Solutions of negatively charged graphene (graphenide) platelets were produced by intercalation of nanographite with liquid potassium-ammonia followed by dissolution in tetrahydrofuran. The structure and morphology of these solutions were then investigated by small-angle neutron scattering. We found that >95 vol % of the solute is present as single-layer graphene sheets. These charged sheets are flat over a length scale of >150 Å in solution and are strongly solvated by a shell of solvent molecules. Atomic force microscopy on drop-coated thin films corroborated the presence of monolayer graphene sheets. Our dissolution method thus offers a significant increase in the monodispersity achievable in graphene solutions.