
AAH* EtOH
A A H ;ir kcal./mble
Compound
Methyl p-toluenesulfonatc'" Ethyl benzenesulfonate1g,20 i-Propyl benzenesulfonate?' hIethyl b r 0 m i d e ~ b , ~ * - - ~ 4 Ethyl bromide3bs12,23 Di-i-propyl phospliorochloridate2j Benzyl chloride2& wPhenylethy1 chloricie*~~ t-Butyl chloride Lithium chloride*^*^ Potassium chl0ride',~7 Tetramethylammonium chlorideb 25 50 V O ~ .% EtOI-I-HzO + € 1 2 0 .
AAF*,
+
-
AND
-0.22 - .34
- .57 -3.1" -.5.1" -t-l.R +0.2
cn, -3 -2.91 +4.3
A A S * VALUES
HPO A4.S
*,
e.u.
+ 5.1 + 6.4 -t11.3
AT
50"
MeOH AAII kral./mole
+,
-0.41 -1.14 -0.34
-
A S ri. i m ,
H,O AAS*,
e
11.
C!.,,
+3.7 3.1 10.4
-14.1 - 1.2.0
- 0.3 - 9.3 - 7.1
+11"
+ 17" +I6
+13 ca. + l a +15.4
-2,40 Change in AH0 or AS0 of solution.
ca -2
ca. +10
-1.66
+1;.2
$3.8 $3.0 -2.06
$-41. G
CII.
-21.8 -12.5 + 1 +l2.0
AAFO,. Expressions for ALLIT+ and A A S + corresponding to that for AAF* in eq. 9 may
sociated) pair of ions,29-31R e and XY, the solvation of Re being treated like that of an ordinary inbe put in the form of eq. 10 and 11. organic i0n.30-32 This amounts to substituting the standard free energy of ionization of RX in the gas AF* = AF*, + AF*, + AFO, (8) phase, A P , , for AF+,, and the standard free energy AAF* = AAFf, AAP, of solution of the ionized RX, AFO,, for AF+, in eq. (9) 8. A A H + = AAH=kS AAHO, (10) Interesting and instructive attempts to estimate & A S * = AAS** + AASO, (11) rates of solvolysis in solution froni the energetics of Equivalent alternative forms of eq. 9 are eq. 12 ionization in the gas phase and the calculated enof solvation of R e and X e have been made and 13 which we have employed p r e v i o ~ s l y I. n~ ~ ~ergetics ~ eq. 12, ( f n x / f * )is the ratio of activity coefficients of by Evans30 and Franklin.31 By einployiiig the RX and transition state, respectively, and ko is the general method of Latimer, Pitzer and Slansky"3for rate constant in the standard solvent. Referring estimating enthalpy and entropy of solvation of all activity coefficients to the gas phase lead+ to triinethylcarbonium halides, Frank1in3l has actueq. 13. .4ccording to the latter equation, the spe- ally been able to calculate rates of solvolysis of 1cific solvolysis reaction rate constant, k, is propor- butyl halides in S07, ethanol which agree, partly tional to the Henry's law constant, HRS, of the fortuitously, to within CIZ. one power of tcii with alkyl halide molecule, and inversely proportional to those observed. Since AF-ks is so important in reducing free enthe Henry's law constant of the solvolysis transition state, IT+. In these terms, AF+s is related to ergy of activation to the observed AF*, predictions regarding the behavior of AF*, AH* or A S * have often been based on the behavior of Ma,,A I P , and k = ko(fi~x/f+) (1%) ASo, of ordinary salts.24 For example, regarding k = K(HRx/II*) (13) the level of A S * values, negative values are usually AAF* = RT A ln H T - IZT A In HKX (14) of the large negative ASc', a n t i ~ i p a t e dbecause ~~ values in solvation of ordinary salts. Because of H + and AFn, is related to H R X . For a given solvent the much greater importance of AF*, over AFO,in change, A A F + is given by eq. 14 as the sum of RT A determining AF* in eq. S , a further impression has In H + and -RT A In H R X . From the observed apparently developed that, for solvent changes, the A In k or A A F* value and A In H R X ,which can be ~ ~ the AAF',, A l F I * , and AAS*, quantities will be much measured, A In H* may be c a l c ~ l a t e d . Thus effects of solvent change on rate can be separated more important than AAFO,, A A I P , and A A S J , in into the separate effects on ground and transition determining the AAF", A U € * and AA.S* quantities associated with the solvent change. Comparing the state, respectively. For purposes of discussion and calculation, the transition state with ordinary salts, one w.odt1 then transition state in a solvolytic ionization often has anticipate a parallelisin between AAF", A U T ' ; or been approximated as the fully forined (and dis- A A S - , and AAFO,, AAFP, and AA.Sn,, respectiucly, of ordinary salts. (19) E. Tommila and J. Juttla, A c t a Chem. Scand., 6, 844 (1952). Comparing the observed facts with pretlictioiis (20) E. Tommila a n d & Lindholm, I. i b i d . , 6 , 647 (1951). based on analogy with ordinary salts, we ii~xyfirst (21) E. Tommila, ibid., 9,975 ( 1 9 5 5 ) .
