Saccharomyces cerevisiae is cultured in a chemostat (continuous

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Saccharomyces cerevisiae is cultured in a chemostat (continuous fermentation) at a dilution rate of 0.5 h^–1. The feed substrate concentration is 10 g.L^–1. The biomass concentration in the chemostat at steady state will be _________g.L^–1.
Assumptions : Feed is sterile, maintenance is negligible and maximum biomass yield with respect to substrate is 0.4 (g biomass per g ethanol).
Microbial growth kinetics is given by
μ = μ_m S
K_s + S

where µ is specific growth rate (h^–1), µ_m = 0.7 h^–1, K_s = 0.3 g.L^–1 and s is substrate concentration (g.L^–1).

1. 1.15 to 2.25
2. 9.65 to 10.75
3. 3.65 to 3.75
4. All of the above

Correct Option: C

(1) X = X_{X / S}		S_R -	K_sD
			μ_m - D

(2) Here X_{X / S} = 0.4	g biomass
	g ethanol

S_R = 10 gL^–1
k_S = 0.3 g L^–1
D = 0.5 h^–1
µ_m =0.7 h^–1

(3) ∴ X = 0.4		10 -	(0.3)(0.5)			= 3.70
			(0.7 - 0.5)