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Saponification in numbers: a worksheet for chemistry classes

Students balance the reaction of triolein with sodium hydroxide, work out a saponification value from molar masses, and then the lye for a real bar of soap. Every answer can be checked against the lye calculator, which writes out each step it takes. Free to print and copy for teaching.

What it covers

For students who have met moles and molar mass.

If the class makes soap Sodium hydroxide is corrosive to skin and eyes, and freshly mixed lye solution can pass 90 °C within moments. Follow your school’s risk assessment. Handling lye safely covers goggles and gloves, the lye into the water and never the reverse, and what to do about a splash.

Worksheet: saponification in numbers

Given: C 12.011, H 1.008, O 15.999, Na 22.990 g/mol. NaOH 39.997 g/mol, KOH 56.106 g/mol.

  1. Triolein, C₅₇H₁₀₄O₆, is the main fat in olive oil: glycerol carrying three oleic acid chains. Write the balanced equation for its reaction with sodium hydroxide, which gives glycerol (C₃H₈O₃) and sodium oleate (C₁₈H₃₃NaO₂).

  2. Work out the molar masses of triolein, glycerol and sodium oleate.

  3. How many grams of sodium hydroxide does 100 g of triolein need?

  4. How many grams of soap and of glycerol does that make? Show that mass is conserved.

  1. A fat’s saponification value is the milligrams of potassium hydroxide that 1 g of it takes. Work out triolein’s.

  2. The Codex Alimentarius standard for olive oil gives its saponification value as 184 to 196 mg KOH/g. Give two reasons it is a range rather than one number.

  3. The calculator uses 190 mg KOH/g for olive oil. Convert that to grams of sodium hydroxide per gram of oil.

  1. A bar is made from 350 g of olive oil (190 mg KOH/g) and 150 g of coconut oil (256.5 mg KOH/g). How much sodium hydroxide saponifies all of it?

  2. Soapmakers weigh 5 % less lye than that, which leaves 5 % of the fat unreacted: the superfat. How much sodium hydroxide do they weigh? Why would a maker leave fat unreacted on purpose?

  3. The sodium hydroxide is dissolved in water to make a 33 % solution by mass. How much water is that?

  4. Coconut oil’s saponification value is higher than olive oil’s. What does that tell you about its fatty acids?

  1. Open the lye calculator with this bar, then “Show the working”. Find each step you worked out. Where does the calculator’s figure differ from yours, and why?

    Open the lye calculator with this bar

From soapformulator.com/teach

Answers
  1. C₅₇H₁₀₄O₆ + 3 NaOH → C₃H₈O₃ + 3 C₁₈H₃₃NaO₂. Each hydroxide breaks one ester bond, so three per molecule.
  2. Triolein 885.45 g/mol; glycerol 92.09 g/mol; sodium oleate 304.45 g/mol.
  3. 100 g ÷ 885.45 g/mol = 0.1129 mol; × 3 × 39.997 g/mol = 13.55 g of sodium hydroxide.
  4. Sodium oleate: 0.1129 × 3 × 304.45 = 103.15 g. Glycerol: 0.1129 × 92.09 = 10.40 g. In: 100 + 13.55 = 113.55 g; out: 103.15 + 10.40 = 113.55 g.
  5. 3 × 56.106 × 1000 ÷ 885.45 = 190.1 mg KOH/g.
  6. Olive oil is a mixture: besides oleic acid its triglycerides carry palmitic, linoleic and other acids (the Codex allows 7.5–20 % palmitic and 3.5–21 % linoleic). Shorter chains mean more molecules per gram, and so more hydroxide per gram, and the mix changes with the olive variety, the place and the year. And a little of the oil (sterols, squalene) never saponifies at all, which lowers the figure.
  7. 190 × 39.997 ÷ 56.106 = 135.4 mg, so 0.1354 g of sodium hydroxide per gram of oil.
  8. KOH: 350 × 0.190 + 150 × 0.2565 = 104.98 g. As sodium hydroxide: 104.98 × 39.997 ÷ 56.106 = 74.83 g.
  9. 74.83 × 0.95 = 71.09 g. Published saponification values are ranges, and a real oil may take more lye than the figure used. With fat left over, the bar cannot be left holding unreacted sodium hydroxide, even when the oil takes more than was assumed.
  10. 71.09 g is 33 % of the solution, so the solution weighs 71.09 ÷ 0.33 = 215.43 g and the water 215.43 − 71.09 = 144.34 g (or 71.09 × 67 ÷ 33).
  11. More hydroxide per gram means more fatty-acid chains per gram, so the chains are shorter: coconut oil is mostly lauric acid (C12, 45–53 % in the Codex), where olive oil is mostly oleic acid (C18).
  12. The steps match to rounding: 104.98 g of KOH equivalent, 74.83 g of NaOH with no superfat and 71.09 g at 5 %, 144.34 g of water; the calculator rounds what it shows. It also shows how far the lye could move across the oils’ published ranges, which is the reason for question 9.

Taking it further