July, 1936
MECHANISM OF S U B S T I T U T I O N REACTIONS
the concentrations of triiodide and vanadic ions, and inversely proportional to the concentrations of the hydrogen and iodide ions. This result is in agreement with the postulation that the single rate determining step is one between hydrolyzed vanadic ions, VOH++, and iodine molecules.
[ CONlRIBLITION FROM
THE
1157
Several possible rapid follow-up mechanisms have been suggested. The salt effect has been measured over the range of ionic strengths from 0.31 to 1.76, and a possible explanation for its large negative magnitude has been advanced. LOS
ANGELES,CALIF.
RECEIVED APRIL23, 1936
CHEMICAL LABORATORY O F THE UNIVERSITY O F CALIFORNIA]
The Mechanism of Substitution Reactions. Substitution of Bromine and Chlorine in Phenylbromo and Phenylchloroacetic Acids by Chloride and Bromide Ions in Aqueous Solution BY M. J. YOUNGAND A. R.
OL50N
When an optically active bromo compound is cases but as is shown by the rate laws, optical purity is in treated with chloride ion, a whole system of reac- no way essential. I t is essential that the assumption that l-phenylchloroacetic acid and l-phenylbromoacetic acid tions is initiated. By making a kinetic study of have the same configuration be correct. This assumption the system of reactions which occurs when 1- is in accord with the opinion of those who have worked bromosuccinic acid is treated with chloride ion with such compounds. in aqueous solution, Olson and Long' were able Apparatus to prove the correctness of the theory of the For all measurements of optical activity a laboratory mechanism of substitution reactions advanced by constructed polarimeter of the Lippich type was used, Olson,2 and by Bergmann, Polanyi and S ~ a b o , ~with monochromatic light (A 5461) obtained from a meraccording to which configurational inversion ac- cury arc and suitable filters. The angle of rotation was determined from the deflection of the image of an illucompanies every single-step substitution. minated scale, four meters distant, produced in a small The present study deals with the kinetics of the plane mirror mounted nearly on the axis of the analyser, corresponding system of reactions produced by and reflected into a telescope parallel to the optic axis by treating 1-phenylbromoacetic acid with chloride means of a periscope arrangement. This device enabled ion in aqueous solution. The results provide rotations to be read directly to 0.007' (1 mm. of scale) and estimated to 0.001'. A given setting can be duplicated to additional confirmation of the above-mentioned 0.005'. A thermostat provided with glass windows was theory. mounted directly on the polarimeter so that tubes did not The relations between the heats of activation have to be removed tor observation. of the various reactions in the succinic system, Experimental Procedure studied by Olson and Long,* are again apparent Due to the slowness with which the phenylhalogenoacetic in this system. The same is true of the tempera- acids dissolve in water, the following procedure was adopted. A weighed amount of the active acid was disture independent factors. Preparation of Materials Phenylbromoacetic acid and phenylchloroacetic acid were prepared from mandelic acid (phenylhydroxyacetic acid) by treatment with the corresponding phosphorus pentahalides, following the procedure given by Walden and Bischoff.s The acids were resolved by fractional crystallization of their morphine salts from methyl alcohol, following the procedure of McKenzie and Clough.6 The products were shown to be chemically pure by the usual analyses. Complete resolution was not obtained in all ( 1 ) A. R. Olson and F. A. Long, T q ~ JOURNAL, s 58, 1294 (1934).
(2) A. R . Olson, J . Chem. Phys., 1, 418 (1933). (3) Bergmann, Polaoyi and Szabo, 2. g h y s i k . Chem., B40, 161 (1933). (4) A. R. Olson and F. A . Long, THIS JOURNAL, 58,393 (1936). ( 5 ) Walden and Bischoff,A n n , 2 7 9 , 122 (1894). (6) McKenzie and Clough, J . Chem. SOG.,93, 818 (1908).
solved in 0.4 cc. of methyl alcohol. To this solution was added the required amount of 2.00 Nperchloric acid (about 10 cc.) followed, after re-solution had occurred, by the required amount of 2.00 N halogen acid (about 10 cc.). The addition of so small an amount of methvl alcohol has no observable effect on the reaction rates. All solutions were prepared at the temperature of the experiment. After the solution process, the material was transferred rapidly to a 30-cm. polarimeter tube and placed in the thermostat. Zero time was taken as the moment of addition of halide ion. The time interval between this addition and the first reading was never more than four minutes. In all experiments the concentrations are: active acid 0.015 M,halide ion 1.00 M , hydrogen ion 3.00 M , unless otherwise specified.
