A computer-enhanced pH study of the formaldehyde–sulphite clock reaction

The formaldehyde-sulphite clock reaction was studied using an Orion SA 720 pH/ISE meter interfaced to an IBM PC. The laboratory software ‘ASYST’ was employed to facilitate data acquisition and data treatment. Experimental pH profiles thus obtained for the first time were simulated by invoking a theoretical model based on the reaction mechanism suggested by Burnett [1]. The variation of rate constants with compositions of reaction mixtures was also discuseed in light of the empirical expression proposed by Bell and Evans [2] for instantaneous rate constant of the clock reaction.


Introduction
The formaldehyde-sulphite reaction has been investigated for decades [1][2][3][4][5][6][7][8]. It has been found that when the two reagents mix with each other, there is a small increase in pH in the reacting system. However, a dramatic rise in pH occurs when the reaction approaches completion. In previous studies on this clock reaction, the time intervals required for the mixing reagents to reach end-points were measured manually using colour indicators. Wagner [3] proposed a mechanism for the process, but it was revised later by Burnett ]. Based on the modified reaction path, Warneck [9] suggested a theoretical model to explain pH profiles of the formaldehyde-sulphite system; no comparison was made, however, between calculated and experimental data. Moreover, the treatment is good for resulting solutions with pH values less than eight. In the present work, a real-time pH measuring system, with a potentiometer connected to an IBM PC [10], was employed to monitor variations of the pH quantity within the formaldehyde-sulphite reaction. In this way errors introduced through the use of colour indicators can be eliminated. The entire pH profiles of the process, as well as end-points, were obtained. A modified formulation based on that proposed before (Warneck [9]) was applied to account for experimental data obtained. In addition, the rate constants obtained were also explained with those predicted from an empirical expression [3].
Mathematical models for the formaldehyde-sulphite reaction The mechanism of the formaldehyde-sulphite clock reaction with the formation of hydroxymethane sulphonate (HMS-) and oxymethane sulphonate (MS2-) is as follows [9]:  (1) [11]. For reaction mixtures, fixed concentrations of formaldehyde (a) 1"41 x 10 -2 M and bisulphate (b) 1"12 x 10 .2 M, and different concentrations of sulphite solutions (c) were used with the presence of 7"79 x 10 .4 M EDTA to give the b/c ratios equal to "0, 8"0 and 14.7 ]. Another set of mixtures with identical compositions were used without the addition of EDTA in order to study the effect of aerial oxidation on the sulphite ion. The experimental procedure as adopted in this work is similar to those given by Burnett [1]. In all measurements, the temperature was kept at 25 C by using a thermostated water bath.
Interfacing hardware and software A computerized pH monitoring system with an IBM PC/ XT interfaced to an Orion SA 720 pH/ISE meter via the RS232C protocol [12] was employed for data acquisition for the formaldehyde-sulphite reaction. Details about the hardware of the system are given in Chau 10].
Programs for data acquisition and treatment were coded using ASYST [13]. ASYST provides real-time display facilities and multi-display of paired data in numerical analyses. Thus the variation ofpH with time can be easily monitored.
A program CLOCKAQC.ASY was developed to acquire pH data for the formaldehyde-sulphite reaction with the interrupt mode for the RS232C protocol being adopted. Paired time and pH data was obtained every 1"37 s and was displayed simultaneously on screen.
The response rate of pH electrode An Orion 9102 BN research grade combination electrode was used in the pH measurements. The response rate of the electrode was checked by using the dipping method 14]. Firstly, a reference solution was prepared by mixing together products of the clock reaction. The Orion pH probe was immersed in the solution for a period of time and the equilibrium pH was measured. Afterward, the electrode was transferred to the mixture solution with reactants but with the absence offormaldehyde. After 30s the electrode was returned to the reference solution. The corresponding change in pH was recored continously to within + 0"01 unit of the equilibrium value using the computerized pH measuring system. The procedure was repeated several times in order to investigate the reproducibility of the electode response.

Simulation of pH profiles
A pH-time plot give the clock time tc at the sharp upturn.
The rate constant kl as shown in reaction (1) correlated to the clock, time by [7] kl tc In [a/(a-b)] (8) Since these two quantities vary with temperature, the pH Eoc plot is preferred for data treatment. A program CONVER.ASY developed in this work was implemented to convert the time factor into the corresponding Eoc quantity through expression: A program called CUBICWS.ASY as coded was then used to compute concentrations of hydrogen ion at given values of Eoc through equation (5). Theorectical pH profiles thus obtained were compared with observed data. Listings of the programs CLOCKAQC.ASY, CONVER.ASY, and CUBICWS.ASY can be obtained from the authors upon request.

