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  Home > JCE Print > Journal of Chemical Education > Issues > 2002  > August  >
Chemical Education Today
Letters
Precision in Microscale Titration
Julian L. Roberts Jr.
Professor of Chemistry Emeritus, University of Redlands, Redlands, CA 92373-5940

Cover
August 2002
Vol. 79 No. 8
p. 941

Full Text
Singh et al. recently described in this Journal a practical microburet and some advantages of microscale titrations (1, 2). However, two of their statements call for critical examination: first, that a microburet made from a 2-mL graduated pipet allows titration volumes to be determined to four significant figures (1); and second, "the data from 50-mL buret(s) are comparable with those obtained using 2.00-mL burets" (2). Although it might be possible to estimate the position of the meniscus in a 2-mL buret to four digits, say 1.643 mL, the usual convention of assuming an uncertainty of ±1 in the least significant digit would imply a relative uncertainty, or relative standard deviation (RSD), of 0.001/1.643 or 0.06%, but the smallest (best) RSD reported by Singh et al. is 0.4%, seven times larger, for the titration of 0.1 M HCl with 0.1M NaOH. For this titration, the volume interval for a bromothymol blue indicator color change is smaller than the volume resolution of the buret (the smallest volume that can be reproducibly delivered, approximately one drop volume). Under these conditions, when the endpoint is approached in a dropwise manner, the minimum uncertainty is equal to the volume resolution of the buret, because the color change can take place anywhere within the last volume increment. So, for dropwise titrations, a good predictor of the optimum relative standard deviation (RSD) is the ratio of volume resolution to buret capacity. For a 2-mL buret of the Singh et al. design, the volume resolution is ~0.01 mL. Thus the predicted RSD would be about 0.01 mL/2 mL or 0.5%, in reasonable agreement with the best data (RSD = 0.4%) reported by Singh et al. (2), showing that there is a measurable uncertainty in the third digit of the volume reading.

Comparing burets with different capacities, a 50-mL buret having a typical drop volume of 0.05 mL has a predicted optimum RSD of about 0.05 mL/50 mL or 0.1%, and a 2-mL microburet about 0.01 mL/2 mL or 0.5% RSD, a factor of five larger. The RSDs for the 0.1 M KHP/0.1 M NaOH titrations were 0.5% and 1%, respectively, calculated from the reported 95% confidence intervals. Spreadsheet simulations of the 0.1 M KHP–0.1 M NaOH titrations shed some light on the discrepancy between the predicted and reported RSDs, showing that the volume intervals for a phenolphthalein indicator color change are ~0.1 mL for the 50mL buret (about two times larger than the 0.05 mL volume resolution) and ~0.01 mL for the 2-mL buret (about equal to the 0.01 mL volume resolution). There are two contrasting ways to view the comparison. On one hand, it shows an advantage of microscale titrations which have sharper endpoints (much larger endpoint slopes, ΔpH/ΔV), as noted anecdotally by Singh et al. (2) and described quantitatively in this Journal by Rossi et al. (3). On the other hand, the comparison is biased in favor of the microburet because the conditions selected result in a titration that is not optimized for a 50-mL buret, the volume interval of the color change (and therefore the uncertainty in the volume measurement) being greater than the volume resolution.

Literature Cited

  1. Singh, M. M.; McGowan, C.; Szafran, Z.; Pike, R. M. J. Chem. Educ. 1998, 75, 371.
  2. Singh, M. M.; McGowan, C. B.; Szafran, Z.; Pike, R. M. J. Chem. Educ. 2000, 77, 625.
  3. Rossi, M. V.; Suárez Iha, M. E. V.; Neves, E. A. J. Chem. Educ. 1990, 67, 65.

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More Information
*  Citation
Roberts, Julian L., Jr. J. Chem. Educ. 2002 79 941.
*  Keywords
Laboratory Equipment / Apparatus; Statistics / Data Analysis
*  History
Created:
Last Updated:
July 23, 2002
March 16, 2005
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