A Paradoxical Effect of the Titrated Volume in Potentiometric Titrations Maura Vincenza Romi, Maria Encarnacih V. Suarez Iha, and Eduardo Almeida Neves Universidade de SHo Paulo, Cx. Post. 20780, SHo Paulo, 01498, Brasil Potentiometric endpoint detection has been considered as an accurate tool in titrimetricmethods, as has been pointed out in the extensive literature on this subject. Text and reference hooks ( 1 4 )mention the effect of the titrated concentration level on the shape of the titration curve, which becomes less and less steep as the concentration goes down, with correspondingly less-sharp first-derivative peaks of a notentiometricsienal. ASIAVvs. WAS = AE. AoH or ADM). 40 reference has'been found with regard to thieffect 0.f the titrated volume of solution at a defined concentration level. We have found experimentally that this volume is a very important parameter, and the present paper discusses this volume effect on the basis of experimental and calculated curves. Results and Dlscusslon Fieure 1shows two exnerimental ~otentiometriccurves of 0.10;0 M sodium carbonate titratei with hydrochloric acid M in twodifferent volumes. 3.000 ml. and a~~ronimatelv0.2 25:00 mL ( ~ i &l a and l h , respectively). The first derivative data were plotted in the conventional manner versus the volumes of the titrant. I t is clear that the potentiometric signal is sharper in a smaller volume (Fig. la). The first peaks in both titrations are smaller than the second ones due to the buffering effecta of HC03- ion. However, a much better definition is found for this first stoichiometric point a t the smaller volume. It is evident that a t smaller volumes e n d ~ o i u t are s much more sharolv . . defined. 1; order to avoid experimental errors, calculated titration curves were used tocheck theeffect of volume in the derivarive curves (a computer program in BASIC language was written fur this purpose). Figure 2 shows a series of firstderivative curves obtained fr%m calculated potentiometric curves (pH vs. V of strong acid) by the titration of a strong
Figure 1. Derivative curves of m e experimental tihatian of 0.1000 M sodium carbonate with 0.2 M hydrochloric acid in two ditiersnt inltiai volumes: (a) 3.000 mL, (b) 25.00 mL.
base with a strong acid, a t 0.1 M concentration level and several titrated volumes. Although activity coefficients may change during the titration, this has not been considered in the calculations because the pH changes are of the same magnitude in the volume increments, a t the considered concentration level, in all calculated curves. After the mass balance calculation, the pH was considered as -log [H+] before the stoichiometric ~ o i n tand . 7.00 for this ~ o i n tafter : this stoichiometric point ;he pH was the difference 14.00 DOH.The incremenu in volumes of the titrant were taken proportional to the titrated volume, respectively: 2.50 mL with an increment of 0.010 mL (Fig. 2a); 5.00 mL with 0.020 mL (Fig. 2h); 10.00 mL with 0.040 mL (Fig. 2c); 25.00 mL with 0.100 mL (Fig. 2d), and 50.00 mL with 0.200 mL (Fig. 2e). With such proportional increments the same percentage of neutralization was achieved a t each titrant addition, with eoual . DH . chanees. The A ~ H / A v d a t afrom several titration curves were pl&d versub volumeof the titrant. Moreelucidative lots are obtained if percent neutralization is used as the abscissa instead of titiant volume, as can he seen in Figure 2. In this way, all x-axis data are plotted within the same abscissa scale, in order to compare the peak heights. In order to understand the volume effect in potentiometric titrations better, as considered in the examples above, let us consider the following arguments: An addition of 0.010 mL of 0.10 M hydrochloric acid to 1.00 mL of water causes a theoretical pH change of 4.0 units, from 7.0 to 3.0, which corres~ondsto a ADHIAVof 400. if this volume of acid were added'to 10.00 m~ht'water,the ;H change would he only 3.0 unim which corres~ondsto a ApHIAV uf 300. It can also be argued that a pro&tional increment, 0.100 mL of acid in 10.00 mL of water, would cause the same 4.0 pH change as observed for 0.010 mL in 1.00 mL of water, which does not appear to be advantageous a t all. But the calculated ApH/ AVfor this condition is only 40 instead of 400 as achieved for 1.00 mL of water. ~
~
Figure 2. meoretical Uerlvativetltration c w e s of strong acid wim strong base, at 0.1 M concennatlon level, for the following titrated volumes (mL) and cmspondins tihant increments (mL): (a) 2.5, 0.010; (b) 5.0. 0.020; (c) 10, 0.040: (d) 2 5 . 0 . 1 0 ( 0 ) so, 0.20.
