Anal Bioanal Chem (2002) 374 : 1132–1140 DOI 10.1007/s00216-002-1578-2
O R I G I N A L PA P E R
Antonio Canals · M. del Remedio Hernández
Ultrasound-assisted method for determination of chemical oxygen demand
Received: 12 June 2002 / Revised: 7 August 2002 / Accepted: 21 August 2002 / Published online: 25 October 2002 © Springer-Verlag 2002
Abstract A method for determination chemical oxygen demand (COD) assisted by use of ultrasound has been successfully evaluated for the first time. The method uses instrumentation simpler and cheaper and, in some instances, safer than that used by previous methods for the same purpose. The new device used for sonication is an all-glass cylindrical sonotrode that can be introduced directly into the reaction mixture. Use of this device enables more efficient interaction between sample and ultrasonic energy. The optimized experimental conditions are high ultrasonic power (55% amplitude, 0.9-second pulses each second), high sulfuric acid concentration (>60%), and a sonication time of 2 min. Under these conditions the method has limitations similar to those of the official COD method with regard to the type of organic compound. It works adequately with easily oxidized organic matter (potassium hydrogen phthalate and dextrose) and other organic compounds difficult to oxidize by conventional methods (e.g. phenol and acetic acid) but the COD values obtained with volatile compounds and difficult organic matter are poor. Chloride is tolerated up to a concentration of 7000 mg L–1 without any masking agent. Gasification of the sample is recommended to improve results; use of air and argon resulted in no significant differences – bubbling with air during sonication resulted in COD values for certified materials and real wastewater samples statistically identical with the certified COD values and those obtained by the classic (open reflux) method. The use of ultrasound energy for COD determination thus seems to be an interesting and promising alternative to conventional oxidation methods used for the same purpose. Keywords Chemical oxygen demand · Ultrasound energy
A. Canals (✉) · M. del Remedio Hernández Department of Analytical Chemistry, University of Alicante, P.O. Box 99, 03080 Alicante, Spain e-mail:
[email protected]
Introduction Because the degradation of organic matter requires oxygen, the organic matter content of a sample of water can be estimated from the amount of oxygen necessary for oxidation of this organic matter. When the oxidation is performed chemically the value obtained is the so-called chemical oxygen demand (COD). Common COD values range between 20 and 50 mg O2 L–1 for slightly contaminated water (e.g. surface water, domestic sewage) to sometimes higher than 100,000 mg O2 L–1 for extremely contaminated industrial wastewater. As an indicator of water contamination by organic matter a rapid, precise, and accurate method for determination of COD is of great importance in environmental analysis. The classic reference (open reflux) method for determination of COD consists in oxidation of the organic matter in the sample, usually by adding a known amount of oxidant (dichromate in sulfuric acid), heating under reflux at high temperature in open containers, and titrating excess of oxidant with ferrous ammonium sulfate [1]. This method suffers from several disadvantages: 1. the overall process is too long – 2–4 h is required for digestion plus additional time for the titration; 2. handling is also considerable, so the likelihood of errors is high and a skilled analyst is required; 3. large amounts of expensive and toxic chemicals are required; 4. straight-chain carboxylic acids are not completely oxidized in the absence of a catalyst (Ag2SO4) and might not be completely oxidized even in the presence of this compound; 5. volatile compounds are only oxidized to the extent with which they stay in contact with the liquid media and the heat generated by addition of sulfuric acid to the flask might drive volatile compounds from the solution; and 6. low selectivity, because some inorganic species (Cl–, N O2− , Fe3+, etc.) cause interferences.
