Repeat Problem 19.H5 except in experiment \(B x_{i n}=0.003, p_{r}=21.4 \mathrm{~atm}\) and \(p_{p}=1.1 \mathrm{~atm}, \theta^{\prime}=0.45\), and a mass transfer coefficient of \(k=4.63 \times 10^{-5} \mathrm{~m} / \mathrm{s}\). Predict \(M, R,{ }^{\prime}{ }^{\prime}\) solv, \(x_{p}\), and \(x_{r}\).

Problem 19.H5

RO experiments are done in a laboratory stirred-tank membrane system at \(45.0^{\circ} \mathrm{C}\). With pure water, we measure the pure water flux \(=17.89 \mathrm{~g} /\left(\mathrm{m}^{2} \mathrm{~s}\right)\) when \(\mathrm{p}_{\mathrm{r}}=15.2 \mathrm{~atm}\) and \(\mathrm{p}_{\mathrm{p}}=1.1 \mathrm{~atm}\). We then do experiment A with a highly stirred system \((M=1.0)\) with \(p_{r}=13.6 \mathrm{~atm}\) and \(p_{p}=1.1 \mathrm{~atm}\) and find \(R^{0}=0.991\). We now plan to do experiment \(B\) with \(\mathrm{p}_{\mathrm{r}}=11.3 \mathrm{~atm}\) and \(\mathrm{p}_{\mathrm{p}}=1.1 \mathrm{~atm}, \theta^{\prime}=0.55, \mathrm{x}_{\mathrm{in}}=0.03 \mathrm{wt} \%\) salt, and a mass transfer coefficient of \(\mathrm{k}=4.63 \times 10^{-5} \mathrm{~m} / \mathrm{s}\). Density of water is \(0.997 \mathrm{~kg} / \mathrm{L}\). Predict M, \(R,{ }^{\prime}\) solv, \(\mathrm{x}_{\mathrm{p}}\), and \(\mathrm{x}_{\mathrm{r}}\) for the new experiment. Use of a spreadsheet or other computer solver is highly recommended.