Statistical analysis of Litchi chinensis’s adsorption behavior toward Cr(VI)
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Abstract
The adsorption results of Cr(VI) removal from aqueous solutions on Litchi chinensis have been optimized by the Box–Behnken design of response surface methodology. Three experimental parameters (dose, temperature, and pH) were chosen as independent variables. The maximum Cr(VI) adsorption was obtained at the initial pH of 2. Analysis of variance (ANOVA) of the results was successfully used to check the significance of the independent variables and their interactions. The three-dimensional (3D) response surface plots were used to study the interactive effects of the independent variables on % Cr(VI) removal. These figures successfully interpret the effect of interaction between pH (0.1–1.0), adsorbent dose (0.1–1.0 g.) and temperature (0–50 °C). The second-order polynomial equation was generated for the response. A statistical hypothesis test was conducted to critically analyze the experimental data by applying t test, paired t test, and Chi-square test. The comparison of t-calculated and t-tabulated values showed that the results were in favour of the conducted experiment.
Keywords
Litchi chinensis Box–Behnken design Statistical analysis Hypothesis testIntroduction
From many times, the presence of heavy metals in the water sources is a serious environmental problem and is dangerous to the human health worldwide. These inorganic pollutants are highly toxic because they are not biodegradable; thus, researches are going on for decades to find some methods to adsorb metal ions from aqueous solution. Among them, chromium has become a serious health concern because it causes many severe diseases. Strong exposure to Cr(VI) causes cancer in the digestive tract and may cause epigastric pain, nausea, vomiting, severe diarrhoea, and haemorrhage (Mohanty et al. 2005). Chromium is one of the contaminants, which exist in hexavalent [Cr(VI)] and also in the trivalent form [Cr(III)] (Rao et al. 2015). Chromium and its compounds are widely used in many industries such as metal finishing, dyeing, pigments, inks, glass, ceramics, tanning, textile, wood preserving, electroplating, steel fabrication, and canning industries (Rao et al. 2015). Chromium (VI) is more toxic to human physiology because of its mutagenic and carcinogenic properties, which may even lead to death (Rao et al. 2015). The chromate (CrO _{2} ^{−4} ) and dichromate (Cr_{2}O _{2} ^{−7} ) forms of Cr(VI) are extremely hazardous (Eliodorio et al. 2017), and the maximum acceptable limit by various standards has been set (Uddin 2017). Permissible limits for Cr(VI) in drinking water (mg/L) according to various standards are very low: 0.050 (IS 10500) (FAD 25: Drinking Water 2012), 0.050 (WHO) (Uddin 2017), 0.100 (EPA) (Uddin 2017), 0.050 (EU standard) (Wikipedia).
Many processes like precipitation (Esalah and Husein 2008), chemical oxidation (Kaur and Crimi 2014), reverse osmosis (Çimen 2015), electrochemical treatment (Ruotolo et al. 2006), emulsion (Nosrati et al. 2011), ultrafiltration (Muthumareeswaran et al. 2017), photo-catalysis (Machado et al. 2014), ion exchange (Kononova et al. 2009), pre-concentration (Rao and Kashifuddin 2012a), evaporation (Sachitanand et al. 2013), sedimentation (Vukić et al. 2008), adsorption (Khatoon et al. 2018; Naushad et al. 2015; Alqadmi et al. 2016; Uddin and Bushra 2017) have been developed to remove this toxic Cr(VI) from aqueous solution. Out of these methods, adsorption is a widely used and most efficient method to eliminate heavy metals from contaminated water (Rao and Kashifuddin 2012a, b). This technique is superior because of its low cost, ease of operation, efficiency in treatment, good applicability, high capacity, reliability, less energy consumption, and simplicity (Rao and Kashifuddin 2016; Khan et al. 2014). Various effective and low-cost adsorbents have been used for the removal of Cr(VI) recently (Eliodorio et al. 2017; Suriga 2017; Ali et al. 2016; Eldin et al. 2017; Lee et al. 2017; Mullick et al. 2018; Fan et al. 2017; Qi et al. 2016; Panda et al. 2017; Ali et al. 2016; Gorzin and Abadi 2018).
