Catalytic oxidation of SO₂ by novel Mn/copper slag nanocatalyst and optimization by Box-Behnken design

Abstract

In this research, the oxidation of sulfur dioxide (SO₂) gases is investigated by Mn/copper slag nanocatalyst (Mn/CS) as a novel catalyst at low temperatures. The removal of SO₂ gas from industrial exhaust is important to reduce environmental pollution. The SO₂ gas in aqueous solution was oxidized and converted to sulfuric acid as an energy source by Mn/CS in the semi-batch reactor (SBR). The characterization of the catalyst was studied using X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX), field emission scanning electron microscopy (FESEM), and Fourier transform infrared spectroscopy (FTIR), simultaneous thermal analysis (thermogravimetry/differential thermal analysis) STA (TG/DTA) techniques, X-ray fluorescence microscopy (XRF) and BET surface area. A Box-Behnken design (BBD) was used for the optimization of influencing factors such as the amount of nanocatalyst, the temperature and the reaction time in the oxidation of SO₂. The graphical counter plots and response surface were used to determine the optimum conditions. The results showed that the nanocatalyst had the most significant effect on SO₂ oxidation compared with the other two variables. Temperature = 283 K, Mn/CS amount = 6 g/L and Time = 60 min were determined as maximum efficiency for oxidation of SO₂.

Introduction

Sulfur dioxide (SO₂) and other gases emitted from specific resources are major pollutants of air. These gases create problems for humans, such as acid rain. There are many processes to reduce sulfur dioxide and other pollutants from the air. Among these methods, the process of removing SO₂ at low temperatures is important. These methods require less energy and equipment [1].

Removal of sulfur dioxide from gas emissions using absorption is a common method to reduce air pollution and environmental risks [2]. Activated carbon and zeolite constitute an exciting group of catalysts, which have been presented recently as potential catalysts for the oxidation of SO₂ to sulfuric acid [3, 4]. Some transition metal ions such as Mn or Cu have been reported for the catalytic oxidation of SO₂ [5].

Mn²⁺ has shown to be a very active catalyst for oxidation of SO₂ in aqueous solution [6]. Copper slag has high mechanical strength and high resistance to temperature changes. It seems to be a suitable material to support Mn ions. In the metallurgical industry, copper slag is produced as a byproduct of the smelting process [7]. Mechanical stability and acidic solution resistance, suitable surface for supporting catalyst on it, non-coagulation and geometric shape and high temperature resistance are the most important properties of copper slag [8]. Optimizing processes reduce costs and increase productivity. Recently, response surface method (RSM) is a mathematical and statistical technique used for modeling and optimization of various processes such as removal of organic and many dyes from different wastewater by different process [9,10,11,12]. The Box-Behnken design (BBD) in RSM is an important design, implement used for optimization of processes. BBD prepares comprehensive results and detailed information even for a smaller number of experiments and positive influences of operating parameters on all responses [13]. The main goal of this study is to optimize the efficiency of SO₂ catalytic oxidation in aqueous solution. In current research, a novel Mn/copper slags nanocatalyst prepared by impregnation method and characterized by XRD, FESEM, EDX and FTIR analysis. The conductometry method is a powerful tool for monitoring SO₂ oxidation and used for determination of catalyst performance. A Box-Behnken design was selected to study the effects of operational parameter such as temperature, reaction time, and amount of nanocatalyst on the efficiency of the SO₂ oxidation process.

