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HNUE JOURNAL OF SCIENCE Natural Sciences 2018, Volume 63, Issue 11, pp. 117-126 This paper is available online at http://stdb.hnue.edu.vn DOI: 10.18173/2354-1059.2018-0079 DETERMINATION OF THE DISSOCIATION CONSTANTS OF ETHYLAMMONIUM AND 2-FUROIC ACID IN AQUEOUS SOLUTION AT 298.15K Bui Thi Minh Anh, Hoang Thi Thu Hong, Nguyen Thu Hien, Nguyen Thi Lien, Dao Thi Phuong Diep and Tran The Nga Faculty of Chemistry, Hanoi National University of Education Abstract. In this study, the dissociation constant of ethylammonium and 2-furoic acid have been determined at 298.15 K using a potentiometric titration method. The ionic strength of all solutions was maintained by 0.50 M of KCl solution. A series of pH was obtained by adding the same of volume of KOH solution into analytical solutions. The dissociation constant was calculated by using the LINEST function of spreadsheet. The value of dissociation constants of ethylammonium and 2-furoic acid which have been determined by this method are (10.684 ± 0.003) and (3.171 ± 0.005), respectively. These values were compared with the known values in some literatures to conclude in accuracy of developed method. Keywords: Dissociation constant, potentiometric titration, ethylamine, 2-furoic acid. 1. Introduction The dissociation constant is the most important parameter to understand the properties of an acid or a base such as physical property, chemical property, biological activity, absorption, chromatographic property in different pH [1]. In the analytical chemistry, it is also used for study and calculation the equilibrium compositions of a given solution [2]. In order to determine dissociation constant of a weak acid and a weak base, some known methods have been used like potentiometric method, solubility measurement, UV-Vis spectroscopy, capillary electrophoresis, calorimetry, NMR spectroscopy, etc. [1, 3]. In many experimental methods to determine the pKa values, a certain parameter is measured as a function of pH [1]. Potentiometric method is known as an inexpensive and simple method to determine the dissociation constant and some thermodynamic parameters [4]. In our investigation, this method has been chosen to determine the pKa of some acids such as acetic acid [5], glutamic acid [6, 7] and we have been gotten accurate results. In potentiometric titration, a sample is titrated with a standard solution (strong acid or strong base) using a pH electrode to monitor the course of titration. Received October 6, 2018. Revised November 15, 2018. Accepted November 22, 2018. Contact Tran The Nga, e-mail address: tranthenga@hnue.edu.vn 117 Bui Thi Minh Anh, Hoang Thi Thu Hong, Nguyen Thu Hien, Nguyen Thi Lien, Dao Thi Phuong Diep and Tran The Nga The structure of acids for this work include: CH3 CH2 NH3 Ethylammonium O COOH 2-furoic acid Dissociation constants of ethylammonium and 2-furoic acid reported in this work were determined by potentiometric titration with KOH solution as follows: (i) Titrate an aqueous solution contain ethylamine and hydrochloric acid. (ii) Titrate an aqueous solution contain 2-furoic acid and hydrochloric acid. Ionic strength of all solutions was maintained by using 0.50 M KCl solution. Data was treated by calculation method using spreadsheet and activity coefficients (γ) was calculated by using the Davies equation as follows [8]:  I  lg  q  0.5115  Zq2    0.2  I  1 I  where I is ionic strength; γq is activity coefficient and Zq is charge of q ion. (1) 2. Content 2.1. Procedure * Chemicals and apparatus - All chemicals which used for this