Consider the advection and dispersion of a conservative nonsorbing solute in a spatially variable but statistically homogeneous velocity field. A Lagrangian approach leads to expressions for the large-time mean and variance of concentration. The expressions require only the macroscopic velocity vector Um, the macrodispersion tensor Dm, and an additional tensor &THgr;. The macroscopic velocities and macrodispersivities are well known from numerous previous studies, but &THgr; is introduced here for the first time. The tensor &THgr; is needed to describe the kinetics of dilution of a plume: Two cases with the same Um and Dm have different dilution characteristics depending on &THgr;. The characteristic times of dilution are given by tensor &THgr;Dm-1. It is demonstrated, for the first time through a Lagrangian approach, that the coefficient of variation of concentration at the center of the plume becomes proportionate to 1/t, as was previously shown in the Eulerian theory of Kapoor and Gelhar <1994a, b>. Expressions for the geometric mean of the dilution index and the reactor ratio are derived. Numerical simulations support the validity of the approach. ¿ 1999 American Geophysical Union