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Titrimetric analysis with adding the titrant by means of electrodialysis
Talanta 58 (2002) 247– 254 www.elsevier.com/locate/talanta
Titrimetric analysis with adding the titrant by means of electrodialysis Anastas Dimitrov Dakashev *, Veselina Todorova Dimitrova Department of Analytical Chemistry, Prof. Dr. Assen Zlataro6 Uni6ersity, 8010 Bourgas, Bulgaria Received 1 October 2001; received in revised form 23 April 2002; accepted 3 May 2002
Abstract A titration method is developed that titrant is added continuously to the analyte by electromigration through an ion exchange membrane. A constant rate of the titrant addition is achieved by keeping the electric current constant. Analyte amount then is proportional to the titration time. The method is applied to the most widely used titrations with a visual end point indication. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Titrimetric analysis; Electrodialysis addition of the titrant
1. Introduction Titrimetric analysis is the most commonly used method of the quantitative chemical analysis. It is performed as a solution of known concentration (titrant) is added to an analyte solution. The process of adding the titrant (called titration) is usually carried out by hand with a burette. There is a number of different sorts of autoburettes. Especially for coulometric titrations the titrant is not added but is generated by an electrochemical reaction directly in the solution to be determined. In the present work an unusual way of doing titration is applied. Electrodialysis is employed to
* Corresponding author. Tel.: + 359-56-858-337; fax: + 359-56-880-249 E-mail address: [email protected] (A.D. Dakashev).
move automatically the titrant toward the solution to be titrated. The electrodialysis process to be used for the titrations instead of a burette is not a new idea. In 1960 Hanselman and Rogers [1] reported a titration method that included electrodialysis. Twelve years later an application of this method was published [2]. A work dealing with this topic has not been proposed since that time. An absence of any interest can be explained by the following arguments. The authors had a misconception. They considered this determination as a coulometric one and investigated the conditions for performing a coulometric titration. The result obtained was one more coulometric titration method but not an alternative version of the titration. The purpose of the work presented here is to create an electrodialysis procedure of adding the titrant applied for all titrations with a visual end-point detection.
0039-9140/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 9 1 4 0 ( 0 2 ) 0 0 2 4 2 - 4
248
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
2. Theory When a voltage is applied between the two electrodes of the electrodialysis titration system,
(Fig. 1), the ions migrate to the opposite sign charged electrodes and pass through the ion exchange membranes from one to another department of the electrodialyzer. An electrical current flows through the system. The ion-titrant is passing from the titrant storage department to the titration vessel, where the chemical reaction underlying the determination is taking place. At the same time water electrolysis and electrochemical oxidation and reduction of the hydrogen and hydroxide ions respectively are occurring at the electrodes as follows: 2H2O+ 2e=H2 + 2OH − 2H+ + 2e=H2 at the cathode and: 2H2O− 4e=4H+ + O2 4OH − − 4e=2H2O+ O2
Fig. 1. General display of the setup for electrodialysis titration.
Fig. 2. Schematic diagram illustrating electrodialysis titration with a cation titrant, cation (K), anion (A), electrodialysis process ( ), dialysis process (----- \ ), electrochemical process (…… \ ), hydrogen ion (H+), hydroxide ion (OH−), cation exchange membrane (CEM), anion exchange membrane (AEM).
at the anode. The selection of a cation or an anion exchange membrane requires the consideration of the following criteria: To ensure penetrating of the ion-titrant into the solution to be titrated. To prevent migrating of the ion-titrant to the nearly electrode cell 1. Not to permit the titrated ion to move in the nearly electrode cell 2. Not to let H+ or OH− ions, generated in the electrode cells, to pass into titrant solution or into solution to be titrated, in a case those ions interfere or simply ‘pollute’ the solutions. A balance for the number of moles, going in or out titrant storage department and electrode cell 1 as well, can be done using the principle for neutrality of the solution. When the titrant is cation, see Fig. 2, (for example a titration of Cl− with Ag+), the following equations can be written: − K ted + d + Kdse − (−A ted)+ (− Adse)= 0
(1)
for the titrant storage department and: H+ec + (−A ted)− (−Adse)= 0
(2)
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
nt = i~/F+ bDC~
249
(7)
where i, ~ and F have the usual meanings, b is a coefficient, and DC is the concentration gradient. If the electrodialysis titration is conducted at a constant current value. And also if DC is constant, i.e. there is a sufficiency of supporting electrolyte, the change in its concentration during titration is negligible. The Eq. (7) then is transformed to: nt = K~
Fig. 3. Schematic diagram illustrating electrodialysis titration with an anion titrant, cation (K), anion (A), electrodialysis ( ), dialysis (----- \ ), electrochemical process (…… \ ), hydrogen ion (H+), hydroxide ion (OH−), cation exchange membrane (CEM), anion exchange membrane (AEM).
