The cost of purifying many chemicals is inversely proportional to their feed concentration over 10 orders of magnitude. This empirical proportionality implies that the key to chemical separation is the free energy of unmixing, that is, to entropic effects. It suggests that pollution abatement involves balancing concentration and toxicity using multi-objective optimization, and hence, a strategy for optimizing pollution abatement is obtained. This knowledge provides insight for policy that incentivizes cleanup of the most important pollutants from contaminated water, whether there is one or many pollutants.