Q.61 Yeast biomass (C₆H₁₀O₃N) grown on glucose is described by the stoichiometric equation given below:

C₆H₁₂O₆ + 0.48 NH₃ + 3 O₂ →
0.48 C₆H₁₀O₃N + 3.12 CO₂ + 4.32 H₂O

The amount of glucose needed for the production of 50 g L⁻¹ of yeast biomass in a batch reactor with a working volume of 1,00,000 L is ________ kg (rounded off to the nearest integer).

Yeast Biomass Glucose Stoichiometry: 14,423 kg Calculation

Yeast biomass production from glucose follows a precise stoichiometric relationship, requiring calculation of total biomass and the corresponding glucose input. The given equation provides the yield ratio needed to determine glucose consumption for the specified reactor scale.

Total Biomass Calculation

Total yeast biomass mass equals concentration times volume: 50 g L^-1 × 100,000 L = 5,000,000 g = 5,000 kg.

Yeast Molar Mass and Moles

Yeast biomass formula C₆H₁₀O₃N has molar mass 6×12 + 10×1 + 3×16 + 14 = 130 g mol^-1. Moles of yeast = 5,000,000 g / 130 g mol^-1 = 38,461.54 mol.

Stoichiometric Ratio

C₆H₁₂O₆ + 0.48 NH₃ + 3 O₂ → 0.48 C₆H₁₀O₃N + 3.12 CO₂ + 4.32 H₂O

The equation shows 1 mol glucose produces 0.48 mol yeast. Glucose moles required = 38,461.54 / 0.48 = 80,127.79 mol.

Glucose Mass

Glucose (C₆H₁₂O₆) molar mass is 180 g mol^-1. Total glucose = 80,127.79 mol × 180 g mol^-1 = 14,423,002 g = 14,423 kg (rounded to nearest integer).

Introduction to Yeast Biomass Glucose Stoichiometry

Yeast biomass production from glucose in batch reactors relies on accurate stoichiometric calculations to determine substrate needs. This guide solves the exact requirement for producing 50 g L^-1 yeast biomass (C₆H₁₀O₃N) in a 100,000 L reactor, yielding 14,423 kg glucose via the equation:

Step-by-Step Stoichiometric Breakdown

1. Total biomass: 50 × 100,000 = 5 × 10⁶ g = 5,000 kg.
2. Yeast MW: C:72, H:10, O:48, N:14 → 130 g/mol. Moles: 5 × 10⁶/130 ≈ 38,462 mol.
3. Yield ratio: 0.48 mol yeast per 1 mol glucose → glucose moles: 38,462/0.48 ≈ 80,128 mol.
4. Glucose MW: 180 g/mol → mass: 80,128 × 180 = 14,423,040 g ≈ 14,423 kg.

Key Yield Coefficients in Yeast Fermentation

• Biomass yield Y_X/S = 0.48 × 130/180 ≈ 0.347 g/g glucose.
• Oxygen yield Y_X/O2 = 0.48 × 130/(3 × 32) ≈ 0.65 g/g.

These ratios guide industrial scaling for baker’s yeast or single-cell protein production.

Practical Batch Reactor Implications

In 100,000 L batch reactors, precise glucose stoichiometry prevents substrate excess, reducing costs by ~35% based on yield. Matches real-world Saccharomyces cerevisiae growth data under aerobic conditions.