APPENDIX A3

Dependence of the Rate Constants on acid Concentration

In strongly acidic media, such as greater than 0.1-M HClO₄, the concentration of acid is not an accurate indicator of the hydrogen ion acid activity (2). A variety of empirically determined ¡°acidity functions¡± have been developed to relate the concentrations of strong acids in a variety of media to the hydrogen ion activities. The acidity function useful for interpreting the results of this experiment is called the Hammett acidity function (H_o). This acidity function determines the hydrogen ion activities of acidic solutions by using indicators whose absorption spectra vary in a regular manner with the hydrogen ion activity (2). The value of H_o that results from this analysis should be directly proportional to the hydrogen ion activity. Charts of HClO₄ concentration vs. H_o are available in the literature (3,4), but unfortunately they are not helpful for the range of acid concentrations employed in this experiment.

     Several experiments have investigated the dependence of the reaction rate of acidcatalyzed epoxide ring openings on acid concentration (5). Brönsted et al. (6) investigated the conversion of glycidol to glycerol using acid concentrations less than 0.02M, well below the range of acidities employed in this experiment, and found that the rate constants increased linearly with acid concentration. Pritchard and Long (7) investigated the same reaction at much higher acid concentrations (greater than 0.6M, much greater than in this experiment), and found the rate constants to be linear with H_o. The range of acidities employed in this experiment falls in between these two experiments, and Figure 7 demonstrates that at lower acid concentrations, the relationship between the rate constants and acid concentration is approximately linear but that deviations from this linear relationship increase with increasing acid concentration. Presumably the rate constants would be directly proportional to H_o if values of H_o were available for the acid concentrations employed. However, the hydrogen ion activity also depends strongly on total electrolyte concentration (because ionic strength affects hydrogen ion activity), and linearly between H_o and the reaction constants likely will be observed only if care is taken not to contaminate the reaction mixture with any ions other than from the perchloric acid.

REFERENCES

1. Noll, E. D. Phys. Teach. 11 (1973) 307.

2. Jones, R. A. Y. Physucal and Mechanistic Organic Chemistry. Cambridge University Press; New York:    1979; 73-80.

3. Hammett, L. P., Deyrup, A. J. JACS 54 (1932) 2721.

4. Rochester, C. H. Acidity Functions. Academic; New York: 1970; 43.

5. Rochester, C. H. Acidity Functions. Academic; New York: 1970; 138-140.

6. Brönsted, J. N., Kilpatrick, M., Kilpatrick, M. JACS 51 (1929) 428.

7. Pritchard, J. g., Long, F. A. JACS 78 (1956) 2667.