Salt, hydrate and free base: converting content so the numbers reconcile

One material, four numbers that are not interchangeable

The same vial can be described by four numbers that all call themselves purity or content, and they are not the same quantity. Anyone who has watched two laboratories disagree over a shipment has usually watched two of these being compared.

Only the last one is a ratio of peak areas. The first three are mass fractions, and each names a different total. Written without the basis, any of them is ambiguous, and a specification line that says 98.0% without saying which of the four it means cannot be tested reproducibly by a second laboratory.

The salt factor is a mass ratio, not a judgement about quality

A salt is the molecule plus a counter-ion, held in a fixed stoichiometry. The fraction of the weighed mass that is the parent molecule is a pure arithmetic ratio of molecular weights:

salt factor = molecular weight of the free base divided by the molecular weight of the salt form

For a monohydrochloride the denominator is the base plus 36.46; for a dihydrochloride, plus 72.92; for a monosodium salt, plus 22.99 minus the mass of the proton displaced. A hydrate adds 18.02 for every water of crystallisation, and a mixed form adds both. Nothing here depends on the supplier, the batch or the method, which is why the factor is the one part of the calculation that can be settled before any material exists.

Take a base of molecular weight 300.00 as an illustration. The numbers below follow from the arithmetic alone.

The last row is the one that catches people. A hydrochloride monohydrate delivers 84.6 grams of molecule per 100 grams of powder. A specification written on the free-base basis and a weighing performed on the salt are then 15 per cent apart before any analytical error is considered, and 15 per cent is far larger than the difference between a good batch and a marginal one.

The factor is only needed when the form on the certificate differs from the form the number is required in. It becomes a mistake when it is applied on top of a certificate that already assigns content on the free-base basis: the correction is then counted twice, and the standard comes out weaker than it should be.

Crystal water belongs to the form, not to the impurity profile

Water in a hydrate is not contamination. It is part of the repeating unit, present in a fixed ratio, and it leaves the crystal only when the form changes. That does not make it harmless to the calculation: in the monohydrate above, water occupies 5.67 per cent of the mass while carrying none of the molecule.

The distinction matters because two water figures are routinely read as one. Karl Fischer titration measures water. Loss on drying measures everything volatile under the test conditions, which includes residual solvent. For a stoichiometric hydrate the specification is expected to carry a water content test, and a procedure specific for water is preferred over loss on drying precisely because the two are not the same measurement. A lot that reads 0.4 per cent by loss on drying and 5.7 per cent by Karl Fischer is not inconsistent: one number counted only the free solvent, the other counted the crystal.

Two practical consequences follow. First, water has to be measured on the same lot and close in time to the content determination, because a hygroscopic solid picks up surface water after the vial is opened and the as-is content moves while the anhydrous content does not. Second, an anhydrous content figure is a statement about the molecule, not about the powder: it will happily report 99.5 per cent for a lot that is one fifteenth water, and a buyer who weighs against it will under-charge the weighing by exactly that fraction.

Where the basis changes a pass into a fail

Impurity thresholds are expressed as a percentage of the drug substance and, for some thresholds, as a milligram daily intake. Both readings move when the basis moves. With the monohydrochloride factor above, a limit written as 0.10 per cent on the free-base basis is 0.089 per cent of the salt, and a result of 0.098 per cent on the salt basis is 0.110 per cent on the base. The same material, measured once, passes under one reading of the specification and fails under the other. Nothing about the sample changed; only the denominator did.

The daily intake version drifts the same way. An impurity at 0.10 per cent of a 500 mg dose of salt is 0.50 mg per day. Described as 446 mg of free base, the same absolute amount is 0.446 mg per day. That difference of 0.054 mg is not noise when a threshold sits at 1.0 mg per day and a product is dosed at the edge of it.

Two habits prevent most of this. Write the basis into the specification line itself, next to the limit, so the number cannot travel without its denominator. And state which form the dose refers to whenever a limit is converted to a daily intake, because a dose of a salt is not a dose of a base.

Area per cent and mass balance never reconcile on their own

A chromatographic area per cent is the target peak divided by the sum of all integrated peaks. Its denominator is the material that reached the detector, so water, chloride and inorganic residue are simply absent from it. A mass balance content starts from 100 and subtracts every measured fraction:

content = 100 - water - residual solvents - residue on ignition - counter-ion - organic impurities

Each subtraction has to come from its own determination, on the same lot: water by Karl Fischer, solvents by gas chromatography, residue on ignition by ashing, the counter-ion by ion chromatography or titration. Residue on ignition does not stand in for the counter-ion, because an organic or volatile counter-ion does not survive the ashing. This is why a mass balance that stops at 97 per cent is usually missing a term rather than describing an impure material, and why the size of the gap should be read against the combined uncertainty of the individual methods.

The same reasoning explains why qNMR and mass balance can be compared with each other but area per cent cannot be compared with either. The qNMR method and the mass balance both aim at the same quantity, content of the named molecule, and they differ in what they can see. Area per cent aims at something else.

Four corrections, always in this order

The order is not arbitrary. Applying them in a different sequence does not give a slightly different answer, it gives a wrong one, because each correction changes the mass that the next one acts on.

1. Fix the target. