Hanspeter Huber Phystkalisch-chemlsches lnstitut der Universitat Klingelbergstr. 80. CH-4056 Basel. Switzerland
Simulation of the Old Nassau Reaction
Stimulated b y a n article in this J o u r n a l (I), we introduced t h e "Old Nassau Reaction" in our laboratow course. T h r e e solutions of KI03, of N a H S 0 3 a n d starch, a n d of HgCIz are mixed together i n this clock reaction, which turns yellow a n d t h e n black. T h e HS03- reduces t h e 103- t o I- which forms t h e yellow HgIz precipitate. With 103- i n excess t h e Idisproportionates finally t o IP, yielding t h e d a r k blue starch complex. Experimentallv t h e reaction times t (when t h e sol u t i m turn;; yellow) and /, (when it turns t~l:tck)are measured. Fmtn a naive point oiview the experiment appears to he much s i m ~ l e rthan-other tvoical introductorv exieriments in kinet& for example, l i t e r hydrolysis. w e accept intuitively t h a t the reaction time is indirectly proportional to the reaction rate. Taking a closer look, however, the reaction turns o u t t o b e much more complicated. We are not dealing with a one step reaction a s usual, h u t with a t least three reactions t h e rates of which are described hv a svstem of simultaneous differential equations. T h i s provides a n opportunity t o teach t h e use of numerical methods i n phvsical chemistry. First the student is introduced to the prinr~plrsuf numerical integration in the mant primitwe way.Thu mrr equation for a iimr order reaction is written as
with the rate equation (8) of the reaction (2). If HgClz is present, there is a further restriction, namely that high concentrations of I- cause HgI2 to precipitate [Hg2+].[I-l2 < 2.2.10-12 moP dm-6
(10)
Results In reality the rate equations are probably more complicated than those indicated above. The mechanism for the reaction is not com-
"
values of Skrabal and Zahorka (3). A titration of a HgClz solution with a KI solution under similar conditions as in the above reaction showed, that a yellow precipitate could only he seen if the concentration of HgIz were larger than mol dm-? In order to fit the experimental data we assumed, therefore, that the reaction mixture turns yellow, when the concentration ofHgIz equals 10Wmol dm-3. A chart of the oxidation states which aids in understanding the redox reactions is eiven in ( 1 ) . With the followine interoretation of stoiehiometry as reaction (1)
To integrate this equation the student is required to write a pragram for an electronic calculator, handling the equation iteratively, starting with the known concentration e , at t = 0 for a given k. By comparing his numerical results with the integrated equation the student gets a feeling for the numerical methods and their dependence on the step-length At. Exercises for more complicated equations and for two coupled reactions complete this learning phase. Next he should read about numerical integration in a standard textbook (McCracken and Dorn, for example) which will enable him to understand a FORTRAN-program we have written for the "Old Nassau Reaction."' The numerical integration is done by the method of Runge-Kutta (2), whereby the condition for the solubility product of HgIn is met by solving a third order equation (Newton-iteration) in each step of the numerical integration. Further details are given
.in..the ...- -annendir ........
The underlying chemistry
If no HgClz is present, then we are dealing with the ordinary Landolt-reaction or "iodine clock," the main reactions of which are
51-+I&-+6Hf-31z+3H20
+ 3 x (I2+ HS03- + H 2 0 lo3-+ 3 HSOs-
-
2 1-
I-
+ SO4-- + 3 H+)
+ 3 SO4-- + 3 H+
(2) (3) (11)
The kinetics of reaction ( l l ) , hawever,.are determined by equation (8). since reaction (3) is very fast. Reaction (11) is autocatalytic since its rate is accelerated by iodide and hydrogen ions. For the overall reaction we can distinguish, therefore, three different phases. Initially no I- is present; therefore, reaction (1) is dominating. Figure 1shows the concentrations of 103- and HS03-versus time for (a), the overall reaetion, and (b),reaction (I), respectively. The curves are identical, and therefore reaction (1) dominates, up toabout 1 sec before all HSOs- is consumed. At this point the I- and Ht concentrations become large enough to make rate (8) comparably fast. We may say that the mechanism of reaction (1) is switching to the mechanism of reaction (11). Figure 2 shows the I- concentrations versus time far three different initial concentrations c, (HSOs-1. The overall reaetion curves (--) all branch off at about the same 1- concentrations from the curves for reaction (1) ( - - - ) , a s expected from the above statements. Following this point the accelerating reaction (11) is dominating until all HSO3is used up.