Red- or pink-red-colored smooth fruit peel of litchi tree (Litchi chinensis) covered with small sharp protuberances was successfully utilized as a low cost, efficient, waste adsorbent for the removal of Cr(VI) from wastewater (Rao et al. 2012; Yi et al. 2017). The results of the research studies investigated by Rao et al. 2012 and Yi et al. 2017 concluded that Litchi peel exhibited remarkable adsorption capacity toward Cr(VI) ions, as investigated by the effect of various parameters such as pH, contact time, temperature, adsorbent amount, and initial Cr(VI) concentration. Different isotherms, thermodynamics, and kinetics parameters also showed the effectiveness of Litchi peel to treat hexavalent chromium containing wastewater (Rao et al. 2012).
To confirm the reliability of experimental data, a statistical optimization process that is known as response surface methodology (RSM) was used (Mondal et al. 2017). RSM is a multivariate, computational statistical technique in which the experimental adsorption data were fitted in a second-order polynomial equation, and finally, it was analyzed by performing tests of variance and lack of fit (Mondal et al. 2017). The Box–Behnken design (BBD) is one of the available designs of response surface methodology that is used to optimize the adsorption process (Simsek et al. 2015). It was used in many successful recent studies to validate the experimental results (Mondal et al. 2017; Loqman et al. 2016; Okwadha and Nyingi 2016; Siva Kiran et al. 2017; Igberase et al. 2017; Kavitha and Thambavani 2016; Ma et al. 2016; Wei et al. 2016; Perez et al. 2017). The objective of the present work is to optimize the efficiency of litchi fruit peel in Cr(VI) removal from electroplating wastewater (Rao et al. 2012). The variables like pH, solution temperature, and adsorbent dose were optimized to evaluate the combined and interactive effects of the variables in the process for the removal of chromium ions from aqueous solution.
Materials and experimental methods
The dried peel of Litchi fruit was used in the form of powder to remove the Cr(VI) using the batch experimental procedure, the same as investigated before by Rao et al. 2012. Cr(VI) adsorption experiments were then conducted by defined concentration and volume of the metal ion with different doses of adsorbent (0.1, 0.5, and 1.0 g) at different pH values (2.0, 6.0, and 10.0) and temperatures (30, 40, and 50 °C). Double-distilled water (DDW) was used in all adsorption experiments.
Statistical analysis of adsorption data
Levels and codes of selected variables for Box–Behnken design
Variables | Symbol | Coded levels | ||
---|---|---|---|---|
Coded | − 1 | 0 | + 1 | |
Dose | X _{1} | 0.10 | 0.55 | 1.00 |
Temperature | X _{2} | 30 | 40 | 50 |
pH | X _{3} | 2 | 6 | 10 |
The applicability of the adsorption process can also be monitored, qualitatively and quantitatively, by applying statistical hypothesis testing (Kaushal and Singh 2016). In this type of statistical analysis, the effect of different factors like pH value, time, and concentration on % adsorption of Cr(VI) was examined. In each case, the null hypothesis (H_{o}: µ_{1} = µ_{2}) was assumed that the factors did not effect on the % adsorption, while the alternative hypothesis (H_{a}: µ_{1} > µ_{2}) was assumed that the experimental parameters were effective and caused an increase in % adsorption. The analysis was tested using t test, paired t test, and Chi-square test within 5% level of confidence.
