# Some Unmodified Household Adsorbents for the Adsorption of Benzalkonium Chloride—A Kinetic and Thermodynamic Case Study for Commercially Available Paper

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Choice of Adsorbent

- Low price and easy availability (commercial sources);
- Good standardization (already ensured by the producer);
- An approximatelly zero value for the 262 nm absorbance of the adsorbent-water mixture, so that it does not interfere with the values provided by BAC;
- A high equilibrium adsorption yield coupled with a low total S-L contact time required until equilibrium.

_{eq}, of the water–BAC–adsorbent mixtures, as well as the corresponding A

_{0}values of BAC aqueous solutions of the same concentration as the tests’ initial ones. In this study, 10 g/L of each adsorbent was employed for C

^{0}

_{BAC}= 1000 mg/L initial BAC concentrations at 18.0 ± 0.1 °C. The adsorption equilibrium yield η

_{eq}(%) was calculated by means of Equation (1). Equilibrium was considered to be achieved when three consecutive absorbance measurements (at different total S-L contact times) did not vary for more than 2%. Figure 2a,b illustrate the results registered during the assessment of criterion 4 for the choice of the most suitable BAC adsorbent.

_{eq}was carried out with absorbance values instead of BAC concentrations because not all adsorbents have negligible A

_{262}values in aqueous media, see sawdust, for example. The first four adsorbents in Table 1 do not add to the overall absorbance value at 262 nm, and the A values in Equation (1) are only due to the presence of BAC. Hence, the corresponding η

_{eq}values of these adsorbents in Figure 2a are pertinent.

_{262}value registered for the bulk liquid phase, the A

_{eq}value of the sawdust–BAC mixtures contains contributions from both species. As a result, the numerator (A

_{0}− A

_{eq}) in Equation (1) is not quantitatively linked with the remaining liquid phase BAC concentration at equilibrium. Hence, the value of η

_{eq}for sawdust in Figure 2a ought to be regarded with reservations.

#### 3.2. Experimental Data and Their Processing Method

_{BAC}was obtained at 262 nm in order to link the absorbance of the liquid phase bulk with the remaining, un-adsorbed BAC concentration. Its mathematical expression is provided in Equation (2), where C

_{BAC}is expressed in mg/L.

_{262}= (0.071 ± 0.014) + (1.184 ± 0.011)×10

^{−3}C

_{BAC}

^{2}

_{adjusted}= 0.9974 value demonstrates the good quality of the calibration. The slope permits the calculus of the molar absorption coefficient for known BAC variants. Because BAC solutions have been prepared from a commercial source with an unspecified BAC-12 and BAC-14 ratio, concentrations are expressed in “overall” mg/L BAC instead of mole/L. Therefore, the slope of Equation (2) is expressed in (mg/L)

^{−1}·cm

^{−1}.

_{BAC}calculus, the A

_{262}values used in Equation (2) were corrected by subtracting the adsorbent’s own absorbance (of an average value of 0.015 as listed in Table 1) from the one of the test’s mixture.

_{BAC}values served to calculate the adsorption capacity q (mg/g), according to Equation (3). C

^{0}

_{BAC}(mg/L) stands for the initial concentration of BAC, whereas C

_{BAC}(mg/L) stands for the one at a certain moment t after process initiation, respectively. C

_{adsorbent}(g/L) is the adsorbent content of the aqueous BAC–solid adsorbent mixture. Hence, q stands for the mass (mg) of BAC adsorbed by 1 g of adsorbent after a certain S-L contact time t.

_{eq}and was determined experimentally in each case.

_{significance}threshold, then the differences are statistically significant [44] (pp. 59–65). Otherwise, they are statistically insignificant. The threshold value depends on the number of degrees of freedom, which, in turn, is related to the number of experimental data subjected to testing.

_{significance}= 2.68. Similar results were obtained for the effect of the initial BAC/paper mass ratio, with F = 1874.4 being much higher than F

_{significance}= 2.41. The results show that both parameters affect statistically significantly the course and outcome of the adsorption process, yet with a far more dramatic influence by initial conditions than the temperature (at least within the range of employed process conditions).