for the electrode cell 1, where K, A and H+ are number of moles for cation, anion and hydrogen ion, symbols: t, se, d, ed, ed+d, and ec mean titrant, supporting electrolyte, dialysis, electrodialysis, electrodialysis accompanied by dialysis, and electrochemically generated respectively. Signs ‘+’ and ‘− ’ show the movement directions, ‘+ ’ for moving in and ‘ −’ for moving out. By these symbols are mentioned the charge signs as well. Eq. (1) and Eq. (2) together give: K ted + d = H+ec + Kdse
(3)
When the titrant is an anion, see Fig. 3, (for example a titration of Ag+ with CNS−), by analogy with Eqs. (1) and (2) and Eq. (3) we obtain: − Kedt +Kdse − (−A ted + d) + ( −Adse) =0
(4)
− OH − ec −Kdse + K ted =0
(5)
A ted + d = OH − ec + Adse
(6)
The Eq. (3) is identical to Eq. (6). The first term in these equations can be expressed by the Faraday’s law equation and the second term by the dialysis equation [3]. Then for the number of moles of the titrant the following equation is obtained:
(8)
where K= i/F+ bDC When the titrant added is equivalent to the analyte, the Eq. (8) can be written for the moles, na, of the analyte: na = K~
(9)
3. Experimental
3.1. Solutions Analytical-reagent grade chemicals were used throughout. Distilled water was used for the preparation of the solutions, except for complexometric titrations, were bidistilled water was implemented. The solutions were standardized by accepted procedures. Hydrochloric acid was standardized by titrating a standard solution of sodium tetraborate decahydrate. The sodium hydroxide and potassium permanganate solutions were standardized by titrating a solution of an exact weight of oxalic acid dihydrate. The iodine solution was standardized by a standard thiosulphate solution, which was determined with a standard potassium dichromate solution prepared directly. A solution of Ca(II) was made up by weighing calcium carbonate and dissolving in hydrochloric acid. A solution of EDTA was prepared directly by weighing the disodium dihydrate. The concentration was also checked against the standard calcium(II) solution. A solution of Fe(II) was prepared immediately before use by direct weighing from (NH4)2Fe(SO4)2 ·6H2O.
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3.2. Membranes Use was made of a cation exchange membrane MK 40 (Russia), an anion exchange membrane MA 40 (Russia), and an ultrafiltration polyacryonitrile membrane, PAN 30 (Bulgaria). The ion exchange membranes were soaked for 24 h in the solutions that passed through the membranes by the time of performing the titration. The ultrafiltration membrane was soaked in water before use.
3.3. Apparatus The electrodialysis titration is performed with a laboratory-build system shown in Fig. 1. It includes an electrodialyzer equipped with a currentgenerating unit. The electrodialyzer consists of four compartments: two electrode cells, a titrant storage compartment, and a titration vessel, separated by three ion exchange membranes. The electrode cells and the titrant storage compartment are made of glass. Their lower ends are sealed by epoxy glue to the pieces of tubings taken from the upper parts of the screw-capped polyethylene bottles. The ion exchange membranes are stuck to the edge of the polyethylene tubings by the caps in which holes are drilled to expose a membrane area of about 12.6 cm2. An aquarium pump is
used to bubble air through the solutions of the electrode cells and the titrant storage in order to stir them. An electromagnetic stirrer is applied for stirring the solution in the titration vessel. The current generating unit consists of a voltage transformer, a current rectifier, two decade resistors (of 1–9 and 0.1–0.9 kV respectively) in series, milliammeter, and two gauze platinum electrodes placed in the electrode cells. By making an appropriate voltage change to the transformer or a change to the resistance of the resistor, the current in the circuit is selected and then checked by the milliammeter. This arrangement assures constant current regime.
3.4. Titration procedure The electrode cells are filled up with the supporting electrolyte solutions and a titrant solution is poured out into the titrant storage. About 80 cm3 of a supporting electrolyte is placed in the titration vessel (for details see Table 1). The stirring is switched on. The electric current is turned on and a proper current value is adjusted. The current is kept constant and the electrodialysis titration is performed continuously. For that purpose analyte solution is introduced in the electrolyte solution of the titration vessel and a
Fig. 4. Calibration graph for electrodialysis titration of Ca2 + with H2Y2 − .