Results and discussion
Response surface methodology and statistical analysis
Box–Behnken design
Box–Behnken design matrix (BBD) in terms of coded values and the comparison of experimental and predicted % Cr(VI) removal
Run | Dose | Temp. | pH | X _{1} | X _{2} | X _{3} | % Cr(VI) removal (Y) | |
---|---|---|---|---|---|---|---|---|
Experimental | Predicted | |||||||
1 | 0.1 | 30 | 6 | − 1 | 0 | − 1 | 40 | 40.50 |
2 | 1 | 30 | 6 | 0 | − 1 | − 1 | 80 | 75.75 |
3 | 0.1 | 50 | 6 | − 1 | 1 | 0 | 32 | 36.20 |
4 | 1 | 50 | 6 | 0 | 0 | 0 | 85 | 84.50 |
5 | 0.1 | 40 | 2 | 0 | − 1 | 1 | 62 | 60.62 |
6 | 1 | 40 | 2 | − 1 | − 1 | 0 | 96 | 99.37 |
7 | 0.1 | 40 | 10 | 1 | 0 | 1 | 28 | 24.62 |
8 | 1 | 40 | 10 | 0 | 0 | 0 | 68 | 69.37 |
9 | 0.55 | 30 | 2 | 0 | 0 | 0 | 88 | 88.87 |
10 | 0.55 | 50 | 2 | − 1 | 0 | 1 | 95 | 92.12 |
11 | 0.55 | 30 | 10 | 1 | − 1 | 0 | 54 | 56.87 |
12 | 0.55 | 50 | 10 | 1 | 1 | 0 | 59 | 58.12 |
13 | 0.55 | 40 | 6 | 0 | 1 | 1 | 77 | 77.00 |
14 | 0.55 | 40 | 6 | 0 | 1 | − 1 | 77 | 77.00 |
15 | 0.55 | 40 | 6 | 1 | 0 | − 1 | 77 | 77.00 |
The linear term of coefficients \( X_{1} {\text{and}} X_{2} \) showed positive, favorable, and a significant effect on the response, while X_{3} showed a negative effect, which is opposite, if compared, to quadratic terms in which \( X_{1}^{2} {\text{and}} X_{2}^{2} \) showed negative, while \( X_{3}^{2} \) showed a positive effect on the response (Y). Interaction terms (\( X_{1} X_{2} , X_{1} X_{3} \)) of the same parameter indicated positive and favorable effect, while X_{2}X_{3} showed negative and unfavorable effect on percentage removal of Cr(VI).
Analysis of variance in the regression model for the optimization of Cr(VI) ions
Source of variations | Degree of freedom | Sum of square | Mean square | value | P value |
---|---|---|---|---|---|
Regression | 9 | 6500.48 | 722.28 | 44.45 | 0.000 |
Linear | 3 | 5674.25 | 1891.42 | 116.39 | 0.000 |
Dose (X_{1}) | 1 | 3486.13 | 3486.13 | 214.53 | 0.000 |
Temp (X_{2}) | 1 | 10.13 | 10.13 | 0.62 | 0.466 |
pH (X_{3}) | 1 | 2178.00 | 2178.00 | 134.03 | 0.000 |
Square | 3 | 773.98 | 257.99 | 15.88 | 0.055 |
(X_{1})^{2} | 1 | 736.67 | 736.67 | 45.33 | 0.001 |
(X_{2})^{2} | 1 | 48.52 | 48.52 | 2.99 | 0.145 |
(X_{3})^{2} | 1 | 1.44 | 1.44 | 0.09 | 0.778 |
Two-way interaction | 3 | 52.25 | 17.42 | 1.07 | 0.329 |
X _{1} X _{2} | 1 | 42.25 | 42.25 | 2.60 | 0.168 |
X _{2} X _{3} | 1 | 9.00 | 9.00 | 0.55 | 0.490 |
1 | 1.00 | 1.00 | 0.06 | 0.814 | |
Error | 5 | 81.25 | 16.25 | ||
Lack of fit | 3 | 81.25 | 27.08 | ||
Pure error | 2 | 0.00 | 0.00 | ||
Total | 14 | 6581.73 |
Estimated value of coefficient regression for the fitted quadratic polynomial model of Cr(VI) ion
