NOVELTY - An electrochemical device, comprises: a positively charged electrode; a negatively charged electrode; a graphene layer comprising graphene having micro-crystalline grain size of 2-15 nm, basal planes that are planar, and a total electrochemical window of at least 3-5 volts; and an electrolyte. The graphene layer covers at least a portion of the positive electrode and/or the negative electrode.    USE - As electrochemical device used to store or provide energy; particularly a symmetric or asymmetric aqueous ultra-capacitor (all claimed), electrochemical sensors, electrochemical pollutant oxidation/reduction reactors, fuel cells, and redox flow batteries.    ADVANTAGE - The graphene layer provides a capacitance of at least 200-700 (preferably 250-675) mu F/cm2. The aqueous ultra-capacitor produces 500-600 (preferably 550) mu J/cm2 of stored energy. The capacitors comprising activated carbon exhibit energy storage of only about 4 mu J/cm2 and the capacitors comprising graphene derivatives have an upper limit of energy storage of only about 60 mu J/cm2. The graphene material is resistant to sulfation and H2 evolution. The graphene material is suitable for use in batteries, such as redox flow batteries, as well as fuel cells. Due to unique structural characteristics, electrochemical properties, and natural hydrophobicity of the graphene material, this material is able to suppress hydrogen gas evolution and/or lead sulfate crystal formation that typically impedes battery/fuel cell performance. Thus, the graphene material provides a complete connective network between electrodes of batteries and/or fuel cells, thus enhances performance and reduces the amount of energetic material typically wasted in these types of systems.    DETAILED DESCRIPTION - An electrochemical device, comprises: a positively charged electrode; a negatively charged electrode; a graphene layer comprising graphene having micro-crystalline grain size of 2-15 nm, basal planes that are planar, and a total electrochemical window of at least 3-5 Volts; and an electrolyte. The graphene layer covers at least a portion of the positive electrode, and/or the negative electrode. The graphene layer is coupled to the positively charged electrode or the negatively charged electrode by an adhesive or a component that facilitates adhesion. The component that facilitates adhesion is an organic solvent. INDEPENDENT CLAIMS are included for the following:    (1) method of making a graphene anode, involving: providing a substrate; depositing the graphene layer on the substrate, where the graphene layer comprises graphene having micro-crystalline grain size of 2-15 nm, basal planes that are planar, and exhibits an anodic potential of at least 2-3 volts; exposing the graphene layer to a support layer comprising an adhesive or that has been exposed to a component that facilitates adhesion; and removing the substrate from the graphene layer; and    (2) method for water remediation, involving: passing non-potable water between the graphene anode and a cathode; applying an electric current using a power source; and isolating potable water.