The Formaldehyde-Sulfite Clock Reaction Revisited Peter Wameck Max-Planck-lnstitut far Chemie, Mainz, Germany (F.R.G.)
The outstanding feature of clock reactions is the sudden appearance of a product some time after the initial mixing of reagents. In thecase of mixing aqueous solutions of formaldehyde and hisulfite a dramatic rise in the pH occurs when the reaction nears completion. This indicates either the production of hydroxyl ions or a loss of protons. The endpoint may he recorded with a pH electrode, or it may he determined visually by the color change of an indicator such as phenolphthalein. Cassen (1) and Cooke (2) have discussed the utility of the title reaction for lecture demonstrations and beginner's chemistry laboratory courses. Measurements of reaction times are fairly easy and the results provide an insight into the principles of reaction kinetics. The interpretation used by Cassen and Cooke is based on a mechanism originally suggested by Wagner (3), who thought that the product of the reaction, hydroxymethane sulfonate (HMS-), is formed via two competing channels involving either HSO; or SO?
+ HSO;
= HOCH,SO;
+ HCHO + SO:-
= HOCH,SO;
HCHO H,O
OH-
+ HSO;
+ OH-
HCHO -OCH,SO;
334
0.4 0.6 0.8 EXTENT OF CONVERSION
1.0
= SO:-
+ H20
+ S O P = -OCH2S0, + Hf = HOCH2SO;
0.2
Formaldehyde-sulflte clwk reaction: Behavlw of pH as a hbmion of the conversion of toward hydroxymethane sulfonate.
and that the second reaction takes over after the first has exhausted the supply of HSO;. In reality, however, the first reaction need not he invoked, because the HSOJSOZ- equilibrium keeps the hydroxyl ion concentration low so long as there is sufficient hisulfite left. Indeed, recent research (4) has shown that for pH > 4 the reaction is carried primarily by sulfite ions, SOf, and free formaldehyde, HCHO. Moreover, in aqueous solution, formaldehyde occurs mainly as the hydrate CH2(0H)? (also called methylene glycol), and free formaldehvde must derive from it bv dehvdration. ~urnetti.5)appears to have been ;he first to point out that under the usual lahoratorv conditions the dehvdration of methylene glycol is the rate-determining step i d that the timing of the color change may he used to determine the associated rate coefficient. Indeed, the rate coefficients calculated by Burnett generally are in good agreement with earlier direct results obtained by Bell and Evans (6) and by LeHenaff (7). Burnett has also discussed various precautions required in the choice of concentrations and experimental procedures for a successful performance of the clock experiments. The purpose of the present note is to discuss the mechanism and the change of pH during the reaction. This discussion, it is hoped, will lead to a better understanding of the overall process. Burnett (5) has assumed that the color change coincides with the completion of hisulfite consumption. This assumption is not self evident and requires further proof. The mechanism for the formation of hydroxymethane sulfonate may he written: CH,(OH),= HCHO
0
K,
= k,/k_, = 5 X
k, = 5.4 X 10% pK = 10.2
Journal of Chemical Education
lo-" (1) (2) (3)
HSOT = S O P
+ H+
pK = 7.2
(4)
The ion equilibria are established rapidly, and the reversal of reaction 2 may he neglected to a first approximation. The following discussion is based on experimental conditions given by Cassen (1) and by Burnett (5). Specifically, the molar concentration of formaldehyde isalwaystaken to he in excess of that of bisulfite and sulfite combined. It is instructive tocalculate thechange of pH asafunction of the formation of hydroxymethane sulfonaw, HMS-. The proton concentration is determined by the charge balance equation, [Na']
+ [H']
= [HSOJ
+ 2[SOF] + [HMS1
+[OH-]
in conjunction with the ion equilibria K,
=
[H*][SO:-]/[HSOJ
= 6.3 X lo-'
and the mass balance equation [SNlo= [HSOJ +[SO:-]
+ [HMS-]
In the range of pH < S the further dissociation of hydroxymethane sulfonate can he neglected to a first approximation. If [HSOJ and [SO:-] are expressed in terms of [S~vloand [HMS-] one obtains acubic equation for [Hf]. However, the cubic term is small compared with the other terms, so that the equation reduces to the quadratic form
I t can he solved in the usual way, most conveniently with a programmable pocket calculator. Results for such calculations are shown in the figure. There is a sharp upturn of the pH, corresponding to a decrease in hydrogen ion concentration, when [HMS-] = 2[S& - [Na+]. This condition is fairly independent of total SN concentration. The sharp rise of the pH indicates the "endpoint" of the reaction. For values of pH > 9 the second dissociation of the sulfonate can no longer he ignored and the procedure for determining the hydrogen ion concentration becomes more comolicated. In the preceding considerations, the condition for reaehing the endpoint was formulated in terns of ISTV~,,,i.e.. the sum of the ihitial molar concentrations of sodi& bisulfke, b = [HSO&, and sodium sulfite, c = [SO:-10, used tomake up the solution. The figure shows that the conversion of initial SN to hydroxymethane sulfonate at the endpoint is incomplete. The deeree of conversion increases with increasing iatio blc. ~ u r n i t(5) t has suggested that the endpoint occurs upon the consum~tionof hisulfite. IHS0;lo. We can now = [HSO;lo check on this assumption by notingtiat N [];: 2[SO%]o. which leads to
