A recently developed method for the simulation of chemical potentials of chain molecules (EVALENCH) is applied here to obtain the chemical potential, the mean square end-to-end distance (R²_n) and the mean square radius of gyration (R²_k) of dilute chains in different athermal media. The environments considered in this work are a frozen network structure, a deformable network matrix and a monomeric solvent at various densities. The properties of all chain lengths smaller than a preset maximum are calculated in a single simulation. A novel method is also presented for locating and computing the fraction of sampling space available to append one segment of an existing chain. This method enhances the range of densities where simulations of chemical potential are feasible. Simulated chemical potentials are compared with the predictions of two theories; good agreement is found in both cases. We find that R²_n and R²_g are reduced as the density of the medium is increased (network or solvent), while they are increased when the network is frozen and as the monomeric solvent size is made larger than that of the chain sites. At the conditions studied here, no direct evidence of chain collapse is observed.