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), k_y/k_x = 2, then y_i equals ____ (rounded off to 3 decimal places).

Question

Accepted Answer

The correct answer is 0.014 to 0.017. GATE 2025 official key: 0.014 to 0.017. The tie-line slope from bulk to interface is −k_x/k_y = −0.5: (0.02−y_i)/(0.002−x_i) = −0.5, combined with y_i = 1.5x_i, gives x_i ≈ 0.0105 and y_i ≈ 0.0158.