The Verification Venue · pointed at a number winemakers trust too much
The Fraction That Does the Protecting
The lab sheet says free sulphur dioxide: 40 milligrams per litre, so the wine is protected. It is not that simple. Only a small molecular slice of a free reading does the antimicrobial work, the size of that slice is fixed by pH alone, and across the ordinary wine range it collapses about fifteen-fold while the number on the sheet does not move at all.
Winemakers measure sulphur dioxide three ways and popular writing constantly conflates them. Total SO2 counts everything in the bottle. Free SO2 counts the part not yet tied up by acetaldehyde and sugars. Molecular SO2 is the sliver of the free pool still in the form of sulphurous acid, and that sliver is the only part that pushes back against bacteria and wild yeast. The lab reports the second number; the third is the one that matters. Below, the relationship is computed live from the acid equilibrium. Drag the pH and watch the protective fraction fall by an order of magnitude while the free reading you dosed to stays exactly where it was.
Five wines from one cellar, each at its own pH · 3.30
Representative mid-points of pH ranges commonly quoted for finished table wines; individual bottles land elsewhere. The tiles set pH only and say nothing about any particular wine. ↓
Molecular fraction of the free pool
3.13 %
of the free reading, set by pH alone
Molecular SO2 actually working (mg/L)
1.25 mg/L
status: meets working target
from 40 mg/L free at pH 3.30
Drag from 3.0 to 4.0 and the fraction falls roughly tenfold per unit of pH. The blue curve is a titration curve, not an arbitrary decline.
Doubling the free reading doubles the molecular slice at any fixed pH. No amount of extra dosing undoes what pH does to the fraction.
The quantity doing the work is the molecular fraction, written α. Sulphurous acid holds its proton in proportion to how much hydrogen ion the wine already carries, and that proportion has a closed form: α = 1/(1+10^(pH−pKa1)), where pKa1 is the first dissociation exponent of sulphurous acid. This page uses pKa1 = 1.81, a mid-range literature value for 25 °C. Published compilations disagree in the second decimal, and the true value drifts with temperature and ionic strength, so treat the second decimal as soft. The shape is a titration curve: at pH 3.0 the molecular share is 6.1 %; by pH 4.0 it is 0.6 %. Nothing about the sulphur in those two barrels differed. The hydrogen ions did it.
This is why the same free reading protects one barrel and abandons another. Dose a crisp white at pH 3.0 to 40 mg/L free and 2.43 mg/L is working. The identical dose in a flat red at pH 4.0 leaves 0.26 mg/L. The sheet shows the same number for both wines. The protection is not the same, and the gap is a 15-fold collapse across the range.
The inverted question: what free reading buys a fixed shield?
Turn the formula around, because that is the question a winemaker actually faces. Hold a target molecular concentration fixed and solve for the free SO2 each pH demands: F = M·(1+10^(pH−pKa1)). The demand climbs about tenfold per unit of pH, and every real wine has a ceiling: regulators cap totals, palates object sooner. Move the pH and watch where the requirement crosses your ceiling. Past that point the target is not difficult. It is arithmetically unavailable.
Free SO2 needed for the target
25.5 mg/L
at the current pH
Ceiling reached at pH
3.98
above this pH the target cannot be met
Around 0.8 mg/L molecular is a commonly quoted working target for table wines. It is a practitioner convention, not a constant of nature.
A stand-in for legal and sensory room combined. No legal figure is printed on this page; see the note below the panel.
Two honest flags. First, the ceiling here is deliberately a slider, not a fact: legal limits in the major wine regions are written against total SO2, which counts the bound pool as well as the free one, and sensory objections usually arrive before legal ones, so this page asserts no jurisdiction's number. Second, the three measurements are not interchangeable, and conflating them is the standard error in popular accounts: a total reading overstates what is available, a free reading overstates what is working, and only the molecular slice protects.
The check · every number recomputed in front of you
Every number on this page flows from one constant, pKa1 = 1.81, and one pair of formulas. The table recomputes the molecular fraction two independent ways in your browser: the closed form, and the same equilibrium solved as a mass balance by bisection with no shared code. The two columns must agree to within 1e-9; a cross is printed if they ever miss. This is a real comparison, not a decoration: change the constant in the source and the third column turns to crosses.
| pH | closing form % | mass balance % | agree (<1e-9) |
|---|
Your current selection, computed both ways:
What is exact: the speciation algebra at a fixed hydrogen-ion activity, its algebraic inversion, and the ceiling boundary formula. The offline verifier reproduces all of it independently, adds limit assertions (the fraction must approach 1 far below pKa1 and 0 far above, which is what makes the curve a titration curve rather than an arbitrary decline), reconciles the call battery, and exits non-zero on any miss. Run it yourself: node research/the-fraction-that-does-the-protecting/verify-the-fraction-that-does-the-protecting.mjs.
What's idealised here, and what's exactly true
Exactly true. For a monoprotic acid whose proton activity is pinned by the surrounding medium, the molecular fraction is exactly α = H/(H+Ka1), which rearranges to the form printed above. The inversion and the ceiling boundary are the same algebra solved the other way. The mass-balance column solves the identical equilibrium equation by bisection, so agreement between the columns certifies the arithmetic, not the chemistry.
Idealised. Wine is treated as a buffer that holds pH fixed while sulphur dioxide speciates. That is a good approximation because the acidity of wine is dominated by tartaric, malic and lactic acids, whose buffering dwarfs a sulphur dioxide addition, but a heavy addition does shift pH slightly and the page ignores that. The second dissociation of sulphurous acid (near neutral pH) is ignored; it is irrelevant below pH 4.5. Activity coefficients are taken as 1; the ionic strength of real wine shifts the effective pKa slightly. The pKa1 used is a 25 °C value and cellar temperatures differ, which moves it.
Representative, not universal. Published pKa1 values for sulphurous acid differ in the second decimal. Any of them produces the same curve shape and nearly the same fifteen-fold collapse across the wine range; the ordering of wines by protection survives the scatter, the third decimal does not. The 0.8 mg/L working target and the ceiling default are conventions rendered as sliders on purpose. Bound, free and total sulphur dioxide are distinct measurements, and this page uses the free measurement exclusively, defining it at every point it appears.