+
The result proves Burnett's suggestion to he correct. It should he noted, however, that [HS0& is not identical with the true concentration of hisulfite existing in the solution at the beginning of the reaction. This concentration is determined by the initial H, which in turn is adjusted by the added, a feature that is also demamount of sulfite onstrated in the figure. The rate of HMS formation is
SO!-]^
d[HMS-Ildt = kz[HCHO][SO~-] whereas that for the formation of HCHO is d[HCHO]ldt = k,[CH,(OH),]
- (k-, + k,[SO;-])[HCHO]
If one applies t h e steady state hypothesis and sets d[HCHO]ldt = 0, one has So long as k-I >> kz[SOi-1, HCHO is in equilibrium with its hydrate, and the rate of HMS- formation will he proportional to both [CHz(OH)z] and [SO:-]. On the other hand, for conditions of kz[SOi-] >> k-l the rate of HMS- formation becomes
Boyce and Hoffmann (4) have reported kz = 5.4 X 106 M-'s-', and Schecker and Schulz ( 8 )have reported k - ~= 20 s-I (at pH = 7). Thus, it is clear that for millimolar concentrations of SN .. with DH > 6.. as aoolied .. in the clock reaction experiments, the second cane holds and the reaction is limited hv the rate of CHAOHb .. . - dissociation. Inteeration of the preceding equations gives
-
has noted that in order to obtain from the measured reaction times At results for kt- in agreement with literature values (6, 7) it is necessary to chose blc >> 1 when using the color change of phenolphthalein as an indicator for the endpoint. Values higher by up to a factor of 2 were ohtained with blc = 1. Several possihle reasons may account for this behavior. One is the pH dependence of kl as determined by Bell and Evans (6) in the form kl = 5.1 X 10-3 2.7 X [H+] 1580 X [OH-]. If the reaction were carried out mainly at or near pH = 8, the effective rate coefficient would be 6.6 X instead at DH = 7. A elance at the fieure shows. of 5.2 X however, that even for blc = 1the reaction proceeds mainly at pH values below 8. Accordingly, the pH dependence of kl should have a very minor influence on the reaction time. A second, perhaps more likely, effect is that the human eye's ability to detect the color change depends on the concentration of phenolphthalein used as an indicator. For acid-base titrations the color change usually is taken to occur near pH = 8.4 (or lIloof the concentration of the pink form of phenol~hthaleinat the eouivalence ~ o i n twhen ) a few d r o ~ of s a 0.190 alcoholic soluti'on of phenhphthalein are used.'ln the orescriotion of Cassen ( I I and Rurnett (5) the concentration bf the phenolphthalein solution is clos& to 1%and in this case the DH for the amearance of color mav be lowered to about p~ = 8. When one starts with a fairl; high pH, as in of color change is reached some the case of blc = 1,. the point . time before the consumption of the initial binulfite concentration, IHSO;ln, iscompleted. From the curve for hlc = 1 in the figu;e and-may estimate that the color change occurs when [HMS-] a 0.8[HSO&. The necessary correction for b in the kinetic equation for klAt does muchto reduce kl to the value ohtained with blc >> 1. The present discussion augments the work of Bumett (5) to show that the formaldehyd+hisulfite clock reaction is well understood in oracticallv all details. Cassen (1) has suggested that the iormalde&de-hisulfite clock reaction mav simulate the method of initial rates as applied to himol e c h reactions. He presented a log-log plot bf llAt versus [CHz(OH)z]oor [S1vloto derive apparent reaction orders: -1 with regard to the concentration of Slv, +1with regard to the concentration of formaldehyde. Burnett (5) has already pointed out that these reartion orders are indeed apparent ones. The reaction is truly of first order in formaldehyde and lSn.l,,results from zero order in SW.The inhihitorv effect of . the longer timkit takes to depiete hisulfite when its initial concentration is raised. In laboratory course work, the seemingly ambiguous interpretation in terms of either a himolecular or a first-order reaction provides an opportunitv to guard the student against premature, falsk~conclus~ons based on a limited data set. The subject thus may serve as a starting point for discussing the validity of proposed reaction mechanisms. Students may also he asked to calculate the pH change during the reaction in accordance with the method discussed here. Literature Cited
+
+
-
~
.~ ~
~
~
~~~
[HMS-1, = [CHz(OH)z],[l- exp(-k,At)] k,At =In [=/(a- b)]
3. Wagner, C. B D I I C ~ ~ ~1929.62.2873-2877. 4. Boyee, S. D.; Haffmann, M. R. J.Phrs. Chern. 1984.88,474M776.
and b = [HMS-It = 2[SW]o - [Na+] where a = [CH~(OH)Z]~ = [HSO;]o. This is the equation adopted by Burnett (5). He
Volume 66 Number 4
April 1989
335