Cathode
Cathode
OH−
Ag+
CNS−
H2Y2−
Ca2+
MnO− 4
Cr2O72−
S2O32−
I3−
C2O42−
Cl−
Ag+
Ca2+
H2Y2−
Fe2+
Fe2+
I2−
S2O32−
Cathode
Cathode
Anode
Cathode
Cathode
Anode
Cathode
Anode
H+
B4O72−
Electrode 1
Ion-titrant
Ion to be determined
Anode
Anode
Anode
Anode
Cathode
Anode
Anode
Cathode
Anode
Cathode
Electrode 2
0.1 M H2SO4 0.1 M NaOH 0.1 M NaNO3 0.1 M NH4NO3 0.1 M Na2SO4
0.1 M KMnO4 0.1 M K2Cr2O7 0.1 M Na2S2O3 0.1 M I2 0.05 M Na2SO4
0.05 M K2SO4 0.1 M K2SO4 0.2 M NaCl 0.05 M Na2SO4
+NH4Cl 0.05 M K2SO4 0.1 M H2SO4 0.2 M NaCl
+NH4Cl NH3
0.1 M Na2SO4 0.1 M Na2SO4 0.1 M NaNO3 0.1 M HNO3 NH3
0.05 M K2SO4 0.1 M K2SO4 0.5 M NaOH 0.5 M NaOH
0.05 M Na2SO4
0.1 M Na2SO4 0.5 M NaOH 0.1 M NaNO3 0.1 M NH4NO3 0.1 M NaCl
MA-40
MK-40
MK-40
MK-40
MA-40
MK-40
MK-40
MA-40
MA-40
MK-40
PAN-30
MA-40
PAN-30
PAN-30
MK-40
MA-40
MA-40
MK-40
–
–
B
A
Electrode cell 2
Electrode cell 1
Titration vessel
Membrane
Supporting electrolyte solutions
0.1 M CaCl2 0.2 M NaCl
0.1 M AgNO3 0.1 M NH4CNS 0.1 M Na2H2Y
–
–
Titrant storage solutions
Table 1 Necessary data for the composition of the electrodialysis titration
MK-40
MK-40
MA-40
MA-40
MK-40
MA-40
MA-40
MK-40
MK-40
MK-40
C
Starch
Diphenylamine Starch
–
Eriochrome black T
Eriochrome black T
FeNH4(SO4)2
Methyl orange Phenolphthalein K2CrO4
Indicator A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254 251
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
252
Table 2 Results for electrodialysis titration with a visual indication
Table 2 (continued) Introduced, mg
Introduced, mg
Found x 9tS/ n, mg
Found x9tS/ n, mg
Relative standard deviation Sr =(S/x)100 (%)
(9) I2 1.28 3.84 5.13 6.40 7.70
1.28 9 0.01 3.84 9 0.02 5.13 9 0.02 6.40 9 0.03 7.70 9 0.03
0.88 0.55 0.45 0.50 0.34
(10) S2O32− 0.29 0.59 0.88 1.17 1.46
0.32 9 0.02 0.59 90.02 0.83 90.03 1.17 90.02 1.49 90.01
3.8 3.1 2.5 1.7 0.77
Relative standard deviation Sr = (S/x)100 (%)
(1) B4O72− 5.92 7.89 9.87 15.8 19.7
5.92 90.15 7.77 90.18 9.75 90.13 15.8 90.14 19.6 90.12
2.5 1.5 1.4 0.92 0.61
(2) C2O42− 1.19 1.78 2.38 2.98 5.95
1.19 9 0.02 1.77 9 0.02 2.41 9 0.01 3.01 9 0.01 3.79 9 0.07
1.6 1.4 0.27 0.45 1.2
(3) Cl− 0.71 1.06 1.42 1.77 2.13
0.71 90.01 1.06 90.01 1.39 90.03 1.78 90.01 2.12 90.01
1.2 0.59 1.8 0.45 0.31
(4) Ag+ 0.54 1.09 1.63 2.18 2.72
0.46 90.02 1.10 90.02 1.70 90.02 2.35 90.03 2.56 90.03
3.9 1.4 1.2 0.90 0.83
(5) Ca2+ 0.80 1.20 1.60 2.00 2.40
0.80 90.01 1.20 90.01 1.60 90.01 1.99 90.01 2.37 90.01
1.5 0.75 0.54 0.59 0.33
(6) H2Y2− 5.80 8.73 11.6 14.6 17.4
5.78 9 0.06 8.73 9 0.03 11.6 9 0.06 14.6 9 0.03 17.2 9 0.03
1.1 0.36 0.56 0.18 0.19
(7)a Fe2+ 1.12 2.23 3.35 4.47 5.59
1.22 9 0.07 2.05 9 0.10 3.59 9 0.07 4.11 9 0.12 5.77 9 0.08
4.4 4.0 1.5 2.4 1.2
(8)b Fe2+ 1.12 2.23 3.35 4.47 5.59
1.06 9 0.02 2.31 9 0.04 3.40 9 0.03 4.35 9 0.02 5.64 9 0.03
1.8 1.4 0.66 0.38 0.41
Number of determination n, 5; t, Students t-value at 95% probability; S, standard deviation. a Fe2+ titrated with MnO4−. b Fe2+ titrated with Cr2O72−.
pretitration is done. When the end point of the pretitration is reached (the indicator changes its colour) a timer is started up and a sample of the analyte is pipetted into the solution. The titration time is read out at the end point but the timer is not switched off and another sample is introduced. In this manner a series of samples can be titrated in succession in the same titrated solution. The results for the first 2–3 titrations are ignored if they differ considerably from the others. The mass of a substance to be determined, ma, is proportional to the titration time, ~: ma = k~ The k-value is previously determined by performing an electrodialysis titration at the same experimental conditions with a known amount of the analyte. A calibration graph method can also be applied. A typical calibration graph is given in Fig. 4.