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Several modifications have been proposed to circumvent these drawbacks [2, 3, 4, 5, 6]. In most of these methods the bottleneck continues to be the digestion time required, sometimes 2 h. To reduce the total analysis time, and hence to increase sample throughput, some automatic methods have been suggested, both in flow-injection analysis (FIA) and in segmented flow analysis (SFA) [7, 8, 9, 10, 11, 12, 13]. All these methods for determination of COD use conventional convective–conductive heating devices. There is a large difference between digestion time in conventional methods (2 h) and in flow methods (a few minutes). This also means that the amounts of energy applied are very different and so oxidation of some organic matter might not be complete for automatic methods heated with conventional conductive–convective systems. Because of this, more efficient ways of heating have been evaluated. Among these, microwave radiation (MW) has been successfully applied, both in batch and FIA [14, 15, 16, 17, 18]. Microwave heating is much more efficient, and thus faster, than conventional conductive–convective heating and the time required for complete oxidation of the organic matter has been reduced to 7 min, instead of approximately 20 min in other FIA methods or 2 h in the conventional semi-micro (closed reflux) method. The higher efficiency of microwave heating has increased sample throughput to 50 samples per hour [16]. Ultrasound is widely used in analytical laboratories. Some applications of this type of energy are solution degasification, cleaning, solid–liquid extraction of organic and inorganic analytes, and aerosol generation [19, 20, 21, 22, 23, 24, 25, 26, 27]. Analyte extraction by use of ultrasonic energy has shown to be an interesting alternative to the common extraction methods, because operation with ultrasonic processors can be performed at ambient temperature and normal pressure, mild chemical conditions can usually be used, and a significant reduction in operating time is achieved. The effects of ultrasound on chemical transformations are not the result of direct coupling of the sound field with the chemical species involved on a molecular level. The reason why power ultrasound can produce chemical effects is through the phenomenon of cavitation. Cavitation is the production of microbubbles in a liquid when a large negative pressure is applied to it. Ultrasound is transmitted via waves which alternately compress and stretch the molecular spacing of the medium through which it passes. Thus the average distance between the molecules in a liquid will vary as the molecules oscillate about their mean position. If a large negative pressure (i.e. sufficiently below ambient) is applied to the liquid so that the distance between the molecules exceeds the critical molecular distance necessary to hold the liquid intact, the liquid will break down and voids will be created (i.e. cavitation bubbles will form). Cavitation bubbles are now subjected to the stresses induced by the sound waves. These bubbles will grow over a few cycles taking in vapor or gas from the medium to an equilibrium size which matches the frequency of bubble resonance to that of the sound frequency applied. The acoustic field experienced by an individual
bubble is not stable, because of interference from other bubbles forming and resonating around it. As a result some bubbles suffer sudden expansion to an unstable size and collapse violently. It is the fate of these cavities when they collapse which generates the energy for chemical and mechanical effects. When these tiny bubbles formed by cavitation collapse, it has been estimated that pressures and temperatures within rise to over 1800 atm and 4300 K, respectively, and thermolysis, supercritical water oxidation, and free-radical oxidation all occur. These conditions often lead to enhanced chemical reactivity. Some chemical effects of ultrasound arise because of the formation during such an implosion of highly reactive radical species which can enter the liquid phase. Sonication of pure water leads to dissociation of water vapor into H and OH radicals [26, 27]. Acceleration of chemical reactions is a feature shared by microwave and ultrasound energies. Although the advantages of microwaves in analytical laboratories are well known [28], major drawbacks are the high initial cost of the equipment and the high temperature and/or pressure that must be used. In previous work [29] we evaluated a novel ultrasoundassisted method for determination of COD. Although the method used instrumentation simpler and cheaper than previous methods used for the same purpose, under optimized experimental conditions (143 W, 126.5 W cm–2; [H2SO4]>60% (v/v); 2 min sonication) the first prototype had the same limitations as the official COD method with regard to the type of organic compounds. It worked successfully with readily oxidized organic matter (e.g. sodium oxalate, glucose, and salicylic acid) but the COD values obtained with more difficult organic matter and real wastewater samples were lower that the theoretical values. The poor oxidation obtained with some samples was explained in terms of low efficiency of the ultrasound energy transfer from the sonic probe (sonotrode) to the reaction mixture. This limitation with the first prototype could be because of the use of a polyethylene intermediate tube filled with water; this was needed because part of the titanium sonotrode (i.e. the cell disrupter) was not resistant to the highly acidic and oxidizing reaction mixture. The aim of this work was, therefore, to evaluate the applicability of an all-glass sonic probe for direct sonication of the highly aggressive media used in COD determinations, so the efficiency of energy transfer between the generator and the reaction mixture would be higher. This new experimental arrangement could be used to suggest a rapid, inexpensive, easy to handle, precise, and accurate ultrasound-assisted method for determination of COD in wastewaters.
