Kinetics of the Decomposition of Hydrogen Peroxide in Acidic Copper

Article pubs.acs.org/IECR

Kinetics of the Decomposition of Hydrogen Peroxide in Acidic Copper Sulfate Solutions Bongani Mlasi,† David Glasser,‡ and Diane Hildebrandt*,‡ †

School of Chemical and Metallurgical Engineering, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2000, South Africa ‡ MaPS Research Unit, University of South Africa (UNISA), Fifth Floor Pha-Pha Building, Corner of Pioneer and Christian De Wet Roads, Private Bag X6, Florida, Gauteng 1710, South Africa ABSTRACT: A study on the decomposition kinetics of hydrogen peroxide in a solution of dilute sulfuric acid with added copper sulfate has been undertaken. The experiments were performed in a vacuum/Dewar flask, and the temperature of the reacting mixture was measured as a function of time. Because the decomposition was exothermic, the relationship between the temperature and time during the decomposition process was used to analyze the reaction kinetics. The decomposition reaction of hydrogen peroxide was found to be first-order, as reported by most of the previous researchers. It was found that, at an initial temperature of 67 °C, the decomposition of pure peroxide in dilute sulfuric acid had a rate constant of 0.0385 min−1. The addition of 5 g of copper sulfate increased the rate constant to 0.265 min−1, and with a further addition of copper sulfate, it asymptoted to 0.463 min−1. It was further rather surprisingly noted that the exothermic reaction was followed by an endothermic one that did not appear to be affected by the change in the amount of copper sulfate in solution. A model was fitted to these data, and it was shown how this kinetic model can be used in practice to design an optimum batch process for copper dissolution in order to minimize the amount of hydrogen peroxide utilized.

■

not the purpose of the work in this paper to try to find a mechanism but rather to measure the kinetics over a wide range of conditions for use in process design. Optimizing and operating any process involving the use of peroxide as a constituent requires a thorough understanding of the kinetics of the decomposition processes of peroxide. In the minerals processing industry, metallic copper is often dissolved in an acidic solution containing hydrogen peroxide. Because of the cost of hydrogen peroxide, the economics of the process are affected by the amount needed for the complete dissolution of the copper. In some early semiquantitative experiments done by the authors, it was found that many times a stoichiometric amount of hydrogen peroxide was needed to dissolve the copper. This was thought to be due to the direct decomposition of hydrogen peroxide rather than the oxidation of copper under the conditions of the experiment. The factors that were thought to be involved are the homogeneous decomposition of hydrogen peroxide as a function of the temperature and the presence of copper sulfate in solution as a product of copper dissolution acting as a catalyst. This paper then looks at doing experiments to get this kinetic information. Because of the very exothermic nature of the decomposition of hydrogen peroxide, it was felt that a very simple way to measure this relatively rapid reaction rate was to measure the temperature as a function of time in a batch reactor of known heat-transfer characteristics. The investigation in this paper was

INTRODUCTION Hydrogen peroxide is used as a reagent to make certain reactions occur. In the decomposition of anazo dye by UV/ H2O2, hydrogen peroxide serves as the source of hydroxyl radicals under UV irradiation.1 In the aerobic biodegradation of hydrocarbons, the decomposition of hydrogen peroxide serves as an important source of oxygen2 and is also used to assist the biological treatment of subsurface contamination.3 Some metal recovery industries utilize peroxide as an oxidant in improving the recovery process of targeted metals. It is proposed that when hydrogen peroxide comes in contact with minerals, it decomposes to the hydroxyl anion (OH−) and hydroxyl radical (HO•),4 which is represented by eq 1. H 2O2 → HO• + OH−

(1)

In a metal leaching process using a sulfuric acid medium, such radicals react with the highly reactive sulfide minerals to yield elemental sulfur, as shown in eq 2.5 2HO• + 2S2 − → 2S0 + H 2O + 0.5O2

(2)

In addition, because the reaction is very exothermic, the catalytic decomposition of hydrogen peroxide can act as a source of high-temperature steam. Also, because hydrogen peroxide is decomposed into oxygen and steam, it has been used to oxidize the fuel in rocket motors.6 The decomposition of peroxide in these cases is represented by eq 3.5 H 2O2 → H 2O +

1 O2 2

(3)

Received: Revised: Accepted: Published:

