Proton-exchange membranes are key solid-state ion carriers in many relevant energy technologies including flow batteries, fuel cells, and solar-fuel generators. In many of these systems, the membranes are in contact with electrolyte solutions. In this paper, we focus on the impact of different HBr, a flow-battery and exemplary acid electrolyte, external concentrations on the conductivity of Nafion, a perfluorosulfonic acid membrane that is commonly used in many energy-related applications. The peak and then decrease in conductivity is correlated with measured changes in the water and HBr content within the membrane. In addition, small-angle x-ray scattering is used to probe the nanostructure to correlate how the interactions of the bromide ion with the fixed sulfonic-acid sites impact conductivity and hydrophilic domain distance. It is also shown that membrane pretreatment has a large impact on the underlying structure/function relationship. The obtained data and results are useful for delineation of optimal operating regimes for flow batteries and similar technologies as well as in understanding underlying structure/function relationships of ionomers in electrolyte solutions.