#### 3.3. Process Kinetics

_{eq}, see Figure 3a, with a pseudo-second-order kinetic rate coefficient k expressed in (g/mg·h), see Equation (4).

**k**and the equilibrium adsorption capacity q

_{eq}, from the intercept and slope of the linear plot of the (t/q) values against t. Figure 3b presents this for the data shown in Figure 3a. Good linearization is observed, proving the suitability of the chosen kinetic model.

_{eq}= 23.53 mg/g, which is practically equal to the experimental 23.56 mg/g value (see also Table 3). Similar matches were found for the other employed experimental conditions. This fact is a further argument in favor of the kinetic model described in Equation (4). Such findings are in agreement with previously reported ones [36,37].

^{2}

_{adjusted}values of the linear regressions from which they were calculated, such as the one in Figure 3b. The last column proves the good quality of the (i) experimental data and (ii) linearizations, hence model fit.

^{2}

_{adjusted}is a strong statistical tool when comparing models with different numbers of independent variables m and data points n. Therefore, it is a better indicator of model quality than the simple R

^{2}, because it shows the variability in the target variable due only to independent variables that actually affect it [44] (pp. 92–108), [46,47]. The relationship between these two statistical parameters is described in Equation (6). It may be observed that, for the same m = 1 (the case here), if n differs, so will R

^{2}, and hence R

^{2}

_{adjusted}. The value of the latter being close to 1 demonstrates that the data fit very well with the proposed equation, in this case, with the second-order kinetic law.

_{a}and the pre-exponential factor Z by means of the linearized Arrhenius law. It fits fairly well (R

^{2}

_{adjusted}= 0.7855) with the four experimental ln(k) vs. 1/T values. Hence, E

_{a}= 73.35 ± 21.26 KJ/mole and ln(Z) = 27.01 ± 8.43 were obtained, pointing to the chemisorption of BAC as the main adsorption mechanism. Previously, similar [31] and opposite (physical sorption) findings [35] have been previously reported, mainly depending on the nature of the adsorbent but also on the initial adsorbate/adsorbent mass ratio.

#### 3.4. Adsorption Isotherms and Mechanism

_{eq}(mg/g), which are quantitatively linked to the BAC retained on the adsorbent’s surface as a function of their corresponding equilibrium remnant concentration in the liquid bulk phase, C

_{eq}(mg/L). Both experimental and calculated q

_{eq}values are provided. The latter are obtained from plots described through the use of Equation (5) and exemplified by Figure 3b. There is a very good match between the q

_{eq}value pairs. Hence, (i) the suitability of the second-order kinetic model is reinforced since the slope of its linearized form (5) serves for the determination of q

_{eq}calculated and (ii) the good quality of the experimental data is proven (see also the corresponding excellent R

^{2}

_{adjusted}values).

_{max}(mg/g), and the adsorption equilibrium constant at that temperature, K

_{L}(L/mg).

^{2}

_{adjsuted}= 0.9562. Hence, at the standard temperature of 298 K, the following were obtained: q

_{max}= 35.09 mg/g and K

_{L}= 11.76 L/g, respectively.

_{exp(i)}and q

_{calc(i)}stand for the i

^{th}experimental and calculated q values, respectively. The denominator represents the average value of q

_{exp}, and n is the number of experiments (here n = 5). The decision variables of the objective function are the sought-after model parameters.

^{2}

_{adjusted}, see Equation (6).

^{2}

_{adjusted}as close to 1 as possible, whereas RMSD and HYBRID ought to be as close to zero as possible.

^{2}

_{adjusted}of 0.988), seconded by the Langmuir (L) isotherm (best R

^{2}

_{adjusted}, yet weakest HYBRID), respectively. A comparison between the experimental values of q

_{eq}and those calculated by these two models is presented in Figure 6. Both seem to do a good job (see also results of Table 4); however, the L-isotherm predicts values that are scattered among the experimental ones, whereas the RP-equation predicts lower q

_{eq}values, regardless of the C

_{eq}level. Hence, despite the better statistical error functions of the RP model, the Langmuir one still holds best. Similar conclusions have been previously reported [32,34,37].