There have been many studies trying to elucidate the mechanism of the hydrogen peroxide decomposition in the presence of copper in both acid and alkaline solutions.7,8 It is © 2015 American Chemical Society

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February 20, 2015 May 15, 2015 May 15, 2015 May 15, 2015 DOI: 10.1021/acs.iecr.5b00642 Ind. Eng. Chem. Res. 2015, 54, 5589−5597

Article

Industrial & Engineering Chemistry Research

where ε is the extent of reaction. Equation 7 is substituted into eq 6 and then integrated to give eq 8.

performed by monitoring the temperature of the reactor contents using a vacuum/Dewar flask as the reactor and immersing the flask in a temperature-controlled water bath to control heat transfer between the flask and the surroundings. This concept of kinetic measurements in an adiabatic system was first suggested by Sturtevant in the 1930s9 using a calorimeter. The Sturtevant approach, as originally proposed, had disadvantages in data analysis because the data obtained in the first 20 min was not used. This technique has been developed through the years such that it is now found to be reliable for chemical kinetic studies.10−14

(T − T0) +

KINETICS FROM TEMPERATURE−TIME DATA Mathematical Analysis of Measured Temperature− Time Data in a Batch System. Heat is released (or absorbed) when reaction occurs, and this leads to an increase (a decrease) in the temperature in the reactor. The differential equation appropriate to such curves is derived from the mass and energy balance for the reaction based on the following assumptions: (i) the laws of mass conservation and energy conservation; (ii) the temperature change is almost entirely attributable to a single reaction; (iii) the heat of reaction is only slightly affected by the temperature; (iv) the specific heat of the system is almost independent of the temperature and composition of the reacting mixture. The mass balance can be related to the energy balance, and then the temperature can be related to the conversion or extent for a single reaction. This results in a differential equation in terms of temperature−time variations for the system. Mass and Energy Balance for the Batch Reactor. In this section, the derivation of the equation derived from the energy and mass balance, which relates the kinetics and thermodynamic parameters of a reaction, is set out. The rate equation for a constant-volume batch reactor is given by eq 4: dC 1 dNA =− A V dt dt

−ΔHrxn Δε mCp

(8)

(9)

⎛ T − Ts ⎞ UA ln⎜ t ⎟= mCp ⎝ T0 − Ts ⎠

(10)

Experiments can be done to measure the heat-transfer characteristics of the flask. A known mass M of water at temperature T0 is placed in the flask, and the flask is kept in a water bath, which is kept at temperature Ts. The change in the temperature of the contents of the flask T can be measured as a function of time t, and these data can be fitted to eq 10 to estimate UA for the flask. This can be used to estimate the constant UA/MCp, which can be inserted in eq 8 to compensate for the heat loss so that an adiabatic system can be approximated. Analysis of the Nature of the Order of the Reaction. An adiabatic batch reactor has an energy balance equation described by eq 11

(4)

mCp

d(ΔT ad) = ( −ΔHrxn)( −rAV ) dt

(11)

where ΔT is the difference between the temperature in the adiabatic reactor at time t and the temperature in the reactor initially, i.e.. at time t = 0. For a constant-volume reaction, the relationship between the reaction rate rA and the concentration CA is given by rA = dCA/dt, and thus eq 11 becomes ad

ΔHrxnV d(ΔT ad) = dCA MCp

(12)

The initial conditions are T(t=0) = T0 and CA(t=0) = CA0. Therefore, integration of eq 12 gives eq 13:

(5)

where ΔHrxn is the enthalpy (heat) of the reaction, mCp is the overall heat capacity of the reactor and contents, UA is the heat-transfer coefficient for heat transfer between the reactor and the bath, Qs is the heating rate due to stirring, ΔT is the temperature difference between the reactor contents and the bath (T − Ts), and Qs dt ∼ 0 because the effect of stirring is negligible in the system; hence, eq 5 becomes

ΔT ad = T − T0 =

ΔHrxnV (CA − CA0) MCp

(13)

If we assume that the rate equation is first-order and that the change in the temperature is fairly small so that we can effectively assume isothermal conditions, we can write CA = CA0 exp( −kt )

(6)

(14)

Thus, combining eqs 13 and 14, we get

The reaction rate and extent of reaction can be related by dε = rate of reaction dt

