For an RO system in which osmotic pressure is a linear function of weight fraction of solute, \(\pi=a^{\prime} x\), show that at the same values of \(\mathrm{x}_{\mathrm{p}}\), the relationship between \(\mathrm{R}, \mathrm{R}^{\mathrm{o}}\), and \(\mathrm{M}\) is

\[ \mathrm{R}=1-\mathrm{M}\left(1-\mathrm{R}^{\circ}\right) \]

What assumptions have to be made to use this relationship for a different RO module?