Abstract

This study provides a strategy for controlling the kinetics of formic acid oxidation by potassium bromide. This strategy resolves the nonlinear deviation of the plot of electromotive force against time and ensures that formic acid oxidation follows first-order kinetics over a wide range of reaction temperatures. The methodology reported here should help instructors optimize their teaching efficiency and provides students with valuable insight into the control of chemical kinetics.

1. Introduction

Br₂ oxidizes formic (methanoic) acid to CO₂ in accordance with the following stoichiometric equation: HCOOH + Br₂ → CO₂ + 2H⁺ + 2Br⁻ (1). The progress of this reaction is described on the basis of HCOOH, Br₂, and H⁺ concentrations. Its progress can also be monitored electrochemically if it occurs in an electrochemical cell. The voltage or electromotive force (EMF) of the cell depends on the concentrations of Br₂ and Br⁻¹. Electrochemical monitoring is a highly convenient approach for following the reaction because the EMF is given by the voltmeter of the electrochemical cell as a function of time. The electrochemical cell has two electrodes. One electrode is simply a piece of Pt that is immersed in the solution. The reduction of Br₂ to Br⁻¹ occurs at this electrode, as follows: Br₋₂ +2e− → 2Br⁻ (2). The second electrode is a calomel (Hg₂Cl₂) electrode that consists of Hg metal in contact with a paste made of insoluble Hg₂Cl₂. The calomel electrode is surrounded by a saturated solution of KCl. The reaction that occurs at this electrode is Hg₂Cl₂ (s) + 2e− → 2 Hg(m) + 2Cl⁻ (3). The saturated KCl solution is held in a glass container the surrounds Hg and Hg₂Cl₂. A small porous plug allows electrical contact between the KCl solution and any solutions that the Hg₂Cl₂ electrode is dipped into while preventing the two solutions from mixing. The EMF of a cell that comprises the Hg₂Cl₂ and Pt electrodes, which are immersed in a solution that contains Br⁻ and Br₂, depends on the concentrations of all the species involved in the two electrode reactions, as depicted in Eqns. (2) and (3). We add Br⁻ ions in such a large excess such that their concentrations remain unchanged during the experiment. Thus, any change in the EMF of the cell is attributable solely to the changes in Br₂ concentration ([Br₂]). The relationship between the cell EMF, E, and [Br₂] can be explained as E = constant + ln [Br₂] (4). We are simply using the EMF as an indicator of [Br₂].

To ensure that [Br⁻] remains unchanged during the experiment, excess amounts of Br⁻ ions are added to the reaction system (20-fold of the amount of HCOOH and H⁺). However, in teaching practice, the reaction does not always follow first-order kinetics over a certain temperature range depending on the excess amount of Br⁻. Thus, the excess amount of Br⁻ is the key parameter that affects the kinetics of the reaction. The appropriate amount of Br^– ensuring that the reaction follows first-order kinetics should be determined and addressed during teaching. Coagulation rate can be reduced by decreasing the size of silica nanoparticles ¹, and a kinetic study has been performed through absorption spectrophotometry ². However, the factors that affect the kinetics of HCOOH oxidation by KBr remain poorly understood. The present work investigates the factors that control the kinetics of HCOOH oxidation by KBr in detail. The appropriate amount of KBr required to ensure that the reaction follows first-order kinetics in teaching practice was studied extensively.

