The net effect on the global atmosphere of a continuous isolated chemical source is considered under idealized conditions. A general framework is described that allows Mi, the steady state global perturbation to the ith species due to the source, to be calculated. This is achieved by exploiting the fact that once the emissions are sufficiently dilute, far from the source, they decay with the timescales of the chemical eigenstates of the background atmosphere. Both Mi and the level of excitation of the longer-lived eigenstates are shown to depend on the details of the mixing of emissions near the source. If the details of the dilution of the emissions plume are known, it is also shown that equivalent emissions can be calculated. Equivalent emissions are designed so that when diluted instantaneously into the background atmosphere they result in the same global perturbation to each species as the original slowly diluted plume. The framework is then applied to test the sensitivity to mixing of a simple O3-NOx-CO-HOx tropospheric chemistry system. Mi is calculated for a NO-CO source of constant strength as the mixing scenario undergone by the emissions is varied. The global increase in O3 due to the source is found to increase with the rate at which emissions are mixed, whereas the global increase in CO is reduced. The equivalent emissions for each plume dilution mechanism are then calculated. In a simple plume box model it is shown that the equilibrium state obtained when the model is forced by emissions that are first diluted in entraining plumes can be reproduced in a standard box model (i.e., with instantaneous mixing of emissions) by the corresponding equivalent emissions. It is argued that the concept of equivalent emissions can be exploited straightforwardly to derive a parameterization of unresolved subgrid plumes in order to reduce systematic error in global models.