+ +
Moelnyn-Hughes, Proc. R o y . SOL.( L o i z d o i z ) , A220, 88G (1953). ( 2 3 ) I. Dostrovsky and E. D . Hughes, J . Chem. Soc., 104 (1940). (24) L. C. Bateman and E. D. Hughes, ibid., 945 (1940). ( 2 5 ) I. Dostrovsky and M. Halman, ibid., 502 (1953). ( 2 6 ) (a) A. H. Fainberg and S. Winstein, unpublished work; (b) A . H. Fainberg a n d S. Winstein, THISJ O U R N A L , 79, 1597 (1957). (37) U'. M . Latimer and C. M . Slansky, i b i d . , 62, 2019 (1940). (28) F. A. Askew, E. Bullock, H . I. Smith, R . K . Tinkler, 0. G a t t y and J. H. Wolfenden, J . C k e m . Soc., 13G8 (1934).
(29) I < , C . Beughan, M. 0 . I,;2 SOC..
SOLVOLYSIS OF L-BUTYL CHLORIDE
Nov. 20, 1957
DISSECTIONO F A A F *
VALUES I N SOLVOLYSIS OF
TABLE IV BUTYL CHLORIDE
INTO
GROUND STATE
5941
AND
TRANSITION STATE CON-
TRIBUTIONS
Solvent, vol. "/o
Temp., "C.
MeOII 70.57, hleOH-HzO 60.5% MeOH-H20 4 9 . 5 % MeOH-Hz0 MeOH 90.17% MeOH-H20 80.09% MeOH-H20 70.4570 MeOH-HzO H2O AcOH AcOH-AczO
0 0 0 0 25 25 25 25 25 25 25
($%)5
2.634 3.951 4,292 4.723 3.350 3.697 4.043 4.390 6.699 3.090 2.895
log ( f i / M ) b
1.231d 2 . 400d 2 . 703d 3 . 127d 1 . 95Qd 2 . 24t5d 2.545d 2 . S46d 4.957' 1,849' 1.869'
A log ( f i / M )
0 1.169 1.472 1.896 0 0.286 ,586 .887 2 998 -0.110 - ,090
AAF
*
0 -2.79" - 3 . 50e -4.12" 0 -1.08" -2.01" -2.80" -6.25 +0.75 3 . OOg
A U * S
0
-1.33 -1.66 -1.75 0 -0.69 -1.21 -1.59 -2.16
S0.60 2.88
AAPbc
0 -1.46 -1.84 -2.37 0 -0.39 - .80 -1.21 -4.09 $0.15 .12
11r.4eOH044?