Experimental All reagents were of analytical grade. Distilled deionized water was used throughout. Reagents were prepared as described for the classic (opened reflux) method [1]. The digestion solution contained 0.0167 mol L–1 K2Cr2O7, 3.0 mol L–1 H2SO4, and 0.11 mol L–1 HgSO4. The acid solution was a solution of 10 g L–1 Ag2SO4 in
1134 H2SO4 (96%, v/v). The indicator for the titration was ferroin, prepared by dissolving 1.485 g 1,10-phenanthroline monohydrate and 0.695 of FeSO4.7H2O in water and diluting to 100 mL. The titrant was a 0.005 mol L–1 aqueous solution of FeSO4(NH4)2SO4.6H2O (FAS), standardized daily against K2Cr2O7. A standard solution of potassium hydrogen phthalate (KHP), corresponding to 1000 mg L–1 COD, was prepared by dissolving 0.851 g KHP in water and diluting to 1 L with water. Appropriate dilution gave solutions of different COD. Potassium hydrogen phthalate was used for optimization studies because it is an excellent primary standard and, it has been previously used for other authors for the same purpose [15]. Certified reference materials (GBW08624b and GBW08626b, National Research Center for Certified Reference Materials, China) were used to validate the proposed method. Certified COD values are 1277 mg O2 L–1 and 4937 mg O2 L–1 for the GBW08624b and GBW08626b, respectively. Real wastewater samples were supplied by an industry located in eastern Spain and a local private water-analysis laboratory (Labaqua, Spain). In this way a broad range of COD values and water types (i.e. industrial, domestic, treated, and untreated, etc.) were analyzed. Blank determinations were performed on distilled water. Figure 1 shows the experimental arrangement of the sonication system used to assist the oxidation of organic matter in COD determination. A 200-W, 24-kHz ultrasonic processor (Dr Hielscher, Teltow, Germany) was used as the sonic probe. An all-glass cylindrical sonotrode (7 mm o.d.; 110 mm long, reference SG7, Dr Hielscher) was introduced directly into the reaction mixture. The temperature of the reaction mixture was optimized and, finally, fixed at 27±2 °C, maintained by use of a Haake (Haake Mess-Technik, Karlsruhe, Germany) model F3-K thermostatted bath . To do this a glass thermostatting two-wall cell (4.08 cm i.d.) was used to contain the reaction mixture. Unless otherwise stated the tip was introduced the maximum distance without touching the bottom of the thermostatting cell (0.7 cm from the surface of reaction mixture) and, finally, the mixture was sonicated for the desired time without stirring. The sonotrode was always immersed the same distance into the reaction mixture, by using a graduated scale located on the supporting rod of the power generator/booster horn/sonotrode system (Fig. 1).
Fig. 1 Experimental arrangement for ultrasound-assisted determination of COD
The mixture to be sonicated was prepared by mixing 2 mL sample, 2 mL oxidant reagent (potassium dichromate and sulfuric acid), and 4 mL acid reagent (sulfuric acid and silver sulfate). After the sonication the dichromate that had not been reduced was titrated against ferrous ammonium sulfate with ferroin sulfate as indicator [1]. Unless otherwise stated, all data are means from three replicate analyses and the error bars show ±one standard deviation. Caution For health reasons, working with a sound reduction box and/or ear protectors is strongly recommended.
Results and discussion Effect of ultrasound amplitude Figure 2 shows the variation of COD values with the amplitude of ultrasonic energy applied. Three different regions are apparent. The first goes from 0% to 45% of the amplitude. In this region the COD values obtained increase continuously with increasing amplitude but the amplitude was insufficient to oxidize the potassium hydrogen phthalate and, hence, the COD values obtained are always lower than the theoretical values (ThOD=100 mg O2 L–1). Without sonication 34% of ThOD is obtained but a minimum intensity of sonication is required to reach the cavitation threshold. In the second region, that from 45% to 70% amplitude, the efficiency of oxidation of KHP is optimum and COD values reach a plateau at 100 mg O2 L–1. Finally, in the third region, for amplitudes ranging between 70% and 90%, the COD values obtained decrease, reaching 80% of the theoretical value. This shape, with a maximum, has previously been observed for other sonochemical systems and can be explained by the large number of cavitation bubbles generated in the solution when a large amount of ultrasonic power enters a system. Many of these bubbles will coalesce forming larger, more longlived bubbles which will certainly act as a barrier to the transfer of acoustic energy through the liquid. Another possible source of loss of efficiency in the transfer of power
Fig. 2 Effect of amplitude. Length of pulses=0.9 s (per second); depth of tip=0.7 cm from the liquid surface; sonication time=2 min; [H2SO4]=56% (v/v); temperature=27±2 °C; ThOD=100 mg L–1
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could be the so-called decoupling effect [30]. From these data, the amplitude was fixed at 55%. At this point it should be remarked that the probe never worked at maximum amplitude (100%), to prevent damage. Comparison of the results obtained with the experimental system used in this work and those obtained with the previous design used for the same purpose [29] confirms that the lack of accuracy obtained with the latter could be because of the special configuration of the experimental arrangement that needs an intermediate tube filled with water. In the previous design the standard sonic probe manufactured from titanium was introduced into this intermediate tube, because it did not resist the highly acidic reaction mixture. The water filling this tube could absorb energy and the two interphases water/tube wall/reaction mixture increase losses of energy by absorption, scattering, and refraction. All these processes might attenuate the sonic energy in the reaction mixture. For this reason the COD values obtained never reached a maximum (Fig. 2 in Ref. [29]) which might mean that the conditions used corresponded to the first region shown in Fig. 2 (i.e. between 0% and 45% amplitude). In the experimental arrangement evaluated in this work the glass sonotrode could be directly inserted into the acid and oxidant reaction mixture and, hence, the efficiency of energy transmission was higher.