(T − TS) dt =

Rearranging eq 9 and integrating it from t = 0, where the temperature of the contents of the flask is T0, to t = t, where the temperature of the contents of the flask is T, yield a relationship that relates the temperature of the reactor contents and the surrounding temperature to the overall heat-transfer coefficient UA:

( −ΔHrxn)( −rA)V dt + Q s dt = mCp dT + UA(ΔT ) dt

( −rA )V =

t

mCp dT + UA(ΔT ) dt = 0

where −rA is the rate of formation of species A, V is the volume of the reacting mixture, NA is the number of moles of A in the reacting mixture, t is the time, and CA is the concentration of A in the mixture. In general, the energy balance for the reactor is described by heat generated by the reaction + heat generated by the stirrer = heat absorbed by the reactor contents + heat transferred through the reactor walls or

( −ΔHrxn)( −rA )V dt = mCp dT + UA(ΔT ) dt

∫0

Determination of the Overall Heat-Transfer Coefficient UA. Consider eq 6 above for the situation in which there is no reaction occurring. This means that the heat generated by the reaction mechanism in eq 6 is equal to zero [(−ΔHrxn)(−rA)V dt = 0]. Therefore, the resulting equation becomes

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−rA = −

UA mCp

T ad − T0 = −

(7) 5590

[CA0 − CA0 exp( −kt )]ΔHrxnV MCp

(15)

DOI: 10.1021/acs.iecr.5b00642 Ind. Eng. Chem. Res. 2015, 54, 5589−5597

Article

Industrial & Engineering Chemistry Research If we consider the steady-state solution, i.e., as t → ∞, where T → T∞ T ∞ = T0 −

ΔHrxnV CA0 MCp

Reaction Vessel. The reaction vessel used was a 500 mL vacuum/Dewar flask with a removable lid made of expanded polystyrene. The lid was pierced to make two holes small enough to allow a temperature probe and syringe needle to be passed through. Stirring was carried out in the flask by means of a magnetic stirrer and was kept constant throughout the experiments at a low speed, enough to agitate the solution to maintain a uniform concentration and temperature.

(16)

Thus, combining eqs 15 and 16 gives T ∞ − T ad =

ΔHrxnV CA0 exp( −kt ) MCp

■

(17)

EXPERIMENTAL PROCEDURE The heated solution of sulfuric acid and copper sulfate (aqueous) was poured into the reaction vessel, and a temperature probe was inserted through the lid. The temperature measured by the thermocouple was recorded on a computer. The temperature in the reaction vessel was allowed to stabilize before the peroxide was added. Hydrogen peroxide was then injected through the second hole in the lid, at a constant but gentle rate intended to allow quick mixing of the reagent. Hydrogen peroxide was introduced at room temperature; thus, the temperature of the solution in the reactor dropped relative to the amount of the oxidant used. The nature of the reaction that follows determines the resultant temperature of the solution: an exothermic reaction has a positive temperature gradient, while an endothermic reaction has a negative gradient. Temperature Profile. Thermocouple Sensitivity. Sulfuric acid is a very strong acid that reacts with most metals. Because the thermocouple used is stainless steel (metallic), it is sheathed in a blown-glass container to act as an insulator against the acidity of the solution. However, because the air surrounding the thermocouple inside the glass reduces the sensitivity of the thermocouple, a small amount of water was poured into the glass to increase the contact surface between the glass and thermocouple. Nevertheless, this insulation sheath causes a delay in the measurement by the thermocouple when it is inserted into a medium. The thermocouple was immersed sequentially in two media, each of different temperature, in order to measure the delay of the response. In the first instance, this device was immersed in tap water at 20 °C. After 3 min, it was removed and immediately afterward plunged into a mixture of water and crushed ice at a temperature of 0 °C. The temperature detected by the probe dropped from 20 to 0 °C in about 20 s, as shown in Figure 2.

∞

Rearranging eq 17 leads to eq 18; thus, a plot of ln(T − Tad) versus time t will give a straight line with slope k. This slope is considered to be the estimated rate constant for the reaction in question.

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⎛ ΔH V ⎞ rxn CA0⎟⎟ − kt ln(T ∞ − T ad) = ln⎜⎜ − ⎝ MCp ⎠

(18)

EXPERIMENTAL: MATERIALS AND APPARATUS The schematic diagram of the experimental equipment is shown in Figure 1.

