A waste stream of alcohol vapor in air from a process was adsorbed by activated carbon particles in a packed bed having a diameter of $4cm$ and length of $10cm$ containing $50g$ of carbon. The inlet gas stream having a concentration $c_o$ of $700ppm$ and a density of

$0\mathrm{.}002\frac{g}{c}{m}^3$ entered the bed at a flow rate of $800c\frac{m^3}{s}.$ Data in Table $1$ gives the concentrations of the breakthrough curve. The break$-$point concentration is set at $\frac{c}{c_o}=0\mathrm{.}05.$ Do as follows:

a$.$ Determine the break$-$point time, the fraction of total capacity used up to the break point, and the length of the unused bed. Also, determine the saturation loading capacity of the carbon.

b$.$ If the break$-$point time required for a new column is doubled, what is the new total length of the column required?

c$.$ Repeat a$.$ and b$.$ if the break$-$point concentration is halved