C1. Derive Eqs. (17-10) for a gas permeator.
C2. Solve Eq. (17-19) for xp as a function of xr.
C3. Derive Eq. (17-31) from shell balances. You should obtain a second-order equation. Do the first integration and apply the boundary condition R = 1.0 at z = 0.
C4. For an RO system where osmotic pressure is a linear function of weight fraction of solute, π = a′x, show that at the same values of xp, the relationship between R, R°, and M is
R = 1 − M(1 − R°)
What assumptions have to be made to use this relationship for a different RO module?
C5. Derive Eq. (17-11e).