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This volume effect is universal and can he observed a t any potentiometric titration, point by point, or with automatic recording, with any potentiometric signal. The only practical adverse effect in dealing with smaller volume is the tendency to add relatively high-volume increments of the titrant, which lead the incremental ratios ASIAV to he lower than the true dSIdV. In spite of that, steeper potentiometric curves with sharper first-derivative curves are always ohserved with titrations a t smaller volumes. A speculation must now be made about the precision and if the procedure a t smaller volumes can he advantageous or not. Rigorously, the derivative potentiometric signal ASIAV with AVmL of the titrant, taken proportional to the titrated volume, is inversely proportional to this titrated volume of solution. This means that the derivative signal increases 10 times when the volume of the titrated solution decreases in the same proportion. Under these comparahle situations, the titration error in volume would he proportionally smaller when using smaller initial volumes. However, the smaller volume error is related to a smaller volume of titrant, which causes the same relative error. After these considerations i t can he argued that, if precision is not increased, why then perform titration a t smaller volume? I t happens that, for a fixed intensive factor (concentration), a smaller extensive factor (weight of substance) is titrated a t a smaller volume condition, with the same theoretical precision as with the higher volume with a higher weight of substance. In practice, the advantage of dealing with smaller volumes is closely related to the precision of the microburet as compared with the macro type. The precision of the results will he the same if hoth deliver volumes with the same number of significant figures. Many modern microburets can deliver smaller volumes with a precision comparahle with that of macrohurets, which deliver higher volumes.
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Journal of Chemical Education
Finally the paradox in the effect of the volume resides in these two considerations: (1) The potentiometric derivative signal decreases with the de-
creased titrated amount of substance at decreasing caneentration and constant volume as normally considered (14). (2) However, these potentiometric signals increase, unexpectedly, with the smaller amount of titrated substance taken at decreasing volumes and constant concentration, which has never been considered (14). Summary
I t has heen demonstrated with hoth experimental and calculated titration curves that, a t lower titrated volumes of solutions and a particular concentration level, sharper peaks were observed for the conventional derivative curves. The increase in the potentiometric signal may compensate the decrease in precision in microtitrations, when smaller volumes of titrant are consumed. Acknowledgment
The authors are greatly indebted to CNPq and FINEP (Brazilian agencies) for financial support. Literature Clted 1. Kolthoff I. M.; Furman, N. H. Pofenfiometric Titration, 2nd ed.; Wiley: New York. 1947; Chapter 11.
2. Kolthoff, I. M.; Stenser,V. A. Volumetric Analysis. 2nd ed.: Intencience:New York, 1942: V o l 1,Chapter 111. 3. Vwd, A. 1. A Test-book of Quonfilolivo lnareonic Anolysis, 3rd ad.: Longmans: London, 1961;Chapter I. 4. Kolthoff, I. M.:Sandeil, E. B.: Mechan, E. J.: Bruckenstein. S. Q u o n t i t n f i ~Chamieol ~ Anolysl~.4th ed.; Mamillan: New York,1971: Chapters 34 and 52. 5. Skoag,D.A.; WestD. M.FundomenfolsofAnolyficolChrmistry,4thed.:Ssndcn:New York. 1962: Chapters 8 and 16. 6. Kennody. J. H. Analytical Chemisfry-Plinciples. 1st ed.: Harmurt: New Yark, 19% Chapfen 7 and 9.
