  We extend Van't Hoff's law for the osmotic pressure to a suspension of active
Brownian particles. The propelled particles exert a net reaction force on the
solvent, and thereby either drive a measurable solvent flow from the connecting
solvent reservoir through the semipermeable membrane, or increase the osmotic
pressure and cause the suspension to rise to heights as large as micrometers
for experimentally realized microswimmers described in the literature. The
increase in osmotic pressure is caused by the background solvent being, in
contrast to passive suspensions, no longer at the chemical potential of the
solvent reservoir. The difference in solvent chemical potentials depends on the
colloid-membrane interaction potential, which implies that the osmotic pressure
is a state function of a state that itself is influenced by the membrane
potential.