_{eq}vs. C

_{eq}plot, each plateau (leveling off) corresponding to a step: the first being explained by chemical and the second by physical processes. The experimental data in Figure 6 exhibit such a shape somewhat, with a leveling off in the 100–320 mg/L C

_{eq}domain. However, there are too few points to correctly apply a double L-model (a sum of two terms, like the Langmuir equation presented in Table 4) [31], with four parameters to be determined from only five q

_{eq}–C

_{eq}pairs.

^{0}by using the Van’t Hoff relationship (11) and the value of the equilibrium constant; however, the latter ought to be dimensionless [51].

_{L}= 11.76 L/g provided by the Langmuir model is not dimensionless. Equation (12) [51] describes a way of computing the dimensionless equilibrium constant K

^{0}

_{e}in such cases:

^{0}= 353.5 g/mole is the dimensionless standardized average molar mass of the employed BAC-12 and BAC-14 mixture (the ratio is unspecified by the provider; however, for the sake of this calculus, a 1:1 value was considered); o$\mathsf{\gamma}$ is the activity coefficient, which was here considered to be equal to 1. The obtained K

^{0}

_{e}value enabled the calculus of ΔG

^{0}with the help of (11) (R = 8.314 J/mole·K, T = 298 K).

^{0}= −20.64 KJ/mole indicates a spontaneous process at 298 K. The magnitude of this adsorption free energy is comparable to those reported for other cationic adsorbates [52], yet it is approximately five-fold higher than values reported for BAC physisorption on powdered activated carbon [37]. Hence, again, a somewhat hybrid chemi- and physisorption mechanism may be assumed for the adsorption of BAC on the studied household paper.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Scheme 1.**The structural formula of benzalkonium chloride (BAC), where n = 8 ÷ 18 stands for the even number of carbon atoms in the chain of the alkyl group.

**Figure 1.**UV absorbance spectrum of the liquid phase for (a) a 500 mg/L aqueous BAC solution, (b) a water-paper mixture containing 10 g/L paper, and (c) a water-BAC-paper mixture containing initially 500 mg/L BAC and 10 g/L paper, at adsorption equilibrium and at 18.0 ± 0.1 °C, respectively.

**Figure 2.**(

**a**) Values of the equilibrium adsorption yield; (

**b**) total S-L contact time until equilibrium. Data describe the 5 different employed adsorbents, with corresponding error bars for triplicate determinations, at 50 mg/g BAC/adsorbent initial mass ratio and 18.0 ± 0.1 °C, respectively.

**Figure 3.**Example of adsorption capacity q vs. total S-L contact time plot (

**a**), and the corresponding plot of the linearized pseudo-second-order kinetic law (

**b**). Data for 50 mg/g initial BAC/paper mass ratio, at 25.0 ± 0.1 °C.

**Figure 4.**Pseudo-second-order rate coefficients k for various adsorbents at 18.0 ± 0.1 °C and 50 mg/g initial BAC/adsorbent mass ratio.

**Figure 5.**The dependence of overall pseudo-second-order rate coefficients k on the BAC/paper initial mass ratio, at 25.0 ± 0.1 °C.

**Figure 6.**Experimental equilibrium isotherm data vs. calculated data for the Langmuir and Redlich–Peterson isotherms, respectively, at 25.0 ± 0.1 °C.

**Table 1.**Comparison among solid BAC adsorbent candidates in terms of price, availability, standardization degree and 262 nm absorbance value in water.