Experimental procedure

Material and apparatuses

Copper slag samples were purchased from Mesbareh Company, Kerman, Iran. The copper-slag-based standard is measured using a glass slide. Hardness of copper slag was much more than silica. Density of copper slag was (3.5 g/cm³). All of the standard gases included N₂, O₂, SO₂ with purity > 99.9% and were purchased from Gas Company, Iran. Other materials were provided by Merck Company. The characterizations of copper slag and Mn/CS were identified using XRD (STOE STADI MP model Germany), FTIR spectrophotometer (PerkinElmer, a spectrum American with the KBr pellet technique), FESEM, EDX (MIRA3-XMU, USA) and XRF (Model: JSX 3201Z). The differential thermal analysis/thermogravimetric analysis (DTA/TG) experiments were carried out in a Netzsch STA 409 C simultaneous thermal analysis (STA). The samples were kept at 100 °C for 30 min, the heating rates were 25 (°C/min) to a final temperature of 1200 °C. BET surface area of materials was determined by N₂ adsorption–desorption method at 77 K, measured using a BELSORP-mini II instrument. The samples were degassed under vacuum at 473 K for 12 h before the BET measurement. The measurements of pH value were performed by a pH meter (Metrohm model 827, Switzerland with an electrode of glass). The pH meter was calibrated before use, with standard buffers (pH 4.0, pH 7.0 and pH 9.0). Input and output gas of the process was identified by a flue gas analyzer (KIGAZ 300, Kimo Company, France). The experimental setup is shown in Fig. 1. The pH and conductivity measurement (Metrohm Model 712) was used for checking the progress of oxidation reaction. The reactor temperature was controlled by external jackets and thermo-bath (RW-0525G).

Fig. 1

Schematic diagram of experimental system: (1–3) N₂, O₂, SO₂ gas cylinder, (4) valve; (5) mass flow controller (MFC); (6) mixing chamber; (7) dryer; (8) thermo-bath; (9) thermal-jacket; (10) semi-batch reactor; (11) mixer; (12) gas distributor; (13) conductometer; (14) pH meter; (15) gas analyzer; (16) tail gas absorber

Preparation of nanocatalyst and oxidation procedure

For activation of copper slag, 100 g of copper slag was added to 500 ml sulfuric acid solution (0.1 M). The sulfuric acid solution was heated to 60° C. The copper slag remained in the hot sulfuric acid solution to 5 h. Copper slags were isolated from acid solution. Copper slags were washed with distilled water several times and finally washed with ethanol. Then samples were dried at 110 °C for 10 h in the oven.

The Mn/CS was prepared by impregnation method; this method has been used in fluidized, suspended and magnetic ion exchange forms [14, 15]. On this basis, the copper slags were placed in aqueous solution including Mn (NO₃)₂ (50%W/V) for 24 h at 60 °C and stirring mixture. After separating the copper slag from this solution, samples were dried at 100 °C for 5 h [16]. Active copper slag and Mn/CS were analyzed by XRD, FTIR, FESEM, TG/DTA, XRF and EDX. In the oxidation process, a gas flow (contains 3000 ppm of SO₂ and 5% of O₂ in N₂) was blown into 250 ml of deionized water in the semi-batch reactor (SBR) until getting a constant conductivity value of 570 µS/cm (corresponds to a HSO₃⁻ concentration of 1.65 × 10⁻³ M) [5]. The changes in the electrical conductivity of the solution were measured by the conductivity meter cell in the reactor. The gas (in the constant pressure) was bubbled with the gas diffuser to surface of catalyst particles. The schematic diagram of the experimental setup for catalytic oxidation of SO₂ gas was illustrated with Fig. 1.

Results and discussion

Nanocatalysts’ characterization

XRD investigation

Analysis of XRD can be utilized to measure peak broadening with crystallite size and lattice strain due to dislocation [17], thus XRD analysis was performed through Cu kα radiation. The data that shows intensity is plotted in a graph based on 2θ on a range of 10°–90°. Figure 2, shows the X-ray diffraction (XRD) pattern of Mn/CS prepared by the impregnation method. The results showed that Mn/CS is well matched with copper slag structure. This indicates that the structure of copper slag is unaltered during the impregnation process. The average crystallite size of the Mn/CS was calculated applying the Debye–Scherer equation [18, 19]:

$$d = \frac{k\lambda }{{\beta_{{}}\,\text{cos}\,\theta }}$$

(1)

where k equals to 0.9 and β is the perfect width at half- maximum (FWHM) of the peak, λ is the wavelength of X-ray used 1.54056 A and θ is the Brage angle. The results showed that the Mn is established on the CS with an average diameter of about 68.43 nm.

