Xanthan gum is produced using Xanthomonas campestris in batch culture. Laboratory

experiments have shown that for each gram of glucose utilized by the bacteria, $0\mathrm{.}23g$ oxygen

and $0\mathrm{.}01g$ ammonia are consumed, while $0\mathrm{.}75g$ gum, $0\mathrm{.}09$ cells, $0\mathrm{.}27$ gaseous $C{O}_2,$ and $0\mathrm{.}13g$

$H_{2}O$ are formed. Other components of the system, such as phosphate can be ignored.

Medium containing glucose and ammonia dissolved in $20,000L$ of $H_{2}O$ is pumped into a

stirred fermenter and inoculated with $x.$ campestris. Air is sparged into the fermenter. The

total amount of off$-$gas recovered during the entire batch culture is $1250kg.$ Because xanthan

gum solutions have high viscosity and are difficult to handle, the final gum concentration

should not exceed $3\mathrm{.}5wt\%.$

a$.$ How much glucose and ammonia are required?

b$.$ What percentage excess air is provided?