Using graphics of logarithmic Concentration (GLC) in the titration of bases and mixture of bases

JOURNAL OF SCIENCE OF HNUE Natural Sci., 2011, Vol. 56, No. 7, pp. 87-99 USING GRAPHICS OF LOGARITHMIC CONCENTRATION (GLC) IN THE TITRATION OF BASES AND MIXTURE OF BASES Dao Thi Phuong Diep(∗), Nguyen Thi Thanh Mai, Phan Thi Thuy Linh and Luu Thi Luong Yen Hanoi National University of Education (∗)E-mail: diepdp@gmail.com Abstract. The general programme, which is to draw the Graphics of Log- arithmic Concentration (GLC) forming the total line, constructed quickly and to exactly determine the pH at the equivalence point and the titration jump in the titration of bases and mixture of bases with strong acid. The study results using GLC (without difficulty in combining and solving the equations of higher degrees) which are in fine agreement with those by the general methods. Keywords: Graphics of Logarithmic Concentration, titration of bases and mixture of base, pH, titration jump. 1. Introduction In the acid-based titration, it is important to have a suitable indicator which experiences a change in colour (end point) as close as possible to the equivalence point (EP) of the reaction. Due to the appearance of the titration jump on the titration curve, we can choose any acid-based indicator which has the pT value ranging within the titration jump with an allowable error [1, 2]. The Graphics of Logarithmic Concentration method [3, 4] has been used to evaluate exactly the pH of the acid-based solutions [5, 6]; to determine the pH at the equivalence point (pHEP) and the titration jump in the titration of acids with strong bases [7]. In this paper, we study the applications of GLC, the general programme has been written with the PASCAL language to draw it with forming the total line constructed, in the titration of bases and mixture of bases. 2. Content The way to construct GLC and the steps in determining pH, equilibria com- ponents in solution (using GLC) are done similarly to the reference [5]. To estimate the pHEP value and titration jump, we study some cases: titra- tion of monoprotic bases, with a mixture of strong and weak bases and mixture of 87 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen monoprotic bases, polyprotic bases, mixture of strong bases and polyprotic bases with strong acids using GLC. 2.1. Example 1 * Titration of 0.10 M NH3 (pKb = 4.76) with 0.10 M HCl (system 1). Estimate the pH at the equivalence point and the titration jump with the error q = ± 0.1% The Graphics of Logarithmic Concentration of system 1 are expressed in Fig- ure 1. Suppose we stop titrating after the equivalence point, the components at the end point are: NH+4 , H2O and excess HCl (C ′ HCl). From the proton conservation law, we have: [H+] = [OH−] + [NH3] + C ′ HCl → [H+]− [OH−]− [NH3] = C′HCl = q.CNH3 = q. C0V0 V + V0 ≈ q. CC0 C + C0 (2.1) with q = C ′ HCl CNH3 - At the beginning of the titration jump: q = −0.1%→ [H+] + 10−4.30 = [OH−] + [NH3] Figure 1. The Graphics of Logarithmic Concentration of the titration of 0.10 M NH3 with 0.10 M HCl (q = ± 0.1%) 88 Using graphics of logarithmic concentration (GLC) in the titration of bases... From Figure 1 we have: the lg[OH−] line is under slung and far from the lg[NH3] line; the lg[H +] line is lower than the lg10−4.30 line → [OH−] ≪ [NH3] and [H+] ≪ 10−4.30 → [NH3] ≈ 10−4.30 → the pH at the beginning of the titration jump (pHB) is defined from the intersection of the lg[NH3] line and the lg10 −4.30 line. From GLC → pHB = 6.23. - At the equivalence point, q = 0 → [H+] = [OH−] + [NH3] ≈ [NH3] → pHEP is determined from the crossing point of the lg[NH3] line and the lg[H+] line: pHEP = 5.27. - At the end of the titration jump, q = 0.1%: → [H+] = [OH−] + [NH3] + 10−4.30 Similarly we have: the lg[NH3] line and the lg[OH −] line is lower than the lg10−4.30 line → [H+] ≈ 10−4.30 → the pH at the end of the titration jump (pHE) is the crossing of the lg10−4.30 line and the lg[H+] line: pHE = 4.30 → the titration jump is 6.23 - 4.30. To check the studied result, we estimate the pH at the equivalence point and the titration jump by the general method - solving an equation of higher degree with one variable. The comparison is shown in Table 1. Table 1. The pH at the equivalence point and the titration jump in the titration of 0.10 M NH3 with 0.10 M HCl (q = ± 0.1%) determined by the GLC and the general method theory calculating Method GLC The general pHEP 5.27 5.27 The titration jump 6.23 - 4.30 6.24 - 4.30 Thus, there is good agreement between the obtained result from the GLC and the calculated theory. 2.2. Example 2 * Titration of the mixture of 0.010 M NaOH and 0.10 M CH3COONa with 0.10 M HCl (system 2). Choose an indicator for this titrimetry if the error is ± 1% To choose the compatible indicator, we need to determine the pH at the equiv- alence point and the titration jump. The Graphics of Logarithmic Concentration of this titrimetry are shown in Figure 2. 89 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen Figure 2. The Graphics of Logarithmic Concentration of the titration of 0.010 M NaOH and 0.10 M CH3COONa with 0.10 M HCl (q = ± 1%) From CH3COO − has pKb = 9.24 > 9, we can only perform the individual titration of NaOH without titration of CH3COO − [1]. The titration reaction: OH− + H+ ⇋ H2O The difference between the components at the end point (H+, OH−, CH3COOH) and at the equivalence point causes the titration error. q = [H+]− [OH−]+[CH3COOH] (CXOH)c with (CXOH)c = C01.V0 V + V0 ≈ C.C01 C + C01 → [H+] = [OH−]− [CH3COOH] + q C.C01 C+ C01 (2.2) - At the beginning of the titration jump, q = - 1%: [H+] + [CH3COOH] + 10 −4.03= [OH−] From the Graphics of Logarithmic Concentration, we can see the lg10−4.03 line is much higher than the lg[H+] line and the lg[CH3COOH] line 90 Using graphics of logarithmic concentration (GLC) in the titration of bases... → 10−4.03 ≫ [CH3COOH], 10−4.03 ≫ [H+]→ [OH−] = 10−4.03. Therefore, the pH at the beginning of the titration jump (pHB) is defined from the intersection of the lg[OH−] line and the lg10−4.03 line → pHB = 9.97. - At the equivalence point q = 0 → [H+] + [CH3COOH] = [OH−] According to the GLC (Figure 2), the lg[CH3COOH] line is much higher than the lg[H+] line→ [CH3COOH] ≫ [H+]→ [CH3COOH] = [OH−]→ the intersection of the lg[OH−] line and the lg[CH3COOH] gives us the pHEP value (the pH at the equivalence point): pHEP = 8.87. - At the end of the titration jump, q = + 1%: [H+] + [CH3COOH] = [OH −]+10−4.03. From the Graphics of Logarithmic Concentration (Figure 2), we can see the lg10−4.03 line is much higher than the lg[OH−] line and the lg[CH3COOH] line is much higher than the lg[H+] line → [OH−] ≪ 10−4.03, [H+] ≪ [CH3COOH] → 10−4.03 ≈ [CH3COOH] → the pH at the end of the titration jump (pHE) is detected from the junction of the lg [CH3COOH] line and the lg10 −4.03 line → pHE = 7.77. To check the studied result, we estimated the pHEP and the titration jump by the general method. From (2.2), we obtained the error equation: q = ( h− Kw h ) . C+ C01 C.C01 + C02 C01 . h Ka+h with h = [H+] (2.3) Solving equation (2.3) with q = 0 and q = ± 1%, we estimated the pHEP and the titration jump. Table 2. The pH at the equivalence point and the titration jump in the titration of 0.010 M NaOH and 0.10 M CH3COONa with 0.10 M HCl (q = ± 1%) determined by different method Method pHEP The titration jump GLC 8.87 9.97 - 7.77 The theory calculat- ing 8.86 9.96 - 7.76 Thus, by two different methods the obtained results are very much the same. From this result, we can choose the indicators of which pT is from 7.77 to 9.97. For example: Phenolphthalein has the pH range from 8 to 10: at pT = 8, the colour changes from pink into colourless; α-naphtholphthalein has the pH range from 7.8 (pink) to 8.7 (greenish blue) or thymol blue has the pH range from 8.0 (yellow) to 9.0 (blue). 