Air at $75\backslash$deg C flows through $8-0\mathrm{.}05-$m long. packed tube of naphthalene spheres at a bulk velocity of $0\mathrm{.}3$ m$/$s $($assuming plug flow$).$ The effective naphthalene surface mass transfer area through the packed tube is $300$ m$?$ per unit volume of the tube. The convective mass tansfer coefficient for this process was found to be $0\mathrm{.}057$ m$/$s$.$ The entering air is free of naphthalene.

The vapor pressure of naphthalene at $75\backslash$deg C is $5\mathrm{.}61$ mmHg $(747$ N$/$m$?).$

a$)$ Derive the bulk naphthalene concentration profile along the tube length.

b$)$ Calculate the bulk concentration of naphthalene in air at the exit of the tube.