Fig. 2

XRD patterns, copper slag and Mn/copper slag nanocatalyst

Field emission scanning electron microscopy (FESEM) investigation

As can be seen from Fig. 3, the prepared nanocatalyst (Mn/CS) is depicted by the field emission scanning electron microscopy (FESEM). The surface morphology and size of samples were identified with FESEM images (before and after the stabilization of manganese). As seen in these images, particle size of the catalyst surface is not equal and also their structure is crystalline. For these reasons, porosity in the Mn/CS was increased.

Fig. 3

FESEM images a copper slag and b, c Mn/copper slag

Energy-dispersive X-ray spectroscopy investigation

The result of the energy-dispersive X-ray spectroscopy (EDX) analyses (Fig. 4, Table 1) shows that the amount of manganese fixed on copper slag is equal to 11.37 wt%. Thus, the EDX confirmed the coating of manganese on the copper slag.

Fig. 4

EDX analyses patterns of copper slag and Mn/copper slag

Table 1 Elemental analyses of copper slag and Mn/copper slag

FTIR spectroscopy investigation

The FTIR spectra of the studied samples are presented in Fig. 5. The copper slag FTIR spectrum in the wave number ranges 400–4000 cm⁻¹ with a resolution of 4 cm⁻¹ by accumulating 32 scans was studied. The wave number accuracy is 0.01 cm⁻¹ and the sampling resolution was 0.09 cm⁻¹, therefore by this method, were identified the functional groups. A peak at 3950 cm⁻¹ exhibited the hydrate minerals such as Mn(OH)₂ and the peak around 3530 cm⁻¹ shows the S–O stretch such as the MnSO₄. The peak of around 1592 cm⁻¹ relates to the C-O asymmetric stretching, whereas a peak at 1408 cm⁻¹ may be due to the bonding in the carbonate ions, indicating the presence of some carbonated mineral, possibly due to the adsorption of CO₂ from the atmosphere. The obtained FTIR spectra of copper slag samples corresponded almost entirely to the spectrum of the Tephroite phase (a-Mn₂SiO₄). This made possible the use of FTIR to determine the composition of tephroite through the established dependency on spectrum bands position on tephroite composition. Adsorption wave number in the spectrum determines the chemical structure of the copper slag. The broad absorption bands of the range of 3100–3600 cm⁻¹ are corresponding to the O–H stretching vibration of water that samples were adsorbed. As shown in Fig. 5 the tephroite structure was appeared in 3487–3576 cm⁻¹ IR bond [20]. This band represents the main stretching vibrations of different OH⁻ groups present in Mn–OH–Al, Al–OH–Al, and Fe–OH–Al units in the octahedral layer therefore sulfur dioxide is an acid gas, active sites accountable for adsorption should have a basic structure [20]. After nanocatalyst preparation, the wavenumber is shifted from 610 to 640 cm⁻¹ and of sharp bands at 636 and 1609 cm⁻¹, corresponding to Si–O stretching modes of bulk sulphates, mainly MnSO₄, in agreement with data from XRD Fig. 2. The peaks of 1150 and 1610 cm⁻¹ are the Si–O and Al–O stretching, the peak of 520 cm⁻¹ is the C–O bending and the bands of 510 and 490 cm⁻¹ are due to Al–O–Si and Si–O–Si bending vibrations, respectively. The FTIR results have proven that Mn as well as placed on the surface of the copper slag.

Fig. 5

FTIR spectra of the studied materials: copper slag and Mn/copper slag

Simultaneous thermal analysis (STA) results

Figure 6 shows the STA results of a Mn/CS sample. The TG curve reveals the occurrence of a marked weight gain in the 375.18–997.84 °C range, following by a weight loss from 997.84 to 1040.13 °C and then slowly decreases weight region of 1040–1200 °C. The exothermic peaks at 515.47 and 765.12 °C in DTA trace can be related to the magnetite $\to$ maghemite and maghemite $\to$ hematite transformations, respectively [21]. The endothermic dip at 1040 °C probably can be associated with the slag melting.

