Your company is considering buying an absorbent material designed to selectively remove solute A from solution.

The solubility of $A$ in the absorbent increases with the liquid concentration $c_{A,l}$ such that $c_{A,S}=1\mathrm{.}5c_{A,l}.$ The

solution is very well mixed and has a constant concentration of $c_A=2\frac{\text{m}\text{o}\text{l}}{m^3}.$ The diffusion coefficient of $A$ in the

absorbent material is $410-7cm\frac{2}{s}.$ The material is available as spherical pellets $1cm$ in diameter.

a$.$ Find the characteristic time constant for absorbent to diffuse through the pellet.

b$.$ What is the Biot number for this system? Is it limited by external convection or internal diffusion?

c$.$ Set up the mass transfer problem with CV$,$ species, flux equation, governing equation, and boundary

$/$initial conditions.

d$.$ How many hours will it take for the solute A concentration to reach $2\mathrm{.}9mo\frac{l}{m^3}$ at a depth of $0\mathrm{.}40cm$ from

the surface of the pellet?Your company is considering buying an absorbent material designed to selectively remove solute A from solution. The solubility of A in the absorbent increases with the liquid concentration $,$ such that $,=1\mathrm{.}5,.$ The solution is very well mixed and has a constant concentration of $=23.$ The diffusion coefficient of A in the absorbent material is $4$x$10-7$ cm$2/$s$.$ The material is available as spherical pellets $1$ cm in diameter. a$.$ Find the characteristic time constant for absorbent to diffuse through the pellet. b$.$ What is the Biot number for this system? Is it limited by external convection or internal diffusion? c$.$ Set up the mass transfer problem with CV$,$ species, flux equation, governing equation, and boundary $/$initial conditions. d$.$ How many hours will it take for the solute A concentration to reach $2\mathrm{.}9$ mol$/$m$3$ at a depth of $0\mathrm{.}40$ cm from the surface of the pellet?