Figure 1. Schematic diagram of the equipment setup for studying the kinetics of the decomposition of hydrogen peroxide.

Sample Preparation. Copper Sulfate. Copper sulfate is a chemical compound that is found in the form of blue crystals. It can be produced as a metal salt from the reaction of copper and sulfuric acid. In order to use homogeneous reactions, different quantities (5, 8, 11, 15, and 20 g) of copper sulfate (CuSO4·5H2O) were weighed out and then dissolved in distilled water. The total volume of the solution for each sample was 100 mL. The solution was then mixed with dilute sulfuric acid. Sulfuric Acid. Concentrated sulfuric acid of 98% concentration was diluted to 1.0 M using distilled water to obtain a total volume of diluted acid of 250 mL. Thereafter, a copper sulfate solution was added, and the final solution was heated on a hot plate to reach a temperature of 70 °C before adding it to the vacuum/Dewar flask. The pH of the solution was not varied in these experiments. A water bath was used for the surrounding temperature: The samples were put in the reactor vessel, which was placed in a bath of water that was maintained at a constant temperature of 30 °C. Addition of Hydrogen Peroxide. In all of the experiments performed, the hydrogen peroxide used had a concentration of 30% in water. Hydrogen peroxide at room temperature was injected into the reactor by means of a syringe with a volume of 50 mL. However, the amount injected was 30 mL for each run.

Figure 2. Rate at which the probe responds when immersed in two solutions of different temperatures. 5591


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The two-probe plot shows a linear relationship; thus, eq 19 is derived from this plot in which the thermometer temperature is expressed in terms of the thermocouple:

It follows that any reaction that occurs within less than about 20 s will not be accurately followed by the thermocouple sensor. Because the decomposition of peroxide in this research occurred over almost 50 min, this probe was suitable for measuring the temperature changes during the reaction. Thermocouple Calibration. A calibrated, certified mercury thermometer was used to calibrate the thermocouple. A range of temperatures between 0 and 81 °C was used for this purpose. Both the thermometer and thermocouple were immersed in the same water bath at different temperatures, and the temperature readings of each were recorded. Figure 3 plots these results so that the readings from each can be compared. For example, when the thermometer recorded 0 °C, the thermocouple read −2 °C.

TC = Tt + 2

(19)

where TC is the corrected temperature equivalent to the thermometer reading and Tt is the actual temperature recorded by the thermocouple.

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RESULTS AND DISCUSSION In these experiments, the initial temperature of the solutions in the reactor was taken as 67 °C. This value was chosen based on semiquantitative experiments that showed that at lower temperatures the rate of copper dissolution was too slow for industrial purposes while at higher temperatures the rate was too fast to ensure adequate control of the process. The reason for the use of 1 M sulfuric acid was also based on previous work. The reactor vessel was placed in a water bath that was maintained at 30 °C, a convenient temperature for a controller. Such temperatures could be changed according to the preference of the experiment to be conducted but were felt to be in the correct region to get adequate results for design purposes. Effect of Varying the Amount of Copper Sulfate. Figure4 illustrates the long-term change in the temperature caused by the reaction of hydrogen peroxide in sulfuric acid when the amount of copper sulfate in the solution was varied. As previously mentioned, an amount of 30 mL of peroxide was added to a 1.0 M solution of diluted sulfuric acid, and the mass of copper sulfate was varied from 0 to 20 g in this series of experiments. The initial temperature was set at 67 °C for each run.

Figure 3. Graphical presentation of the temperatures obtained from the thermocouple and thermometer.

Figure 4. Temperature−time profile for 1.0 M sulfuric acid with 30 mL of hydrogen peroxide added in the presence of 0, 5, 8, 11, 15, and 20 g of copper sulfate, all with an initial temperature of 67 °C, while the water bath was kept at 30 °C. 5592


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Figure 5. Log−linear plots of the tail of the curves from Figure 4.

