Glucose is converted to ethanol in a packed$-$bed reactor using immobilized S$.$ cerevisiae cells entrapped in Ca$-$alginate beads. The specific rate of ethanol formation is $0\mathrm{.}15$ g ethanol$/$g cell$-$h$,$ and the average cell concentration in the alginate bead is $25$ g$/$L and the alginate beads occupy $70\%$ of the bed volume $($the other $30\%$ is liquid that the feed flows through$).$ Assume that growth is negligible so that the cell concentration is constant, and that the bead sizes are sufficiently small such that the no diffusion limitation of substrate and product in the bead. The feed flow rate is F$=400$ L$/$h and contains glucose at a concentration of $100$ g$/$L$,$ the bed diameter is $1$ m$,$ and the bed length is $5$ m$.$ Glucose is converted into ethanol at a yield of $0\mathrm{.}5$ g ethanol$/$g glucose. Determine the glucose and ethanol concentrations at the exit of the bed.