$7\mathrm{.}6$ Prediction of the Break$-$Point Time in Fixed$-$Bed Adsorption At low concentra$-$

tions, the equilibrium for the antibiotic novobiocin and Dowex $21K$ anion exchange resin

is linear,

$q_i=125c_i^{**}$

for $q_i$ and $c_i^{**}$ in units of milligrams per milliliter. For the range of concentrations

where this isotherm is valid, the mass transfer coefficient $K_a$ averages $82h^{-1}.$ Assuming

a linear isotherm, estimate the break$-$point time $($where $\frac{c_i}{c_{i0}}=0\mathrm{.}05)$ in a fixed$-$bed

adsorber with a bed length of $20cm$ and superficial velocity of $40c\frac{m}{h}.($Data from

P$.$ A$.$ Belter, F$.$ L$.$ Cunningham, and J$.$ W$.$ Chen, "Development of a recovery process

for novobiocin," Biotechnol. Bioeng., vol. $15,$ p$.533,1973.)$