The Formation of Mandelic Acid from Phenylhalogenoacetic Acids.-The detailed mechanism
11%
.1
M. J. YOUNGAND A. R. OLSON
Vol. 58
kl(Br-1
l-C6HsCHOHCOOH (r)
~-Ct,H&HOHCOOH(r)
1
ka(Cl-)
of the reactions between phenylbromoacetic acid or phenylchloroacetic acid and water, by which mandelic acid, hydrogen ion and halide ion are produced, is not completely understood in spite of the amount of investigation to which it has been s ~ b j e c t e d . ' ~ The ~ ~ ~ specific rate, measured by the rate of formation of hydrogen ion, is in accord with the assumption that the undissociated acid reacts more slowly than its ion. Measurement of the decrease of optical activity with time makes it necessary to suppose that the ion can react with water in either of two different ways, one reaction producing a d-mandelic acid, and the other an I-mandelic acid. The following mechanism can account for this effect and is a t the same time in accord with the theory that inversion in configuration accompanies each single-step substitution.
0 (inversion a t C( 1))
Reactions (l), ( 2 ) and the sequence (3), (4) lead to a mandelic acid of configuration opposite to that of the CaH6CHXCOOH. The sequence (3), ( 5 ) , involving a double inversion a t C(1), leads to a mandelic acid of the same configuration as that of the C&CHXCOOH. The relative amounts of levo and dextro mandelic acids depend on the relation between the specific rates of the various reactions under the conditions of the experiment. Although we failed to isolate the postulated lactone, a similar compound is known to be formed in the hydrolysis of bromosuccinic acid. When the hydrogen-ion concentration is large, this mechanism predicts that 2-CeHaCHXCOOH (1) (2) ki (1) C6H5-CHX-COOH HzO ----f will disappear a t a specific rate kl ( ( k ~ k3) CgHsCHOHCOOH + H + + X - (inversion at C(1)) k,/(H+)}, where k, is the dissociation constant of C6H&HXCOOH, and that d and I mandelic acids will appear a t specific rates kl { ( k ~4kBfl)ka/(H+)) and k d 1 - P)K,/(H+), respec(1) ( 2 ) ka tively, where p is the fraction of the lactone hy(3) CeH6-CHXCOO- + C~HS-CH-C=O + X - drolyzing by reaction (4) and (1 - p) the fraction 'O/ hydrolyzing by reaction ( 5 ) . If the specific rate (inversion at '(I)) of disappearance of Z-C6HsCHXCOOHis repre(1) ( 2 ) fast sented by K , the specific rates of production of + HzO* +C~HF,-CH-COOH* (4) CaHs-CH-C=O 1 and d mandelic acid can be represented by K(cY), I OH 'O/ and K ( l -a), respectively, where CY = 1- { k&,/ (inversion at C ( 2 ) ) [kl(H+) h k a hka]). (7) (a) Senter and Tucker, J . Chew. Soc., 109, 690 (1916); (b) Rate Laws Senter, i b i d . , 107, 908 (1915); ( e ) Senter and Drew, i b i d . , 107, 638 ( 1Y 1.5). Following the system of reactions and the no(8) A . McKenzie and N. Walker, i b i d . , 107, 168,; (191,7). 'tntion shown in Fig. 1, we can write the differen(9) A M. Ward, { h i d , , 1184 (19%).
+
+
+
+
+
+
MECHANISM OP SUBSTITUTION REACTIONS
July, 1936
tial equations for the rate of change of the concentration of each substance.
+ kt(Br-)y + ka(Br-)z - k,(Cl-)x - ksx (2) dy/dt = -kl(Br-)y + kl(Br-)x + k3(Br-)w - k4(C1-)y - k s y (3) dw/dt = -kZ(Cl-)w + kz(CI-)z k3(Br-)m + k4(C1-)y - k6w (4) dZ/dt = -kz(Cl-)~ + Rz(Cl-)w ks(Br-)z + kc(c1-)2 - k@ ( 5 ) drjdt = ksax + ks(1 - a)y + kaaw + ks(1 - a)z + k s a ~+ ks(1 ( 6 ) ds/dt = ksay + k s ( 1 (7) d(Br-)/dt = k4(C1-)(x + y) k3(Br-)(w f z ) + k d x + Y) d(Cl-)/dt = -kr(Cl-)(x + y) + (8) (1) dx/dt = -kt(Br-)x
(Y)X
CY)W
kdBr-)(w -I-z )
+
+
Additional assumptions: (1) kl > > ka SO that 4CHBrCOOH is racemized as fast as it is formed; i. e., (x y) = 0; K 6 makes no contribution to ( I - s). (2) (Cl-) is so small that &(el-) and kr(C1-) are negligible. (3) (Br-) = constant Ratelaw: (e -e,)/@, - 0,) = e-[ka(Br-)+kslt,8 , = ks(w - Z)ocs(2a - l)/(kdBr? f ks)
