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Sample and charge
The ore sample, its true gold grade and the flux recipe. A lead button of 25 to 35 g is the usual aim.
Furnace
Fusion and cupellation temperatures and the size of the bone-ash cupel.
Process time
Move through the three stages, or press Play.
Layers
Model checks
The science
What a fire assay does
Gold in an ore is far too thinly spread to weigh directly. Fire assay concentrates it in three steps: fusion in a crucible at about 1,150 °C, cupellation at about 950 °C, and parting with nitric acid. The result is a bead of pure gold whose mass, divided by the sample mass, is the grade.
1. Fusion: litharge, flour and the lead button
The charge is ore plus litharge (PbO), borax and soda ash as flux, and flour as the reducing agent. Carbon in the flour reduces some litharge to metallic lead: C + 2 PbO → 2 Pb + CO2. The heavy lead droplets fall through the molten slag, collect gold and silver on the way and join into a button at the bottom. The mass of lead is therefore tied to the flour: mPb = mflour fC (2 × 207.2 / 12.011) η, with carbon fraction fC = 0.40 and a reduction efficiency η. The rest of the litharge stays in the slag, so lead atoms are conserved: lead in the button plus lead left as PbO equals lead in the litharge charged. Collection of gold from the melt follows an S-curve in fusion temperature (a teaching model: 50 % at 1,050 °C).
2. Cupellation: oxidising the lead away
The button goes into a porous cupel of bone ash in a hot oxidising furnace. Lead oxidises to PbO (2 Pb + O2 → 2 PbO), the liquid litharge soaks into the cupel, and the noble metals stay behind as a bead. The oxidising surface of the button scales as m2/3, so dm/dt = -k(T) m2/3, which integrates exactly to m(t) = (m01/3 - k t / 3)3 and takes t = 3 m01/3 / k. The rate constant follows an Arrhenius law with Ea = 150 kJ/mol. A cupel absorbs about its own mass of litharge; if the button makes more PbO than that, the cupel is saturated and lead is left in the bead.
3. Losses
Too cold (below about 880 °C) the button freezes before the lead is gone. Too hot, silver and a little gold are lost into the cupel and lead vapour carries metal away. The curves in the third graph are smooth teaching models of these two effects, centred on the 950 °C that assayers choose.
4. Inquarting, parting and the assay ton
A gold bead with too little silver will not part cleanly, so silver is added so that the ratio Ag : Au is about 3 : 1. Hot nitric acid dissolves the silver and leaves the gold. The grade is c = mAu / msample. One assay ton is 29.167 g, chosen so that each milligram of gold from one assay ton means exactly one troy ounce per short ton: 1 mg / 29.167 g = 34.286 g/t = 31.1035 g / 907.185 kg.
Model checks on this page
(1) Lead atoms are counted in moles before and after fusion. (2) The cupellation time from stepping the differential equation with RK4 is compared with the closed form. (3) The assay-ton conversion is recomputed from the troy ounce and the short ton.
Honest simplifications
Real assays depend on ore chemistry (sulphides, tellurides, copper), slag acidity, crucible attack and operator skill. The efficiencies, S-curve and loss laws here are teaching approximations, not laboratory constants; only the stoichiometry, the m2/3 rate law and the unit conversion are exact.
What to try
Set the flour to 0 and see no lead button forms. Raise it until the button reaches 25 to 35 g. Shrink the cupel until it saturates and watch lead stay in the bead. Lower the cupellation temperature below 880 °C and the button freezes; raise it above 1,000 °C and the silver and gold losses climb. Try a very low grade (1 g/t) with one assay ton and look at the bead mass in the last graph: it is only a few hundredths of a milligram.