91 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen 2.3. Example 3 * Titrate the mixture of 0.10 M NaOH and 0.10 M NaClO (pKb = 6.47) with 0.10 M HCl (system 3). Evaluate the ability of the individual titration of each base in this mixture if the error is ± 1% The GLC of system 3 are shown in Figure 3. Figure 3. The Graphics of Logarithmic Concentration of the titration of the mixture of 0.10 M NaOH and 0.10 M NaClO (pKb = 6.47) with 0.10 M HCl (q = ± 1%) Because 5 < pKb(ClO−) = 6.47 < 9, in this case we could perform the individual titration of each base in the mixture [1]. Similarly to two cases mentioned above, from the difference between the com- ponents at the end point and at the equivalence point we could easily establish the error equation. Combining this equation with GLC (Figure 3) we would estimate pHEP and titration jump quickly in two cases: individual titration of NaOH and total titration of two bases: - First case: The individual titration of NaOH: [H+] = [OH−]− [HClO]− qI. C.C01 C + C01 (2.4) pHEP1 = 10.10 and the first titration jump: 10.70 - 9.53 - Second case: The total titration of two bases: 92 Using graphics of logarithmic concentration (GLC) in the titration of bases... [H+] = [OH−] + [ClO−]− qII. C(C01 + C02) C + C01 + C02 (2.5) pHEP2 = 4.47 and the second titration jump: 5.77 - 3.13. The studied result from GLC was in good agreement with the one obtained from general method solving 6 equations of higher degrees with one variable (Table 3). Table 3. The pH at the equivalence point and the titration jump in the titration of the mixture of 0.10 M NaOH and 0.10 M NaClO with 0.10 M HCl (q = ±1%) determined by different methods Titration Method pHEP The titration jump The individual titration of the strong base GLC 10.10 10.70 - 9.53 The general method 10.11 10.72 - 9.50 The total titration of the two bases GLC 4.47 5.77 - 3.13 The general method 4.50 5.84 - 3.17 The results obtained from the Graphics of Logarithmic Concentration show the ability of the individual titration of each base in the system 3. We can use thymolphthalein (pT = 9.40: the colour changes from blue into colourless or alizarine yellow (pT = 10.10: the colour changes from violet into yellow for defining the concentration of NaOH. With the second step, we can use methyl red (pT = 5.00: the colour changes from yellow into pink - orange; methyl orange (pT = 4.00: the colour changes from yellow into pink - orange or bromocresol green (3.80 - 5.40: the colour changes from blue into yellow for the titration of two bases. Through the titration of the mixture of a strong and a weak monoprotic base, we can infer that the ability in individual titration of A− in the mixture of two weak monoprotic bases A− (Kb,A, C01) and B − (Kb,B, C02) depends on the relation- ship between two base equilibrium constants (assume that Kb,A > Kb,B) and the concentration of two bases. According to [2] base A− can be titrated individually if pKb,B - pKb,A > 6 (with q ≤ 0.1%) and if pKb,B - pKb,A > 4 (with q ≤ 1% ), with C01 ≈ C02. 2.4. Example 4 *Titrate the mixture of 0.010 M NH3 (pKb,NH3 = 4.76) and 0.010 M NaOCl (pKb,ClO− = 6.47) with the 0.010 M HCl (system 4) if the error is ± 1% 93 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen The GLC of system 4 are expressed in Figure 4. Figure 4. The Graphics of Logarithmic Concentration of the titration of the mixture of 0.01 M NH3 (pKb,NH3 = 4.76) and 0.01 M NaOCl (pKb,ClO− = 6.47) with 0.01 M HCl (q = ± 1%) From ∆pKb= pKb,ClO−−pKb,NH3= 6.47− 4.76 = 1.71 < 4 and pKb,ClO− < 9, we could not perform the titration of each individual base, so we must titrate the total bases NH3 and ClO −. The error equation was established from the proton conservation law with zero level is the end points component or from the difference between the components at the end point and at the equivalence point: [H+] = [OH−] + [ClO−] + [NH3] + qII. C.