Fig. 6

STA (TG/DTA) traces of Mn/copper slag

XRF characterization

In order to determine the catalyst chemical composition XRF was carried out (Table 2). Based on the results, the percentage of manganese in the Mn/CS sample is greater than that of Cs. These values confirm the EDX results.

Table 2 XRF analyses of copper slag and Mn/copper slag

Figure 7 shows the adsorption–desorption isotherms and BET surface area for the Copper slag, and Mn/CS. The BET surfaces area of Copper slag, and Mn/CS were determined 152.46 and 268.37 (m²/g) respectively. It seems that supporting of nano particle Mn on the CS has been increasing the BET surface area of the catalyst.

Fig. 7

Adsorption–desorption isotherms and BET surface area for the copper slag (a) and Mn/CS (b)

Catalytic activity

The schematic diagram of the reactor system was shown in Fig. 1. The catalytic reaction was carried out in a glass reactor (glass thickness 80 mm). The sulfur dioxide gases in the presence of a catalyst and water-soluble oxygen performs the following reactions [22]:

$${\rm SO}_{2({\rm g})} + {\rm H}_{2} {\rm O} \to {\rm HSO}_{3({\rm aq})}^{ - } + {\rm H}^{ + }$$

(2)

$${\rm HSO}_{3({\rm aq})}^{ - } + \frac{1}{2}{\rm O}_{2} \xrightarrow{{{\rm catalyst}}} {\rm SO}_{4}^{2 - } + {\rm H}^{ + }$$

(3)

$${\rm SO}_{2({\rm g})} + \frac{1}{2}{\rm O}_{2} + {\rm H}_{2} {\rm O} \xrightarrow{{{\rm catalyst}}}{\rm SO}_{4}^{2 - } + 2{\rm H}^{ + }$$

(4)

As shown in Eqs. (2–4), the products of the oxidation of SO₂ are ${\rm SO}_{4}^{2 - }$ and H⁺. Thus, the oxidation of the SO₂ can be directly related to the change in solution conductivity and pH. Effect of catalyst (Mn/CS) amounts to conductivity and pH of solution show in Figs. 8 and 9.

Fig. 8

Conductivity variation for different amounts of (Mn/CS)

Fig. 9

Effect of amounts of Mn/CS on solution pH

With the advancement of the reaction, the concentration of hydrogen and sulfate ions increases and the electrical conductivity of the solution increases and pH of solution decrease. If the catalyst is not present, the electrical conductivity of the solution and pH will remain constant. Therefore, the reaction is not carried out without the presence of a catalyst.

The results of these experiments used for Box-Behnken experimental design. The present study, based on SO₂ gas, was carried out at considerably lowered temperatures of SO₂.

The oxidation efficiency of nanocatalyst for SO₂ is calculated using the following Eq. (5):

$$\eta = \frac{{\left| {{\rm Ec}_{\rm in} - {\rm Ec}_{\rm fi} } \right|}}{{{\rm Ec}_{\rm in} }} \times 100$$

(5)

Where SO₂ oxidation efficiency η (%) is, Ec_in is the initial conductivity of SO₂ aqueous solution (0.570 mS/cm), Ec_fi is the final conductivity of aqueous solution.

The proposed mechanism

Iron, copper and manganese are present in the form of oxides or hydroxides at the copper slag surface metal oxides play an important role in the industrially employed heterogeneously catalyzed autoxidation of sulfur(IV) oxides, for example the production of sulfuric acid with the help of vanadium pentoxide as catalyst. These activities probably depend on the nature of the metal oxide or hydroxide. In general, metal oxides exhibit different catalytic activity, which is probably related to the different bond strengths of oxygen to the metal surface. The catalytic activity of a metal oxide increases with decreasing energy of the metal–oxygen bond. For the heterogeneous oxidation of sulfur(IV) oxides, it is assumed that both oxygen and sulfur(IV) are adsorbed on the surface of the metal oxide [4].

