A number of processes contribute to the decrease in solute concentration in the near surface; these include leaching and degradation. The combined effect of all loss processes is termed dissipation; its converse is termed persistence. In this paper we derive analytical expressions for the statistics of the time for a chemical, which undergoes linear equilibrium sorption and first-order degradation under the influence of a random series of rainfall events, to dissipate to a specified concentration. Rainfall is characterized by a random time between events and a random storm depth, both of which are assumed to be exponentially distributed. Analytical expressions for the mean and variance of the time for dissipation to 50% (DT50) and 10% (DT90) of the applied concentration are derived. The model is in qualitative agreement with empirical observations of pesticide dissipation. The model results indicate that on average these solutes tend to dissipate exponentially with time. Rapid dissipation initially, followed by slower dissipation later, is more likely to occur. This may contribute to observations of apparent multirate dissipation which can be explained without recourse to sorption or biological kinetics. A larger average storm magnitude and/or more frequent storms reduce the mean and increase the coefficient of variation of dissipation times. A normal distribution, parameterized using the derived statistics, approximated the probability distribution of dissipation times reasonably well. On the basis of this we obtain a measure of the potential amount of chemical available for rapid off-site leaching at a given time since application.