I
Gerald Corsaro University of Akron Akron. Oh1044325
I
Salt and Sdvent Effects on Reaction Mechanism
One objective in transition state theory is t o explain medium influence on properties of the activated complex. The substitution reaction S2032- + BrCH200- a [cornplex]3-
-
K.
K.IrlA1
k.'/rtAl
k.'
+
(1)
log k = log ko + log m + log r e - log rt (3) lag h' = log ko' + log yn + log ye + l o g y ~- log yt (4) The y t term refers to the activity coefficient of the activated complex with a net charge of 3- for reaction between simple anions and 2- or 1- if cations are 1+ and 2+ valence. The Dehye-Hiickel limiting law expression substituted for the y terms gives log kz = log ho + 2AZnZePi2 (5) lag kz' = log ho' + 2AZ~Znnl'~~ (6) The prime notation is for reactions involving metal ions. For reaction between simple anions eqn. (5) gives a slope of +4A for plots of log kz versusI1I2and -8A for eqn. (6). The ko and ko' terms replace (kTlh)(Kt)of expression (2) and are the rate constants a t zero ionic strength. If reaction (1) is between simple anions of sodium salts in dilute aqueous medium ko is found a t 0.248 LM-I min-' a t 25OC and eqn. (5) is obeyed. Davies ( 1 , 2 ) used the available literature ( 3 , 4 ) rate data in which Ca2+.. Mp2+. ,. . and Ba2+ salts were used t o varv the ionic strength, I. lleshowed that cations form asswiated ion and BrAc-. and utilizine their disscxiation oairs with S1O.'- " equilibrium constants, including those for ion pairs with monovalent cations, he calculated all free ions and associated ion pair concentrations taking part in reaction and/or contributing to the ionic strength. I t was possible to allocate reactant concentrations for (5) and (6) separately. Davies thus confirmed the expectations of (6) and evaluated ko' for reactions involving Mg2+,Ca2+,and Ba2+. It should be noted that whereas ko'values are over 400 times the kovalue expression (6) accounts for only a small contribution to the overall rate of reaction. Table 1summarizes the ko' values reported by Davies along ~~
ton Pair
Sz03CH2C002- Br-
provides an illustrative example. It is the objective of this article to review the published rate data for eqn. (1) and show how theorv accounts for the oarticipation of cations in reaction nwchanisk and the influence of solvent and its consequence in effecting this participation. A correlation hetween cation lattice ionsize and ragconrjtants is demonstrated. Accordine to Bronsted and transition state theory, ionic rractions proreed via the formation of an activated c&nplen. The rate of reaction is assumed proportional to the concentration of activated complex with t h e latter remaining in equilibrium with reactant ions. One writes according to transition state theory the rate constant dependency hT h = -KiYars (2) h yt in whichKt is the eauilibrium constant between complex and reactants and t h e y terms are the activity coefficients togive it thermodvnamic consistencv. For reactions in which cations take part & additional term,&, is required in the numerator of eqn. (2). Hereafter, A, B, and M refer to hromoacetate, thiosulfate, and metal ions. Expression (2) with and without cation may be put in the forms
~~~
Table 1. Correlation Between Cation Size and Rate Constant
~~
-
with data added to show a correlation between cation size and rate constant. The values of K. are eauilibrium constants for formation of ion pairs. The K& for B; was extrapolated from the other values since the observed K, value does not fit the otherwise almost linear plot, K , versus r. The ion pair MgBrAc+ makes negligible contribution to expression (6) although i t is significant in calculating I.The parallel trends of K.lr and ko% suggest that an intermediate [S203MBrAc]forms prior to the transition state whose concentration is determined by that of (MSz031and in turn on the radius, rM of the cation, M. If alkali metal salts are used to orovide the anions. a reaction medium of low dielectric constant will enhance foimation of ion pairs, MS203- and MBrAc. Although few Kg values for such ion pairs are available for mixed solvents, the values listed for NaS70~-and KS701- are in excess of 200. The free en-&& difference, b ~of ,an ion in some specified reference state and in a given solvent environment is AG = G - (?(ideal)= -hTln) The total free energy of an ion is given by