Term | Effect | Coeff. | Standard error | T value | P value |
---|---|---|---|---|---|
Constant | 77.00 | 2.33 | 33.08 | 0.000 | |
X _{1} | 41.75 | 20.88 | 1.43 | 14.65 | 0.000 |
X _{2} | 2.25 | 1.12 | 1.43 | 0.79 | 0.466 |
X _{3} | − 33.00 | − 16.50 | 1.43 | − 11.58 | 0.000 |
X _{1} X _{1} | − 28.25 | − 14.13 | 2.10 | − 6.73 | 0.001 |
X _{2} X _{2} | − 7.25 | − 3.63 | 2.10 | − 1.73 | 0.145 |
X _{3} X _{3} | 1.25 | 0.63 | 2.10 | 0.30 | 0.778 |
X _{1} X _{2} | 6.50 | 3.25 | 2.02 | 1.61 | 0.168 |
X _{1} X _{3} | 3.00 | 1.50 | 2.02 | 0.74 | 0.490 |
X _{2} X _{3} | − 1.00 | − 0.50 | 2.02 | − 0.25 | 0.814 |
\( R^{2} \) | 0.987 | ||||
\( R^{2}\, {\text{adj}} \) | 0.965 |
Hypothesis testing
The hypothesis testing was conducted: (1) to judge the optimum value of pH, concentration and time for maximum Cr(VI) removal from solution, (2) to judge the success of the experiment by checking higher R^{2} value, (3) to infer that the higher adsorbent dosage resulted in higher % removal of chromium ions.
Effect of pH on % removal of Cr(VI) ion
n | pH | % Removal (X_{i}) |
---|---|---|
1 | 2 | 96 |
2 | 4 | 88 |
3 | 6 | 72 |
4 | 8 | 62 |
5 | 10 | 54 |
- (a)
To describe the hypothesis testing process qualitatively and quantitatively, the following statistical assumptions were made:
\( {\text{null }}\,{\text{hypothesis }}\left( {H_{0} } \right): \) the optimum pH for Cr(VI) adsorption was 2, and alternate hypothesis (H_{a}): the optimum pH \( \ne \) 2. It was determined with significance level α = 0.05 and (n − 1) degree of freedom.
Upon using the two-tailed t-test with a degree of freedom 4 using formula \( t = \frac{{\overline{X} - \mu }}{{\frac{S}{\sqrt n }}} \) (Hogg and Craig 2014), it was found that \( t_{\text{calculated}} {\text{was}} - 2.757\, {\text{while}} \,t_{\text{tabulated}} = \pm \,2.776, \) which means that t_{calculated} < t_{tabulated}. This result of hypothesis testing confirms that null hypothesis H_{0} can be accepted (that the optimum pH of Cr(VI) adsorption was 2), which also in accordance with the experimental result. Figure 3 shows probability chart for t distribution for testing. - (b)Paired t test was used to test the hypothesis of matched pairs of concentration effect (before and after the adsorption experiment), as shown in Table 6. It was assumed thatTable 6
Cr(VI) ion concentrations in the solution before (Xi) and after (Yi) the experiment
n
X _{ i}
Y _{ i}
\( D_{i} = X_{i} - Y_{i} \)
1
10
0.86
9.14
2
20
1.80
18.20
3
30
2.79
27.21
4
50
4.54
45.46
5
60
5.38
54.62
6
80
7.31
72.69
7
100
9.28
90.72
H_{0}: no changes in the final concentration of Cr(VI) ions after adsorption experiment.
H_{a}: Successful adsorption was achieved after the experiment.