(C01+C02) C + C01+C02 (2.6) with qII. C.(C01+C02) C + C01+C02 = 10−4.17 Combining eq. (2.6) with GLC in Figure 4, we easily determined the titration jump and the pHEP of system 4: - At the beginning of the titration jump, pHB is defined from the intersection of the lg[ClO−] line and the lg10−4.17 line → pHB = 5.83. - The pH at the end of the titration jump (pHE) is detected from the junction of the lg[H+] line and the lg10−4.17 line → pHE = 4.17 - Similarly, pHEP is the crossing of the lg[ClO −] line and the lg[H+] line: pHEP = 5.00. These results were in good agreement with the results estimated by the general method: the titration jump is from 5.84 to 4.17 and the pHEP = 5.00. 94 Using graphics of logarithmic concentration (GLC) in the titration of bases... Thus, we can select the indicator, which has pT from 4.17 to 5.84 (such as methyl red) for this titrimetry. 2.5. Example 5 * Define the titration jump of the titration of 0.10 M NH2CH2CH2 NH2 (A 2−) with 0.10 M HCl (system 5) if the error is ± 1%; pKbi=4.072; 7.152 The GLC of system 5 are expressed in Figure 5. Figure 5. The Graphics of Logarithmic Concentration of the titration of 0.10 M NH2CH2CH2NH2 with 0.10 M HCl (q = ± 1%) From pKb2 < 9, ∆pKb= pKb2−pKb1 = 7.152 - 4.072 < 4, we have to per- form the total titration of two steps of ethylenediamine with the error of titrimetry calculated by equation (2.7): q. 2.C.C0 C + 2C0 = [H+]− [OH−]− [HA−]− 2[A2−] (2.7) + At the beginning of the titration jump, q = - 1% → q. 2.C.C0 C + 2C0 = −10−3.17 → 10−3.17+[H+] = [OH−] + [HA−] + 2[A2−] From GLC (Figure 5), we can see: the lg10−3.17 line is higher than the lg[H+] line; the lg[HA−] line is higher than the lg[A2−] line and the lg[OH−] line → [H+] ≪ 10−3.17; [OH−] ≪ [A2−] ≪ [HA−] → [HA−] ≈ 10−3.17. 95 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen Therefore, pHB is defined from the intersection of the lg[HA −] line and the lg10−3.17 line: pHB = 3.17. - Similarly, pHEP is the crossing of the lg[HA −] line and the lg[H+] line: pHEP = 4.17; and pHE is the crossing of the lg10 −3.17 line and the lg[H+] line: pHE = 5.17. These results corresponding with those which were calculated by solving equa- tions of higher degrees with one variable h = [H+], which were combined from the error equations (2.8), with αHA− and α 2− A are the concentration ratio of HA − and A2−, respectively: pHEP = 4.16; the titration jump: 5.16 - 3.17. q = (h−Kw h ) C + 2C0 2C.C0 − 1 2 (αHA− + 2αA2−) (2.8) We can choose the acid - base indicators which have 3.17 < pT < 5.17 for the titrimetry in system 5 (for example: methyl orange, pT = 4.00, the colour changes from yellow into orange - pink; bromocresol green, (3.8 < pT < 5.4), the colour changes from blue into yellow, etc. 2.6. Example 6 * Define the pH at the equivalence point and the titration jump of the titration of 0.10 M Na3PO4 with 0.10 M HCl (system 6) if the error is ± 1% and pKbi = 1.68; 6.79; 11.77 GLC with the sum-lines of system 6 are shown in Figure 6. From ∆pK1= pKb2−pKb1 = 6.79−1.68 > 4 and pKb3 > 9, we could carry out the individual titration of the first and second steps, the third step was not titrated. The first step: PO3−4 +H + → HPO2−4 From the difference between the components at the end point (H3PO4, HPO 2− 4 , PO3−4 , H +, OH−) and at the equivalence point (HPO2−4 , H2O) we can easily establish the error equation (2.9) at the first step. The second step: PO3−4 +2H + → H2PO−4 Similarly, the error equation for the second step is presented in equation (2.10). 