work are pro-analysis (PA). Chemicals consist of potassium chloride, potassium hydroxide, oxalic acid dihydrate, hydrochloric acid, borax, ethylamine, 2-furoic acid and deionized water. - Apparatus for this investigation include an analytical balance, a pH meter, a N2 system, some burettes, pipettes, and some beakers. The pH meter was calibrated by the buffer solutions of pH 4.010, 7.010 and 10.010 at (298.15 ± 1) K. - Solutions were prepared following: Sample Concentration (mol.L-1) Concentration (mol.L-1) 1 Ethylamine C01 = 4.551×10-3 HCl C02 = 4.577×10-3 2 Ethylamine C01 = 3.414×10-3 HCl C02 = 4.577×10-3 3 2-furoic acid C01 = 2.239×10-3 HCl C02 = 5.130×10-3 4 2-furoic acid C01 = 3.024×10-3 HCl C02 = 5.130×10-3 All solutions were prepared in 0.5M KCl solution. Sample 1 and sample 2 were titrated by using 1.125×10-2 M of KOH solution while sample 3 and sample 4 were titrated by using 2.451×10-2 M of KOH solution. * Titration process For each analytical sample, a 25.00 mL aliquot was taken exactly into a 100 mL beaker. Each time, a 0.20 mL or 0.40 mL of KOH solution was added into sample and shake well until having an equilibrium. Record the pH values as a function of volume of alkaline solution. During the experiments, nitrogen (99.99%) was purged through the titration beaker and temperature was fixed (298.15 ± 1) K. Each solution was titrated twice and calculated the average values. The titrated results were shown in the Table 1. 118 Determination of the dissociation constants of ethylammonium and 2-furoic acid in aqueous solution… Table 1. The titrated results of 04 samples (V = volume of KOH solution (mL); V0 = 25.00 mL of each sample; pH1 = pH of sample 1; pH2 = pH of sample 2; pH3 = pH of sample 3; pH4 = pH of sample 4) pH3 pH4 0.00 2.407 2.403 4.80 3.049 2.977 10.805 10.674 0.20 2.424 2.421 5.00 3.097 3.014 7.80 10.820 10.698 0.40 2.441 2.438 5.20 3.145 3.053 3.563 8.00 10.835 10.716 0.60 2.460 2.455 5.40 3.198 3.092 9.851 3.716 8.20 10.853 10.737 0.80 2.479 2.473 5.60 3.256 3.135 2.00 10.049 3.946 8.40 10.864 10.752 1.00 2.498 2.492 5.80 3.321 3.181 2.40 10.175 4.416 8.60 10.879 10.776 1.20 2.519 2.511 6.00 3.393 3.230 2.80 10.274 6.315 8.80 10.888 10.790 1.40 2.540 2.530 6.20 3.473 3.282 3.20 10.351 9.112 9.00 10.898 10.807 1.60 2.561 2.551 6.40 3.567 3.337 3.60 10.418 9.636 9.20 10.915 10.824 1.80 2.584 2.572 6.60 3.680 3.399 4.00 10.474 9.884 9.40 10.927 10.839 2.00 2.607 2.594 6.80 3.823 3.469 4.40 10.525 10.057 9.60 10.937 10.856 2.20 2.630 2.615 7.00 4.020 3.544 4.80 10.564 10.196 9.80 10.942 10.870 2.40 2.656 2.637 7.20 4.344 3.628 5.20 10.605 10.298 10.00 10.958 10.882 2.60 2.681 2.660 7.40 5.452 3.731 5.40 10.625 10.346 10.20 10.896 2.80 2.708 2.684 7.60 8.912 3.853 5.60 10.643 10.385 10.40 10.910 3.00 2.735 2.709 7.80 9.878 4.015 5.80 10.660 10.424 10.60 10.924 3.20 2.763 2.734 8.00 10.227 4.252 6.00 10.678 10.464 10.80 10.937 3.40 2.793 2.761 8.20 10.443 4.723 6.20 10.696 10.492 11.00 10.952 3.60 2.825 2.789 8.40 10.594 - 6.40 10.713 10.525 11.20 10.965 3.80 2.857 2.816 8.60 10.712 9.474 6.60 10.730 10.551 11.40 10.980 4.00 2.892 2.845 8.80 10.801 9.997 6.80 10.750 10.578 11.60 10.995 4.20 2.928 2.877 9.00 10.876 10.291 7.00 10.761 10.601 11.80 11.006 4.40 2.966 2.908 9.20 10.939 10.482 7.20 10.777 10.627 12.00 11.015 4.60 3.006 2.942 9.40 10.995 10.619 V pH1 pH2 V pH1 pH2 0.00 4.180 3.280 7.40 10.791 10.650 0.40 5.724 3.351 7.60 0.80 9.104 3.448 1.20 9.642 1.60 V pH3 pH4 V 2.2. Result and discussion 2.2.1. Construct the theory for calculation of pKa of ethylammonium and 2-furoic acid (a) For ethylammonium (signed HA+), we have HA+ ↔ H+ + A Ka in which: Ka  (H  )  (A) [H  ]11  [A]   K ca   1 (HA ) [HA ]1 (2) 119 Bui Thi Minh Anh, Hoang Thi Thu Hong, Nguyen Thu Hien, Nguyen Thi Lien, Dao Thi Phuong Diep and Tran The Nga At every time of titration process of a mixture of ethylammonium (HA +) and hydrochloric acid with KOH, we have [H+] + [HA+] + [K+] = [OH-] + [Cl-] (3a) or C01V0 K w C02 V0 h11 CV h  .    