GATE 2022 CH – Question 32
Consider interphase mass transfer of a species $S$ between two immiscible liquids $A$ and $B$. The interfacial mass transfer coefficient of $S$ in liquid $A$ is twice of that in liquid $B$. The equilibrium distribution of $S$ between the liquids is given by $y_S^A = 0.5y_S^B$, where $y_S^A$ and $y_S^B$ are the mole-fractions of $S$ in $A$ and $B$, respectively. The bulk phase mole-fraction of $S$ in $A$ and $B$ is 0.10 and 0.02, respectively. If the steady-state flux of $S$ is estimated to be 10 kmol h$^{-1}$ m$^{-2}$, the mass transfer coefficient of $S$ in $A$ is ________ kmol h$^{-1}$ m$^{-2}$ (rounded off to one decimal place).
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Correct answer: 221.09 to 223.31
Explanation
Let $k_A = 2k_B$. The flux is the same on both sides of the interface: $k_A(0.10 - y_i^A) = k_B(y_i^B - 0.02)$ with $y_i^A = 0.5y_i^B$. Dividing by $k_B$: $2(0.10 - 0.5y_i^B) = y_i^B - 0.02$, so $0.22 = 2y_i^B$ and $y_i^B = 0.11$, $y_i^A = 0.055$. Then $N = k_A(0.10 - 0.055) = 10$ gives $k_A = \frac{10}{0.045} = 222.2$.