Solute $A$ is absorbed from a gas into water in a packed bed operating at steady state. The absorber operating pressure and temperature are $1 \: \mathrm{atm}$ and $300 \: K$, respectively. At the gas-liquid interface
$$y_{i}=1.5 x_{i}$$
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 $\left(k_{y}\right)$ to that on the water-side $\left(k_{x}\right), \frac{k_{y}}{k_{x}}=2$, then $y_{i}$ equals $\_\_\_\_\_\_$ (rounded off to $3$ decimal places).