from Figure 7 that the greater the amount of copper sulfate, the greater the first-order rate constant for decay will be. The values of these rate constants with the amount of copper sulfate added are shown in Table 1. It should be noted that doing these plots to get the so-called first-order rate constants is contingent on the fact that the exothermic reaction is essentially complete before the endothermic reaction starts; these results appear to justify this assumption. As previously mentioned, the slopes of the regression curves in Figure 7 provide the estimated rate constants for the firstorder reaction for each corresponding amount of copper sulfate. The data from Table 1 are plotted in Figure 8. It can be seen that Figure 8 shows a saturation effect in that, as more copper sulfate is added, there is a smaller effect of each addition and the rate constant seems to asymptote to a maximum value. Model for the Relationship between the Rate Constant for the Decomposition Reaction and the Amount of Copper Sulfate. In this section, the methodology used to model the relationship between the various amounts of copper sulfate and the estimated rate constant in Figure8 is explained. Nonlinear regression techniques were used in the process of fitting the appropriate model to the experimental data. Certain aspects of the proposed model, such as the coefficient of determination (R2), confidence interval, and error bars, had to be considered to evaluate how scientifically plausible the best-fit values are. Coefficient of Determination (R2). By definition, the coefficient of determination (R2) is taken to be the amount of variation in the dependent variable that is explained by the regression line in terms of the predictor variable.15 This was used to quantify the degree of fit between the proposed model and the experimental data. As a rule of thumb, a value of R2 ≥ 0.99 is required for a very good fit.16 Nonetheless, a value of R2 ≥ 0.95 is considered to be a standard value that is accepted by

In Figure 5, the log plots of the temperature versus time curves for the data in Figure 4, for times greater than 5 h, have been plotted. Because their slopes are almost equal to that of the pure water result, we can assume that the decomposition of hydrogen peroxide in the reactor is essentially complete after 5 h and just the cooling process (heat loss from the flask to the water bath) is taking place. These slopes could then be used to correct the curves in Figure 4 to obtain the corrected adiabatic curves in Figure 6A. These so-called “adiabatic curves” show the heat transfer corrections give curves that asymptote to horizontal straight lines as expected from “adiabatic curves”. Figure 6A shows an exothermic reaction (occurring in the first 15 min or so) followed by an endothermic reaction, which dominates for times longer than 15 min. The increase in the amount of copper sulfate caused a greater increase in the maximum temperature rise, but the final temperatures seemed to be unaffected. Figure 6B displays the corrected adiabatic temperature rise for the first 15 min of the six experiments that form the subject of Figure 4. The results show that during this initial period the adiabatic temperature rises to its maximum value. Furthermore, an increase in the amount of copper sulfate also results in an acceleration of the initial rate of the temperature rise (and thus the reaction rate). The curves in Figure 6B exhibit a slight S shape, but in the latter part of the curve, they look as if the temperature might approach the maximum temperature exponentially. In order to study the exothermic reaction, the natural logarithm of the difference between the highest temperature that the graph reaches in Figure 6B (T∞) and the corrected adiabatic temperature rise (Tad) are plotted against time in Figure 7. The curves are all reasonably linear, indicating that a first-order reaction is occurring. A regression was done to obtain a first-order rate constant for each experiment. It is clear 5593


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Figure 6. (A) Results from Figure 4 corrected for heat losses. So-called “adiabatic curves” that show the heat-transfer corrections give curves that asymptote to horizontal straight lines, as expected from “adiabatic curves”. (B) Adiabatic temperature rise plot from Figure 4 in which only the first 15 min duration is considered.

statisticians’ worldwide.15 It is important to note, however, that although the coefficient of determination (R2) describes the closeness of the fit of the curve to the practical data, this does not guarantee the accuracy of the estimated parameters. Confidence Intervals of the Parameters. The point of regression is basically to find a best fit between the model and experimental results using parameters in the model. However, one of the other key factors to draw a plausible scientific conclusion is the precision of the values of the parameters. For this to be achieved, the concept of the confidence interval is introduced.

Laboratory-gathered data are subject to error. It is therefore essential to define best-fit parameters and an estimate of their confidence interval to allow one to take the variability inherent to the measurements into account in the regression.17,18 Error Bars. Error bars normally indicate how accurate the experimental data are because they focus on the reproducibility of the experimental data. The concept of error bars operates in a manner very similar to the confidence band because it also uses regions in which the reproducibility of the data point lies. Model Selection. From Figure 8, one can see that the rate constant could be thought of initially to depend linearly on the 5594


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rate constant when no copper sulfate is added in the solution. mCuSO4 is the mass of copper sulfate added in the reacting solution. The fitting parameters of this empirical model are a and b. The estimated rate constant is a function of the added copper sulfate because when no copper is added, the rate constant is

k(mCuSO4 = 0 g) = k 0

(21)