2. Methods

The rate law is assumed to be rate = k [HCOOH]^a [Br₂]^b[H⁺] , where a, b, and c are orders with respect to HCOOH, Br₂, and H⁺, respectively. The experiment aims to determine these orders. An electrochemical cell facilitates the measurement of [Br₂]. Thus, the reaction rate can be conveniently expressed in terms of the rate of Br₂ loss, and the following equation is obtained through calculus: d[Br₂] = −k [HCOOH]^a [Br₂] ^b [H⁺ ] ^c dt (5). The negative sign in Eqn. (5) implies that [Br₂] decreases as the reaction progresses. To simplify the kinetics of this reaction, we formulated reaction mixtures in which the amounts of HCOOH and H⁺ are large excesses compared with those of Br₂ to ensure that the reactant concentrations remain constant throughout the reaction. The rate law can then be written as d[Br₂]/dt = −k_app [Br₂]^b, where k_app = k[HCOOH]^a [H⁺]^c (6). Here, initial k_app is the apparent rate constant and not a true rate constant because its value depends on the initial concentrations of HCOOH and H⁺. We first test the hypothesis that the order, with respect to Br₂, is 1, that is, b = 1. The rate law can be then integrated as follows: d[Br₂]/dt = −k_app [Br₂], 1/ [Br₂ ] d [Br ₂⁻] = −k _app dt, ln [Br₂ ] = −k_appt + A (7), where A is the constant of integration. The form of Eqn. (7) suggests that the reaction is the first order in Br₂; a plot of In [Br₂ ] against t should provide a straight line with slope −k_app. Eqn. [4] demonstrates that the cell EMF is directly proportional to ln[Br₂], E = constant + ln [Br₂] (4). This equation can be rearranged to yield ln [Br₂ ] = E − (constant). Substituting this expression for ln[Br₂] into Eqn. (7) yields E − (constant) = − k_app t + B (8). This equation can be simplified as E, k_app t, B, where B is a constant at a given temperature. Equation (8) implies that the plot of E against time will present a straight line of slope −k _app. If E is given in volts and t is given in seconds, the usual SI units for all the other quantities provide an apparent first-order rate constant, k_app, in s⁻¹. When plotted in this way, the data should be fitted with a straight line, thus confirming that the reaction follows the first order in Br₂.

3. Experimental

The following apparatuses were used: SunyLAB200 nonpaper recorder, precision super constant-temperature baths, saturated Hg₂Cl₂ electrode, Pt electrode, magnetic stirrer, thermostat jacket reactor, split voltage junction box, pipettes (5, 10, 25, and 50 mL), bottle washer, and suction bulb.

The following reagents were used: 2.00 and 4.00 M HCOOH, 2.00 M HCl, 1 M KBr, 0.02 M Br₂ (0.0075 M Br₂ reagent was prepared), 1 M KBr, and deionized water.

The nonpaper recorder, constant-temperature baths, and voltage junction box are connected with a wire. The power switch is turned on. The import and export of the thermostat jacket reactor are connected to the import and export of the constant-temperature bath trough, and the reactor is placed on the magnetic stirrer. The temperature of the constant-temperature baths is set to 25 °C. The reagents (75 mL of deionized water, 10 mL of KBr, 5 mL of HCl, and 5 mL of Br₂) are added to the reactor with a pipette. The total volume of reagents is 100 mL. The thermometer, Pt electrode, and Hg₂Cl₂ electrode are separately inserted into the reactor. Then, the magnetic stirrer is turned on, and the potentiometer of the voltage junction box is adjusted. The EMF is read on the nonpaper recorder and allowed to reach a constant value after 5–10 minutes of continued magnetic stirring. The stabilization of EMF suggests that Br₂ has been completely produced. The stoichiometry of this reaction is expressed as follows: 5Br⁻ + BrO₃ + 6H⁺→3Br₂ + 3H₂O. The EMF readings linearly increase with time after the addition of 5 mL of 0.1 M HCOOH. The reaction is stopped after 15–25 minutes. The EMF is plotted against time (in seconds). The best-fit straight line is then drawn and its slope is determined.

Separate kinetic runs at 25 °C, 30 °C, 35 °C, 40 °C, and 45 °C are conducted by changing the concentration of HCOOH (0.10 or 0.20 M) and the volumes of KBr (10, 15, 20, 25, 30, or 35 mL). The suggested sets of initial reactant solution concentrations, KBr volumes, and temperature are listed in Table 1.

4. Results and Discussion

The stoichiometry equation of this reaction shows that its rate decreases with the addition of different volumes of KBr. Table 2 indicates that the rate constant k decreases as the volume of KBr increases, and the rate constant k is larger under 0.2 M HCOOH than that under 0.1 M HCOOH. The change in EMF against time with the addition of different volumes of KBr at 25 °C is shown in Figure 1. The slopes of the best-fit straight lines for EMF against time sharply decrease when 10, 15, and 20 mL of KBr are added. This decrease, however, becomes gradual when 25, 30, and 35 mL of KBr are added. Thus, the decrease in the rate of HCOOH oxidation depends on the added volumes of KBr. Time and EMF are linearly related. This relationship indicates that the reaction follows first-order kinetics. Therefore, the addition of different volumes of KBr affects the kinetics of HCOOH oxidation.

