A litre of vegetable oil (about 1.04 mol) needs at least 3 mol of methanol, which is 126 mL, to become methyl esters, and the parent’s 200 mL is a 4.8-to-1 mole ratio that pushes the reversible reaction to completion. The mass balance gives 10.4% of the oil’s mass as glycerol and 924 g of esters from 920 g of oil, and shows that 3.5 g of NaOH equals 4.9 g of KOH, so the parent’s 7 g of KOH is 1.4 times too much.
Part of Biodiesel Production
The quantitative balance of the transesterification reaction: molar masses, reagent amounts, product masses and what the parent’s rules of thumb imply.
The Reaction And Its Molar Masses
Take the oil as triolein, C₅₇H₁₀₄O₆, a standard stand-in for a vegetable oil’s average triglyceride. Atomic masses: C 12.011, H 1.008, O 15.999, Na 22.990, K 39.098.
| Substance | Formula | Molar mass (g/mol) |
|---|---|---|
| Triglyceride (triolein) | C₅₇H₁₀₄O₆ | 885.45 |
| Methanol | CH₃OH | 32.04 |
| Fatty acid methyl ester (methyl oleate) | C₁₉H₃₆O₂ | 296.49 |
| Glycerol | C₃H₈O₃ | 92.09 |
| NaOH | 40.00 | |
| KOH | 56.11 |
Triglyceride + 3 CH₃OH → 3 methyl ester + glycerol. Mass check: 885.45 + 3 × 32.04 = 981.58 and 3 × 296.49 + 92.09 = 981.56. The two sides agree to rounding, so the formulas are balanced.
Per Litre Of Oil
Assume a density of 0.92 kg/L for oil (a typical recalled figure; use your own oil’s), 0.792 for methanol and 0.88 for the esters (recalled).
- Moles of oil: 920 g ÷ 885.45 = 1.039 mol, about 1.04 mol.
- Methanol needed: 3 × 1.039 = 3.117 mol × 32.04 = 99.9 g = 99.9 ÷ 0.792 = 126 mL.
- The parent’s 200 mL = 158.4 g = 4.94 mol, a ratio of 4.94 ÷ 1.039 = 4.8 to 1 against the stoichiometric 3 to 1. About 74 mL per litre of oil (200 − 126) is excess that is later removed or recovered.
- Esters made: 3.117 mol × 296.49 = 924 g (more than the 920 g of oil, because each ester carries a methyl group from methanol). At 0.88 kg/L that is 924 ÷ 0.88 = 1,050 mL: 1.05 L of biodiesel per litre of oil if nothing is lost. The parent’s “about 1:1” is a fair working figure once washing, soap and glycerin carry-over take their share.
- Glycerol made: 1.039 × 92.09 = 95.7 g, which is 95.7 ÷ 920 = 10.4% of the oil’s mass and 95.7 ÷ 924 = 10.4% of the biodiesel’s. For 10 L of biodiesel (8.8 kg at 0.88 kg/L) that is 8.8 × 0.104 = 0.91 kg of glycerol, 0.91 ÷ 1.26 = 0.72 L of pure glycerol. The parent’s 1-1.5 L of “glycerin” per 10 L of biodiesel therefore implies the crude layer is about 48-72% glycerol by volume (0.72 ÷ 1.5 to 0.72 ÷ 1.0), the rest being soap, methanol, lye and water. It is consistent.
The Catalyst: Where The Parent’s KOH Figure Goes Wrong
The lye is a catalyst, so its amount is set by chemistry of the oil’s acidity and by convention, not by 1:1 stoichiometry. But NaOH and KOH do the same job mole for mole, so equivalent masses follow from molar masses:
- 3.5 g NaOH = 3.5 ÷ 40.00 = 0.0875 mol, about 8.4% of the moles of oil.
- The same moles of KOH: 0.0875 × 56.11 = 4.9 g. The ratio is 56.11 ÷ 40.00 = 1.40, so KOH is needed at 1.4 times the NaOH mass.
- The parent gives 7 g of KOH per litre, which is 0.1248 mol, 1.43 times the NaOH figure in moles. Either the KOH figure is double what it should be, or it is intended as a higher dose. This page cannot say which; it flags the 7 g as inconsistent with the 3.5 g NaOH rule and uses 4.9 g where equivalence is meant. The titration method that follows is derived for NaOH and must also be scaled by 1.40 for KOH (Oil Preparation & Titration).
Free fatty acid consumes base mole for mole: 1 g of NaOH (0.025 mol) neutralises 0.025 × 282.46 = 7.06 g of oleic acid, which is 0.77% of a 920 g litre of oil (Free Fatty Acid Problem).
Ethanol Instead Of Methanol
Ethanol (46.07 g/mol) can in principle replace methanol: 3.117 mol × 46.07 = 143.6 g, 182 mL per litre of oil, 1.44 times the methanol volume at the same mole count. It must be nearly water-free, which is the work of Dehydration to Fuel Grade, and ethyl esters separate less readily from glycerin. The corpus has no sourced procedure for it and this page does not write one. Its importance: methanol in a post-collapse world is a finite salvaged stock (the parent’s equipment list says “salvage from fuel and solvent stores”) while ethanol can be made (Ethanol Fuel Production).
Energy Check
200 mL of methanol is 158.4 g; at about 19.9 MJ/kg that is 3.15 MJ. A litre of biodiesel holds about 37 MJ/kg × 0.88 = 32.6 MJ (recalled heating value). The methanol is therefore about 9.7% of the fuel’s energy, partly carried into the product and partly recoverable. Farm and press energy is not counted here.
Sources And Assumptions
- Atomic masses (standard values).
- Densities 0.92 (oil), 0.792 (methanol), 0.88 (esters), 1.26 (glycerol) and heating values 19.9 and 37 MJ/kg are recalled constants, not opened.
- Triolein as a stand-in for the oil: a real oil is a mixture, so the figures move a few per cent.
The numbers are for planning, not for handling
Every reagent here is hazardous. Methanol is toxic through skin and vapour and blinds, lye burns, and the mixture is flammable; see Methanol Hazards and work only with eye protection, gloves and ventilation, away from flame.
What’s Next
- Learn next: Lye Catalyst, for using these figures in practice
- Combine with: Free Fatty Acid Problem, the main reason the real dose differs