Charge storage in electrochemical double-layer capacitors (EDLCs) is via the adsorption of electrolyte counterions in their positive and negative electrodes under an applied potential. This study investigates the EDLC-type charge storage in carbon nanotubes (CNT) electrodes in aqueous acidic (NaHSO4), basic (NaOH), and neutral (Na2SO4) electrolytes of similar cations but different anions as well as similar anions but different cations (Na2SO4 and Li2SO4) in a two-electrode Swagelok-type cell configuration. The physicochemical properties of ions, such as mobility/diffusion and solvation, are correlated with the charge storage parameters. The neutral electrolytes offer superior charge storage over the acidic and basic counterparts. Among the studied ions, SO4 2- and Li+ showed the most significant capacitance owing to their larger solvated ion size. The charge stored by the anions and cations follows the order SO4 2- > HSO4 - > OH- and Li+ > Na+, respectively. Consequently, the CNT//Li2SO4//CNT cell displayed outstanding charge storage indicators (operating voltage ∼0-2 V, specific capacitance ∼122 F·g-1, specific energy ∼67 W h·kg-1, and specific power ∼541 W·kg-1 at 0.5 A·g-1) than the other cells, which could light a red light-emitting diode (2.1 V) for several minutes. Besides, the CNT//Li2SO4//CNT device showed exceptional rate performance with a capacitance retention of ∼95% at various current densities (0.5-2.5 A·g-1) after 6500 cycles. The insights from this work could be used to design safer electrochemical capacitors of high energy density and power density.