The single-fluid Magnetohydrodynamic (MHD) equations for electrolytes in the presence of a magnetic field are derived from multi-fluid MHD equations with ion-neutral collisions in partially ionized conductive fluids. The dispersion relationship of MHD waves is also investigated, which is different from that for plasmas or liquid metals. Based on the equations, we find that MHD waves are dispersive in electrolytes, and the critical frequencies for excitation of Alfven waves vary with magnetic field or conductivity, so the exciting of MHD waves is severely restricted in electrolytes with relatively low conductivity except at an extremely low frequency or when it is permeated by a considerably strong ambient magnetic field. These theories are applied to seawater to estimate the magnetic field vibration caused by the large-scale motion of seawater (e.g., ocean currents or tides). It is found that high frequency waves are dampened severely in seawater, while low frequency waves can propagate over a long distance without much attenuation.