Yeast Growth on Glucose — Observed vs. Maintenance-Corrected Yields: 04-BS-13, Undated paper, Q4

Question 4: Yeast Growth on Glucose — Observed vs. Maintenance-Corrected Yields (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

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The printed "molecular weight of yeast = 25 g/mol" does not match the yeast biomass formula given in the same equation, C₄H₇NO₂ (computed MW = 4(12)+7(1)+14+2(16) = 101 g/mol) — a misprint. MW = 101 g/mol is used throughout (all three other given MWs — glucose 180, ethanol 46, glycerol 92 — check exactly against their formulas, confirming only the yeast value is corrupted). The product yield in part (b) is taken as the ethanol yield, since ethanol is the fermentation product of interest formed even under the aerobic (Crabtree-type overflow) conditions described.

Given.

Quantity	Value
Glucose, MW	180 g/mol
Yeast (C₄H₇NO₂), MW	101 g/mol (corrected; printed 25 g/mol fails the formula check)
Ethanol, MW	46 g/mol
Glycerol, MW	92 g/mol
Yeast, glycerol coefficients	0.43 gmol/gmol glucose each
Ethanol coefficient	0.035 gmol/gmol glucose
μ_max, m_e, m_p	0.4 h^-1, 0.2 h^-1, 0.1 h^-1

Find. (a) Y_XS and Y'_XS; (b) Y_PS and Y'_PS (ethanol).

Approach. Convert the molar stoichiometric coefficients to mass yields using the (corrected) molecular weights, then apply the Pirt-type maintenance correction to each yield — the same $1/Y_{obs} = 1/Y_{true} + m/\mu$ form used for biomass in Q3, applied here with $m_e$ for biomass and $m_p$ for product.

(a) Biomass yield, observed and maintenance-corrected. $$Y_{XS} = \frac{0.43 \times 101}{180} = \boxed{0.241 \text{ g/g}}$$ $$\frac{1}{Y'_{XS}} = \frac{1}{Y_{XS}} - \frac{m_e}{\mu_{max}} = \frac{1}{0.241} - \frac{0.2}{0.4} = 4.144 - 0.500 = 3.644\ \Rightarrow\ Y'_{XS} = \boxed{0.274 \text{ g/g}}$$
(b) Product (ethanol) yield, observed and maintenance-corrected. $$Y_{PS} = \frac{0.035 \times 46}{180} = \boxed{0.00894 \text{ g/g}}$$ $$\frac{1}{Y'_{PS}} = \frac{1}{Y_{PS}} - \frac{m_p}{\mu_{max}} = \frac{1}{0.00894} - \frac{0.1}{0.4} = 111.8 - 0.25 = 111.55\ \Rightarrow\ Y'_{PS} = \boxed{0.00896 \text{ g/g}}$$ Since $Y_{PS}$ is already small, the maintenance term ($m_p/\mu_{max}=0.25$) is a much smaller relative correction here than for biomass — ethanol formation in this system is overwhelmingly growth-associated, with only a small maintenance-driven contribution.

Quantity	Value
Y_XS (observed)	0.241 g/g
Y'_XS (maintenance-corrected)	0.274 g/g
Y_PS, ethanol (observed)	0.00894 g/g
Y'_PS, ethanol (maintenance-corrected)	0.00896 g/g
(for reference) Y glycerol	0.220 g/g

Topic: Mass-yield coefficients from stoichiometry and the Pirt maintenance correction, applied to both biomass and product.

Key relations: $Y_{i/S} = (\nu_i M_i)/(\nu_S M_S)$ from a balanced equation; $1/Y_{obs}=1/Y_{true}+m/\mu$ for any yield, biomass or product.

Why this works: Observed stoichiometric coefficients already embed the maintenance substrate draw at the specific $\mu$ the equation was measured at; the Pirt correction backs that out to recover the maintenance-free (true, maximal) yield.

Common pitfall: Using an uncorrected/garbled molecular weight (as printed for yeast here) silently propagates into every downstream yield — always sanity-check a given MW against its own stated molecular formula.

Source: Shuler & Kargi, Bioprocess Engineering: Basic Concepts, Ch. 6 (Pirt maintenance model, Luedeking–Piret product formation).

Question 4 of 9: Yeast Growth on Glucose — Observed vs. Maintenance-Corrected Yields

Question 4: Yeast Growth on Glucose — Observed vs. Maintenance-Corrected Yields (20 marks)