- ,152 1.28 1.07 .21 - ,390 1.28 0.75 .53 - .062 -0.47 - .55 .08 ,412 -1.49 - .89 - .56 ,780 -2.30 -1.24 -1.06 1.287 -3.02 -1.26 -1.76 1.727 -3.75 -1.39 -2.36 2.184 -4.59 -1.61 -2.98 log H R ~p ,being vapor pressure in mm. and N being mole fraction, respectively, of t-butyl chloride. log H R X ,molarity, -RT A In ( p / M ) . Based on data of Olson, RuebsaIf,of t-butyl chloride being employed instead of mole fraction, N . men and Clifford.37 e Based on data of Fainberg and LVin~tein.~"f Calculated from data of Grunwald and L V i n ~ t e i n . ~ ~ 9 Based on the assumed3" E* = 26.4 kcal./niole. * Calculated from the interpolated values of Olson and Half0rd.~6 EtOH EtOH 90% EtOH-HnO 80% EtOH-HnO 70% EtOH-Hn0 60% EtOH-Hz0 50% EtOH-H20 40% EtOH-H2O
25 25 25 25 25 25 25 25
3.037 2.799 3.225 3.778 4.210 4.772 5.260 5.761
1.807' 1.569h 1.897h 2.3 i l h 2.739" 3.24@ 3 . 686h 4 . 143h
look a t the A S * values. These are generally negative for solvolysis of t-butyl chloride in most solvents, and this is true also for other substrates listed in Table 111, most of them being substances whose solvolysis is not However, that A S * is not always negative'O~~~ is shown by the high positive A S * value for t-butyl chloride in water and highly aqueous Going on to compare the effects of the solvent change, MeOH -+ HOH, with the expectations based on AAFO,, AAHO, or AASO, of ordinary salts, it is, of course, obvious that A A F * has the expected sign based on such an analogy. Further, A A S * i s substantially positive just as are the AASO, values for salts. Because of the relatively low entropy of water with its relatively highly organized liquid structure,27t33 substantial positive AASos values are observed for ordinary salts, this being +35 e.u. for potassium chloride (Table 111). For all the substances listed in Table 111, regardless of the preference for solvolysis mechanism, positive values of A A S * are the rule. In the case of t-butyl chloride, it is interesting specifically to compare the observed A A S * of +13 e.u. with the value of AASO, for trimethylcarbonium chloride of +31 e.u. given by Franklin's treatment.31 Comparing A A H * for the solvent change, MeOH -+ HOH, with A m o s for salts, we note that A U T * is - 1.7 kcal./mole (-2.9 for EtOH + HzO), while A A H o s for lithium or potassium chloride has the opposite sign. However, A A P , does have a negative sign ( - 2.1 kcal./niole) for tetrarnethylammonium chloride, which might be expected3*to be a better model for trimethylcarbonium chloride than lithium or potassium chloride. Again, it is interesting to compare the A A H value of - 1.7 kcal./ mole with the AAHO, value obtained for the model
*
for trimethylcarbonium chloride employed by Franklin.31 For the latter value, Franklin's treatment gives +3.8 kcal./niole. With t-butyl chloride as the substrate in solvolysis, there are sufficient available data on Henry's law constant^^^,^^,^^ to indicate from the outset that A A F * values due to solvent change cannot be discussed on the basis of AAF*, values alone. I n Table IV is given the dissection of A A F * values into the component AAF*s and A A P , parts. I n this table, all the A A F values are referred to methanol as the standard sclvent. Focusing attention on the pure solvents for the moment, i t may be seen that A 1F does tend to be associated mainly with a corresponding change in AAF+,, except for the change to water as solvent. For solvent changes such as MeOH -+ HOH or EtOH + HOH, A A P , values, relating to effects on the ground state, are of major importance.38 For these solvent changes, AAFO, is ca. twice as large as A A F * s . How difficult i t is to calculate the effect of solvent change on rate from first principles may be illustrated for the MeOH + HOH change by combining Franklin's A A P , value3' (which is used as an approximation t o AAF*,) with the A A F Q v value given by Henry's law constants. A A P , , evaluated as AAHos - TAASO,, is -5.5 kcal./mole a t 25".
*
(36) A. R . Olson and R . S. Halford, THIS JOURNAL, 69, 2644 (1937). (37) A. R . Olson, W. C. Ruebsamen and W. E. Clifford, ibid., 76, 5265 (1954). (38) The AAFo, value for the solvent change, MeOH HzO, is in principle separable into AAHO, and AASO, values from data on the temperature coefficients of the Henry's law constants. However,
-
as far as we know, the necessary data are unavailable. On the basis of the behavior of other halides, for example, chloroform, the AAFo, value fa! t-butyl chloride may be due mainly to the entropy term [E. Grunwald, Thesis, U.C.L.A., 1947; A. E . Remick, "Electronic Interpretations of Organic Chemistry," John Wiley and Sons, Inc., New York, N. Y., 1943, p . 3491.
t
51
I I
IB--
A__.
64
os
06 Moie
Fraction
I(
H,O
Fig. 1 -Plot of AH*, 4F+, and -Tis* as inole fmction H2O for solvolysis of t-butyl chloride 111 dioxmic-€T?O niivtures a t 25 0”.