Fig. 4 Effect of sulfuric acid concentration. Amplitude=55%; length of pulses=0.9 s (per second); depth of the tip=0.7 cm from the liquid surface; sonication time=2 min; temperature=27±2 °C; ThOD=100 mg L–1
In the second region, from 0.5 to 0.9 s, the efficiency of oxidation of KHP increases noticeably, with COD values reaching the ThOD value at a pulse time of 0.9 s. This pulse time was therefore used in all the experiments. To prevent damage the probe was never used at maximum pulse time (1 s). Effect of sulfuric acid concentration
Effect of pulse timing The instrument can be used in pulse mode, to enable rhythmic processing of media. With a pulse setting of “1” the reaction mixture is sonicated without interruption whereas with a pulse setting, for example, of “0.5” the mixture is sonicated for 0.5 s and then sonication stops for 0.5 s. Hence in pulse mode the ratio of sound-emission time to cyclic pause time can be adjusted continuously from 0% to 100% per second. The effect of pulse timing on the COD values obtained is shown in Fig. 3, in which two different regions are apparent. The first region goes from pulse times of 0 to 0.5 s. In this region COD values were constant at 60 mg O2 L–1.
Figure 4 shows that COD values increased linearly with acid concentration until finally, for acid concentrations >66%, COD values reached a plateau at 100 mg O2 L–1 (i.e. ThOD). Hence, the higher the concentration of acid, the higher the COD values obtained. Similar trends have also been observed for other systems irradiated with ultrasound [29, 31] or microwaves [16]. At acid concentrations between 66% and 70% the COD values obtained were not significant different from the ThOD; in this work, therefore, 66% (v/v) was selected. The advantage of the experimental arrangement studied in this work is reflected in this experimental variable. Standard sonic probes manufactured with titanium cannot be introduced directly into the highly acidic reaction mixture and, hence, the efficiency of interaction between the ultrasound energy and sample decreases. For this reason in our previous work the highest COD value obtained during optimization with KHP was 70% of the ThOD [29]. The glass sonotrode used in this work can be introduced directly into the highly acidic and oxidizing reaction mixture. This increases the efficiency of energy transmission from the sonotrode to the sample and, hence, it is possible to reach the ThOD value. Effect of sonication time
Fig. 3 Effect of length of pulses. Amplitude=55%; depth of the tip= 0.7 cm from the liquid surface; sonication time=2 min; [H2SO4]= 56% (v/v); temperature=27±2 °C; ThOD=100 mg L–1
The effect of sonication time on the COD values obtained is shown in Fig. 5. COD values increase with sonication time during the first minute of irradiation, then reach a constant value of 100 mg O2 L–1 (i.e. ThOD). The same
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Fig. 5 Effect of sonication time. Amplitude=55%; length of pulses= 0.9 s (per second); depth of the tip=0.7 cm from the liquid surface; [H2SO4]=66% (v/v); temperature=27±2 °C; ThOD=100 mg L–1
Fig. 6 Effect of temperature. Amplitude=55%; length of pulses= 0.9 s (per second); depth of the tip=0.7 cm from the liquid surface; sonication time=2 min; [H2SO4]=66% (v/v); ThOD=100 mg L–1
behavior has been observed in the ultrasound-assisted extraction of metals [31, 32] and organic compounds [33], the ultrasonic generation of some anions [20], and microwave assisted COD determination [17]. With our previous experimental design in which a metallic cell disrupter was used the highest COD value obtained was 60% of ThOD [29]. At this stage of the work irradiation for 2 min was selected because after this time the potassium hydrogen phthalate was completely oxidized without elevation in its temperature.
the COD values obtained were equal to the ThOD. The temperature was, therefore, always fixed at 27 °C, because this temperature was easier to maintain constant.
