Problem $4(20$ pts$)$

A $10-$liter stirred tank is used to cultivate mouse myeloma cells. Dry air is sparged from the bottom at $1$

$\frac{L}{m}in$ to supply $O_2$ to the system. The gas composition of the outlet is $16\%$ of $O_2,3\mathrm{.}5\%C{O}_2,6\mathrm{.}5\%$ wa$-$

ter vapor and the balance $N_2.$ The ambient pressure and temperature are $1$atm and $37C.$ The dissolved

$O_2$ in the reactor is controlled at $20\%$ of saturation with ambient air.

$($a$)$ Assuming steady state, what is the volumetric $O_2$ transfer coefficient $K_{L}a?$

$($b$)$ The specific OUR of myeloma cells is $5{10}^{-11}$mmo$\frac{l}{c}$ell$-h.$ What is the cell concentration?

$($c$)$ What is the respiratory quotient $($RQ$)?$ Assume that the mole fraction of $C{O}_2$ in the ambient air is

negligible. The universal gas constant $R=0\mathrm{.}082L^{**}at\frac{m}{m}ol-K.$