V  V0 h11  K a V  Vo h1 V  V0 1 1 (3b) where h = (H+) is activity of H+ ion and γ1 is activity coefficient of ±1 ion (in this study γ1 = 0.691 obtained from equation (1)). 1 Substitute 1  1  1.448 and transform the (3b) expression, we obtain Kw V  V0 CV  C02 V0 h1 (h  )1  01   01 h C V0 C V0 h1  K a (4) The left-hand of (4) expression was defined as Q term Kw V  V0 CV  C02 V0 Q  (h  )1  01  h C V0 C01V0 So, equation (4) is Q h1 h1  (1  Q) → Ka  h1  K a Q (5) (6) Using the statistics according to least square method for n experimental points, we have n K a (HA )    h  (1  Q)  Q  1 i 1 n  Q (7) 2 i 1 (b) Similarly for 2-furoic acid (signed HA), we obtain n K a (HA)     (1  Q)  hQ  1 i 1 n    (1  Q)  i 1 (8) 2 1 where the Q value was calculated by (5) expression. It will be obtained from known experimental values include h, V0, V, C01, C02, C and 1 . So, the dissociation constant (Ka) will be calculated from equation (7) (for ethylammonium) and equation (8) (for 2-furoic acid) by using the LINEST function in spreadsheet. 2.2.2. Calculate the pKa of ethylammonium and 2-furoic acid from experimental data Using the titration data in Table 1, the titration curve of 04 samples were shown in Figure 1. 120 Determination of the dissociation constants of ethylammonium and 2-furoic acid in aqueous solution… Figure 1. The titration curve of samples Based on the titration data, the equivalent volumes of KOH and reactive ratio were estimated as follows: Table 2. The equivalent volumes of KOH and reactive ratio of acids with KOH Sample Equivalent volume of KOH Reactive ratio at equivalent point 1 0.202 Ethylammonium : KOH ≈ 0 2 2.55 Ethylammonium : KOH ≈ 0 3 7.50 2-Furoic acid : KOH ≈ 1 4 8.40 2-Furoic acid : KOH ≈ 1 (a) For ethylamine Because of a base, ethylamine is going to react with hydrochloric acid in the initial solution to form ethylammonium ion. Thus, before titration, sample 1 and sample 2 contain ethylammonium and the excess of HCl. Based on the reactive ratio at equivalent point in Table 2, we see that only the excess of HCl in sample react with KOH while ethylammonium does not. This mean that ethylammonium is a very weak acid and it does not react with KOH to appear an individual titration jump. Therefore, its pKa is only calculate after the equivalent point when sample is a buffer solution (in range pH > 10 and sample contain ethylamine and ethylammonium). According to the (5) expression, the values of Q, Y  h1  (1  Q) were calculated from experimental data and shown in Table 3. Table 3. The value of Q, Y of sample 1 and sample 2 Sample 1 V pH Q Sample 2 Y V pH Q Y -11 2.80 10.274 0.795 1.578×10 4.80 10.196 0.787 1.961×10-11 3.20 10.351 0.770 1.486×10-11 5.20 10.298 0.757 1.772×10-11 3.60 10.418 0.745 1.411×10-11 5.40 10.346 0.743 1.676×10-11 4.00 10.474 0.720 1.361×10-11 5.60 10.385 0.728 1.620×10-11 4.40 10.525 0.696 1.315×10-11 5.80 10.424 0.715 1.555×10-11 121 Bui Thi Minh Anh, Hoang Thi Thu Hong, Nguyen Thu Hien, Nguyen Thi Lien, Dao Thi Phuong Diep and Tran The Nga 4.80 10.564 0.670 1.304×10-11 6.00 10.464 0.703 1.478×10-11 5.20 10.605 0.646 1.272×10-11 6.20 10.492 0.688 1.457×10-11 5.40 10.625 0.635 1.254×10-11 6.40 10.525 0.675 1.403×10-11 5.60 10.643 0.623 1.242×10-11 