0
02
04 Mole
08
06 Fraction
IO
H,O
*,
Fig. 3.-Hot of AU AF* snc~- TAST c9. mole fraction H20 for solvolysis of t-butyl chloride ill EtOH-H20 n t 25 0”.
-..
ward solvent composition for the various binary solvent systems. 9 The behavior of Ail* and A S * for solvolysis of t butyl chloride is most simple in the non-aqueous solvent pairs. In mixtures of acetic and formic acids, substantially the entire contribution to the AFI increase in rate in going froin acetic to formic acid , is a 5.8 kcal./mole decrease in AI$*, A S * remaining almost constant at -3.2 i 0.8 e.u. The latter, however, does show a shallow minimum a t 75% AcOH-HCOOH. I n dioxane-formic acid mixtures, decrease in A I l T and increase in A S * are ca. equally responsible for increase in rate as the formic acid content is increased. Still a different behavior is apparent in the solI ...~. .. .... c 02 0.4 :!,: 0.8 vent mixtures involving water plus an “inert” solMole Fraction H,O vent, e.g., acetone-water and dioxane-water mixFig. ~ . - - P Mof AR*, AF* ant1 - T A S * us. m o ~ cfrnc- tures. Here the principal contribution to increase tiori 1420 for solvolysis of t-butyl cliloritlc i n AcOII--€T~O in rate is made by increasing AS*, A€I* being roughly constant. This is shown graphically for the mixtures at 95.0’. dioxane-water mixtures in Fig. 1. The character shown bv AII”, involving a weak niaxiniuni a t ca. Addition of AAFO, gives -9.G kcal./mole for AAF*, water and a marked minimum a t 83 mole -G.2 kcal./mole being the observed value. The dis- 60 mole Yfl water, is real, being well outside of experiiiiental in rate. crepancy corresponds t o a factor of Binary Solvents; AH* and A S * vs. Mole Frac- error. The situation becomes more complex for acetic tion.-Thermodynamic quantities of activation for solvolysis of t-butyl chloride have now been acicl-water mixtures, as shown in Fig. 2. Here AII* macle available for the complete composition ranges passes through a minimum a t cn. ST, inole 5; water, of a number of binary solvent pairs. These data per- and - TAS* through a maximum at ru. 20 niolc % mit an examination of the variation of the thernio- water. This plot is fairly characteristic of thosc dynamic quantities of activation in solvolysis with solvent mixtures in which both components are solvent composition, and they reveal a number of hydroxylic. Thus, the plots for formic acid-watcr striking features. Some of these features become and methanol-water mixtures are quite similar, apparent when AF+, AH*, and - TAS* are plotted and even ethanol- water, discussed further below, against mole fraction of the more rapid component shows a resemblance. n‘ith acetic acid-water of each binary solvent pair, as in Figs. 1, 2 and 3. mixtures, the principal contribution to increasing There exists a considerable diversity of behavior rate over the first two-thirds of the solvent range is o f the thcrmoclynaniic quantities of activation to- from the decrcase in M I * , A S - being rclatively \
?
‘k
2
’r,
~~~~~~
~
_
i
~
r0
SOLVOLYSIS OF t-BUTYL CHLORIDE
Nov. 20, 1957
constant. I n contrast, in the high water region, the effect of AS* becomes increasingly important, sufficiently so as to outweigh by far the actual reversal of the trend in AH*. The most complex behavior of AH* and A S * is observed in ethanol-water mixtures. Thus, while A F * is a monotonically decreasing, relatively characterless function of solvent composition, AH* and - TAS* go through some remarkable reversals. Roughly describing the behavior, from pure ethanol water, the chief contribution to to ca. 85 mole 70 decrease in A F f is decrease in AH In the last 15 mole of water, an enormous increase in AS* dominates the picture, more than compensating for the reversal in the trend of AH*. I n this case, AH* drops six kcal./mole over the first 85 mole %, then rises three kcal./mole in the last 15 mole % of water. The A S * value remains relatively constant a t -4.6 + 2.2 e.u. over the first 55 mole %, and then abruptly rises more than 15 e.u. in going the rest of the way to pure water.39 Complex behavior of AH* toward solvent variation has also been reported by T ~ m m i l a for ~ ~hyr~~ drolysis of methyl, ethyl and i-propyl benzenesulfonates in acetone-water and dioxane-water mix-
*.
