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We present an efficient method for determining temporal moments of concentration for a solute subject to first‐order and diffusive mass transfer in steady velocity fields. The differential equations for the moments of all orders have the same form as the steady state nonreactive transport equation. Thus temporal moments can be calculated by a solute transport code that was written to simulate nonreactive steady state transport, even though the actual transport system is reactive and transient. Higher‐order moments are found recursively from lower‐order moments. For many cases a small number of moments sufficiently describe the movement of a solute plume. The first four moments describe the accumulated mass, mean, spread, and skewness of the concentration histories at all locations. Actual concentration histories at any location can be approximated from the moments by applying the principle of maximum …