4. Results and discussion In the present work the titration is performed with an electrodialyzer (Fig. 1), in which the electrodes are separated from the titrant solution.
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
This design avoids titrant to be involved in an electrochemical reaction as well as titrant solution to be preserved from the water electrolysis products. However when acids and bases are titrated, it is suitable the titrant solution to be placed in one of the electrode cells as the electrode product is actually the titrant itself. In this case the electrodialysis device is simplified. A visual end point detection is chosen for the electrodialysis titrations. The voltage applied between electrodes, in order to realize electrodialysis process, interferes with an electrometric (potentiometric, amperometric) end point indication. The electrometric indication is possible if an intermittent titration is performed. It was found out that when the electric circuit of the electrodialysis system is disconnected, the titration goes on by means of dialysis. The dialysis rate increases if the dialysis is preceded by electrodialysis. The dialysis depends strongly on the current value of the electrodialysis process went earlier. By these reasons the intermittent titration becomes complicated and is not to be recommended. When electrodialysis titration continues for a long time a difficulty in end point indication arises. An unclear change in the indicator colour is observed for some visual indicators such as methyl orange or eriochrome black T. It is due to the decreased indicator concentration, caused by the adsorption of the indicator on the membrane or penetration through it. A proper way of dealing with this is simply to add some more indicator. If the rate of electrodialysis addition of the titrant is not high enough a smooth change of the indicator colour is achieved and a sharp end point indication cannot be attained. The conditions for electrodialysis titrations are found experimentally to fulfill the requirement for the titrant addition rate mentioned above. The factors that influence the titrant addition rate are membrane area, current and ion transport number, so that the membrane area and the current can be selected. The membrane area chosen is as big as possible for the titration setup. The choice of the current value is limited by the fact
253
that at high current values the membrane is heated and can be damaged. So a different current value is chosen for every single titration. Current values in an interval from 20 to 80 mA are used in the work. The supporting electrolyte solution provides a conductivity and in this way determines the current value. When the supporting electrolyte concentration is 0 0.01 mol dm − 3, a change in the concentration, by the time of titration, varies the current value. Supporting electrolyte concentrations E0.05 mol dm − 3 are used throughout this work. It was found that in the beginning of performing the titration the titrant addition rate is lower then increases. As a result the titration time for the first two or three samples is longer than the next one. If the first results differ considerably they have to be ignored. Redox electrodialysis titrations using an oxidizing ion as a titrant, such as MnO4 − , Cr2O72 − and J3 − are impossible with an MA 40 anion permeable membrane used in this work. A PAN 30 ultrafiltration membrane was applied instead. Despite the fact that this membrane is not a selective one, the electrodialysis titration is fulfilled. The use of Eq. (9) to calculate analyte quantity requires knowledge of the k-value. It depends on the experimental conditions. The k-value is previously determined by performing an electrodialysis titration with a known amount of the analyte. In this work calculations were made with a linear regression computer program using Eq. (9). A calibration graph method can also be applied for this purpose. Fig. 4 shows an example of a calibration graph. A standard titrant solution is required for the titrations. A standard analyte solution is needed instead for the electrodialysis titration proposed in this work. The presented electrodialysis method is checked for its application to the most frequently used titrimetric determinations implementing a visual indication. The results are given in Table 2. Those results are regarded as satisfactory. There is not a systematic error. For the proposed electrodialysis method the
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A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
titrant addition rate depends on the current value and a constant rate is achieved by keeping the current constant. That’s why current is the only parameter that has to be regulated while the time to be measured. Such technique appear to be simple, convenient and suitable for automation. Instruments for this purpose are commercially available (these for the constant current coulometry). The membranes manufactured at present are stable, the current can be strictly kept constant and an exact timing can be made. The results for
electrodialysis titration, in principle, would not be less accurate and precise than those for the usual titrations.
References [1] R.B. Hanselman, L.B. Rogers, Analytical Chemistry 32 (10) (1960) 1240. [2] V.G. Barikov, O.A. Songina, T.G. Sereda, Manufactory Laboratory 38 (6) (1972) 641 in Russian. [3] S.T. Hwang, K. Kammermeyer, Membranes in Separation, Chemistry, Moscow, 1981.
