Example 5: XANTHAN GUM PRODUCTION
Xanthan gum is produced using \textit{Xanthomonas campestris} in batch culture. Laboratory experiments
have shown that for each gram of glucose utilized by the bacteria, 0.23 g oxygen and 0.01 g ammonia
are consumed, while 0.75 g gum, 0.09 g cells, 0.27 g gaseous $CO_2$, and 0.13 g $H_2O$ are formed.
Other components of the system such as phosphate can be neglected. Medium containing glucose and
ammonia dissolved in 20,000 liters of water is pumped into a stirred fermenter and inoculated with
\textit{Xanthomonas campestris}. Air is sparged into the fermenter; the total amount of off-gas recovered
during the entire batch culture is 1250 kg. Because xanthan gum solutions have high viscosity and are
difficult to handle, the final gum concentration should not be allowed to exceed 3.5 wt%.
(a) How much glucose and ammonia are required?
(b) What percentage of excess air is provided?
1 g glucose + 0.23 g $O_2$ + 0.01 g $NH_3$
$\rightarrow$ 0.75 g gum + 0.09 g cells + 0.27 g $CO_2$ + 0.13 g $H_2O$