r
+10
tures. I n a paper which became available t o us since our work was first presented,' Tommila and co-workers12report a complex pattern of AH* vs. solvent composition for hydrolysis of ethyl bromide, t-butyl bromide and t-butyl chloride in aqueous acetones. Further, Hyne and Robertson18 have observed shallow minima in A H * near pure water for solvolysis of methyl benzenesulfonate in aqueous methanol, ethanol and 2-propanol. A B C Classification.-When A S * is plotted z's. AH*, as in Figs. 4, 5 and 6 , for solvolysis of tbutyl chloride in the various binary solvent sys1+4 +IO1
I -
+2
+51
--
I-
1-2 /
~
+5
59.13
I
I
t I
-15
I
-
1-4
I I
190 v@l % Dioxane -2oL
L
- H20
- - - -. ~
--1-22 24 +-6 A H * , kcol /mole
I
~
20
Fig. 4.-Plot of A S * vs. AH* for solvolysis of t-butyl chloride a t 25.0': 0, AcOH-H~O; 8, AcOH-HCOOH; 8 , HCOOH-Hz0; 0 , dioxane-HCOOH ; C), dioxane-HtO. (39) The variations of AH* and A S * with solvent composition are not independent of each other. One limitation on the lndependence of their variation can be derived from the observation that AF decreases monotonically as "20 changes from 0 to 1. Mathematically, this can be expressed by theinequality, dAF */d < 0. Substitution of (AH - T A S f ) for AF and rearrangement of terms This exlead to the inequality, dAH*/dN=,O < d(TAS*)/dNH,o. presses the requirement that, whatever variation the slope of AH* us. goes through, it is always exceeded algebraically by the slope of the curve o f TAS u s . NHZO. Thus, changes in slope of one curve are always accompanied by related changes in slope of the other. (40) E . Tommila and E. hlerikallio, Suomen Kemislilehfi, 26B, 79
*
*
*
(1953).
*
:-5 O l
lo'
\
2b
22 24 A H ' . k c o l / m@le
26
Fig. 6.-Plot of A S * us. AH* for solvolysis of t-butyl chloride in EtOH-H20 mixtures a t 25.0".
tems, rather complex curves are obtained, the most complex being the plot for the ethanol-water mixtures in Fig. 6. For discussion, comparison and tabulation purposes, i t is convenient to set u p a symbolic terminology for characterizing the behavior of the thermodynamic quantities of activation toward solvent variation.
S . WINSTEINAND :ARNOLD H. FAIKRERG
5944 TABLE V
lines from the lower right-hand side of the plot to the upper left. Since AF* decreases continuously, the plot of A S * us. AH*, however it changes direcmr/iii I tion, is constrained to cut each 45" line once and > 1 4 1 only once. In general, it can do this in one of three 1 ---c Tl/,T2 < ways: A, both A H * and AS*increase; B, AH* dewhile A S * increases; C, both A H * and A S * ( T ~ / T ~ ~ L creases ) decrease. These classes are given in Table V along with the signs of ( a A I " * / b A F + ) , (bAS*/bAF*) and (bAST/dAII+). For classes A and C, the sign
SUMMARY OF THERMODYNAMIC CLASSIFICATION b A H + / bas+/ bas*/ b l F + / Class ~ A F +~ A F + b S € F b.V (1
A B c
D E F
-
+ +
+
+ +
+
+
-
-
+
+
t
+
+
-
-
-
-t
1
SCRE~~E
-
TABLE TI CORRELATION OF SOLVOLYSIS RATESWITII Y Compound
t-Butyl chloride
Seopentyldimethylcarhinyl chlorideg Dineopentylmethylcarbinol chlorideg Di-isopropyl phosphorocliloridxt~~~ Ethyl dichloroacctatc41
l l c t h y l benzenesuIfoiiate'R
Temp., OC.
