The first-order rate constant in a unimolecular reaction is a measure of the probability that the reaction will occur per unit time, measured in an interval that is small enough so that this probability is small. It is impossible to predict the exact time at which a particular molecule will react; because of the random nature of the process, we can just calculate probabilities. Because the probability of survival for each individual molecule decreases exponentially with time as e-kt, the rate constant of the process can be calculated from the experimental determination of a large number of survival times. This is now possible for certain reactions thanks to the development of single-molecule techniques, in which individual molecules are observed in real time one-by-one in equilibrium conditions.
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