Question $1$

An absorption tower is used to remove contaminant A from the effluent of a wastewater stream.

Here a solvent is contacted with the gas stream so that the concentration of contaminant in the

solvent increases along the column. The spatial profile of the concentration of $A$ in the solvent along

the column $($with $3m$ height$)$ is described as:

$\frac{d^2{C}_A}{d{z}^2}-4\frac{d{C}_A}{dz}+3C_A=2z-f$

where $C_A$ is the concentration of $A$ in the solvent, and $z$ is the axial position. $f$ is an identifier

dependent on the last digit of your URN.

As an example, students with last digit of URN of $1$ use $f=1.$

a$)$ Develop an algebraic equation to represent $C_A=f(z).$ The equation should contain two

constants, namely A and $B.$

b$)$ Both constants are derived from experimental measurements, but concentrations inside the

column are not practically measurable. Propose suitable boundary conditions to evaluate

both constants.

c$)$ Based on your answer in part $($b$),$ if the inlet concentration of $A$ in the solvent is $2mo\frac{l}{L},$

create a plot $($using MS Excel$)$ to represent $C_A=f(z).$