J. Comput. Chem. Jpn., Vol. 5, No. 1, pp. 29 38 (2006) Microsoft Excel, 184-8588 2-24-16 e-mail: yosimura@cc.tuat.ac.jp (Received: July 28, 2005; Accepted for publication: October 24, 2005; Published on Web: February 28, 2006) VBA Microsoft Excel ph ph Excel ph : Excel,,,, 1 [1] [2, 3] [3 5] Lotus 1-2-3 [6, 7] [5] Microsoft Excel ( ) http://www.sccj.net/publications/jccj/ 29
ph 2 S T V S, V T ml ; ; q H2 OV total + q BS+ ; q AS; VS + q BT+ ; q AT; VT = 0 q H2 O =[H + ];[OH ; ] V total = V S +V T : (1) ph q A; moll -1 ph q B+ moll -1 K a1, K a2,, K an K b1, K b2,, K bm q;, q+ (2), (3) n ik Ai i=1 [H + ] i i q A; = n C A K Ai = K Ai K aj : (2) 1 + i=1 [H + j=1 ] i n ik Bi i=1 [OH ; ] i i q B+ = n C B K Bi = K Bi K bj : (3) 1 + i=1 [OH ; ] i j=1 C A, C B q AS; S H n A Σ A q A; S T V S V T (1), (2), (3) ph V T V T (1) ph V T VBA Excel ph (1) Q net (ph) 0 [5] Excel (bisection method) ph Q net ph = - ph = Q net,- Q net =0 ph Figure 1 f (x A ) f (x B ) f (x) =0 x A x B x C =(x A + x B )/2 f (x C )=0 f (x A ) f (x B ) f (x C ) x C x A x B Figure 1. The procedure of bisection method. 30 J. Comput. Chem. Jpn., Vol. 5, No. 1 (2006)
3 V T ph Excel pk a 2.90, 4.34, 5.66[8] 5.00 10-3 M 100 ml 1.00 10-1 M q AS; q cit; q cit; (2) q cit; = K A1 [H + ] + 2 K A2 [H + ] 2 + 3 K A3 [H + ] 3 1 + K A1 [H + ] + K A2 [H + ] 2 + K A3 [H + ] 3 C cit = 10pH;pK a1 + 210 2pH;pK a1;pk a2 + 310 3pH;pK a1;pk a2 ;pk a3 1 + 10 ph;pk a1 + 10 2pH;pK a1;pk a2 + 10 3pH;pK a1 ;pk a2 ;pk a3 C cit q BT+ q NaOH+ = C NaOH = 0.1 Figure 2 V T =0 ph A7 A8 ph ph = -5 19 A9 ph ((A7+A8)/2) B7 I7 Figure 2 7 ph = -5 q H2O q cit; q NaOH+ Q net B7 I7 B8 I9 ph =19 ph = 7 Q net Q net A10 A11 ph Q net I9 Q net =0 ph A7 A9 A10 A11 Q net ph A9 A8 A10,A11 Figure 2 A10, A11 Q net ph -5 7 A9 A12 B7 I9 B10 I12 ph (4) Q net Figure 2 A10 I12 3 A13 I15 A16 I18 52 ph 2.698 ph (1) V T V T = 5.53 10-15 ml 0 V T H3 ph A162 Excel V T V T ph V T ph 1 1ml 25 ml Figure 3(1) L2 L27 0 25 1 ph V T H3 =L2 V T L2 ph V T =0 ph A162 M2 (=A162 ) L2 (0 ml) ph (2.698) M2 L V T =1,2,, 25 ml L2 M2 ph L3 1ml L2 M2 ph = 2.843 ph M3 L4, L5 http://www.sccj.net/publications/jccj/ 31
Figure 2. The worksheet for calculating ph by bisection method, an example of citric acid - NaOH titration at 0 ml titration volume. The ph values can be calculated by substituting given titration volumes for H3 cell. V T ph L2 M27 ffigure 3(1)g Figure 3(2) V T L2 L2 OK V T M2 ph ph V T ffigure 3(3)g Figure 4 ph 15 ml V T 1 ml 0.2 ml 25 ml 126 Figure 3(1) L2 M127 Figure 4 0.2 ml 32 J. Comput. Chem. Jpn., Vol. 5, No. 1 (2006)
Figure 3. Usage of table in Excel. (1) selecting input and output data area, (2) setting of dialog box, (3) output data. 4 1.50 10-2 M 100 ml 1.00 10-1 M 5.00 10-3 M 1.00 10-1 M q NH4OH+ (3) pk b = 4.76[8] Figure 4. Simulated titration curves. CO 2 CO 2 ph [9] http://www.sccj.net/publications/jccj/ 33