Vol. 79
A X D THE
A B C CLASSIFICATION
h-0. of points
Solvent rnnFe
50.0 411 solvents 0-1007, EtOH-HZ0 0-100% MeOI-I-H20 O-l00% AcOH-HCOOII n-ioo% I-ICOOH-H~O O-lOOY, AcOR-H~O 0-90 vol. 7, dioxan-H20 0-90 vol. % hIe2CO-H20d 0-80 vol. yo dioxane-HCOOH 2 5 . 0 70-90 vol. % EtOH-H:O 50.0 70-90 vol. 7, EtOH-IS20 25.0 80-100 vol. yo EtOH-H20 5 0 . 0 80-100 V O ~ .% EtOH-If20 25.0 O-l00% EtOH-H2O" 30.0 O - l O O ~ , EtOH-H$O 35.0 50-70 V O ~%. hlcpCO-HsO 4 5 . 0 30-811 vol. % iLle2CO--I120 50.0 0-1007, EtO€I-IT20, hZeOH-FT20 7 5 . 0 O - l O O ~ , EtOH-H.0, RIcOlT-~I-120 50.0 O-l00% EtOH-H& 76.0 0-100% EtOH-1.120 50.0 0-100y0 hIeOH-HpO 73.0 0-1007, MeOH-TT&
69 19 1I (1 8 11 10 7 5 4
1 -14 5
4 3 4
1s I6 13 10 ti
nt
log- ko
ya
Class
0.974 -3.716 0.043 . 974 - 3 . 698 . Ot52 oC,,B;eC,5Al,,,l ,983 -3.693 .(I41 oCisB,,Ai,o , 9 2 6 -3.676 ,012 oC3:B100 1.070 -3.990 ,027 oC.isAloo 0.901 - 3 , 6 7 6 ,044 oCnoBSjAloo 1 ,007 - 3 . 774 .027 3jAGaBh5Alno 1 000 -3.779 ,038 aoAsoBgoAlno 0.960 -3.723 .004 35B100 .8;i6 -3.704 ,007 ,853 - 2 . 4 1 1 ,009 2sBco .C,O3 -2.302 .OOS .fil? -1.186 .0!3 ocit ,376 -:3.426 .Of37 ,411 - 2 , 6 8 8 ,047 oA!no ,701 -7.281- ,018 .(E -6.903 . O O i &, , 2 2 0 -4,503 ,025 ,217 -3.511 .023 ,214 - 4 502 .0%1 oB,,Aioo ,211 --3.516 ,027 . 2 Z i -4.516 , 0 1 2 ,,B,jAi,o
25.0 0-80 mt. % Me2CO-I120 7 .411 -6.,562 ,033 5 0 . 0 0--80 rvt. % Me2CO-H20 7 ,441 -5.338 ,034 ~ C ~ ~ S O B ~ S A I O O 2%. 0 0-90 wt. % diosane-H?O 9 ,440 -6.543 ,024 5 0 . 0 0-90 rvt. % dioxane-HzO 10 .440 -.5 333 ,029 2oA5sBsnC~5Aloo 30.0 O-lOO% EtOI€-HaO, MeOH A ,284 -4.819 ,052 %-Propylbenzeue2 5 . 0 0-90 wt. Yo h1e2CO-H20 7 ,454 -6.816 ,044 zjAioCgoAioo s~lfonate'~~~~ 50 fl 0-90 \vt. % hIe2CO-H.0 7 .4,Xl -5.617 ,031 Ethyl bromidec*'2 -10.0 0-85 wt. % l I e ~ C O - H Y O 20 .339 -6.787 ,031 60.0 0-85 W. 7 0 hZe?CO-HnO 20 ,364 -L5.950 ,030 rsA,,C,rAioo Probable error of the fit.42 The value for 60% EtOH--H20 was far out of line and was omitted. e Based on Y values calculated or interpolated from Tomniila's'2 data on solvolysis rates of t-butyl chloride in presumably the same solvents. Tommila, et aZ.,'2 recently have reported solvolysis data for t-butyl chloride in 18 R.Ie2CO-H20 mixtures a t several temperatures. Their data are in essential agreement with those repcrted in this and the previous paper3c in the high water region (.TII~,-, = 0.83 to 1.00), but differ seriously from our data in the low water region.
The classification system may be defined with the aid of a plot of A S * V.S. AH+ as shown in the inset in Fig. 6. In such plots, arrowheads may be placed on the curves to indicate the direction of increasing Y or increasing mole fraction of the more rapid component of a binary solvent set, e.g., X H , ~ .b'hen the A S + axis is laid out in units of TIS* (kcaI./mole), as in Figs. 4, 5 and 6 , a line of unit slope is a line of constant I F * . Values of A F * decrease as one crosses these iso-free energy
of b ( A S * ) / d ( A H + )is positive, while for cIassB, the
sign is negative. When a linear relation obtains between the thermodynamic quantities of activation, classes A, B and C are prescribed by definite boundary values of the slope a in eq. 5 relating A X * and AF+. Thus, a is less than 0 for A, between 0 and 1 for B and greater than 1 for C. Classes A, B and C suffice for neutral solvolysis of neutral substrates, for which solvolysis rate in-
SOLVOLYSIS OF BUTYL CHLORIDE
Nov. 20, 1957
5045
TABLE VI1
+d
LINEARFITSOF THERMODYNAMIC DATATO AH* = a A F * Compound
&Butyl chloride
T,emp., "L.
