LETTERS TRratlons of Monoprotic Aclds wRh Sodlum Hydroxide Contaminated by Sodlum Carbonate To the Editor:
The effect of the contamination of sodium hydroxide titrant by carbonate on the shape of the titration curves of acids of various strengths has been examined by Michalowski 11988.65.1811. All his deductions are formally correct , on the assumption ihat the sum C of the concentrkions of hydroxide, C1, and of carbonate, C2, in the titrant solution is constant in all titrations with the same titrant batch. However. a reconsideration shows that this very assumption does not reflect the most common practical situation; therefore, some of the conclusions can be misleading if taken as general rules. In fact, a constant degree of contamination must be considered as an exception rather than the rule: the titrant can be contaminated by atmospheric carbon dioxide after standardization. or carbon dioxide can evolve from the solution during the titration. As contamination entails the substitution of two moles of hvdroxide bv one mole of carhonate, it is more useful t o consider the totai"equiva1ent" concentration of base. C, = CI 2 C2. as the constant parameter. ~ i g u i e1~depicts titration curves o f a strong acid (Co = 1.00 X 10-2) with a base of Ct = 0.100 M, affected by various contents of carbonate, expressed in terms of the ratio E = 2 CJCt. Figure 1B deals similarly with the case of a moderately weak acid (pK. = 3.0). ~
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weaker than carbon dioxide (pK. = 6.3) and that it cannot he exploited in practice even for appreciably stronger acids. Only with nonvolatile, strong or moderately weak, acids can the pH break a t the first equivalence point be enhanced (with a corresponding improvement in the precision of the titration) by expelling the carbon dioxide (by boiling the solution or by purging i t with an inert gas). The second eouivalence point, which, as seen above, corresponds to the ;ormation bf hydrogen carbonate, is quite steep for acids with pK. 5 6.3 and can be exploited provided that the degree of contamination by carbon dioxide is strictIv constant from the time of the standardization of the base to titration. this .. the .--~ - ~ - In - ~ ~ case. however. loss of carbon dioxide during the titration [1986,63,691] causes a negative error; as this loss is oracticallv unavoidable. titration to the second equivalence'point should be avoided in accurate work. ~
G. Glorglo Bomb! and Carlo Macch The UniverriPf. Via Manolo 1 1-35131 Padova, Italy
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To the Edltor:
My paper [1988, 65, 1811 and the note cited by G. G. Bombi and C. M a c d present two of an infinite number of possibilities of mathematical transformations of the formula V = V,(CJ,
- [HI + K,I[Hl)I(C, + riC, + [HI - K,I[Hl) (1) ..
but only a few of them have a defined chemical interpretaK1[H])l(K2[HI2 KI[H] 1) and tion; a = (%[HI2 further notations in eq 1are given in ref I. In my paper, D and C were introduced. Both terms are easily interpreted. D is the mole fraction of MzC03 in a mixture with MOH, and C is the sum of concentrations of the two comoounds. Such an ootion is the most natural one and, moreover, leads to the simplest form of expression fur Z,.as eiven in mv article. The exorension for C corresoonds with t i e title of ;he paper. Bombi and Macca started bv considerine a C M solution of uncontaminated MOH. This solution is t i e n contaminated hv dissolution of COr, in it. Neglecting the volume change caused by two opposite factor; evaporation of water a i d dissolution of Con, one can denote the total concentration of remaining MOH by CI; concentration of M+ originating from M&O3 thus formed is 2C2. Then the postulated equation C = C1 2Cz expresses, simply, the concentration balance of M+ in the titrant. This leads to an alternative, althoueh less natural. chemical definition of the terms and to resukng changes in the shapes of the corresponding curves (under the assumption that eq 1 was applied for this purpose). Concludine, one can state that the two treatments can be considered asalternatives.
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The true equivalence point, a t which the total amount of base (hydroxide carbonate) is equal to the initial amount of acid [titration ratio FI = 1, VACI 2 C2) = Vocal is indicated by the first inflection point. The products of the titration reactions are water and carbon dioxide; therefore, the contaminant has been restored to its original form and does not interfere with the stoichiometry of the titration. After this eouivalence ooint, the carbon dioxide is titrated t o yield hydrogen carbonate: plateau is developed a t a pH equal to the pK. value for the carbon dioxidehydrogen carbonate pair (6.3). and a second equivalence point is ohserved a t a titration ratio value of F 2 = 2/(2-El. Unfortunately, the pH break a t the first equivalence point is fairly high only for relatively concentrated strong acids and decreases with increasing pK, of the analyte. I t is obvious that the first equivalence point does not appear for acids
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1072
Journal of Chemical Education
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Tadeusz Mlchalowski Jagiellonlan University 30-060 Krakow. Poland