6.60 10.551 0.661 1.379×10-11 5.80 10.660 0.611 1.232×10-11 6.80 10.578 0.648 1.345×10-11 6.00 10.678 0.600 1.215×10-11 7.00 10.601 0.634 1.326×10-11 6.20 10.696 0.590 1.196×10-11 7.20 10.627 0.623 1.289×10-11 6.40 10.713 0.579 1.180×10-11 7.40 10.650 0.611 1.262×10-11 6.60 10.730 0.569 1.162×10-11 7.60 10.674 0.600 1.227×10-11 6.80 10.750 0.561 1.131×10-11 7.80 10.698 0.590 1.190×10-11 7.00 10.761 0.548 1.134×10-11 8.00 10.716 0.577 1.177×10-11 7.20 10.777 0.539 1.116×10-11 8.20 10.737 0.567 1.149×10-11 7.40 10.791 0.529 1.104×10-11 8.40 10.752 0.553 1.145×10-11 7.60 10.805 0.519 1.091×10-11 8.60 10.776 0.547 1.098×10-11 7.80 10.820 0.510 1.074×10-11 8.80 10.790 0.534 1.094×10-11 8.00 10.835 0.502 1.055×10-11 9.00 10.807 0.524 1.075×10-11 8.20 10.853 0.496 1.024×10-11 9.20 10.824 0.515 1.054×10-11 8.40 10.864 0.486 1.018×10-11 9.40 10.839 0.504 1.040×10-11 8.60 10.879 0.479 9.972×10-12 9.60 10.856 0.496 1.016×10-11 8.80 10.888 0.468 9.974×10-12 9.80 10.870 0.486 1.003×10-11 9.00 10.898 0.458 9.930×10-12 10.00 10.882 0.475 9.977×10-12 9.20 10.915 0.454 9.620×10-12 10.20 10.896 0.466 9.824×10-12 9.40 10.927 0.446 9.488×10-12 10.40 10.910 0.458 9.659×10-12 9.60 10.937 0.437 9.422×10-12 10.60 10.924 0.450 9.482×10-12 9.80 10.942 0.424 9.532×10-12 10.80 10.937 0.442 9.337×10-12 10.00 10.958 0.421 9.234×10-12 11.00 10.952 0.437 9.099×10-12 11.20 10.965 0.431 8.934×10-12 11.40 10.980 0.427 8.680×10-12 11.60 10.995 0.425 8.419×10-12 11.80 11.006 0.418 8.311×10-12 12.00 11.015 0.408 8.275×10-12 Using equation (7), we have gotten the dissociation of ethylammonium as follows: 122 Determination of the dissociation constants of ethylammonium and 2-furoic acid in aqueous solution… Sample Ka 1 2 Average pKa (2.021 ± 0.016)×10 -11 10.694 ± 0.003 (2.121 ± 0.020)×10 -11 10.673 ± 0.004 -11 10.684 ± 0.003 (2.071 ± 0.013)×10 References pKa = 10.636 [2]; 10.630 [9]; 10.650 [10] (b) For 2-furoic acid In Figure 1, the titration curve of 2-furoic acid like in shape as titration curve of ethylammonium and they only appear one equivalent point. However, unlike ethylammonium, we prove that both hydrochloric acid and 2-furoic acid react with KOH completely at the equivalent point (the number of moles of KOH is equal the total number of moles of HCl and 2-furoic acid). Therefore, the pKa of 2-furoic acid will be calculated before the equivalent point when sample is also a buffer solution (in range pH < 4.0 and sample contain 2-furoic acid and 2-furoat salt). According to the (5) expression, the values of Q was calculated from experimental data. And next we calculate the values of Y = h×Q, X  1  (1  Q) and shown in Table 4. Table 4. The values of Q, X, Y of sample 3 and sample 4 Sample 3 Sample 4 V pH Q Y X V pH Q Y X 1.20 2.519 0.288 8.721×10-04 1.031 1.20 2.511 0.241 7.451×10-04 1.098 1.40 2.540 0.291 8.395×10-04 1.026 1.40 2.530 0.250 7.364×10-04 1.087 1.60 2.561 0.300 8.241×10-04 1.014 1.60 2.551 0.256 7.217×10-04 1.077 1.80 2.584 0.303 7.908×10-04 1.008 1.80 2.572 0.264 7.075×10-04 1.066 2.00 2.607 0.313 7.735×10-04 0.995 2.00 2.594 0.270 6.894×10-04 1.056 2.20 2.630 0.321 7.531×10-04 0.983 2.20 2.615 0.281 6.815×10-04 1.041 2.40 2.656 0.326 7.211×10-04 0.976 2.40 2.637 0.292 6.737×10-04 1.025 2.60 2.681 0.335 6.988×10-04 0.962 2.60 2.660 0.303 6.626×10-04 1.009 2.80 2.708 0.345 6.763×10-04 0.949 2.80 2.684 0.315 6.523×10-04 0.992 3.00 2.735 0.355 6.543×10-04 0.933 3.00 2.709 0.325 6.365×10-04 0.977 3.20 2.763 0.369 6.363×10-04 0.914 3.20 2.734 0.337 6.225×10-04 0.959 123 Bui Thi Minh Anh, Hoang Thi Thu Hong, Nguyen Thu Hien, Nguyen Thi Lien, Dao Thi Phuong Diep and