In reaction with oxygen Mn²⁺/CS is converted to Mn³⁺/CS [4, 22]:

$${\text{Mn}}^{2 + } /{\text{CS}} + {\text{O}}_{2} \to {\text{Mn}}^{3 + } /{\text{CS}} + {\text{O}}_{2}^{ - }$$

(6)

Sulfur dioxide gases dissolved in water and then carry out the following reactions:

$${\rm SO}_{2 } \cdot {\rm H}_{2} {\rm O} \rightleftarrows {\rm H}^{ + } + {\rm HSO}_{3}^{ - }$$

(7)

$${\rm HSO}_{3}^{ - } \rightleftarrows {\rm H}^{ + } + {\rm SO}_{3}^{2 - }$$

(8)

Mn²⁺/CS and Mn³⁺/CS performs the following reactions:

$${\rm Mn}^{2 + } /{\rm CS} + {\rm HSO}_{3}^{ - } \rightleftarrows {\rm Mn}^{2 + } /{\rm CS} + {\rm SO}_{3}^{2 - } + {\rm H}^{ + }$$

(9)

$${\rm Mn}^{3 + } /{\rm CS} + {\rm HSO}_{3}^{ - } \rightleftarrows {\rm Mn}^{2 + } /{\rm CS} + {\rm SO}_{3}^{ - } + {\rm H}^{ + }$$

(10)

$${\rm Mn}^{3 + } /{\rm CS} + {\rm SO}_{3}^{2 - } \rightleftarrows {\rm Mn}^{2 + } /{\rm CS} + {\rm SO}_{3}^{ - }$$

(11)

The ${\rm SO}_{3}^{ - }$ is reacted with oxygen and produces ${\rm SO}_{5}^{ - }$:

$${\rm SO}_{3}^{ - } + {\rm O}_{2} \to {\rm SO}_{5}^{ - }$$

(12)

The following reactions generate ${\rm SO}_{4}^{2 - }$:

$${\rm SO}_{5}^{ - } + {\rm Mn}^{2 + } /{\rm CS} + {\rm H}^{ + } \to {\rm Mn}^{3 + } /{\rm CS} + {\rm HSO}_{5}^{ - }$$

(13)

$${\rm HSO}_{5}^{ - } + {\rm Mn}^{2 + } /{\rm CS} \to {\rm Mn}^{3 + } /{\rm CS} + {\rm SO}_{4}^{ - } + {\rm OH}^{ - }$$

(14)

$${\rm SO}_{4}^{ - } + {\rm Mn}^{2 + } /{\rm CS} \to {\rm Mn}^{3 + } /{\rm CS} + {\rm SO}_{4}^{2 - }$$

(15)

Design of experiments using Box-Behnken

In this study, the aim at the optimization was to find conditions that gave the maximum oxidation yield. Box-Behnken a design was also identified the relationship between the controllable input parameters and the response variable. Initial concentration of SO₂ in solution after blowing gas is constant in all experiments. Three variables, including temperature (X₁), time (X₂), and nanocatalyst concentration (X₃) are responsible to change the solution conductivity. A three factor, three levels in a Box-Behnken design was established for further optimization for each variable; three levels were promised and encoded by (−1, 0, +1).