Titrimetric analysis with adding the titrant by means of electrodialysis Anastas Dimitrov Dakashev *, Veselina Todorova Dimitrova Department of Analytical Chemistry, Prof. Dr. Assen Zlataro6 Uni6ersity, 8010 Bourgas, Bulgaria Received 1 October 2001; received in revised form 23 April 2002; accepted 3 May 2002
Abstract A titration method is developed that titrant is added continuously to the analyte by electromigration through an ion exchange membrane. A constant rate of the titrant addition is achieved by keeping the electric current constant. Analyte amount then is proportional to the titration time. The method is applied to the most widely used titrations with a visual end point indication. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Titrimetric analysis; Electrodialysis addition of the titrant
1. Introduction Titrimetric analysis is the most commonly used method of the quantitative chemical analysis. It is performed as a solution of known concentration (titrant) is added to an analyte solution. The process of adding the titrant (called titration) is usually carried out by hand with a burette. There is a number of different sorts of autoburettes. Especially for coulometric titrations the titrant is not added but is generated by an electrochemical reaction directly in the solution to be determined. In the present work an unusual way of doing titration is applied. Electrodialysis is employed to
* Corresponding author. Tel.: + 359-56-858-337; fax: + 359-56-880-249 E-mail address: [email protected] (A.D. Dakashev).
move automatically the titrant toward the solution to be titrated. The electrodialysis process to be used for the titrations instead of a burette is not a new idea. In 1960 Hanselman and Rogers [1] reported a titration method that included electrodialysis. Twelve years later an application of this method was published [2]. A work dealing with this topic has not been proposed since that time. An absence of any interest can be explained by the following arguments. The authors had a misconception. They considered this determination as a coulometric one and investigated the conditions for performing a coulometric titration. The result obtained was one more coulometric titration method but not an alternative version of the titration. The purpose of the work presented here is to create an electrodialysis procedure of adding the titrant applied for all titrations with a visual end-point detection.
0039-9140/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 9 1 4 0 ( 0 2 ) 0 0 2 4 2 - 4
248
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
2. Theory When a voltage is applied between the two electrodes of the electrodialysis titration system,
(Fig. 1), the ions migrate to the opposite sign charged electrodes and pass through the ion exchange membranes from one to another department of the electrodialyzer. An electrical current flows through the system. The ion-titrant is passing from the titrant storage department to the titration vessel, where the chemical reaction underlying the determination is taking place. At the same time water electrolysis and electrochemical oxidation and reduction of the hydrogen and hydroxide ions respectively are occurring at the electrodes as follows: 2H2O+ 2e=H2 + 2OH − 2H+ + 2e=H2 at the cathode and: 2H2O− 4e=4H+ + O2 4OH − − 4e=2H2O+ O2
Fig. 1. General display of the setup for electrodialysis titration.
Fig. 2. Schematic diagram illustrating electrodialysis titration with a cation titrant, cation (K), anion (A), electrodialysis process ( ), dialysis process (----- \ ), electrochemical process (…… \ ), hydrogen ion (H+), hydroxide ion (OH−), cation exchange membrane (CEM), anion exchange membrane (AEM).
at the anode. The selection of a cation or an anion exchange membrane requires the consideration of the following criteria: To ensure penetrating of the ion-titrant into the solution to be titrated. To prevent migrating of the ion-titrant to the nearly electrode cell 1. Not to permit the titrated ion to move in the nearly electrode cell 2. Not to let H+ or OH− ions, generated in the electrode cells, to pass into titrant solution or into solution to be titrated, in a case those ions interfere or simply ‘pollute’ the solutions. A balance for the number of moles, going in or out titrant storage department and electrode cell 1 as well, can be done using the principle for neutrality of the solution. When the titrant is cation, see Fig. 2, (for example a titration of Cl− with Ag+), the following equations can be written: − K ted + d + Kdse − (−A ted)+ (− Adse)= 0
(1)
for the titrant storage department and: H+ec + (−A ted)− (−Adse)= 0
(2)
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
nt = i~/F+ bDC~
249
(7)
where i, ~ and F have the usual meanings, b is a coefficient, and DC is the concentration gradient. If the electrodialysis titration is conducted at a constant current value. And also if DC is constant, i.e. there is a sufficiency of supporting electrolyte, the change in its concentration during titration is negligible. The Eq. (7) then is transformed to: nt = K~
Fig. 3. Schematic diagram illustrating electrodialysis titration with an anion titrant, cation (K), anion (A), electrodialysis ( ), dialysis (----- \ ), electrochemical process (…… \ ), hydrogen ion (H+), hydroxide ion (OH−), cation exchange membrane (CEM), anion exchange membrane (AEM).