-
(6) Initial conditions: (x - y) = (x - y ) ~= A , (w - z ) = 0, ( r - s) = 0, (Cl-) = 1 M, (Br-) = 0, (H+) = 2 M Additional assumptions: (1) k8(Br-) can be neglected, ( 2 ) ks < < ks, (3) (Cl-) = constant, (4) e, = 0 (experimentally true) ) Re-[%(Cl-)tksl~ Rate law: e/eo = (1 + R ) e - Q ( f -
R
+ kdw + z )
For the determination of the angle of rotation only the quantities ( x - y ) , (w - z) and (r - s) need be calculated, for 0 = C,(x - y ) CZ(Wz) C3(r - s). For the evaluation of the six specific rates, a series of experiments was devised each involving only one unknown specific rate. ‘This series, and the corresponding integrated rate laws, are shown in Table I. TABLE I (1) Initial conditions: (x - y) = ( x - y)o, (w - z ) = 0, ( Y - s) = 0, (C1-) = 0, (Br-) = 1 M , (H+) = 2 M Additional assumption: kl > > k6 so that ks can be neglected. (Br-) = constant Rate law: €)/Cia e-2k1(Br-jf =i
1159
= ICz/G]kr(C1-)/[2KtA
2kz(Cl-) Q(t) = [ 2 k J
- ksl
+ kr(Cl-)
e-[k4(C1-)+kslf)/(kq(c1-)
+ k~(Cl-) + k, + kslt - 2k1A[(1 + k6)I.
The rate laws for experiment series (l), (a), ( 3 ) and ( 5 ) follow in a perfectly straightforward manner from the differential equations; those for experiment series (4) and (6) involve an intcgral of the form I = l e - (~+b)f+la(l-e-~~)/bIdt
We have been unable to evaluate this integral exactly in terms of elementary functions. Olson and Long handled it by means of a series expansion and term by term integration. We have found the following procedure more convenient in this case. Integration by parts gives
(2) Initial conditions: (x - y) = 0, (w - Z ) = (W - z ) ~ , I = ( (1 - e - ( a + b ) f + [ a ( l - ~ - ~ ~ ) / h\ l / ( a + b ) (Y - s) = 0, (Cl-) = 0, (Br-) = 0, (H+) = 2 M Additional assumption: Since (C1-) remains small, a$’e-:~+Zb)f+[a(l--e-~’)/bl dt / ( a b) kz(C1-) can be neglected compared to ks Ratelaw: (e e,)/(o, e,) = ,-hi, 8 , = C~ The second integral can be neglected for two rea(w - z), (2a - 1)
(I
+
-
{
1
+
-
sons. The integrand is smaller by a factor ebf,
-
(3) Initial conditions: (x - y) = 0, (w z ) = (w - Z)O, and the coefficient a is small compared to 1, in (I - s) = 0, (Cl-) = 1 M , (Br-) = 0, (H+) = the time units empfoyed. The error introduced 2 M by this neglect is never more than 0.3%. Additional assumption: (Cl-) = constant - e,) = e-[2kz(C’-)+ka~‘, The constants appearing in expressions (l), Rate law: (e - €),)/(e0 (a), (3) and ( 5 ) can be evaluated by calculating e, = C,(W - z)oka(2a - 1)/{2k2(c1-) k s ] one value from each observation and averaging , - z) (4) Initial conditions: A = ( x - y) = (x - y ) ~ (w the results in the usual manner, or by obtaining = 0, (Y s) = 0, (C1-) = 0, (Br-) = 0, (H+) = 2 M a value of the slope of the line Additional assumptions: none In (0 - e,)/@, - 0,) = -kt Rate law: (e - 8 , ) / ( % - e,) = using the method of least squares. The exprese - ( Z k ~ A + K d t + ( 2 k 1 A ( 1 - - e - ~ ~ ~ ) / he), = C,(x - Y ) ~ (4) and (6) cannot be solved explicitly for sions (2a - l)k5/(2klA ks) the unknown specific rates kg and k4, respectively. (,5) Initial conditions: (x - y) = 0, (w - Z ) = (w - z)a, In these cases a value of the specific rate was de(r - s) = 0, (CI-) = 0 , (Rr-) = 1 M ,(H+) = tcrniinetl by a trial and error process to fit ant' 2 A1
+
-
+
M. J. YOUNGAND A. R. OLSON
1160
observation ; the remaining observations were plotted on a curve calculated using this constant, and agreement was found satisfactory in all cases. The results obtained are given in Tables IIVIII. The values of K(ca1cd.) are those obtained from the activation energies and temperature independent factors shown in Table VIII. All times are in minutes unless otherwise specified.