The Box-Behnken is a high-quality design in the sense that it could be fitted in the quadratic model. In the current experiments, the effects of three independent variables on response performance and optimal conditions were investigated by engaging with BBD and RSM [23, 24]. Among all RSM designs, Box-Behnken design requires fewer runs (for example 15 runs at three-parameter experimental design) and lets calculations of the response function at intermediate levels and provides estimation of the method efficiency at any experimental point within the range studied through careful analysis [25]. In this study, the optimization of experimental conditions for SO₂ oxidation using conductivity meter process was studied using Box-Behnken method of RSM. In order to calculate the influence of operating parameters on the SO₂ oxidation, three main factors and three levels for each one was chosen: temperature (°C) (X₁), Reaction time (min) (X₂), and nanocatalyst concentration (g/L) (X₃) as shown in Table 3. Each variable was studied at three levels the low (−1), medium (0) and high (+1). With statistical analysis of the obtained experimental data, a second-order polynomial Eq. (16) was achieved as an empirical model that describes the response surface. The behavior of the system is clarified by the following quadratic equation [26]:

$$Y = \beta_{0} + \sum \beta_{i} X_{i} + \sum \beta_{ii} X_{i}^{2} + \sum \beta_{ij} X_{i} X_{j} ,$$

(16)

where Y is the response (SO₂ oxidation efficiency), β₀, β _i , β _ii and β _ij are coefficients of the intercept, linear, square and interaction effects, respectively. The optimum response and also the process parameters were also determined. Test of F in the ANOVA analysis is used for evaluating model variance in residual variance. The variance is almost identical, this ratio is almost one, which indicates that the probability that each of the factors has a significant effect on the response. The statistical significance of the model and the coefficient was analyzed by means of F-test and P value, respectively [27]. In the present study, the SO₂ oxidation process was investigated to treat with different operating conditions such as temperature (10–30 °C), nanocatalyst amount (1.2–6 g/L), reaction time (20–60 min) using (SBR). The number of experiments (n) needed for the development of BBD is defined as:

$$n = 2k(k - 1) + C_{0}$$

(17)

where K is the number of factors and C₀ is the number of repeated central points. Three factors and three levels (for each factor) of BBD were occupied to optimize and check the effect of operation variables on the responses.

Table 3 Experimental ranges and levels of independent variables

A Box-Behnken design was selected to study the effects of three influencing variables on the response (oxidation efficiency). The reward using of Box-Behnken designs to include the fact that they are all spherical designs and require factors to be run at only three levels. Some of these designs also provide orthogonal blocking and if separate runs, need into blocks the Box-Behnken design, designs are available that let blocks be used in such a way that the approximation of the regression parameters for the factor influences are not affected by the blocks [27]. In all 15 runs the experiments were conducted in triplicate and all results attained from the Box-Behnken design is summarized in Table 4. The observed values and predicted response value with residuals for the runs are shown in Table 4. It shows the experimental results of SO₂ oxidation versus model results. The tip collections of the diagonal line demonstrate that the difference between the experimental and predicted values was less and good fit of the model is obtained.

Table 4 Coded factor levels for a Box-Behnken design of a three-variable system

All 15 runs were first carried out and used to build a mathematical model to describe the process and the experimental results along with the design matrix are presented in Table 4. It was found that the relationship between SO₂ oxidation yields and the three operating parameters (i.e., temperature, Amount of catalyst and Time) was fitted to a second order polynomial equation. The predicted values of the efficiency were obtained from quadratic model fitting techniques for the Oxidation efficiency (%) using the software minitab 17. The response functions (with the determined coefficients) for Oxidation efficiency are presented by Eq. (18). The ANOVA analysis indicates a linear relationship between the main effects of the amount of nanocatalyst, temperature and time. The final mathematical equation in terms of the actual variable (confidence surface above 95%) as determined by Minitab software 17 is given below:

$$Y \; =\; 45.984 - 0.08637x_{1} - 0.05556x_{2} - 7.33x_{3} + 2.6282x_{3}^{2} + 0.01792x_{2} \times x_{3}$$

(18)

The equation reveals that there was a significant synergistic effect (p value = 0.0001) of the concentration of amount of nanocatalyst on the percent SO₂ oxidation efficiency. The amount of nanocatalyst, that had a more coefficient (7.33x₃), is more important.