Adsorbent | Price (EUR/kg) | Availability | Standardization Degree ^{1} | Absorbance at 262 nm |
---|---|---|---|---|

White household paper towel | 7.5 | Easy (retail) | - −
- Controlled and constant quality ensured by the producer;
- −
- (42.68 ± 0.18) g/m
^{2}outer surface; - −
- (6.42 ± 0.24)% relative humidity.
| 0.015 ± 0.012 |

Light blue viscose household cloth | 30.2 | Easy (retail) | - −
- 70% viscose, 30% polyester
^{2}; - −
- Controlled and constant quality ensured by the producer;
- −
- Approximately 18.9 g/m
^{2}outer surface.
| 0.018 ± 0.009 |

White tea filter paper | 82.2 | Easy (retail) | - −
- Controlled and constant quality ensured by the producer;
- −
- (16.99 ± 0.05) g/m
^{2}outer surface; - −
- (4.31 ± 0.17)% relative humidity.
| 0.018 ± 0.008 |

White cotton string | 16.7 | Easy (retail) | - −
- Controlled and constant quality ensured by the producer;
- −
- Thickness
^{2}of 1 mm; - −
- Approximately
^{2}250 g/100 m.
| 0.003 ± 0.003 |

Sawdust | 0.16 | Easy (household) | - −
- Quality and composition dependent on source;
- −
- Approximately 24% relative humidity;
- −
- (254.5 ± 3.8) g/L dry bulk density.
| From 0.38 to 3.60 |

^{1}As ensured by the producer.

^{2}As indicated by the producer.

**Table 2.**Pseudo-second-order rate coefficients k as a function of temperature, at 50 mg/g initial BAC/household paper towel mass ratio.

T (K) | 100 × k (g/mg·h) | R^{2}_{adjusted} |
---|---|---|

291 ± 0.1 | 4.74 ± 0.08 | 0.9932 |

298 ± 0.1 | 7.00 ± 0.23 | 0.9997 |

308 ± 0.1 | 10.44 ± 0.17 | 0.9971 |

318 ± 0.1 | 72.93 ± 1.68 | 0.9889 |

**Table 3.**Equilibrium data: BAC adsorption capacities q

_{eq}(mg/g) vs. their corresponding equilibrium remnant concentration in the liquid bulk phase, C

_{eq}(mg/L). Experimental and calculated data, at 25 ± 0.1 °C.

C_{eq}(mg/L) | q_{eq}—Experimental(mg/g) | q_{eq}—Calculated(mg/g) | R^{2}_{adjusted} |
---|---|---|---|

63.63 ± 4.03 | 18.64 ± 0.02 | 18.69 ± 0.04 | 0.9980 |

135.98 ± 2.09 | 23.90 ± 0.07 | 23.87 ± 0.02 | 0.9998 |

264.36 ± 2.11 | 23.56 ± 1.04 | 23.53 ± 1.01 | 0.9997 |

477.76 ± 9.13 | 27.22 ± 0.01 | 27.25 ± 0.01 | 0.9993 |

672.30 ± 11.17 | 32.77 ± 1.05 | 33.33 ± 0.07 | 0.9980 |

Model ^{1,2} | Equation | Parameters ^{3} | RMSD | HYBRID | R^{2}_{adjsuted} |
---|---|---|---|---|---|

Langmuir ^{1} | $q=\frac{{q}_{max}{K}_{L}{C}_{eq}}{1+{K}_{L}{C}_{eq}}$ | q_{max} = 35.088K _{L} = 11.760 | 2.777 | 56.052 | 0.956 |

Freundlich ^{1} | $q={K}_{F}{{C}_{eq}}^{\frac{1}{n}}$ | K_{F} = 7.900n = 4.762 | 1.719 | 18.135 | 0.886 |

Dubinin–Radushkevich ^{1} | $q={q}_{s}\mathrm{e}\mathrm{x}\mathrm{p}(-{k}_{ad}{\epsilon}^{2})$ | q_{s} = 3.10^{−4}k _{ad} = 27.719 | 3.079 | 53.815 | 0.674 |

Temkin ^{1} | $q=\frac{RT}{{b}_{T}}\mathrm{l}\mathrm{n}\left({A}_{T}{C}_{eq}\right)$ | b_{T} = 472.270A _{T} = 0.530 | 1.861 | 21.275 | 0.852 |