Effect of temperature There is some controversy about the effect of temperature on sonochemical processes. Some authors have stated that in reaction kinetics the effect of ultrasound is higher at lower temperatures [34, 35] whereas the ultrasound-assisted extraction of organic additives increases with temperature [33]. Performance passing through a maximum is very common in the variation of sonochemical effects with temperature [26, 30], although the temperature of maximum benefit depends on the sonochemical process studied. For this reason experiments were performed at 10 °C, 27 °C, and 49 °C. Figure 6 shows the COD values obtained at these temperatures. Two main conclusions can be obtained from this figure. No change in COD value was obtained for temperatures between 10 °C and 27 °C but a significant reduction of 45% in the ThOD was obtained when working at 49 °C. This is a clear indication that the beneficial effect of sonication is mainly because of a chemical rather than thermal effect [29]. One possible explanation of this behavior could be that any increase in temperature will increase the vapor pressure of a medium and so lead to easier cavitation but less violent collapse. This will be accompanied by a decrease in viscosity and surface tension. At temperatures approaching the solvent boiling point, however, many cavitation bubbles are generated concurrently. These will act as a barrier to sound transmission and dampen the effective ultrasound energy from the source which enters the liquid medium [26, 30]. When the temperature was fixed between 10 °C and 27 °C
Effect of sonotrode depth into the sample Because the depth of the sonotrode in the reaction mixture might cause variation in the COD values obtained [29], experiments were performed to optimize this variable. The tip of the glass sonotrode was placed at two positions, 0.2 cm and 0.7 cm from the surface of the reaction mixture. To reproduce the immersion positions a graduated scale was attached to the supporting rod of the power generator/booster horn/sonotrode. Because the mean COD values were 43% and 104% of ThOD when the sonotrode tip was placed at 0.2 cm and 0.7 cm, respectively, the sonotrode was inserted the maximum distance into the solution but always without touching the bottom of the vessel with the tip. Effect of interferences Chloride ions are the most important interference in COD determination because they are amenable to oxidation by dichromate and can precipitate the silver used as catalyst. This problem is usually solved by adding HgSO4 to the sample. The concentration of HgSO4 required is related to the concentration of chloride in the sample. Hence, if this interference could be reduced or even eliminated the method would be more environmentally sound. Automated methods of analysis are a good choice to reduce or even eliminate this interference. When digestion was performed by flow injection chloride was tolerated up to concentrations of 30,000 mg L–1 and 10,000 mg L–1 when Ce(IV) was used as oxidizing agent or microwaves as heating method, respectively [10, 17]. In this work interference from chloride was investigated by use of the standard solutions (100 mg L–1 COD, as KHP) containing no HgSO4 and chloride levels between 750 and 7000 mg L–1. The results given in Fig. 7 show that the method can toler-
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Fig. 7 Effect of chloride concentration on COD values. Amplitude=55%; length of pulses=0.9 s (per second); depth of the tip=0.7 cm from the liquid surface; sonication time=2 min; temperature=27±2 °C; [H2SO4]=66% (v/v); ThOD=100 mg L–1
ate chloride up to 7000 mg L–1 without the need for the addition of mercury(II) sulfate. Application to other organic compounds To evaluate its applicability this new ultrasound-assisted oxidation method was also used to determine the COD values of six organic compounds of known theoretical oxygen demand (ThOD) [29]. The results are given in Table 1. The ratios of measured and theoretical COD values are between 0.22 (pyridine) and 1.01 (dextrose). On the other hand, five different types of compound can be monitored. The first group includes the readily oxidized compounds such as dextrose, which is completely oxidized. The second group includes volatile compounds such as ethanol or 1-butanol. The experimental COD values obtained with such compounds range from 52% to 62% of the theoretical values. The experimental system used is open and heat could be generated in two ways. The first could be when sulfuric acid is added to the sample; in this work, however, this temperature never was higher than 37 °C. A second explanation could be that during cavitation the bubbles act as very high-temperature microreactors (e.g. 4200 K inside a cavitation bubble containing nitrogen in water at ambient temperature and pressure) [26], so the temperature changes on a micro scale but not on a macroscale. Irrespective of mechanism it Table 1 Results from use of the ultrasound-assisted method to determine the COD of different organic compounds Organic compound
