A new method approximates transport properties of a homologous series of poly(oxyethylene-ethylene carbonate) copolymer-lithium bis(fluorosulfonyl)imide (LiFSI) solid polymer electrolytes (SPEs)-using both dilute and concentrated solution theories. A chemical equilibrium model uses published Fourier-transform infrared data to estimate the concentrations of positively charged ion aggregates, of free anions and negatively charged ion aggregates, of charge-balanced ion aggregates, and of lithium ion adducts with ether and carbonyl oxygen groups in the copolymer. Ion shuttle-hopping and bulk self-diffusivities are estimated using published cation transference number, glass transition temperature, and ionic conductivity data using species concentrations from the chemical equilibrium model. Over a broad range of copolymer composition, salt concentration, and temperature, both ion shuttle-hopping and bulk diffusion contribute to ion transport. The method has been more generally validated for homogeneous and amorphous solid polymer electrolytes consisting of polymers containing aliphatic ether and carbonate groups with LiFSI and lithium bis(trifluoromethylsulfonyl)imide, including polyethylene oxide SPEs.