Consider an interphase mass-transfer process for the chlorine dioxide ($ClO_{2}$)-air-water system at $20 ^{\circ } \mathrm {C}$, where $ClO_ {2}$ gas (solute A) is sparingly soluble in water. At the current conditions of operation, the mole fraction of $\mathrm{ClO}_{2}$ in the bulk gas phase is $y_{A}=0.040$ and the mole fraction of $\mathrm{ClO}_{2}$ in the bulk liquid phase is $x_{A}=0.00040$. The mass density of the liquid phase is $992.3 \mathrm{kg} / \mathrm{m}^{3}$ and is not dependent on the very small amount of $\mathrm{ClO}_{2}$ dissolved in it. The molecular weight of water is $18 \mathrm{g/gmole}$, and the molecular weight of $\mathrm{ClO}_{2}$ is 67.5 g/gmole. The total system pressure is 1.5 atm. The liquid film mass-transfer coefficient for $\mathrm{ClO}_{2}$ in water is $k_{x}=1.0$ gmole/m$^{2} \cdot \mathrm{ s }$, and the gas film mass-transfer coefficient $\mathrm{ClO}_{2}$ in air is $k_{G}=0.010$gmole/m$^{2} \cdot s \cdot atm$. The equilibrium distribution data for the $\mathrm{ClO}_{2}$-water-air system at $20^{\circ} \mathrm{C}$ are provided below:

$\begin{array}{llllllll}\hline \scriptstyle{p_{A}} & \scriptstyle{{100E-02}} & \scriptstyle{{3.00E - 02}} & \scriptstyle{{5.00 \mathrm{E} - 02}} & \scriptstyle{{7.00 \mathrm{E} - 02}} & \scriptstyle{{1.00 \mathrm{E} - 01}} & \scriptstyle{{1.10 \mathrm{E} - 01}} \\ \scriptstyle{{x_{\mathrm{A}}}} & \scriptstyle{{2.40 \mathrm{E} - 04}} & \scriptstyle{{7.19 \mathrm{E} - 04}} & \scriptstyle{{1.15 \mathrm{E} - 03}} & \scriptstyle{{1.64 \mathrm{E} - 03}} & \scriptstyle{{2.34 \mathrm{E} - 03}} & \scriptstyle{2.58\mathrm{E} - 03} \\ \scriptstyle{{p_{\mathrm{A}}}} & \scriptstyle{{1.20 \mathrm{E} - 01}} & \scriptstyle{{1.30 \mathrm{E} - 01}} & \scriptstyle{{1.40 \mathrm{E} - 01}} & \scriptstyle{{1.50 \mathrm{E} - 01}} & \scriptstyle{{1.60 \mathrm{E}-01}} \\ \scriptstyle{{x_{\mathrm{A}}}} & \scriptstyle{{2.81 \mathrm{E}-03}} & \scriptstyle{{3.06 \mathrm{E}- 03}} & \scriptstyle{{3.28 \mathrm{E} - 03}} & \scriptstyle{{3.52 \mathrm{E} - 03}} & \scriptstyle{{3.78 \mathrm{E} - 03}} \\ \hline\end{array}$

a. Plot out the equilibrium line in $p_{A}-c_{A L}$ coordinates, and the operating point $\left(p_{A}, c_{A L}\right)$. Is the process gas absorption or liquid stripping?
b. What is the equilibrium relationship as n equal to?
c. What is $k_{L}$ for the liquid film?
d. If the $\mathrm{ClO}_{2}$ mole fraction in the bulk gas phase is maintained at 0.040 under 1.5 am total system pressure, what is the maximum possible dissolved $\mathrm{ClO}_{2}$ concentration (gmole A/$\mathrm{m}^{3}$) in the liquid phase that could possibly exit the process-i.e., $c_{A L}^{\circ}$?
e. What are the compositions at the gas-liquid interface, $p_{A, i}$ and $c_{A L, i}$?
f. What is $K_{y}$, the overall mass-transfer coefficient based upon the overall gas-phase mole fraction driving force? There are several valid approaches for calculating $K_{y}$ based on the information provided. Show at least two approaches that lead to the same result.
g. What is the mass-transfer flux $N_{A}$ for $\mathrm{ClO}_{2}$ in units of gmole/m$^{2} \cdot$s?