ThOD (mg L–1)
COD (mg L–1)
RSD (%)
Dextrose Ethanol 1-Butanol Phenol Acetic acid Pyridine
102 158 119 114 107 133
103 98 62 114 101 29
19 22 27 15 17 24
seems that a significant fraction of these volatile compounds is probably lost before being oxidized by the dichromate. The third group includes aromatic derivatives such as phenol. This compound is completely oxidized under the optimized experimental conditions used. The fourth group includes straight-chain carboxylic acids such as acetic acid. This type of compound is not oxidized in the absence of a catalyst and might not be completely oxidized even in the presence of a catalyst [36, 37]. In our previous work on ultrasound-assisted digestion of organic matter the COD obtained with this compound was 10% of the theoretical value [29]. With the new device used in this work, however, this compound is completely oxidized. Finally, the fifth group includes organic compounds that are poorly oxidized, for example pyridine, because this compound is difficult to oxidize even with more efficient oxidation methods [16, 17]. Relative standard deviation (RSD) values for the results obtained using the ultrasound-assisted method were always below 20%, with the exception of pyridine, ethanol, and 1-butanol, for which values of 24%, 22%, and 27%, respectively. These high RSD values are mainly because of the small COD values obtained with these compounds.
Application to reference materials As a first step in the validation of the new sample pretreatment method two COD reference materials were analyzed. The values obtained are showed in Table 2. Results shown in columns two and three were obtained without bubbling gas whereas results shown in columns four and five were obtained by bubbling air. Data given without bubbling in this table show that the COD value obtained with the reference sample of lower COD value is statistically not different from the certified value; there is, however, a significant difference from the certified material of higher COD, at the significance level used (95%) [38].
Application to real samples The ultrasound-assisted method for determination of COD was used, without bubbling, to determine the COD of three real wastewater samples from an industrial plant. Table 3 compares the COD values obtained by use of the new diTable 2 Results from use of the ultrasound-assisted method to determine the COD of reference materialsa Certified value (mg L–1)
COD (mg L–1)
tcalb
COD (mg L–1)
tcalb
1277±1.2 4937±0.7
963±22 3028±20
2.55 5.57
1010±12 3184±27
3.73 2.81c
aValues
Without bubbling
With bubbling (air)
after “±” are relative standard deviations (n=2, 95%) [38]
bt =4.30 (n=3, 95%) [38]; t =12.71 tab tab cnumber of replicates=2
1138 Table 3 Comparison of classic and ultrasound-assisted methods for determination of the COD of wastewater samplesa
aValues after “±” are relative standard deviations bClassic method [1] cF =39.00 (n =n =3, 95%) tab 1 2 [38]; ttab=2.78 (n1 + n2 – 2=4, 95%) [38] dt =4.303 (degrees of freetab dom=2, 95%) [38]
Sample CODb (mg L–1) 1 2 3 4 5 6 7 8 9 10 11
11286± 7 6799± 4 11133± 8 54±47 119±35 53±19 215±10 1300±15 585±47 735±58 1235±33
Without bubbling
With bubbling (air)
COD (mg L–1)
Fcalc
tcalc
COD (mg L–1)
Fcalc
tcalc
9923±12 4582±18 8619±14 – – – – – – – –
2.37 7.28 1.93 – – – – – – – –
1.71 4.42 2.84 – – – – – – – –
10258±21 6419± 4 12493± 7 70±14 63± 4 76±15 165±10 1366±19 338± 4 507±14 1270± 7
8.39 1.39 1.02 6.68 342 1.29 1.93 1.82 347 37.9 3.73
0.77 1.66 1.87 0.054 2.321d 0.229 0.147 0.001 1.547d 0.003 4×10–4
gestion method and those obtained by use of the classic method. The data listed in Table 3 show that, without gas bubbling, for the three real samples analyzed there are no significant differences between the precision obtained with the classic and ultrasound-assisted methods (i.e. Fcal values were always