Thus, k0 is read off as the y intercept in Figure 8. At low concentration of copper sulfate (bmCuSO4 ≪ 1), the reaction constant becomes linearly dependent on the mass of copper sulfate, that is k − k 0 = amCuSO4

Thus, the initial slope of the rate constant curve in Figure 8 gives the value of the parameter a. Furthermore, if mCuSO4 is increased sufficiently such that bmCuSO4 ≫ 1, then the equation for the rate constant becomes a k = + k0 (23) b

Figure 7. ln(T∞ − Tad) for the decomposition of hydrogen peroxide with different amounts of copper sulfate against time. In this case, 0, 5, 8, 11, 15, and 20 g of copper sulfate are in solution with 1.0 M sulfuric acid, and 30 mL of peroxide is added. The experiments are done with an initial temperature of 67 °C.

Thus, the reaction constant does not depend on the mass of copper sulfate at high concentration and asymptotes to a/b + k0. Now the graph for eq 20 is shown in Figure 8 as the solid line. The coefficient of determination (R2) is 0.99. The error bars represent a confidence level of 95%. The solid line crosses the error bars in the last five points of the experimental data. This signifies that the fitted model curve is within the margin of error associated with each measurement. However, the initial point at 0 g mass of copper sulfate has no significant variability, so there is no error bar plotted on the graph. Confidence on the Optimized Parameters (a and b) for the Model. The constants in eq 20 have been optimized at a confidence level of 95% and are listed in Table 2.

Table 1. Estimated Rate Constants with the Corresponding Amount of Copper Sulfate Added mass (g) of CuSO4

estimated rate constant (k)

mass (g) of CuSO4

estimated rate constant (k)

0 5 8

0.03858 0.2659 0.3145

11 15 20

0.3999 0.4331 0.4637

(22)

Table 2. Values of a and b in Equation 20 Computed at a Confidence Level of 95% k0 (min−1) a (g−1 min−1) b (g−1)

3.858 × 10−2 8.333 × 10−2 1.278 × 10−2

±0.03158 ±0.07643

The value of a is estimated to be 0.08333, while b is 0.1278. Table 3 shows the data for the value of the rate constant versus the mass of copper sulfate added with 95% error bands. Endothermic Reaction. Up until now, we have only focused on the exothermic part of the curves in Figure 6A, that is, the very initial parts. However, there is also a substantial, but slower endothermic reaction, which becomes apparent for times

Figure 8. Reaction rate constants estimated from Figure 7 versus the amount of copper sulfate added in comparison with the theoretical best fit to the proposed model at a confidence level of 95%.

Table 3. Data for the Plot of the Mass of Copper Sulfate against the Estimated Rate Constant (k) Showing 95% Error Bands

concentration of copper sulfate but then saturates; that is, the rate constant becomes independent of the concentration of copper sulfate. A simple function that has this property is described below: amCuSO4 k − k0 = 1 + bmCuSO4 (20) where k is the rate constant, which is a function of the mass of copper sulfate present in the solution; thus, k0 represents the 5595

mass (g) of CuSO4

k

k+

k−

Δk

0 5 8 11 15 20

0.0386 0.2659 0.3145 0.3999 0.4331 0.4637

0.0410 0.291 0.3398 0.4287 0.4687 0.5004

0.0361 0.2408 0.2893 0.3711 0.3976 0.427

0.0025 0.0251 0.0253 0.0288 0.0356 0.0367


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concentration [H2O2]o but is otherwise zero-order. This is the simplest shrinking particle model for the dissolution of a solid,21 but one could, of course, use more complex models. We can then say the economic cost of the hydrogen peroxide addition is C, where this factor contains the rate of hydrogen peroxide decomposition as well as the relative cost of hydrogen peroxide to the value of copper dissolved. This optimization is equivalent to the following equation amCuSO4 C= + k0 1 + bmCuSO4 (26)

greater than around 15 min. When this work started, it was believed that there was only a single exothermic reaction19 taking place, namely H 2O2 → H 2O +

1 O2 2

(24)