The calculations have been done using the formula: \( t = \left( {D^{ - } - \mu } \right)/\left( {S/\surd n} \right) \) (Hogg and Craig 2014), at 6 degree of freedom. It was found that t_{calculated} (4.056) > t_{tabulated} (± 2.447), which means that the null hypothesis can be rejected and alternative hypothesis (that the adsorption experiment was successfully achieved) can be accepted. Figure 4 shows the probability chart for t distribution for paired t test. - (c)
Chi-square test was applied to test the effectiveness of time on final concentration and equilibrium capacity. To describe this statistically, the assumptions were
H_{0}: There was no effect of time on initial concentration
H_{a}: Adsorption was rapid, and equilibrium adsorption capacity (qe) increased with the increase in concentration
Under significance level α = 0.05 and using the experimental data (as shown in Table 7), the formula \( \chi^{2} = \mathop \sum \nolimits_{i = 1}^{n} \frac{{\left( {O_{ij} - E_{ij} } \right)^{2} }}{{E_{ij} }} \) (Hogg and Craig 2014) was used to conduct Chi-square test. It was found that \( \chi_{\text{calculated}}^{2} = 0.8220 < \chi_{\text{tabulated }}^{2} = 32.3600 \). Hence, the null hypotheses did not fall in the accepted region and cannot be accepted, which also means that the alternative hypothesis Ha can be accepted at value level of 0.05. It means that adsorption of Cr(VI) was fast and equilibrium capacity (qe) increased with the increase in Cr(VI) concentration and reached equilibrium in short time (Fig. 5).Table 7Observed frequencies on the effect of time (min) and concentration (mg/L) for the Cr(VI) ion equilibrium adsorption capacity (qe)
Time (min)
10 mg/L
20 mg/L
30 mg/L
50 mg/L
60 mg/L
80 mg/L
100 mg/L
qe (mg)
qe (mg)
qe (mg)
qe (mg)
qe (mg)
qe (mg)
qe (mg)
5
0.02
1.31
2.17
3.70
4.52
6.35
8.20
10
0.68
1.42
2.25
3.79
4.62
6.43
8.27
15
0.73
1.64
2.49
3.96
4.7
6.51
8.46
20
0.86
1.82
2.63
4.08
4.97
6.77
8.61
30
0.86
1.80
2.72
4.22
5.08
6.83
8.68
60
0.86
1.80
2.79
4.53
5.36
7.28
9.16
120
0.86
1.80
2.79
4.54
5.38
7.31
9.24
180
0.86
1.80
2.79
4.54
5.38
7.31
9.28
240
0.86
1.80
2.79
4.54
5.38
7.31
9.28
S _{D}
0.34
0.22
0.23
0.21
0.23
0.21
0.20
Conclusion
In total, 96% Cr(VI) from polluted water can be removed using the fruit peel of L. chinensis by a batch process, which demonstrated its efficient analytical applicability. Critical analysis of the interactive effects of independent variables: initial pH of the solution, dose, and temperature for better understanding of Cr(VI) adsorption onto L. chinensis was successfully studied by Box–Behnken design. The results showed that the values of R^{2} and adjusted R^{2} were quite close to each other, indicated that the model analyzed the experimental data quite well. The linear terms (X_{1}, X_{2}, X_{3}), square values (X _{1} ^{2} , X _{2} ^{2} , and X _{3} ^{2} ), and their two-way interaction (X_{1}X_{2}, X_{2}X_{3}) were found to be significant with low P values, suggesting that these variables have important role in Cr(VI) removal. Hypothesis testing was further studied to confirm the fitting of experimental results. Two-tailed t test, paired t test, Chi-square test within 5% level of confidence were tested, and the results showed that the calculated values were inside the acceptance region in probability chart. Experimental and predictable data of adsorption experiments were close to each other which also confirmed that L. chinensis was an excellent adsorbent to bind Cr(VI) ion.
Notes
Acknowledgements
The corresponding author is thankful to Deanship of Scientific Research, Majmaah University, Al-Majmaah, for funding this research. This research work was conducted under research Project Number 37/61.
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