GATE 2025 CH – Question 56
Solute $A$ is absorbed from a gas into water in a packed bed operating at steady state. The absorber operating pressure and temperature are 1 atm and 300 K, respectively. At the gas-liquid interface $y_i = 1.5x_i$ where $y_i$ and $x_i$ are the interfacial gas and liquid mole fractions of $A$, respectively. At a particular location in the absorber, the mole fractions of $A$ in the bulk gas and in the bulk water are 0.02 and 0.002, respectively. If the ratio of the local individual mass transfer coefficients for the transport of $A$ on the gas-side ($k_y$) to that on the water-side ($k_x$), $\frac{k_y}{k_x} = 2$, then $y_i$ equals ____ (rounded off to 3 decimal places).
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Correct answer: 0.006 to 0.026
Explanation
In the two-film model the flux through the gas film equals the flux through the liquid film: $k_y(y - y_i) = k_x(x_i - x)$. So $2(0.02 - y_i) = x_i - 0.002$, with $x_i = \frac{y_i}{1.5}$. Then $0.04 - 2y_i = 0.6667y_i - 0.002$, so $0.042 = 2.6667y_i$ and $y_i = 0.01575 \approx 0.016$.