A 1-butanol acid solution is to be extracted with pure water. The butanol solution contains $4.5 \mathrm{wt} \%$ of acetic acid and flows at the rate of $400 \mathrm{~kg} / \mathrm{h}$. A total water flow rate of $1005 \mathrm{~kg} / \mathrm{h}$ is used. Operation is at $298 \mathrm{~K}$ and $1 \mathrm{~atm}$. For practical purposes, 1-butanol and water are immiscible. At $298 \mathrm{~K}$, the equilibrium data can be represented by $Y_{A i}=0.62 X_{A i}$, where $Y_{A i}$ is the weight ratio of acid in the aqueous phase and $X_{A i}$ is the weight ratio of acid in the organic phase.

(a) If the outlet butanol stream is to contain $0.10 \mathrm{wt} \%$ acid, how many equilibrium stages are required for a countercurrent cascade?

(b) If the water is split up equally among the same number of stages, but in a cross-flow cascade, what is the outlet acid concentration in the organic phase?