Effect of the variables

To study the effect of three independent variables (x₁, x₂ and x₃) on the characteristics of SO₂ oxidation and entrapment efficiency, analysis of the variance (ANOVA) was performed. The final equations were simplified to contain only significant parameters (p value < 0.05). Suitability of the model was tested using analysis of variance (Table 5). The adjusted R² calculates the amount of variation explained by the form after adjusting to the number of parameters in it. The high value of R²-adjusted designates the high fitness of the model [28]. The ANOVA was also conducted for each answer and the results are presented in Table 5, demonstrating the fact that the predictability of the model is at 95% of confidence surface. Response functions predictions are consistent with experimental data (R² = 99.95).

Table 5 ANOVA test for response function

Accuracy of the model

The analysis of variance tests is a usual statistical method of the different fields. The analysis of variance provides a statistical process that determines the means of several groups are equal or not. F value is used to test the significance of the model, individual variables and their interactions [29, 30]. The p value is used to check the significance of the coefficient and p value < 0.05 shows that the model is significant and higher than 5% model is not significant. The results were analyzed using the analysis of variance a regression model, the coefficient of determination (R²), adjusted R-square, statistical-diagnostic and response plots. The F value (48586.56) indirectly suggests that the model is significant. In addition, the p value of the model is less than 0.05, that it is a significant and eligible model. The large value of F indicates that most of the variation in the response can be demonstrated by the regression equation in the Eq. (18). The analysis of variance in (Table 5), Indicates that the second-order polynomial model in term Eq. (18) was statistically significant and adequate to represent the actual relationship between the efficiency and the significant variables, with a very small p value (0.0001) and (R² = 0.9995). The positive coefficient of the term, X1, indicates that the amount of catalyst is pertaining to a synergy influences on the oxidation efficiency (p value < 0.0001). The ANOVA results also revealed the synergy effect of the amount of catalyst on the oxidation efficiency (p value < 0.0001).

Diagnostics of model adequacy

The natural probability graph is a graphical material that Fig. 10a shows that the remainder of the response is normally distributed. As is evident in Fig. 10a, the obtained point consistently appears on a linear relationship and has indicated that the random error was independently and normally distributed. The results demonstrated that the model applied to the data was significant and sufficient to represent the relationship between the response and the independent variables. Summary of the ANOVA results is shown in (Table). Histogram of Fig. 10b and fitted to value Fig. 10c shows the classification of data’s is normal.

Fig. 10

Diagnostic plots for the Box-Behnken model adequacy. a normal probability plot of residuals, b Histogram, c residual versus fitted values and d Residual versus run the numbers

The residuals were analyzed to determine the accuracy of the model. To recognize the validity of the prediction, the predicted values of was compared with experimental ones and they are presented in Fig. 11. These results show that the predicted and experimental values are in a good agreement as painted by all points arranged to the diagonal line. The coefficient of the regression model (R²) was 0.9995, which indicated that the regression model was statistically significant. Moreover, the R²-Adj value was 99.97%, indicating a high degree of correlation between the experimental and predicted efficiencies.

Fig. 11

Actual and predicted plots using Box-Behnken design

According to the results, the model in Eq. (17) shows that time has no significant effect on the oxidation of SO₂. These observations are not surprising and, in fact, match the results one at a time [31].

Three-dimensional response surfaces and contour plots

Response surface plots and contour plots and are useful for the model equation and recognizing the character of response surface. A simple examination of the effect of experimental variables on responses is 3D response levels and corresponding contrast components [32]. The resulted surface response 3D plots of efficiency as a function of two independent variables are shown in Fig. 12. Figure 12a, b depicts the interaction of each two variable by keeping the other at its central level for SO₂ oxidation, thus Eq. (18) is used to be drawing the plots. The common interaction between temperature and nanocatalyst amount on the SO₂ oxidation efficiency can be best translated from the response surface contour diagram (Fig. 11a), which indicates that SO₂ oxidation efficiency directly related to nanocatalyst amount.

