Ching and Ruthven (1985) found that the equilibrium of glucose on an ionexchange resin in the calcium form was linear for concentrations below $50 \mathrm{~g} / \mathrm{L}$. Their equilibrium expression at $303 \mathrm{~K}$ is $Y_{A i}=1.961 X_{A i}$, where $X_{A i}$ is the glucose concentration in the resin ( $\mathrm{g}$ of glucose per liter of resin) and $Y_{A i}$ is the glucose concentration in solution ( $\mathrm{g}$ of glucose per liter of solution).

(a) We wish to sorb glucose onto this ion-exchange resin at $303 \mathrm{~K}$ in a countercurrent cascade of ideal stages. The concentration of the feed solution is $15 \mathrm{~g} / \mathrm{L}$. We want an outlet concentration of $1.0 \mathrm{~g} / \mathrm{L}$. The inlet resin contains $0.25 \mathrm{~g}$ of glucose/L. The feed solution flows at the rate of $100 \mathrm{~L} / \mathrm{min}$, while the resin flows at the rate of $250 \mathrm{~L} / \mathrm{min}$. Find the number of equilibrium stages required.

(b) If five equilibrium stages are added to the cascade of part (a), calculate the resin flow required to maintain the same degree of glucose sorption.