Figure 5. Comparison between normal distribution and generated data. Figure 6. Citric acid - NaOH titration curve with and without carbonic acid contamination. q H2CO3; (1) pk a 6.35, 10.33[8] 5.00 10-4 M q H2CO3; 0.2 ml 25 ml ph 0.2 ml 0.2 ml Excel =Norminv(Rand(),0,2.5) 0 2.5 (65536 ) 0.00277 2.49 0 2.5 Figure 5 0.2 ml 2% 0.002 0 25 ml Figure 2 L2 ph M 0.2001 ml 5.00 10-3 M 100 ml 1.00 10-1 M ph 2.726 0.2 ml ph 2.73 ph 5 [9] pk 5 Figure 4 34 J. Comput. Chem. Jpn., Vol. 5, No. 1 (2006)
Table 1. Estimated pk a and concentrarion of citric acid. no contamination and error CO 2 contqamination CO 2 contamination and round-off error pk a C/mM pk a C/mM pk *1) a sd *2) C/mM *1) sd *2) 2.92 5.01 2.92 5.03 2.91 0.047 5.00 0.0202 citric acid 4.35 4.98 4.35 5.02 4.36 0.0129 5.07 0.0556 5.64 5.00 5.66 5.17 5.67 0.0142 5.14 0.0955 6.47 0.360 6.49 0.117 0.352 0.0890 10.33 0.581 10.38 0.0406 0.604 0.0299 14.00 12.86 12.44 1.64 1.80 2.46 *1) average value of 5 times trials. *2) standard deviation ph ph ph Figure 6 Table 1 3 pk a pk a 5mM pk a Table 1 pk a 6.47 10.33 pk a 5.66 pk a 6.47 2 0.2 pk a pk a 14 1.00 10-1 M ph pk a 14 Table 1 ph pk a pk a 14 6 Microsoft Excel VBA http://www.sccj.net/publications/jccj/ 35
Figure 2 Figure 3 pk a3 pk a1-100 Excel PC PC F9 ph Q net Excel PC [1],, http://www.tuat.ac.jp/ mt2459/members/yosimura/ TCAS/index.html [2],. http://www.i-t-c.co.jp/eigyo/product/tekitei/ [3] Takuya, Java Forest >, http://clustera.skr.jp/java/tcurve.html [4],,, B, 30, 51 (1986). [5],, JAPC, 12, 403 (1990). [6] L. S. Reich and S. H. Patel, Am. Lab., 27(8), 36 (1995). [7] L. S. Reich, Am. Lab., 29(24), 29 (1997). [8], II, 4, (1993). [9],,, J. Comput. Chem. Jpn., 2, 49 (2003). 36 J. Comput. Chem. Jpn., Vol. 5, No. 1 (2006)
Simulation of Acid-Base Titration Curve by Using Table-Function in Microsoft Excel Norio YOSHIMURA Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho Koganei, Tokyo 184-8588, Japan e-mail: yosimura@cc.tuat.ac.jp A simulation method for acid base titration was developed by using not VBA programming but fundamental functions of Microsoft Excel. For calculating a ph value corresponding to a given titration volume, an approximation is need. In this study, the approximation was computed on a worksheet of Excel. Moreover, for simulating a titration curve, the ph value must be calculated for every dropping of titrant. The simulations were performed by using table which is one of the fundamental functions of Excel. Using this method, not only weak acid (base) strong base (acid) titrations such as citric acid sodium hydroxide and ammonium hydroxide hydrochloric acid, but also weak acid weak base titrations such as citric acid ammonium hydroxide were simulated. The effect of errors, which arise from carbonic acid contamination and the round-off operations of titration volumes and ph values, on titration curves were discussed. Keywords: Excel, Table, Titration curve, Simulation, Bisection method http://www.sccj.net/publications/jccj/ 37
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