We are extracting pyridine from \(500 \mathrm{~kg} / \mathrm{h}\) of a feed that is \(15.0 \mathrm{wt} \%\) pyridine and \(85.0 \mathrm{wt} \%\) water using \(225 \mathrm{~kg} / \mathrm{h}\) of pure chlorobenzene as the solvent. Assume water and chlorobenzene are immiscible. The equilibrium is \(\mathrm{y}_{\mathrm{pyr}}=2.2 \mathrm{x}_{\mathrm{pyr}}\) with \(\mathrm{y}=\mathrm{wt} \%\) pyridine in extract, and \(\mathrm{x}=\) \(\mathrm{wt} \%\) pyridine in raffinate. A counter-cascade is used. If we desire a final concentration of \(\mathrm{x}_{\mathrm{N}}=4.0 \mathrm{wt} \%\) pyridine in the exiting raffinate \(\left(\mathrm{x}_{\mathrm{N}}\right)\),

a. What is the outlet \(\mathrm{wt} \%\) of the pyridine in the extract phase, \(\mathrm{y}_{1}\) ?

b. How many equilibrium stages are required?