Mass balances and rates in a fermenter (15 points). In a batch fermentation with yeast (X) using substrate (S), a valuable pharmaceutical product (P) is produced. The volume of the culture is constant at 250 L. The experimental data for your process is shown below:

t (h)	S (g/L)	X (g/L)	P (g/L)
0.0	50.0	0.13	0.00
0.2	50.0	0.13	0.00
0.4	50.0	0.13	0.00
0.6	50.0	0.13	0.00
0.8	50.0	0.17	0.00
1.0	49.9	0.21	0.00
1.2	49.9	0.27	0.00
1.4	49.8	0.34	0.01
1.6	49.8	0.43	0.01
1.8	49.7	0.55	0.01
2.0	49.6	0.70	0.01
2.2	49.4	0.89	0.02
2.4	49.3	1.13	0.02
2.6	49.0	1.43	0.03
2.8	48.7	1.82	0.04
3.0	48.4	2.32	0.05

*Units for X are in grams dry cell weight per L.

(8) In the region of exponential growth, calculate the following specific rates: m^max, qsmax , and qpmax .

(2) In the region of exponential growth, what is the yield of grams P produced per grams S consumed?

(3) At t=5h, what are the concentrations of X and P in the fermenter?

(2) Suppose you scale up the process from 250 L to 1,000 L. The 1,000 L is operated at the same process conditions (temperature, pH, initial concentrations, etc.) as the 250 L process. At the 1,000 L scale, what is q_S? At the 1,000 L scale, how many grams of S are in the fermenter at t=5h?