"in which G' represents solvent media but non-electrostatic contributions; the other terms are potentials. The first is the potential at a distance r (radius) from the center of an ion with charge Zie. The last term is the potential at this same point hut due to counter charge of the first ion distributed over a spherical surface a t an effective distance, llx, when present in a mixed ion atmosnhere around the first term ion. The Debye-Huckel parame'ter, x , depends on .ZZi2e and hence, on I so that at I = 0 the term vanishes, G(ideal) = G' Zi2e2/2Dr and Zi2eZdW = -kTlny or log y = -AZi21'12 on substitution for x. This is the expression substituted in (3)and (4) to give (5)and (6). Hence, the latter would give linear plots of log k versus Ill2with slopes and kxtraoolated loe ko and log ko' which in t&n dependsin the dielectric values dependent OA; constants of the reaction media. What is required are expressions showing how log ko and log ko' are related to dielectric constant, D. 'I'l~edielertrir constant of a solvpnt mixture or pure liquid rellects the facility with which dipolar constituents may orient or order in an electric field. since the charged activated complex and reactant ions provide such fields, a difference in o r ( l e h g for r e a r t n n ~and ~ complex depends on the magnitude and difference of charges. For reaction ( 1 ) as written one expects as a result of such ordering an entropy difference between activated complex and reactants which is negative. With cation participating in the reaction either a lesser negative A S is expected or even a positive value since the activated comolex containine cation would have a lesser charge. These ASthmagnitudesmake up the major part of AGf relatkd to K + by AGt = -RTlnKt. The aforementioned ordering of
+
Volume 54, Number 8, August 1977 1 483
solvent constituents mav also affect the encounter frequency of reactants if the latter's mohility is diffusion controlled. Superimposed on these solvent effects are the repulsion or attraction forces which should depend on Coulomb's law. If a reference state is chosen as I = 0 and D = m the Coulombic forces vanish and Zi2e2 AG = G - C(idea1) = -kTlny = (9) ?nr Substitution of (9) in (3) leads to the Scatchard (5)expression (10) and when substituted in (4) gives (11) lag ko = log ko., -
ZA' ZI?]; rA rB
The ha values are the observed rate constants extrapolated
to zero ionic strength and h o = m is the rate constant for D = m or 11D = 0. N is the Avagodro number, R the gas constant in ergs, and e the electronic charge (esu). Substituting the sign and numerical values for the Z terms one obtains (-2Ne2/2.3 RTr)(l/D) expression (lo), (+Ne2/2.3 RTr)(l/D) and (+4Ne2/2.3 RTr)(l/D) for expression (11) for monovalent and divalent cations. The slopes log ho versus 11D and log h d versus 1/D depend on a value for r t , the distance of closest aonroach of reactant ions formine the activated complex, .. which isusually takenequal tor,,,rlr,and r ~ . T h ~ s a s s u m p t i o n i i not valid if divolar species are invol\.ed in reaction. hut the relative magnikde and signs of the slopes can he compared with those from observed rate data. The data of LaMer and Davis ( 6 )for reaction (1) in aqueous solutions of amino acids, sucrose, and urea (D = 70-100) gave log ho versus 1ID slopes of --30. The data of Corsaro and Morris (7) for reactions using three alkali metal salts of the anions in iPrOH-Hz0 mixtures (D= 30,35.3,42.5, and 49.7) gave log ho' versus 1/D slopes -16 and a log hot versus rlD single linear plot with all rate constants falling on the plot. With calcium salts in EtOH-Hz0 mixtures (D = 2&12.5), data not previously published, the slope was -+62. These slopes are in conformity with the expressions of (10) and (11) with regard to sign and relative magnitudes. Table 2 gives a summary of rate constants observed for one
484 1 Journal of Chemical Education
Table 2. Ion Pair
'.k
Summary of Observed Rate Constants LM-' min-'
k-'I?
k.'.Dh.80
of the iPrOH-H70 solvent mixtures (D = 35.3) The same average is found for h o ' . / ~r.80 in the other t hree solvent mixtures where 1) is the dielectric constant ot reaction medium and 80 is the D value for water at 25'C. These results may he interpreted in the same manner as for the behavior of divalent cations in water with regard to ion size and ion pair concentration. The constant value for h0'.D/r.80 indicates that all ho' values are leveled to a single cation size and the dielectric constant for water. This result suggests that simple Coulombic electrostatic forces contribute to the formation of intermediate and a transition state complex. The log ho'versus 1/D lot we refer to is actuallv that for the overall rate extrapolated to zero ionic strength, and tht: positi\.e A,pe n:flects the oredominance of ion natr effects oi the I o w r dielectric constant media. The analvsis of the data discussed should have nossible application in areasdreartion mechanism u>hereversalt and sol\.ent etfects nre manifwt. For exnmple, t h r hgdrolvsis of ortho esters of hcnmicacid is cntnlyrrd in sodium laurvl s d fate solutions ( A ) . The reaction pruceeds \,isa carbonium ion intermediate which is presumkd adsorbed on the micelle pseudo surface. The addition of a series of alkali-metal salts, Li-Cs, reduces the rate almost in proportion to the size of the cation. This effect is usually attributed to the hydrophobic nature of the cations, but more likely association of these with the sulfate ion end of the lauryl chains preempts carbonium ion adsorption. This association is enhanced if the polarity of the micelle stern layer is low as has been suggested (9). Lllerature Cited 11) 0auies.C. W..and Williams, I. W.. Trons.ForodaySor. 1547 119581. (2) Dsvies,C.W.,Pmgrass Ramelion Kinrflcr. 161 119611. (31 L ~ M < I . V .~ . F . ~d = ~ ~ D w.. . R J. . chamso
