ethanol from wood

Ethanol from wood: yield versus theoretical

Problem

The first ethanol-from-cellulose plant (Germany, 1898) used dilute acid to hydrolyze cellulose to glucose.
It managed to produce 7.6 L of 100% ethanol per 100 kg of wood. We can assume that 50 % of the wood is
cellulose and that this can be hydrolyzed completely to same mass of glucose. The density of ethanol is $0.789\text{kg/L}$

$M_{\text{glucose}}=180\text{g/mol}$; $M_{\text{EtOH}}=46\text{g/mol}$.

Question: how far is this yield compared with the theoretical yield?

Solution

1. Reaction. Fermentation of glucose gives two ethanol and two CO₂ per glucose:

${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6⟶2{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}+2C{\mathrm{O}}_2$

2. Glucose available. Per 100 kg of wood we have 50 kg glucose:

$m_{\text{glucose}}=0.50\times 100\text{kg}=50\text{kg}=50\times 10^3\text{g}$

$n_{\text{glucose}}=\frac{50\times 10^3\text{g}}{180\text{g/mol}}=277.8\text{mol}$

3. Theoretical ethanol. Fermentation yields two moles of ethanol per mole of glucose:

$n_{\text{EtOH}}=2\times 277.8\text{mol}=555.6\text{mol}$

$m_{\text{EtOH}}=555.6\text{mol}\times 46\text{g/mol}=25.56\times 10^3\text{g}=25.6\text{kg}$

4. Actual ethanol. The reported volume expressed as mass:

$m_{\text{EtOH}}=7.6\text{L}\times 0.789\text{kg/L}=6.0\text{kg}$

5. Yield.

$\text{Yield}=\frac{6.0\text{kg}}{25.6\text{kg}}\approx 0.235=23.5\%$

Answer: the 1898 process reached about 23.5% of the theoretical yield.

Discussion

• The theoretical maximum is $\frac{2\times 46}{180}=0.51$ g ethanol per g glucose. The process gave about 0.12 g per g of glucose-equivalent.
• Possible reasons for the low yield: incomplete hydrolysis of cellulose, degradation of glucose by hot acid, lignin-derived fertmentation inhibitors, incomplete fermentation, and losses in distillation. Biomass used for growth and by-products (glycerol, acetic acid) also lowers the yield.
• Even in modern fermentations the practical limit is about 90–95% of theoretical, because some glucose supports cell growth and by-product formation.

Check questions

• Why is the theoretical yield 2 mol ethanol per mol glucose, and what happens to the other carbon?
• Which steps of the 1898 process would you change first to raise the yield?