Clearly something more complex must be happening. Because this reaction happens even when there is no copper sulfate present, it is likely to be the result of the presence of sulfuric acid. Now it is known that hydrogen peroxide can react with sulfuric acid to produce Caro’s acid.20 Caro’s acid (or peroxymonosulfuric acid) is said to be an equilibrium product obtained by mixing hydrogen peroxide with sulfuric acid. H 2O2 + H 2SO4 ↔ H 2SO5 + H 2O

Solving this gives us the final concentration of the solution that we require:

(25)

mCuSO4 (C − k)/[a − b(C − k)]

This is usually thought to occur only in concentrated solutions at low temperature.20 However, because these reactions at 67 °C are quite fast, perhaps some Caro’s acid is produced and soon decomposed. If this is the case, its decomposition must be endothermic. This point has not been followed at this stage but could be the focus of more work in the future. Copper Dissolution. As mentioned in the Introduction, the motivation for this work was to be able to minimize the high usage of expensive hydrogen peroxide during the dissolution of copper. For this purpose, it is not as important to know the mechanism of the reaction as the kinetics. The kinetics of how much the dissolved copper increases the decomposition rate of hydrogen peroxide has now been measured and modeled. It will now be shown how this information can be used in practice to minimize the usage (and thus cost) of hydrogen peroxide during copper dissolution. In order to use the above results, we need to clarify various features of the copper dissolution. We first of all presume that the dissolution of copper will be done in a batch process. We consider that a batch of copper-containing material is added to a volume (to be determined) of 1 M sulfuric acid at 67 °C. In order for the reaction to take place, there needs to be a certain minimum oxidation potential in the dissolving solution. This minimum oxidation potential effectively means that a certain minimum hydrogen peroxide concentration (which we call [H2O2]o) must be maintained in the solution. We presume that this concentration in the solution is maintained by the continuous addition of extra peroxide. It is the total amount of peroxide added to completely dissolve all of the copper in that batch that we wish to minimize. A little thought will suggest what this means that we wish to stop the process when the copper is completely leached such that at this point the marginal value of the copper leached is equal to the marginal cost of the peroxide used at that time. That is, we wish to dissolve all of the copper, and at the time when the last copper is being dissolved, the economically weighted value of the rate of copper dissolution must be equal to the economically weighted value of the rate of hydrogen peroxide being used. Because we wish to dissolve all of the copper, the problem boils down to choosing the relative volume of the initial acidic solution to be added to the copper containing batch reactor so that the final copper concentration in solution when all of the copper is dissolved is the correct final concentration determined by the optimization described above. To make this a bit more concrete, let us assume that the rate of copper dissolution depends on the hydrogen peroxide

(27)

Hence, we can work out the volume of the initial acid solution that we need to add per batch.

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CONCLUSION Different amounts of copper sulfate were used, namely, 0, 5, 8, 11, 15, and 20 g, which were added to a 1.0 M sulfuric acid solution and heated to an initial temperature of 67 °C. A total of 30 mL of hydrogen peroxide, which was at room temperature, was injected into the heated solution. It was observed that there was a relatively fast exothermic reaction, which was ascribed to the decomposition of peroxide, followed by a slower endothermic reaction. It was observed that the amount of copper sulfate added affected the rate of decomposition of peroxide because the higher the amount of copper sulfate, the faster the reaction occurred. It is worth noting that the change in the amount of copper sulfate had no apparent effect on the rate of the endothermic reaction. Rate Determination. This study has shown that an increase in the amount of copper sulfate in the reacting solution increases the rate of decomposition of peroxide. It was further found that the decomposition of peroxide to the maximum temperature measured followed a first-order model.22 When the first-order rate constants were plotted against the amount of copper sulfate present, the rate constant at low concentrations of copper sulfate increased with increased copper sulfate concentrations but asymptoted to a constant value as the amount of copper sulfate increased. A simple rate expression that showed a saturation effect was chosen with two constants. The constants were estimated, and the model was shown to give a good fit to the experimental results. Because the endothermic reaction was unaffected by the presence of copper, it was not further analyzed. It was suggested that the decomposition of hydrogen peroxide was not a simple process because it was possible that Caro’s acid was formed, and what we saw was the decomposition of this as well as that of hydrogen peroxide directly. Finally we have shown that in using these kinetics we can, in principle, work out how to optimize a batch copper dissolution process to minimize hydrogen peroxide usage.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 5596


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REFERENCES

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Kinetics of the Decomposition of Hydrogen Peroxide in Acidic Copper

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