In practice, under initial conditions and increasing temperature, the relationship between EMF and time is nonlinear. Thus, the effect of temperature on reaction kinetics should be explored. Figure 2 shows the change in EMF against time under different volumes of KBr over the temperature range of 30 °C-45 °C for the 0.10 M HCOOH (a, c, e, g) and 0.20 M HCOOH (b, d, f, h) systems. The slopes of the 0.10 and 0.20 M HCOOH reaction systems increases as the temperature increases, and the reaction order is temperature-sensitive. The curve of EMF against time is correlated with the reaction kinetics. If the curve of EMF against time is linear, then the reaction follows first-order kinetics. Otherwise, the reaction follows second-order kinetics if the relationship between EMF and time is nonlinear. For the 0.10 M HCOOH system, the relationship between EMF and time is linear if the temperature is lower than 30 °C for all volumes of KBr, indicating that the reaction follows first-order kinetics.

The plot is nonlinear and the reaction order changes if the volume of KBr is less than 25 mL. Therefore, the kinetics of HCOOH oxidation can be controlled through the addition of different volumes of KBr. Thus, the oxidation kinetics of the 0.10 M HCOOH reaction system over the temperature range of 25 °C-45 °C can be controlled through the addition of 25–35 mL of KBr.

To investigate the effect of temperature, the plots of EMF against time for the 0.1 and 0.2 M HCOOH systems with The reaction order and relationship followed by the 0.20 M HCOOH reaction system is almost the same as those followed by the 0.10 M HCOOH reaction system. However, the 0.20 M HCOOH reaction system is more sensitive to temperature than the 0.10 M HCOOH reaction system. Specifically, when the temperature exceeds 35 °C and the volume of KBr is less than 25 mL, the relationship between EMF and time is nonlinear (Figure 2 d, f, h). The nonlinear deviation of the curve becomes more pronounced with increasing temperature. Conversely, the plot of EMF against time is linear if the volumes of KBr exceed 25mL under all temperatures, and the reaction order follows first-order kinetics. the same volumes of KBr at different temperatures were compared. As shown in Figure 3, when the volumes of KBr are 10, 15, and 20 mL, the plots of the 0.1 and 0.2 M HCOOH reaction systems appear linear over the temperatures of 25 °C and 30 °C. This result indicates that the reaction follows first-order kinetics. Otherwise, the reaction follows second-order kinetics under increasing temperatures as indicated by the fitting of the correlation coefficient by a third-order square. In general, the slope of the plot of the 0.2 M HCOOH reaction system is larger than that of the plot of the 0.1 M HCOOH reaction system, indicating that the reaction rate of the former system is faster than that of the latter. Meanwhile, as shown in Figure 4, if the volumes of KBr exceed 25 mL, all the plots are linear at 25 °C – 45 °C. Thus, the reaction kinetics can be controlled by adjusting the volume of KBr.

5. Conclusion

The reaction rates of HCOOH oxidation are adjusted through the addition of different volumes of KBr. HCOOH oxidation under the reaction temperatures of less than 35°C can be controlled to follow first-order kinetics through the addition of 10-35 mL of KBr. This effect is confirmed by the linear relationship between EMF and time at 35 °C. However, if the reaction temperature exceeds 35°C, the reaction rate increases, the curves of EMF against time become nonlinear, and the reaction follows second-order kinetics. Furthermore, if the added volumes of KBr exceed 25 mL, the reaction rate decelerates and the curve of EMF against time becomes linear over the temperature range of 25°C-35°C, indicating that temperature and concentration do not affect the reaction order under the present conditions. Therefore, the addition of KBr is an effective approach to control the kinetics of HCOOH oxidation. This approach can be widely applied in laboratory work.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 21676232) and Classroom teaching reform of Department of Education of Zhejiang Province.

References