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Silva, Pereira, and Sabadini, in their recent paper in this Journal (1), ask “Can an indicator solution change color upon dilution? Our usual experience in chemistry suggests to us that such behavior is impossible.” They then complete the paradox by saying “However, the answer to the question is affirmative, as shown in this paper.” The resolution of the paradox is to realize that dilution of a buffered solution of an indicator will not appreciably change the pH (no change in color), but dilution of a solution that contains only the indicator will certainly change the pH if the pH is not initially 7 (possibly a change in color). The experiment they describe involves a special case in which there is a change in color upon dilution of an unbuffered indicator solution.
This special case is characterized by a pKa value for the indicator, called pKIn, of 5. We can estimate (2) that a 0.0001 molar solution of a weak acid whose pKa is 5 should have a pH of about 2.5 + 2, or 4.5. This sets the pH of the solution on the acidic side of the pKa, where the acidic form of the indicator will predominate. This possibility corresponds quite well to point 6 in Table 1 of the supplemental materials. For this point the reported indicator concentration is 1.092 × 10−4 M, the reported pH is 4.13, the ratio of [In−] to [HIn] was determined to be 0.123, and the log of this ratio is −0.91. The Henderson–Hasselbalch equation states that pKIn = pH − log[In−]/[HIn], and so pKIn must equal 4.13 − (−0.91), or 5, the value reported in the paper.
Dilution of this solution by a factor of 10 should change the pH to 4.5 + 0.5, or 5.0 (2). This possibility corresponds pretty nearly to point 1 in Table 1 of the supplemental materials. For this point the reported indicator concentration is 0.182 × 10−4 M, the reported pH is 5.28, and the ratio of [In−] to [HIn] was determined to be 1.013. Thus dilution by a factor of 10 changed the ratio of [In−] to [HIn] from 0.123 to 1.013; that is, as the solution was diluted by a factor of 10 the fraction of the indicator in the form of the conjugate base went from about 1/9 to about 1/2. Further dilution would make the solution even less acidic, and finally, as the pH approached 7, practically all of the indicator would be present in the basic form; the color change would be complete.
In order to see a color change upon dilution of an unbuffered solution of an indicator of the form HIn, the pKa of the indicator should be 2 or more units on the acidic side of 7 so that dilution can take the pH of the solution to the basic side of the pKa, but not so far on the acidic side of 7 that the solubility limit of the indicator will prevent the indicator from setting the pH initially to the acidic side of the pKa. For example, if the pKa is 3, it will take a 0.01 M solution to set the pH to 2.5 (2).
“Can an indicator solution change color upon dilution?” A better answer is: Only if the solution is unbuffered and the pKa of the indicator, HIn, lies between about 3 and 5.
Literature Cited
- Silva, C. R.; Pereira, R. B.; Sabadini, E. J. Chem. Educ. 2001, 78, 939–940.
- Ault, Addison. J. Chem. Educ. 1999, 76, 936–938.
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