I
-
R. K. Cosarove. P. W. Kina. -.
and A. C. Norris Portsmouth Polytechnic Portsmouth, Honts, England
Ion Association and Ionic Reaction Rates An investigation of the brornoacetate-thiosulfate reaction
The reaction which occurs in aqueous solution between bromoacetate and thiosulfate ions is an uncomplicated bimolecular process remarkably free from interfering side reactions (1, b) The object of the present paper is to show how this reaction can he used to demonstrate the way in which the rate of an ionic reaction is influenced by the formation of ion association complexes (ion pairs). No student experiment to describe this effect has been reported previously. Ion Association and lonic Reactions
The quantitative description of the effect of ion association on the rate of an ionic reaction was developed by Wyatt and Davies (3) and Davies and Williams (4). These workers applied the theory to their own (3) and to previous ( 1 , 5 ) data for the bromoacetate-thiosulfate reaction in the presence of alkalineearth cations. For example, when magnesium nitrate is added to a dilute mixture of sodium thiosulfate and sodium bromoacetate, zhe ion pairs MgSz03 and MgBrAc+ are formed in significant concentrations.' These species participate in processes which are concurrent with the reaction between the unassociated ions. SnOP BrA(SnOsBrAc8-) BOIAc'- + Br- (1) MgSnOa+ BrAo- + (MgSnOaBrAc-) Mgz+ + S20aAc2-+ Br- (2) S~OBI- MgBrAct (MgS2OaBrAc-) Mga+ S10aAe2- Br- (3) MgSn01 MgBrAcf (Mg&OaBrAc+)
+
+
+
=
=
--+ +
2Mg2+
+
+ Br-
S20aAc4-
(4)
and BrAc-, the contribution of route (4) can be neglected. Application of the Br@nsted-Bjerrum theory of the primary salt effect (6) to this mechanism gives the overall rate of reaction, v , as the sum of three componentsz u = (ktfPfi/fd[S~08~-1 [BrAc-I (klfi/fi)LMgS~Od[BrAc-I (k~j~f~/ft)[S~O~'-l[MgBrAc+l (5) where the free ion concentrations are those which remain after ion association, f ~f , ~ and , f~are the activity coefficients of uni-, hi- and tervalent ions, respectively, and the activity coefficient of the uncharged species MgSzOaisassumed to beunity. The activity coefficients for the charged species are readily calculated from the Davies equation (7) log f, = -Az,'[I'/./(l I ' h ) - 0.311 = -AeePF(I) (6)
+
+
+
Here z, is the valency of the ith kind of ion, A is a constant (= 0.509 I'/l mole-'/' for water a t 25°C) and, for most ions, the function F ( I ) increases with increasing ionic strength, I, up to I = 0.5 mole 1-'. Now the ion pair concentrations can he eliminated from eqn. (5) by defining their dissociation constants thus MgSzOse Mgs+ + SzOa2KZ= IMgn+l[SzOa'~lfi'/[MgSIOal (7) MgBrAe+ == Mg'+ + BrAcK2 = [Mgnf] [BrAc-1 fif,/[MgBrAc+lj, (8) With these substitutions, and the simplification f&ja = l/j2derived from eqn. (6) v = [SnOa2-][BrAc-] (k& (k~/K~)fiYMg'+l (ka/Kdfzz[Mg"1 I (9)
+
+
However, the reaction is accurately bimolecular under all conditions and so3 v = k.[S10s2-l,[BrAc-I, (10)
Reactions (2)-(4) show clearly that ion association catalyses the overall reaction by reducing the electrostatic repulsion between the reactants. If the bimolecular rate constants a t infinite dilution for the processes (1)-(4) are k~to ka, respectively, then, on electrostatic grounds, a ! is expected to be less than ka. Since also the concentrations of MgS20a and MgBrAo+ are small compared with those of S2OaZ-
Here, k, is the experimental rate constant and the suffix s refers to the stoichiometric reactant concentration. Hence, from eqns. (9) and (10) after rearrangement and defining k' = (kz/K~ ka/KJ k' = ((k.[S103z-l(I[BrA~-lr/[S10~~-I [BrAc-I) k,/f*l/[Mga+lf%* (11)
'Under these conditions, the concentrations of the species NaSnOl-, NaBrAc and MgNO3+are negligible. 'In eqn. (5), the first term on the right hand side exhibits a positive, the second s. zero, and the third a negative salt effect. In the absence of ion association, the combination of eqns. (9) and (10) produces the standard farm of the Brdnsted-Biemm equation, k. = k,/f2.
