In a fermentation process sugar $($A$)$ is converted to ethanol $($C$)$ in the presence of yeast $($B$)$ in a batch reactor. In

a simple model the process can be presented as:

$A+B4C+4C{O}_2,-r_A=k{C}_A{C}_B$

The starting solution contains $10$ weight percent of sucrose $(C_{12}{H}_{22}{O}_{11})$ in water.

a$.$ Find the reaction time needed to achieve $99\%$ conversion of the sucrose for an initial yeast

concentration of $10M.$ Initial experiment found that if the concentration of yeast is

maintained at $1M,$ the reaction takes $2$ hours to achieve $99\%$ conversion of sucrose.

Assume the density of the solution equals the density of water.

b$.$ Determine to total cycle time of the process. Use time values from Table $5\mathrm{.}3$ for $t_f,t_e,$ and

$t_c.$