Fig. 12

Response surface plots for the Box-Behnken design: a 3D plot of efficiency versus amount of nanocatalyst and temperature, b 3D plot of efficiency versus amount of nanocatalyst and time, c. 3D wafer plot of amount of nanocatalyst and time

As shown in Fig. 12a, b efficiency increases with increase in nanocatalyst amount and the temperature (or time) increase is not significant role in increasing the efficiency of SO₂ oxidation. As shown in 3D wafer plot Fig. 12c, efficiency increases with increasing reaction time and the amount of nanocatalyst.

The interaction effects of catalyst concentration and reaction time

The BBD was effectively used to optimize and study the interactive effect of SO₂ oxidation in surface Mn/CS. The contour plot of the influence of the operating parameters on the SO₂ oxidation efficiency is depicted in Fig. 13. Contour plots efficiency (%) versus amount of nanocatalyst and contour plot efficiency (%) versus temperature are presented in Fig. 13a, b. It is important to note that Fig. 13a represents the evolution of influence amount of nanocatalyst versus time. It can be seen that with the increase in amount of nanocatalyst, the efficiency (%) increases.

Fig. 13

Contour plot describing for SO₂ oxidation efficiency as a function of amount of nanocatalyst versus temperature. a Contour plot of efficiency (%) versus amount of nanocatalyst [g: time (min)]. b Contour plot of efficiency (%) versus temperature (°C); time (min)

Under optimal conditions, by means of a catalyst, repeatabilty was perefectly done. Copper Slag has relatively high activity compared to other catalysts such as Mn-activated carbon and Mn/zeolite [4, 6]. This observation is probably related to the higher diffusivity of the reaction intermediates (most of them electrically charged) in a structure. Moreover, the copper slag has the advantage of allowing loading (by ion exchange) more amount of Mn²⁺.

Conclusions

In this research, oxidation of SO₂ was done using Mn/CS as nanocatalyst in a (SBR) in the low temperature range of 10–30 °C. In order to simulate SO₂ gas industrial in bench scale experimental SO₂ oxidation reaction to oxygen dissolved in aqueous solution catalyzed by Mn/CS was studied using conductivity measurement methods. FESEM images, EDX analysis, FTIR spectroscopy, XRD pattern, XRF, TG/DTA analysis and BET surface area were used to study Mn/CS. High capacity of copper slag for adsorption of manganese ions increases the reaction rate of the oxidation of SO₂ gas. The Box-Behnken design was used to investigate the effect of reaction time, temperature and amount of nanocatalyst on SO₂ oxidation experiments. The SO₂ oxidation process was optimized with respect to three main parameters; temperature, time, and nanocatalyst amount, using BBD. A second polynomial quadratic was fitted with experimental values (R² = 0.9995).

According to the results, it can be concluded that the application of this SO₂ oxidation process has great potential to be economically and industrially. The fitted model is in a good agreement with the experimental data, so a good correlation coefficient for the quadratic model was gained as 0.9995. The statistical design method predicts a maximum conversion to 99% for the optimum values of three process variables, reaction temperature 10 °C, nanocatalyst amount 6 g/l and reaction time 60 min. The results indicate that for oxidation of SO₂ in the low temperature (10–30 °C) Mn/CS is very active. One of the advantages of this method is the production of sulfuric acid and the removal of SO₂ gas from industrial exhaust. This finding indicates that SO₂ oxidation using Mn/CS is likely related to the excellent catalytic activity of Mn/CS at low temperatures. Maximum efficiency for oxidation of SO₂ at temperature = 283 K, Mn/CS amount = 6 g/L and Time = 60 min was determined.

Catalytic processes have been reported for the oxidation of SO₂ using a hematite catalyst in the presence of hydrogen peroxide as an oxidizer [33]. The use of hydrogen peroxide increases process costs. Another catalyst such as Ce promoted V₂O₅ and CuO/Al₂O₃ are reported for oxidation of sulfur dioxide, which is carried out at high temperatures. In this study, catalytic oxidation is carried out using a new catalyst (Mn/CS) without the use of expensive oxidizers and at ambient temperatures [34, 35].