Since k, and ica are bimolecular rate constants and K1 and Kzhave units of mole 1-1, kt is effectively a termolecular rate constant and is a measure of the efficiency of the magnesium ion in catalyzing the reaction. The individual rate constants kz and ks cannot be determined separately without further assumptions (8) hut k' can he derived from eqn. (11).
626
/
Journal of Chemical Education
+
If the theory and assumptions on which eqn. (11) is based are correct, the value of k' should he independent of the ionic strength. Furthermore, if q = k ' p then log p = log k'
-8AN)
veniently taken a t 15-20 min intervals, i.e., a. titration is made a~oroxi~ll&teIv everv 10 min. ~~, I n an cxtcndcd form, the experitneut l m also hem used with success as aprojcct for afital year student.
..
Table 1. Rate Constants (k.) at 25'C for the BromoacetoteThiosulfate Reaction in the Presence of Moanesium Nitrate INaBrAol. = [Na3S20aJ. 5 X lo-' mole 1-1
Materials. Sodium bramoscetate is not readily s v d able but is easily prepared by dropwise neutralization of redistilled (9) bromoacetic acid with sodium hydroxide using phenolphthalein as indicator.' The preparation is carried out in ethanol and, after recovery, the precipitated salt is found to contain 99.9 f 0.2y0 of the theoretical bromine content so that recrystallisation is unnecehssry. The salt keeps indefinitely when stored in the dark under vacuum and aver phosphorus pentoxide. All other reagents are rwenrcb grade chemicals. K i n ~ l ? r&p.prrtmenls. A rexrtiun mixture ir pnparcd from IOU ml of a suck solution of u.tll .I1 sodium thiuwlfate and 100 ml of a solution containing 0.01 M sodium bromoacetate and the required concentration of magnesium nitrah6 Thus, the initial cancentra.tions Of both reactants are always 0.005 M and the starting concentrations of the inert salt are conveniently obosenas5.0, 7.5, 10.0, 12.5, 15.0, 17.5,20.0, and22.5 X 1 0 - W . The bromoacetatenitrate solutions are readily prepared by diluting to a total volume of 500 ml, 100 ml 0.05 M sodium hromoacetate and 50, 75 ml, etc. of stock 0.1 M magnesium nitrate solutions. When the 100-ml aliquots of the reactant solutions, contained in stoppered 500-ml conical flasks, have reached the temperature of a water bath thermostatted a t 25.00 f 0.05'C, the reaction is begun by pouring one solution into the other and transferring the total volume back to the empty flask. A stopwatch or clock is started midway through the mixing. At suitable times, t minutes, after the start of the reaction, 25-ml aliquots me withdrawn from the reaction mixture and pipetted into a quantity of ice-cold -0.0025 M iodine solution (containing 4% w/v K I ) just insufficient to react with the remaining thiosulfate. One gram iodine-free potassium iodide and 5 ml of s. 4% w/v solution of sodium starch glycollate are added and the titration completed with iodine solution from a buret. The total titre, T 4 is proportional to the concentration of thihsulfate a t the time of sampling. Two 25-ml aliquots of ice-cold 0.005 M sodium thiosulfate (prepared by dilution of the stock 0.01 M solution) are also t~tratedwith the iodine solution and the mean titre, T. is proportional to the initial concentration of thiosulfate. Both T tand TOare estimated to f0.01 ml, but a blank correction of 0.06 ml is subtracted from these titres since, with the standard procedure used here, this volume of iodine solution is required to produce s detectable coloration at the endpoint (straw-yellow in the presence of excess KI). Thus, for each sample, the rate constant, k., is calculated from the usual bimaleculsr formula in the form (To - Tt)/0.005(Tt
- 0.06)t 1 mole-'
min-I
-
-
[Mg(NOd.l.