VOl. 58 TABLEVI1 kr C1- +d-CsH6CHC1COOH Br-
+
I-C&CHBrCOOH runs
k4
3 2 2
0.01582 ,003610 .001253
322,54 307.92 298.1
Reaction
TABLEI1 ki
4- Br-
= d-C6Ht.CHBrCOOH f Rr-
(Br-)
No of moles/
T, OK.
runs
288.1 298.1 298.1 303.23 307.02 310.70
Mean deviation,
%
ki
liter
2 2 3 2 2 1
0.984 .208 .965 ,965 .964 ,960
0.004358 0 . 5 .01198 .1 .01268 .3 ,01984 .3 .02974 1 ,04294 ..
kt calcd.
0.004363
.. ..
,01251 .0209 ,03020 .04294
TABLEI11 ks 1-CeHsCHClCOOH Hz0 +CsH6CHOHCOOH H C C1-
+
T, O K .
No. of runs
323.1 308.1 298.1
2 2 2
+
Mean deviation,
k6
2.20 x 10-4 3.65 X lo-& 1.03 X
+ yo
2 2 2
TABLEIV 1-CsHsCHClCOOH NO.
+ '21-
k2
= d-CdIsCHCICOOH f C1Mean deviation,
kobed. =
Of
T,O K . runs
Zkz(Cl-)+ks
%
k,
(Cl-)
308.1 2 5.067 X lo-' 2.00 1.178 X lo-' 323.1 2 2.660 X 10-5 2.00 6.100 X lo-'
1.6 1.5
+ Br- +d-C6H6CHBrCOOH
+ c1-
No. of runs
322.54 308.05 298.1
6 5 2
bobad.
=
ks(Br.-) + h
(Br-)
3.260 X 10-3 7.326 X lowr 2.457 X lo-'
0.980 .980 ,980
ka
Mean deviation, %
ks, calcd.
3.114 X lo-' 7.104 x 10-4 2.402 X
1.5 1.9 2.0
3.104 X 10-a 7.141 X lo-' 2.397 X lo-'
TABLEVI k5
l-CsHaCHBrCOOH
+ HnO +d-C&CHOHCOOH + H f + Br-
T,OK.
No. of runs
324.0 307.92
2 2
+ C1-
Br-
+ C1-
kr
0.00174 0.000318
Ecn~./mo~e
A X 10-9 (set.moles-' litera)
17,971 * 150 21,683 20,016 * 87 19,805 * 100
3.13 4.74 1.90 6.93
KO values of E and A for the hydrolysis reactions (Tables I11 and VI) were calculated for they would be of doubtful significance since the specific rates are complex averages over several reactions. The listed probable errors are mean deviations from the average of the values of E calculated for each temperature interval. It can be shown that the introduction of the assumption of incomplete inversion in configuration, giving rise to the system of reactions appearing in Fig. 2, where the Greek letters represent in each case the fraction of the reaction occurring without inversion, results in an alteration of the rate laws which is not detectable except in the case of expression 6. In this case the new rate law is e/eo = (1 + R)e-Q(O - R e - [ Z k ~ ( C I - ) + W ~ where R = C&,(Cl-)(l - 2e)/C1[2klA 4-
+ +
k4(Cl-)(l - 2 ~ ) kr - 2kz(C1-)
+ kr(CI-)(l
(2klA(1
ka'
T, O K .
+ Rr-
I-C6H6CHBrCOOH I-CsHsCHClCOOH ~-CRH&!HC~COOH f 1-CoHsCHBrCOOH
Q(I) = (2kiA
TABLEV l-CsHaCHCICOOH
kr, calcd. 0.01576 .003632 .001250
TABLEVI11
Results
l-CeHsCHBrCOOH
+
No. of
T,O K .
-
2 ~ ) kslt
-
- e-[kr(CI-)+kjll)/[ka(Cl-)
- ks] + k611
The effect which this modification has on the calculated value of 6 for various times and for various values of B is shown in Table I X for the TABLEIX Time min.
0 cm. c = 0
0 -15.76 10 11.18 20 7.27 3.98 30 1.21 40 50 +1.09 2.45 60 4.52 70 5.75 80 6.75 90 7.54 100 9.48 150 9.72 200
A0 0.03
c =
0
0 +0.01 .02 .03 .03 - .03 - .03 - .03 - .03 - .02 - .01 - .01
-
A0 = 0.05
0
+O.Ol .02 - .03 .04 .06 - .06 - .05 - .05 - .04
+ -
-
.03
.02 .01
f
A0 = 0.07
0 +O.Ol f .03 * 00 - .05 - .07 - .08
- .O9 - .os - .OS - .07 - .0:3 - .O1
1161
MECHANISM OF SUBSTITUTION REACTIONS
July, 1936
d-GHrCHOHCOOH(s)