25.0
Solvent range
Class
EtOH, AcOH, MeOH, HCOSHz, HCOOH 90-100 V O ~ .7 0 EtOH-Hz0 50-90 V O ~ .yo EtOH-Hz0 0 EtOH-H?O 35-50 V O ~ .7 0-35 V O ~% ' . EtOH-H20 80-100 vol. % MeOH-H20 40-80 vol. % MeOH-H20 0-40 vol. yo hIeOH-HZ0 0-70 vol. yo MeOH-HzO 70-100 vol. % MeOH-H20 0-100% AcOH-HCOOH 75-100 vat. % ' AcOH-HCOOH 0-75 V O ~ .% AcOH-HCOOH O-lOO% HCOOH-Hz0 80-100 V O ~ .% ' HCOOH-Hz0 14.3-80 V O ~ .% HCOOH-Hz0 0-14.3 V O ~ .yo HCOOH-Hz0 80-100 mole % AcOH-H20 45-80 mole % ' AcOH-HzO 15-45 mole yo AcOH-H20 AcOH-H20 0-15 mole ' dioxane-HzO 0-90 vol. % 70-90 vol. yo dioxane-Hz0 60-70 vol. yo dioxane-HZO 40- 60 vol. yo dioxane-HZ0 0-30 vol. % dioxane-HzO 0-30 vol. % dioxane-HzO' 30-50 vol. % ' dioxane-HzOC 0-90 vol. % MeZCO-H20 ' dioxane-HCOOH 0-80 vol. %
r0
Neopentyldimethyl carbinyl chloride9 Dineopentylmethyl carbinyl chloride9 1-Chloro-2-meth yl-propan2-01~~ 2,3-Di~hlorodioxane~~
5 4 5 5 8 3 5 5 7 4 6 3 4 8 4 4 2 4 3 4 3 10 3 2 3 4 4 3 7 5
0.17 .31 .08
.I1 .19 .O1
.08 .l5 .04
.02 .22 .01
.07 .49 .05 .03 * .
.09 .02 .07
.31 .49
.11
.. .02 .10 .ll .10 .72 .04
50.0
70-90 V O ~% . EtOH-Hz0
3
.Ol
50.0
80-100 VOI.% ' EtOH-H20
4
.14
5 5 10
3 5
8 5 . 1 0-80 V O ~ .% ' EtOH-Hz0 25.0 0-75 vol. % dioxane-HZO ' Me2CO-Hz0 2 5 . 0 0-90 vol. % Methyl chloromethyl dioxane-alcohol ether46 25.0 benzene-alcohol CCl4-alcohol 0-80 vol. % dioxane-2-chloroethanol Ethyl chloromethyl ether45 25.0 40-80 vol. % ' dioxane-EtOH Dichlorodimethyl ether46 2 5 . 0 0-80 vol. yodioxane-EtOH p-Xitrobenzyl bromide46 50.0 50-90 wt. yo dioxane-Hz0 Benzoyl chloride47 25.0 60-95 vol. yo Me~CO-HnO Methanesulfonyl chloride48 5 0 . 0 50-85 wt. % dioxane-HzO Diisopropyl phosphorochloridate25 50.0 0-100 V O ~ .% ' EtOH-HzOd Ethyl dichloroacetate4' 50.0 50-70 vol. % MezCO-H20 Methyl p-toluenesulfonate1* 5 0 . 0 9 pure alcohols Ethyl 5 0 . 0 0-85 wt. % MezCO-HzO Ethyl bcnzenesulfonate'9~4~5 0 . 0 92.5-98 wt. % Me2CO-H20 0-92.5 wt. yo MeZCO-H20 0-95 wt. dioxane-HzO 0-95 V O ~ .% CeHs-EtOH 0-80 vol. % MezCO-EtOH
1
24100
d,
r b
kcal.jmole kcal./mole
a.