(10"mola 1-9 5.0 7.5 10.0 12.5 15.0 17.5
Experimental Procedure
=
~.
(12)
and a plot of logq against F ( I ) should give a straight line of slope, -8A (= -4.072 l1/%ole-"3. The experiment now to be described is designed to produce the necessary data with which to evaluate k' and test these postulates.
k.
~
*.
(I mole-. min-1 )
0.568 f 0.005 0.018 f 0.002 0.650 f 0.005 0.083 f 0.003 0.722 f 0.008 0.738 -t 0.006 0.748 f 0.005 0.785 rt 0.005
20.0 22.5
Results and Discussion
Typical rate constants, k,, obtained by students for the above experiments are shown in Table 1. The results show clearly the overall positive salt effect. They also demonstrate that k, is readily determined with an error less than *I%. To interpret these data it is necessary to know the values of the rate constant, kt, and the dissociation constants, K I and 5. I n their analysis, Davies and Williams (4) took k l = 0.247 1 mole-' min-' and K1 = 0.0145 mole I-' and K2= 0.28 mole I-I (the smaller the value of K the more stable is the ion pair) and these values are used here. As eqn. (11) shows, the calculation of k' also requires a knowledge of the concentrations of the free ions and the activity coefficient fi. Since the values of these parameters depend intrinsically on one another and upon the ionic strength, they must be determined by a series of successive approximations. The iterative procedure is best illustrated by expressing the relevant equations in algebraic form. Let and
and [MgBrAef] = R
then [Ns+] = 3B
In this laboratory, students work in pairs and, when provided with the stock solutions, each pair carries out two reactions during a. 4-hr laboratory period. If time is limited, the first reaction should be started as soon as possible and the second about 10 min later. Usina the same buret for all titrations. the mean vahle of TO,wlridl is ~ppliral~le to hoth rcnctims, can hc dctcrmi~rrd bcfore t l a tirst snnqlle i- rakcn about 40 rnin after the start of the rcnrtion. Further a r q h ncvcn f n m each mixtwe are ron~
~~
Equations (7) and (8) become Bromoacetic acid produces skin blisters, and the preparation is best carried out by an experienced technician. The sodium salt is not a vesicant. The tbiosulfate and bromoacetate solutions are not stable for long periods and should be freshly prepared (1).
On rearrangement, eqn. (13) gives a quadratic in P from which Volume 48, Number 9, Sepfember 1971
/
627
Table 2.
Effect of MgSO3 and MgBrAc+ Ion Pairs on the
Bromoacetate-Thiosulfate Reaction at 25°C
The other root of this quadratic is not calculated since it predicts a value of P > B, a result which has no physicalsignificance. Division of eqn. (13) by eqn. (14) and transposition gives R = K,BP/[&f,(B - P ) KIP] (16)
+
Also
[NaBrAcl. = [Na,SOzI. = 5 X 10-8 male IMg-
(N04,I. (101 mole 1-1)
IMsS308l iMgBrAat1 (10. mole
1-1)
(10" mole
I-?
0.04 0.38 0.50 0.06 0.60 0.08 0.69 0.09 0.11 0.76 0.82 0.12 0.88 0.13 0.93 0.15 Mean value of k' =
5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5
I
fi
(mole
I-?