Hill ^{2} | $q=\frac{{q}_{sH}{{C}_{e}}^{{n}_{H}}}{{k}_{D}+{{C}_{e}}^{{n}_{H}}}$ | q_{sH} = 7191.3k _{D} = 744.214n _{H} = 0.168 | 2.268 | 41.914 | 0.865 |

Redlich–Peterson ^{2} | $q=\frac{{K}_{R}{C}_{e}}{1+{a}_{R}{C}_{e}^{g}}$ | K_{R} = 3673.7a _{R} = 464.983g = 0.790 | 1.720 | 27.914 | 0.988 |

Toth ^{2} | $q=\frac{{K}_{T}{C}_{eq}}{{\left({a}_{T}+{C}_{eq}\right)}^{\frac{1}{t}}}$ | K_{T} = 7.492a _{T} = 0t = 1.266 | 1.707 | 27.388 | 0.848 |

Radke–Prausnitz ^{2} | $q=\frac{{a}_{RP}{K}_{RP}{C}_{eq}^{{\beta}_{R}}}{{a}_{RP}+{K}_{RP}{C}_{eq}^{{\beta}_{R}-1}}$ | a_{RP} = 3112.800K _{RP} = 7.493ᵝ _{R} = 0.220 | 1.708 | 27.504 | 0.857 |

^{1}Two-parameter adsorption isotherm models.

^{2}Three-parameter adsorption isotherm models.

^{3}Units of parameters for the isotherms, whit the calculus performed with C

_{eq}values expressed in g/L: Langmuir—q

_{max}(mg/g) maximum monolayer coverage, K

_{L}(L/g) adsorption equilibrium constant; Freundlich—K

_{F}(mg/g) approximate indicator of adsorption capacity, n (dimensionless), with 1/n indicating adsorption strength, a model coefficient; Dubinin–Radushkevich—q

_{S}(mg/g) theoretical saturation capacity, k

_{ad}(mole

^{2}/KJ

^{2}) a measure of adsorption equilibrium constant, ε (dimensionless) Dubinin–Radushkevich isotherm constant, a model coefficient; Temkin—A

_{T}(mg/g) binding constant, b

_{T}(dimensionless) Temkin isotherm constant; Hill—q

_{sH}(mg/g) Hill saturation capacity, k

_{D}(L/g) Hill–Deboer isotherm constant, n

_{H}(dimensionless) model coefficient; Redlich–Peterson—K

_{R}(L/g) Redlich–Peterson isotherm constant, a

_{R}(g/mg) a measure of maximum adsorption capacity, g (dimensionless) model exponent with values between 0 and 1; Toth—K

_{T}(L/g) Toth isotherm constant, a

_{T}(mg/g) maximum adsorption capacity, t (dimensionless) heterogeneity factor; Radke–Prausnitz—a

_{RP}(mg/g) maximum adsorption capacity, K

_{RP}(L/g) Radke–Prausnitz isotherm constant, β

_{R}(dimensionless) model exponent.

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## Share and Cite

**MDPI and ACS Style**

Bitay, E.; Csavdari, A.
Some Unmodified Household Adsorbents for the Adsorption of Benzalkonium Chloride—A Kinetic and Thermodynamic Case Study for Commercially Available Paper. *Toxics* **2023**, *11*, 950.
https://doi.org/10.3390/toxics11120950

**AMA Style**

Bitay E, Csavdari A.
Some Unmodified Household Adsorbents for the Adsorption of Benzalkonium Chloride—A Kinetic and Thermodynamic Case Study for Commercially Available Paper. *Toxics*. 2023; 11(12):950.
https://doi.org/10.3390/toxics11120950

**Chicago/Turabian Style**

Bitay, Enikő, and Alexandra Csavdari.
2023. "Some Unmodified Household Adsorbents for the Adsorption of Benzalkonium Chloride—A Kinetic and Thermodynamic Case Study for Commercially Available Paper" *Toxics* 11, no. 12: 950.
https://doi.org/10.3390/toxics11120950