Tran The Nga 3.40 2.793 0.381 6.130×10-04 0.897 3.40 2.761 0.350 6.074×10-04 0.941 3.60 2.825 0.393 5.889×10-04 0.879 3.60 2.789 0.362 5.892×10-04 0.924 3.80 2.857 0.408 5.671×10-04 0.857 3.80 2.816 0.378 5.775×10-04 0.900 4.00 2.892 0.423 5.432×10-04 0.835 4.00 2.845 0.394 5.629×10-04 0.877 4.20 2.928 0.440 5.202×10-04 0.811 4.20 2.877 0.407 5.409×10-04 0.858 4.40 2.966 0.459 4.965×10-04 0.784 4.40 2.908 0.426 5.264×10-04 0.831 4.60 3.006 0.478 4.714×10-04 0.756 4.60 2.942 0.443 5.060×10-04 0.807 4.80 3.049 0.499 4.457×10-04 0.725 4.80 2.977 0.461 4.865×10-04 0.780 5.00 3.097 0.519 4.159×10-04 0.696 5.00 3.014 0.481 4.668×10-04 0.751 5.20 3.145 0.545 3.903×10-04 0.659 5.20 3.053 0.502 4.448×10-04 0.721 5.40 3.198 0.572 3.623×10-04 0.620 5.40 3.092 0.525 4.250×10-04 0.687 5.60 3.256 0.600 3.326×10-04 0.580 5.60 3.135 0.549 4.020×10-04 0.654 5.80 3.321 0.629 3.002×10-04 0.538 5.80 3.181 0.573 3.775×10-04 0.619 6.00 3.393 0.661 2.676×10-04 0.491 6.00 3.230 0.599 3.530×10-04 0.581 6.20 3.473 0.695 2.339×10-04 0.442 6.20 3.282 0.626 3.274×10-04 0.541 6.40 3.567 0.731 1.981×10-04 0.389 6.40 3.337 0.655 3.016×10-04 0.499 6.60 3.680 0.769 1.607×10-04 0.334 6.60 3.399 0.685 2.737×10-04 0.456 6.80 3.823 0.810 1.219×10-04 0.275 6.80 3.469 0.715 2.428×10-04 0.413 Using equation (8), we have gotten the dissociation of 2-furoic acid as follows: Sample pKa (7.031 ± 0.163)×10 -4 3.153 ± 0.010 4 (6.460 ± 0.039)×10 -4 3.190 ± 0.003 Average (6.745 ± 0.084)×10-4 3.171 ± 0.005 3 References 124 Ka 3.164 [10]; 3.160 [11] Determination of the dissociation constants of ethylammonium and 2-furoic acid in aqueous solution… 2.3. Discussion The known researches show that the dissociation constants will be determined exactly if the composition of sample is a buffer [7, 12]. Based on this conclusion, the pH > 10.0 (for ethylammonium) and pH < 4.0 (for 2-furoic acid) were chosen for calculating pKa values because observation on titration curve (Figure 1) indicate that the pH of these ranges increase very slowly when adding KOH solution. This means that they are the buffer solutions. Moreover, according to (4) expression, the value of Q is alpha value of ethylammonium and 2-furoat. So, when 0.200 < Q < 0.800 (see in Tables 3 and 4), the compositions of samples consist of a conjugate acid/base pair. Dissociation constant was determined in this area will have a high accuracy. This study have determined dissociation of ethylammonium and 2-furoic acid are 10.684 and 3.171, respectively. Compare with some values in known literatures, these values are consistent and have high reliability. This proves that the potentiometric titration method and the chosen calculation method are correct and convenient. The decreasing the number of experiments and the simplicity in calculating will save time and cost but the accuracy was still ensured. Therefore, this method can be applied to determine the thermodynamic dissociation constants for new acids, bases which are unknown dissociation constants. 3. Conclusions The potentiometric titration method have been modified and applied in a optimal condition to titrate samples of ethylammonium and 2-furoic acid. Dissociation constants of ethylammonium and 2-furoic acid were calculated by using LINEST function of spreadsheet. The pKa of ethylammonium and 2-furoic acid are (10.684 ± 0.003) and (3.171 ± 0.005), respectively. These values have a high accuracy and reliability. It could be used for learning and calculation in analytical chemistry. REFERENCES [1] Bebee P., Vrushali T., and Vandana P., 2014. 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