1-1
F(I) (mo~e'/s
0.508 0.0334 0.481 0,0404 0.462 0.0474 0.444 0.0546 0.429 0.0617 0.416 0.0690 0.404 00762 0.393 0.0835 110.0 i 3.0 1' mole-'
I
-
0.1445 0.1552 0.1646 0.1730 0.1805 0.1873 0.1935 0.1991
k'
,& ,in-,) 112.6 113.6 108.6 109..4 113.1 108.7 103.6 110.2
min-1
where c , is the concentration of the ith kind of ion and log f, = - Z.O36[I'/r/(l + 1%) - 0.311 (18) The choice of a quadratic solution for P allows the initial value of R to be set equal to zero. Starting with f, = 1 (effectively I = O), the calculation of the unknown parameters proceeds in the following order: P, eqn. (15); R, eqn. (16); I,eqn. (17) and f2,.eqn. (18). Repetition of this cycle produces a consistent set of values P, R, and f2 for each reactant concentration. k' is then calculated from the algebraic form of eqn. (11) k' = [kJP/(B - P)(B - R) - kr/fil/(C - P - R)fna Table 2 shows the results of these calculationss carried out for each of the mixture compositions shown in Table 1. The extent of formation of the MgS20~species is found to be from 8-19% of the initial concentration of thiosulfate ion while the formation of the less stable MgBrAc+ is only 0.8-3% of the original concentration of bromoacetate. The most striking feature of the results, however, is the constant value of k' for which the standard deviation is only +2.7% over the range of ionic strengths studied. While the theory described earlier in this paper is also applicable to the results of .LaMer and Fessenden ( I ) and Von Kiss and Vass ( 5 ) , alternative algebraic equations may be needed. For example, identical algebraic equations can he used to analyse Von Kiss and Vass's data, ( A ) ,for the addition of magnesium nitrate to the reaction but their data, (B), for the addition of magnesium sulfate and LaMer and Fessenden's data, ( C ) , but for the reaction between magnesium thiosulfate and bromoacetate different equations are required, the former since MgSOl and NaSOn- ion pairs must be accounted for and the latter because no inert salt is added. Without presenting the detailed calculations made by the present authors (lo), the appropriate iterative procedures give values for k' from data (A), 116.9 * 5.0; (B), 106.9 * 5.5; and (C), 110.9 8.5 1 mole-' min-1. The excellent agreement between these values and the present figure leads to an overall
*
T h e cdculations were performed on an ICL 4130 computer and programmed in the ALGOL 60 language. Copies of the program w i t h supplementary n o t e s may be obtained from ACN o r RKC. After three iteration cycles, subsequent values of k', usually agree to within 0.1 so that hand c&ulation is not too tedious.
628 / Journal of Chemical Education
Bromomceate-thiaulfote rooctim at 25'C. Vorldlon of log q with F I I ) for the readion in tho prorencs of magnesium cations.
*
mean value from the four sets of data of k' = 111.2 7.2 1 mole-' min-'. In the figure, log q is plotted against F(I)-the graph is constructed by drawing a straight line through the points plotted from the results in Table 2 and a point on the log q axis cofresponding to the overall mean value of k' (log k' = 2.046). The slope of the line, -4.09 1'/' mole-'/', is in good agreement with the predicted value. Clearly, these data provide strong evidence for the validity of the Wyatt-Davies treatment and the ratio kl/kl 450 1mole-' indicates the catalytic effect of the ion association.
-
Acknowledgment
The authors wish to thank D. R. Chandler and P. M. Colligan who assisted with the development stages of this work. Literature Cited (1) L*Mzn, V. K., AND Fess~xnen.R. W., J . Anrev. Cham. Soc.. 54, 2351 (1932). (2) LAMER, V. K., A N D K ~ N E M. ~ ,E., J . Amcr. Cham. Soc., 57, 2862 (1935). (3) WYATT,P. A. H..AND D A Y I ~C.~ W.. , Tvona. Foroday Sor.. 45, 774 (1949). DAvlea. C. W.. *No W I L L I A I 8 . I. W.. TIGM. F a ~ d a f ,SOC.,54. 1547 (4) .. (1958). (5) vow KIBB.A,. A N D V u s . P.. 2.Anorv. Ails. Cham.. 217,305 (1934). (6) Awrs, E. S.. "Solvent Emots on Reaction Rates and Meohanisms." Acsdemio Praas. New York, 1966. p. 21. (Several physics1 chemistw textbooks d v a less oomorehensive but ouite aatiafaotor~derivations .I t h e Br$nsted-Bierrum equation). (7) D ~ v r e a C. . W., "Ion Association." Butterworths, London. 1962. (8) D ~ v r e s C. , W., "Progress in Reaction Kinetics" (Edilor: Ponrsn, G.). Pergamon Press. New York, 1961, Volume 1, p. 161. l Chemistry" (3rd Ed.) Longmana, (9) VOOEL. A. I.. " P r ~ c t i c ~Organio New York, 1956, p. 429. (10) COSO~OVE. R. K., KINO. P. W., A N D N o R ? I ~ .A. C.. manuscript in
prep8ration.