for the electrode cell 1, where K, A and H+ are number of moles for cation, anion and hydrogen ion, symbols: t, se, d, ed, ed+d, and ec mean titrant, supporting electrolyte, dialysis, electrodialysis, electrodialysis accompanied by dialysis, and electrochemically generated respectively. Signs ‘+’ and ‘− ’ show the movement directions, ‘+ ’ for moving in and ‘ −’ for moving out. By these symbols are mentioned the charge signs as well. Eq. (1) and Eq. (2) together give: K ted + d = H+ec + Kdse
(3)
When the titrant is an anion, see Fig. 3, (for example a titration of Ag+ with CNS−), by analogy with Eqs. (1) and (2) and Eq. (3) we obtain: − Kedt +Kdse − (−A ted + d) + ( −Adse) =0
(4)
− OH − ec −Kdse + K ted =0
(5)
A ted + d = OH − ec + Adse
(6)
The Eq. (3) is identical to Eq. (6). The first term in these equations can be expressed by the Faraday’s law equation and the second term by the dialysis equation [3]. Then for the number of moles of the titrant the following equation is obtained:
(8)
where K= i/F+ bDC When the titrant added is equivalent to the analyte, the Eq. (8) can be written for the moles, na, of the analyte: na = K~
(9)
3. Experimental
3.1. Solutions Analytical-reagent grade chemicals were used throughout. Distilled water was used for the preparation of the solutions, except for complexometric titrations, were bidistilled water was implemented. The solutions were standardized by accepted procedures. Hydrochloric acid was standardized by titrating a standard solution of sodium tetraborate decahydrate. The sodium hydroxide and potassium permanganate solutions were standardized by titrating a solution of an exact weight of oxalic acid dihydrate. The iodine solution was standardized by a standard thiosulphate solution, which was determined with a standard potassium dichromate solution prepared directly. A solution of Ca(II) was made up by weighing calcium carbonate and dissolving in hydrochloric acid. A solution of EDTA was prepared directly by weighing the disodium dihydrate. The concentration was also checked against the standard calcium(II) solution. A solution of Fe(II) was prepared immediately before use by direct weighing from (NH4)2Fe(SO4)2 ·6H2O.
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A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
3.2. Membranes Use was made of a cation exchange membrane MK 40 (Russia), an anion exchange membrane MA 40 (Russia), and an ultrafiltration polyacryonitrile membrane, PAN 30 (Bulgaria). The ion exchange membranes were soaked for 24 h in the solutions that passed through the membranes by the time of performing the titration. The ultrafiltration membrane was soaked in water before use.
3.3. Apparatus The electrodialysis titration is performed with a laboratory-build system shown in Fig. 1. It includes an electrodialyzer equipped with a currentgenerating unit. The electrodialyzer consists of four compartments: two electrode cells, a titrant storage compartment, and a titration vessel, separated by three ion exchange membranes. The electrode cells and the titrant storage compartment are made of glass. Their lower ends are sealed by epoxy glue to the pieces of tubings taken from the upper parts of the screw-capped polyethylene bottles. The ion exchange membranes are stuck to the edge of the polyethylene tubings by the caps in which holes are drilled to expose a membrane area of about 12.6 cm2. An aquarium pump is
used to bubble air through the solutions of the electrode cells and the titrant storage in order to stir them. An electromagnetic stirrer is applied for stirring the solution in the titration vessel. The current generating unit consists of a voltage transformer, a current rectifier, two decade resistors (of 1–9 and 0.1–0.9 kV respectively) in series, milliammeter, and two gauze platinum electrodes placed in the electrode cells. By making an appropriate voltage change to the transformer or a change to the resistance of the resistor, the current in the circuit is selected and then checked by the milliammeter. This arrangement assures constant current regime.
3.4. Titration procedure The electrode cells are filled up with the supporting electrolyte solutions and a titrant solution is poured out into the titrant storage. About 80 cm3 of a supporting electrolyte is placed in the titration vessel (for details see Table 1). The stirring is switched on. The electric current is turned on and a proper current value is adjusted. The current is kept constant and the electrodialysis titration is performed continuously. For that purpose analyte solution is introduced in the electrolyte solution of the titration vessel and a
Fig. 4. Calibration graph for electrodialysis titration of Ca2 + with H2Y2 − .