Reaction (2) may further be divided into the following steps: (3) 2 I-
+ lo3-+ 2 H+ $2 10I-
+ H+
+ IOH + H+
-
IOH
+ IO-
(slow)
(4)
IOH (fast)
(5)
IZ+ Hz0 (fast)
(6)
In the computer program the following rate equations (3) for reactions (1) to (3) were assumed
Noto, that the mechanism listed in (4), (51, and (6) is in agreement 320 1 Journal of Chemical Education
Figure 1. Concenhations of lo8- (-) and HSOS- (- - -) versus time. (a) is the overall reaction. (b) reaction (1) alone. The initial reaction mixture contained 0.014 mot dm+KiO,and 0.029 moi dm-3 NaHS03. Initially curves (a)and (b). are identical, which ;how that reaction ( I ) is dominating
0
1 ,
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0 5 10 15 t(S1 Figure 2. Concenhationsof I- for mree dilferent initial Mncennations c.(HS03-) (0.029.0.02175and0.0174 ml dm-=).For each oeselheoverall reaction (-) and reaction (1)alone (- - -1 are plotted. The arrows pointing to the branchings mol drnPshaw that reaction (11)is at an I-concentration of about 1.6. initiated at approximately the same I- concentration. The initial concenhation c, (lo,-) was 0.014 mol dm-3. Then, in a third phase, only reaction (2) remains and proceeds in a less hectic way. Up td now we were dealing with the ordinary Landolt-reaction ([H&I2] = 0).The additional effect due to the yellow HgI? precipitate is shown in Figure 3. If HgCl* is present in the mixture, the I- concentration is "buffered" a t a certain level until all Hg2+ is precipitated as Hg12. This leads to adelay in the "explosion"of reaction (11) and therefore in t z .
Ftwe 3 Concenuat MS 01 :r-)and I, 1- - -1 rem.9 lme h case (at me nnal reactlon m xlure contaned 0 014 mol dm-'KI0,and 0 029 mol dm-' NaHSO? and in case lbl 0 00222 mol dm-3 HgCI, n add loon The buffernng of m e concentration in case (b) results In a delay of the sudden formation of I,.
.
of one of the equations hy stoichiametry would be possible but does not accelerate the integration. A main problem is the very abrupt change in concentrations at t 2 , which forces us to choose a variable step-length. The step-length is adapted to keep the change in the concentrations small compared to the concentrations themselves (except nt the begmninr, when wme ronr~ntrstit,nsnrezen>l. Near r z the * t e p - I ~ n g_\r~ hhec~mcsverv small, uhirh results in relatiwly Imr (:PI'-times and requires renscma1,ly hidh precisiun. Thew pr;blems are more severe-with larger rate consta& We therefore limited ks to 3WW dm3 mol-' s-', and k l and kzshould not be varied too much either. .~ The I h r a t w n of the 1- runcentrariun hg Hzz' was taken intuaccount thrwch the mequality 110,.i n r a r h s t q r drheintegration the inequalgtg IS tested, and i f the ronwntraticmi are ruu large, the rorresponding equation is solved and the concentrations are reduced. The equation is of third order and is solved by a Newton-iteration with a first approximation of zero far the correction term. Supersaturation [I1was not taken into account in the calculation since the effect on the reaction rate will be negligible. ~~
Literature Cited (11 Alyea. H. N., J.CHEM. EDUC.,54,167(19771. (2) MeCrsleken. D. D..and Dorn, W. S.,"Numcrieal MethodsandFortran Pco~ramming: Wiley. New York. 1964. (81 Skrabni, A,. and Zaharks. A,. 2. E l e k t r o c h m 33.42 (1927). (4) Barnford. C. H.. and Timer. C. F. H.. "Com~r,rehen%iveChemicsl Kincfice,"Vol. 6. El-
Appendix The FORTRAN-program integrates a system of three simultaneous differential equations by the method of Runge-Kutta. The elimination
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Listing available from author upon request.
Volume 56. Number 5, May 1979 / 321
