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Bath bombs

Two parts bicarbonate to one part citric acid is the rule everybody repeats. The reaction wants 1.31 parts, so the usual mix carries about half again more bicarbonate than the acid can use. That is fine — the surplus is filler and buffer — but it means adding more of it does nothing at all for the fizz.

The two reagents
g
Sodium bicarbonate, NaHCO3
g
Anhydrous. The monohydrate carries water and weighs more per mole — convert first.
The rest of the dry mix
g
Cornflour, SLSA, clay, salts
g
A mica, an oxide, a lake or a dye, as powder: only one permitted for cosmetics where you sell.
Liquids

Water starts the reaction, so this is the part that decides whether it sets in the mould or fizzes in the bowl.

g
g
g
Your mould
cm
The size the mould is sold at. Both halves together make one sphere.
g/cm³
Weigh one finished bomb from your own mould and divide by its volume.

fill in the bicarbonate and the citric acid

Ingredient list
By its CI number, as its supplier’s data sheet gives it (CI 77491). It goes after the other ingredients; a US label names it as its FDA listing does (Iron Oxides).

Several ingredients in one line: their names comma-separated, heaviest first.

Calculated at soapformulator.com, every value sourced. Check the figures against your own scale.

The formula, and where it comes from 
3 NaHCO₃ + H₃C₆H₅O₇ → Na₃C₆H₅O₇ + 3 CO₂ + 3 H₂O

bicarbonate needed = citric acid × 3 × M(NaHCO₃) ÷ M(citric acid)
                   = citric acid × 1.3118
CO₂                = (citric acid consumed ÷ 192.124) × 3 × 44.009
liquids %          = Σ liquids ÷ total × 100
colour %           = colour ÷ total × 100          # held to its supplier's maximum
bombs              = ⌊total ÷ (V × ρ)⌋            # V = π/6 × d³
  • Neutralisation of citric acid by sodium bicarbonate: 3 NaHCO₃ + H₃C₆H₅O₇ → Na₃C₆H₅O₇ + 3 CO₂ + 3 H₂O. Molar masses NaHCO₃ 84.007 g/mol, anhydrous citric acid 192.124 g/mol, CO₂ 44.009 g/mol (IUPAC 2021 standard atomic weights).
  • The craft’s 2:1 bicarbonate-to-citric-acid ratio by weight. A convention, and deliberately bicarbonate-rich: the surplus is filler and buffer, not reagent. — Not the stoichiometric ratio, which is 1.312:1.
  • Working convention: total liquid ingredients around 1–4 % of the mix. Below it the bomb crumbles; above it the reaction starts in the bowl. — Strongly dependent on humidity, on whether the liquid is water-based or anhydrous, and on how fast it is mixed in. A habit of the craft, not a measured threshold.
  • Only a colour permitted for cosmetics: in the EU and Great Britain one listed in Annex IV of Regulation (EC) No 1223/2009 and used under its conditions (Art. 14(1)(c)); in the US one listed for cosmetics in 21 CFR 73 Subpart C, or in 74 Subpart C from certified batches. How much goes in is its supplier’s figure: 21 CFR 73.2496 lets mica colour cosmetics “in amounts consistent with good manufacturing practice”, with no number. — Micas, oxides, lakes and dyes are used at rates too far apart for one figure to stand for them, so the engine has none of its own.
  • Packing density of a pressed bath bomb, ≈ 1.1–1.4 g/mL depending on press force. The default assumes hand-packed spheres. — Calibrate by weighing one finished bomb from your own mold.

The reaction

Three molecules of bicarbonate for one of citric acid, giving sodium citrate, water and three of carbon dioxide. By weight that is 1.312 g of bicarbonate per gram of acid.

Why the surplus is not waste

The bicarbonate the acid cannot reach gives the bomb its body and its float, and buffers the bath. Cutting it to the reaction’s ratio makes a small, dense bomb that fizzes hard and briefly.

Setting in the mould

Around one to four per cent liquid is where most makers work. Below it the bomb crumbles; above it the reaction starts while you are still mixing. Humidity moves the whole window, so the figure that worked in January may not in July.

Common questions

Is 2:1 wrong, then?
No. It is just not the reaction’s ratio, and knowing the difference tells you which ingredient actually changes the fizz. At 2:1 the acid is the limit, so more acid gives more fizz and more bicarbonate gives none.
I have citric acid monohydrate.
It is 210.14 g/mol against 192.12 for the anhydrous, so 100 g of monohydrate is 91.4 g of acid. Enter that figure. The water it carries also counts towards your liquids.
How much gas is that, really?
A 120 g bomb at 2:1 gives roughly 27 g of carbon dioxide, about 15 litres at bath temperature. It comes off over a minute or two rather than at once, which is why the bomb travels around the tub.
What is the fragrance limit?
A bath bomb is IFRA category 9, the same as bar soap. The figure itself is on your supplier’s certificate of conformity and differs per fragrance; the fragrance and allergens page works it out against the finished weight.

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