We are doing RO experiments with a completely mixed laboratory unit. Data: \(\mathrm{K}_{\text {solv }}^{\prime} / \mathrm{t}_{\mathrm{ms}}=1.387 \mathrm{~g} /\left(\mathrm{atm} \mathrm{m}^{2} \mathrm{~s}\right)\). Assume solutions have same density as water \(=997 \mathrm{~kg} / \mathrm{m}^{3}\). Osmotic pressure of sodium chloride is \(\pi=\mathrm{a}^{\prime} \mathrm{x}\) where \(\mathrm{x}\) is in weight fraction, \(\pi\) is in atm, and at \(25.0^{\circ} \mathrm{C}, \mathrm{a}^{\prime}=705.9 \mathrm{~atm} /\) (weight fraction).

Experiment B. With a very high stirrer speed so that there is no concentration polarization, we do an experiment with a feed that is \(0.077 \mathrm{wt} \%\) sodium chloride in water. Cut (in weight units) \(\theta^{\prime}=0.22\), and measured inherent retention is \(\mathrm{R}^{\mathrm{o}}=0.996, \mathrm{~T}=25^{\circ} \mathrm{C}, \mathrm{p}_{\mathrm{p}}=1.1 \mathrm{~atm}\), and \(\mathrm{p}_{\mathrm{r}}=12.06 \mathrm{~atm}\).

Experiment C. A feed with \(0.093 \mathrm{wt} \%\) sodium chloride was separated with \(\mathrm{T}=25^{\circ} \mathrm{C}\), a permeate pressure of \(1.1 \mathrm{~atm}\), and a retentate pressure of \(15.2 \mathrm{~atm}\). Cut (in weight units) \(\theta^{\prime}=0.26\). Stirring speed was lower, and concentration polarization is expected. \(\mathrm{R}=0.992\) was measured.

a. What is the value of concentration polarization modulus \(\mathrm{M}\) in experiment \(\mathrm{C}\) ?

b. What are the values of \(\mathrm{x}_{\text {out }}, \mathrm{x}_{\mathrm{p}}\), and solvent flux \(\mathrm{J}_{\text {solv }}\) in experiment \(\mathrm{C}\) ?