10−3.30 = qI. C.C0 C + C0 = [H+]− [OH−] + [H2PO−4 ] + 2[H3PO4]− [PO3−4 ] (2.9) 10−3.17 = qII. 2.C.C0 C + 2C0 = [H+]− [OH−] + [H3PO4]− [HPO2−4 ]− 2[PO3−4 ] (2.10) 96 Using graphics of logarithmic concentration (GLC) in the titration of bases... Figure 6. The Graphics of Logarithmic Concentration of the titration of 0.10 M Na3PO4 with 0.10 M HCl (q = ± 1%) Combining two error equations (2.9), (2.10) and GLC (Figure 6) with using the sum-line, we could quickly determine the following values: pHEP1 = 9.67 (pHEP1 is the crossing of the lg([OH−] + [PO3−4 ]) sum-line and the lg[H2PO − 4 ] line); the first titration jump: 10.30 - 9.03 (pHB is defined from the intersection of the lg([OH −] + [ PO3−4 ]) sum-line and the lg10 −3.30 line; pHE is the crossing of the lg[H2PO − 4 ] line and the lg10−3.30 line). Similarly, from Figure 6 we can see: pHEP2 is detected from the junction of the lg[H3PO4] line and the lg[HPO 2− 4 ] line; pHB is defined from the intersection of the lg[HPO2−4 ] line and lg10 −3.17 line; pHE is the crossing of the lg[H3PO4] line and the lg10−3.30 line: pHEP2 = 4.73; the second titration jump: 5.37 - 4.10. To check the studied results, we estimated the pH at the equivalence point and the titration jump by the general method - solving equations of higher degrees with one variable which are combined from the error equations (2.11) and (2.12). qI = (h−Kw h ) C + C0 C.C0 + αH2A− + 2αH3A − αA3− (2.11) qII= (h−Kw h ) C + 2C0 2C.C0 − 1 2 (αHA2− + 2αA3− − αH3A−) (2.12) The comparison is shown in Table 4. 97 D.T.P. Diep, N.T.T. Mai, P.T.T. Linh and L.T.L. Yen Table 4. The pH at the equivalence point and the titration jump in the titration of 0.10 M Na3PO4 with 0.10 M HCl (q = ±1%) determined by different methods Step Method pHEP The titration jump The first step GLC 9.67 10.30 - 9.03 The general method 9.69 10.21 - 9.16 The second step GLC 4.73 5.37 - 4.10 The general method 4.75 5.53 - 3.98 From Table 4 we can see: the pHEP and the titration jump defined promptly and visually in the titration of 0.10 M Na3PO4 with 0.10 M HCl by the Graphics of Logarithmic Concentration (with construction of the sum-line) corresponding with those by the general method (but solving the quintic equations is very difficult). Thus we can choose the indicators, pT of which is from 9.03 to 10.30 for the first step (such as thymolphthalein (9.4 < pT < 10.6), the colour changes from blue into colourless). Then the indicators can be chosen for the second step such as methyl red, pT = 5.0, the colour changes from yellow into orange - pink; or bromocresol green (3.8 < pT < 5.4), the colour changes from blue into yellow. In the titration a mixture of strong base and polyprotic base, the values of pHEP and the titration jump are defined similarly. 3. Conclusion We constructed the general programme to draw the Graphics of Logarithmic Concentration (GLC) with forming the total line to quickly and exactly determine the pH at the equivalence point and the titration jump in the titration of bases and mixture of bases. The results of defining the pH at the equivalence point and the titration jump by GLC (without difficulty combining and solving the equations of higher degrees) were in good agreement with those by the general method. The programme has been written with the PASCAL language. REFERENCES [1] Dao Thi Phuong Diep, Do Van Hue, 2007. Analytical Chemistry. The Basis of Quantitative Chemical Analysis. Hanoi National University of Education Publish- ing House (in Vietnamese). 98 Using graphics of logarithmic concentration (GLC) in the titration of bases... [2] Nguyen Tinh Dung, 2007. Analytical Chemistry. Part III: ”The Methods of Quantitative Chemical Analysis”. Education Publishing House, Hanoi, 4th Edi- tion (in Vietnamese). [3] Christie G. Enke, 2000. The Art & Science of Chemical Analysis. John Wiley & Sons, Inc. [4] Kennedy, John H, 1990. Analytical Chemistry. Principles, Saunders College Pub- lishing, New York. [5] Nguyen Tinh Dung, Dao Thi Phuong Diep, Truong Thanh Vuong, 2005. Estima- tion of Equilibria Components in Complex Acid-Base Systems Using Logarithmic Concentration Diagram. Journal of Science of Hanoi National University of Edu- cation, No. 1, pp. 56-60 (Vietnamese). [6] Dao Thi Phuong Diep, 2005. Using Logarithmic Concent