Final answer:
To estimate the time to reach 98% conversion in an acid-catalyzed poly-esterification reaction, if 82 minutes were needed to go from 98% to 99%, we can estimate the same amount of time, 82 minutes, was needed to go from 97% to 98%, assuming consistent reaction rates near completion.
Step-by-step explanation:
The student asked how to calculate the estimate of the time needed to reach a 98% conversion in an acid-catalyzed poly-esterification reaction if the conversion increased from 98% to 99% in 82 minutes. This type of problem typically involves understanding the nature of the reaction kinetics. However, without explicit information about the kinetics of the reaction (whether it's first-order, second-order, etc.), we must make assumptions, or at least estimate based on the provided information. In many chemical reactions, especially those approaching completion, the rate significantly decreases as the reactants are consumed. Assuming that an equal amount of time was required to go from 97% to 98% as from 98% to 99%, we could estimate that the time required to reach 98% conversion was also likely 82 minutes before the last measurement was taken. Therefore, the best estimate with the given information would be option (b) 82 minutes.