Cathode
Cathode
OH−
Ag+
CNS−
H2Y2−
Ca2+
MnO− 4
Cr2O72−
S2O32−
I3−
C2O42−
Cl−
Ag+
Ca2+
H2Y2−
Fe2+
Fe2+
I2−
S2O32−
Cathode
Cathode
Anode
Cathode
Cathode
Anode
Cathode
Anode
H+
B4O72−
Electrode 1
Ion-titrant
Ion to be determined
Anode
Anode
Anode
Anode
Cathode
Anode
Anode
Cathode
Anode
Cathode
Electrode 2
0.1 M H2SO4 0.1 M NaOH 0.1 M NaNO3 0.1 M NH4NO3 0.1 M Na2SO4
0.1 M KMnO4 0.1 M K2Cr2O7 0.1 M Na2S2O3 0.1 M I2 0.05 M Na2SO4
0.05 M K2SO4 0.1 M K2SO4 0.2 M NaCl 0.05 M Na2SO4
+NH4Cl 0.05 M K2SO4 0.1 M H2SO4 0.2 M NaCl
+NH4Cl NH3
0.1 M Na2SO4 0.1 M Na2SO4 0.1 M NaNO3 0.1 M HNO3 NH3
0.05 M K2SO4 0.1 M K2SO4 0.5 M NaOH 0.5 M NaOH
0.05 M Na2SO4
0.1 M Na2SO4 0.5 M NaOH 0.1 M NaNO3 0.1 M NH4NO3 0.1 M NaCl
MA-40
MK-40
MK-40
MK-40
MA-40
MK-40
MK-40
MA-40
MA-40
MK-40
PAN-30
MA-40
PAN-30
PAN-30
MK-40
MA-40
MA-40
MK-40
–
–
B
A
Electrode cell 2
Electrode cell 1
Titration vessel
Membrane
Supporting electrolyte solutions
0.1 M CaCl2 0.2 M NaCl
0.1 M AgNO3 0.1 M NH4CNS 0.1 M Na2H2Y
–
–
Titrant storage solutions
Table 1 Necessary data for the composition of the electrodialysis titration
MK-40
MK-40
MA-40
MA-40
MK-40
MA-40
MA-40
MK-40
MK-40
MK-40
C
Starch
Diphenylamine Starch
–
Eriochrome black T
Eriochrome black T
FeNH4(SO4)2
Methyl orange Phenolphthalein K2CrO4
Indicator A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254 251
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
252
Table 2 Results for electrodialysis titration with a visual indication
Table 2 (continued) Introduced, mg
Introduced, mg
Found x 9tS/ n, mg
Found x9tS/ n, mg
Relative standard deviation Sr =(S/x)100 (%)
(9) I2 1.28 3.84 5.13 6.40 7.70
1.28 9 0.01 3.84 9 0.02 5.13 9 0.02 6.40 9 0.03 7.70 9 0.03
0.88 0.55 0.45 0.50 0.34
(10) S2O32− 0.29 0.59 0.88 1.17 1.46
0.32 9 0.02 0.59 90.02 0.83 90.03 1.17 90.02 1.49 90.01
3.8 3.1 2.5 1.7 0.77
Relative standard deviation Sr = (S/x)100 (%)
(1) B4O72− 5.92 7.89 9.87 15.8 19.7
5.92 90.15 7.77 90.18 9.75 90.13 15.8 90.14 19.6 90.12
2.5 1.5 1.4 0.92 0.61
(2) C2O42− 1.19 1.78 2.38 2.98 5.95
1.19 9 0.02 1.77 9 0.02 2.41 9 0.01 3.01 9 0.01 3.79 9 0.07
1.6 1.4 0.27 0.45 1.2
(3) Cl− 0.71 1.06 1.42 1.77 2.13
0.71 90.01 1.06 90.01 1.39 90.03 1.78 90.01 2.12 90.01
1.2 0.59 1.8 0.45 0.31
(4) Ag+ 0.54 1.09 1.63 2.18 2.72
0.46 90.02 1.10 90.02 1.70 90.02 2.35 90.03 2.56 90.03
3.9 1.4 1.2 0.90 0.83
(5) Ca2+ 0.80 1.20 1.60 2.00 2.40
0.80 90.01 1.20 90.01 1.60 90.01 1.99 90.01 2.37 90.01
1.5 0.75 0.54 0.59 0.33
(6) H2Y2− 5.80 8.73 11.6 14.6 17.4
5.78 9 0.06 8.73 9 0.03 11.6 9 0.06 14.6 9 0.03 17.2 9 0.03
1.1 0.36 0.56 0.18 0.19
(7)a Fe2+ 1.12 2.23 3.35 4.47 5.59
1.22 9 0.07 2.05 9 0.10 3.59 9 0.07 4.11 9 0.12 5.77 9 0.08
4.4 4.0 1.5 2.4 1.2
(8)b Fe2+ 1.12 2.23 3.35 4.47 5.59
1.06 9 0.02 2.31 9 0.04 3.40 9 0.03 4.35 9 0.02 5.64 9 0.03
1.8 1.4 0.66 0.38 0.41
Number of determination n, 5; t, Students t-value at 95% probability; S, standard deviation. a Fe2+ titrated with MnO4−. b Fe2+ titrated with Cr2O72−.
pretitration is done. When the end point of the pretitration is reached (the indicator changes its colour) a timer is started up and a sample of the analyte is pipetted into the solution. The titration time is read out at the end point but the timer is not switched off and another sample is introduced. In this manner a series of samples can be titrated in succession in the same titrated solution. The results for the first 2–3 titrations are ignored if they differ considerably from the others. The mass of a substance to be determined, ma, is proportional to the titration time, ~: ma = k~ The k-value is previously determined by performing an electrodialysis titration at the same experimental conditions with a known amount of the analyte. A calibration graph method can also be applied. A typical calibration graph is given in Fig. 4.