a
0.14 0.96 -24.63 1.86 13.56 0.36 - 9.09 1.3'3 75.00 -2.63 - 7.12 1.24 13.24 0.38 50.18 -1.37 50.34c -1.39" 75.51' -2.48c 0.23 0.95 - 9.25 1.32 5.42 0.72 39.69 -0.90 -25.42 2.16 34.22 -0.66 153.62 -6.66 -16.24 1.58 2.23 0.84 18.02 0.15 48.71 -1.31 23.79 -0.09 26.47 -0.18 2.81 0.79 18.63 0.11 50.70 -1.41 47.24' -1.22' 60.51' -1.8GG 23.77 -0.09 9.66 0.53 21.52
.03
2.31
1.03
.22 .14 .16
42.89 6.10
7.83
-0.59 0.66 0.57
7
.13 .14 .13
58.37 65.41 32.67
-1.51 -2.34 2.08
5 3
.27 .06
27.04 -45.12
-0.63 2.14
9
.57
129.21
-4.12
4 9 10 8 9
.06 .24 .35 .29 .12
-28.59 28.32 24.86 79.68 25.43
1.69 -0.29 -0.16 -2.16 -0.165
-
TABLE V1I
(continued)
Temp.. Colllpourld
OC.
Solvent range
Class
50.0 56-90 wt. % hlezCO-H20 27.2-56 wt. % MczCO-H~O Ok27.d wt. 70Me2CO-H20 i-Propyl bcnzeiic 50.0 0-99 wt % MezCO-H20 sulfonntelg~zl 0-95 wt. yo dioxane-HzO il-70 vol. yo CsH6i-PrOI-I 0-30 vol. Yo C6H6-EtOH 2 3 . U 0 - T O wt. % dioxaiic-I-I2C) 25.0 I) -8%wt. yo dioxane-HzO 25.0 0-52 wt. 70dioxane-IIzO 0-20 w t . yo nIeOH-HzO Propionic acidU41 25.0 0-82 rvt. % diosatie--Il?O Hydrogen clkxklc2: 2 5 . 0 O ~ - l O O ~i\IeOH-H20 o Sodium cliluridezi 25,O O-lOOyo XlcOII-~€-120 l'robablc error of the h e a r fit.4z KO.of pieces of data fitted. t e s t ) . ii No experitnerital data between 0 and 60 vol. % EtOH-HzO. 011 LJI* ant1 A S * calculated froiri first-order rate constants. n-Propyl benzcnesulfonatez1
creases monotonically as Y or iV of the more rapid solvent component increases; ie., ( b A F " / b N ) is negative. For the sake of generality, classes D, E and F, where ( d A F + / b N ) is positive, are included and defined in Table 17. In the example shown in Fig. 5, i t is clear that in traversing the iso-free energy lines of decreasing value in going from methanol to water, the plot starts in the C class, shifts t o B, and then to A. This leads to a convenient shorthand description of the data, C B A. It is useful to append subscripts to the letters designating the solvent range covered for each class, in terms of mole 7; of the more rapid component. Thus, for the methanol-water case, the complete description of the relative contributions of S I * and A S " to the solvolysis rate of ~ o ~ type . t-butyl chloride is given as o C a ~ B ~ ~ AThis of designation is particularly useful where only restricted portions of solvent ranges have been iiivestigatetl. In Table VI and V I 1 are listed these classificatioiis for the present data on t-butyl chloride, as well as for a number of compounds for which suiEcient data were available from the literature. I n most cases, the solvent compositions a t which a transition from one class to another occurs could not be accurately estimated; for this reason, the figures designating solvent composition were in most As a cases rounded offto the nearest 5 mole further simplification, only the major and mainbiguously established regions of the curvcs are clescribed. Thus the coiiiplex plot in Fig. 6 for tbutyl chloride in ethanol-water, which iiiight be ( 4 1 ) 1'. A I S a i r a n d IC, S . Aniis. THISJIJIJRNAI., 77, 3.182 (1955). (12) (a) A . 11. 11argenu:l and C . X I . l l u r p h p , "Alathernatics uf I'liysirs .rnd Chemistry," D. Van Xmtrand C o , Tnc., Kew I'ork, N. T., 19 i 3 p . 502; (I,) \V,J . Youden. "Statistical Afethuils for Chemists," Joliii \V:lcy a n d S
