Use of the Bubbling Reactor with the $${\mathbf{Ru(bpy)}}_{\mathbf{3}}^{\mathbf{2+}} {\mathbf{/S}}_{\mathbf{2}} {\mathbf{O}}_{\mathbf{8}} ^{\mathbf{2 - }}$$ Photosystem for Measuring the Rate of Water Oxidation as Promoted by Different Manganese Oxides