4. Results and discussion In the present work the titration is performed with an electrodialyzer (Fig. 1), in which the electrodes are separated from the titrant solution.
A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
This design avoids titrant to be involved in an electrochemical reaction as well as titrant solution to be preserved from the water electrolysis products. However when acids and bases are titrated, it is suitable the titrant solution to be placed in one of the electrode cells as the electrode product is actually the titrant itself. In this case the electrodialysis device is simplified. A visual end point detection is chosen for the electrodialysis titrations. The voltage applied between electrodes, in order to realize electrodialysis process, interferes with an electrometric (potentiometric, amperometric) end point indication. The electrometric indication is possible if an intermittent titration is performed. It was found out that when the electric circuit of the electrodialysis system is disconnected, the titration goes on by means of dialysis. The dialysis rate increases if the dialysis is preceded by electrodialysis. The dialysis depends strongly on the current value of the electrodialysis process went earlier. By these reasons the intermittent titration becomes complicated and is not to be recommended. When electrodialysis titration continues for a long time a difficulty in end point indication arises. An unclear change in the indicator colour is observed for some visual indicators such as methyl orange or eriochrome black T. It is due to the decreased indicator concentration, caused by the adsorption of the indicator on the membrane or penetration through it. A proper way of dealing with this is simply to add some more indicator. If the rate of electrodialysis addition of the titrant is not high enough a smooth change of the indicator colour is achieved and a sharp end point indication cannot be attained. The conditions for electrodialysis titrations are found experimentally to fulfill the requirement for the titrant addition rate mentioned above. The factors that influence the titrant addition rate are membrane area, current and ion transport number, so that the membrane area and the current can be selected. The membrane area chosen is as big as possible for the titration setup. The choice of the current value is limited by the fact
253
that at high current values the membrane is heated and can be damaged. So a different current value is chosen for every single titration. Current values in an interval from 20 to 80 mA are used in the work. The supporting electrolyte solution provides a conductivity and in this way determines the current value. When the supporting electrolyte concentration is 0 0.01 mol dm − 3, a change in the concentration, by the time of titration, varies the current value. Supporting electrolyte concentrations E0.05 mol dm − 3 are used throughout this work. It was found that in the beginning of performing the titration the titrant addition rate is lower then increases. As a result the titration time for the first two or three samples is longer than the next one. If the first results differ considerably they have to be ignored. Redox electrodialysis titrations using an oxidizing ion as a titrant, such as MnO4 − , Cr2O72 − and J3 − are impossible with an MA 40 anion permeable membrane used in this work. A PAN 30 ultrafiltration membrane was applied instead. Despite the fact that this membrane is not a selective one, the electrodialysis titration is fulfilled. The use of Eq. (9) to calculate analyte quantity requires knowledge of the k-value. It depends on the experimental conditions. The k-value is previously determined by performing an electrodialysis titration with a known amount of the analyte. In this work calculations were made with a linear regression computer program using Eq. (9). A calibration graph method can also be applied for this purpose. Fig. 4 shows an example of a calibration graph. A standard titrant solution is required for the titrations. A standard analyte solution is needed instead for the electrodialysis titration proposed in this work. The presented electrodialysis method is checked for its application to the most frequently used titrimetric determinations implementing a visual indication. The results are given in Table 2. Those results are regarded as satisfactory. There is not a systematic error. For the proposed electrodialysis method the
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A.D. Dakashe6, V.T. Dimitro6a / Talanta 58 (2002) 247–254
titrant addition rate depends on the current value and a constant rate is achieved by keeping the current constant. That’s why current is the only parameter that has to be regulated while the time to be measured. Such technique appear to be simple, convenient and suitable for automation. Instruments for this purpose are commercially available (these for the constant current coulometry). The membranes manufactured at present are stable, the current can be strictly kept constant and an exact timing can be made. The results for
electrodialysis titration, in principle, would not be less accurate and precise than those for the usual titrations.
References [1] R.B. Hanselman, L.B. Rogers, Analytical Chemistry 32 (10) (1960) 1240. [2] V.G. Barikov, O.A. Songina, T.G. Sereda, Manufactory Laboratory 38 (6) (1972) 641 in Russian. [3] S.T. Hwang, K. Kammermeyer, Membranes in Separation, Chemistry, Moscow, 1981.