Results and discussions
Electrode response and error estimation The response rate of the Orion pH electode was investigated by using the formaldehyde-sulphite solution with a concentration ratio of b/c 1"0. This solution composition should proceed the largest and the most rapid pH change of the various reactions being studied. curves obtained from the dipping method. In these plots, the time interval between two consecutive points is 1"37 s, the minimum time required for the pH system to acquire a reading. After being immersed into the reference and the mixture solutions, the electrode was dipped into the reference solution again where measurements started at point 1. The interval between points and 2 for the dipping step should not be included in continuous measurement. After point 2, the pH readings rose sharply at a rate of 2"54 + 0"33 pH/s between points 2 and 3. The rate then dropped to 0"53 + 0"37 pH/s for the next time interval. Finally, the pH values attained the equilibrium value of 11" 13 + 0"01 unit at point 5.
Rechnitz and Hameka [15] proposed an expression for cation-sensitive glass-electrode response in continuous measurements. However, it was found that the response curve of the Orion pH probe did not follow predictions from their expression probably owing to the nature of electrodes involved.
Table lists the response time of the Orion pH sensorthree successive intervals of 4.11 s (= 3 x 1"37 s) from points 2 to 5 were required for the glass electrode to attain an equilibrium value. In continous pH recording, a total time lag of 4.11 s is required for the computerized measuring system in obtaining one datum accurately.
Hence, the maximum error introduced in the pH-time profile of the clock reaction under study would be the corresponding change in pH at a given time and 4.11 s later. In this way, the relative errors for pH measurements can be estimated. With the presence of appreciable amount of bisulphite ions, pH rises slowly with time as reaction proceeds. However, when the bisulphite concentration decreases to certain extent, the pH of the reaction mixture increases abruptly, as shown in Figure 2, and then becomes constant at the completion of the reactions. It is interesting to note that the initial pH value of a reaction mixture varies with the relative amount ofbisulphite and sulphite present. The smaller the b/c ratio of a system (or the more the amount of sulphite added),, the higher will be the initial pH value.
The errors introduced in the pH-time plots for the formaldehyde-sulphite reaction can be estimated using the method suggested previously for continuous measurements. Plots (d) to (f) of the calculated relative pH error (in %) against time corresponding to the pH profiles (a) to (c) respectively are shown in figure 2. For systems with b/c 1"0, 8"0 and 14"7 respectively, the first 90%, 93% and 96% of the processing time before completion of the reaction have errors of less than 3% and the errors increase to a maximum of 18%, 16% for the remaining time.
The clock times of the formaldehyde-sulphite reaction were determined with the consideration of the final pH values to be within +0"01 unit of the equilibrium values. The time lag factor for the electrode response had been considered in evaluating these quantities. Then values for kl were determined through equation (8). Table 2 lists the clock times, the rate constants kl, and the final pH values thus determined for three different concentration compositions of the formaldehyde-sulphite reaction at 25 C. The maximum error estimated for the clock times determined is +3%. As mentioned previously, concentrations of formaldehyde and bisulphite solutions were kept constant in the study, only the sulphite concentration varied for different reaction mixtues. The one with b/c 1"0 has the highest amount of hydroxide ion at the start of the reaction (figure 2). Since both suIphite and hydroxide ions catalyse the dehydration of methylene   Simulation of experimental pH profiles Experimental and theoretical pH Eoc plots for the formaldehyde-sulphite reaction with the b/c ratio having values of "0, 8"0 and 14" 7 are given in figure 3. In general, the simulated curves generated from the cubic equation  (5) agrees almost perfectly with the experimental one, with only a small deviation appears at the beginning of the reaction. This arises from the residual oxygen dissolved in the deionized water. A small amount of sulphite ions are oxidized by the oxygen to give sulphate ions whose conjugate acids are more acidic than those of the bisulphite. Therefore, the observed initial pH of the mixture is lower than the theoretical value in which no such factor being considered. The effect of aerial oxidation of sulphite ions becomes more prominent with the amount of sulphite ion being decreased for systems with a higher b/c ratios. This explains why discrepancies between the calculated and the observed pH values at the beginning, as well as in the middle of the clock reactions, increase with the b/c ratios (see figure 3).
In all cases with different b/c ratios, equation (5) gives no physical acceptable roots (or pH) beyond the clock times of the reactions. When tc, a limiting value of Eoc is obtained from equation (5) (10). Figure  Time t (s) Figure 5. The instantaneous rate constant kl-time plots derived from equation (10)for the formaldehyde-sulphite reaction with three different concentration ratios b/c of 1"0, 8"0 and 14"7 at 25C. obtained in the manner. It can be seen that the initial rate for the system with b/c 1"0 is high with respect to the other two systems with higher concentration ratio because reaction (1) is catalysed by the presence of sulphite ion. As the reaction proceeds, the concentration of OHincreases and the curve rises rapidly around the tc region (figure 5) resulting in very large kl values. Similar  the experiments were carried out. More accurate results can be obtained by using finer chemicals and an inert atmosphere.

Conclusion
A computerized pH measuring system, including an IBM PC/XT and an Orion SA 720 pH/ISE meter, was used to monitor pH changes in the formaldehyde-sulphite clock reaction. Data acquisition and treatment were achieved through the use of ASYST.
A mathematical model based on the mechanism suggested by Burnett [1 was devised to explain experimental pH profiles at three different concentration compositions with success. The rate constants, kl and clock times for the reactions were correctly predicted. In addition, the kl values for different solution compositions were compared with those evaluated from the expression for instantaneous rate constant. From the present work, it has been shown that aerial oxidation of sulphite had marked effect on the reaction under study.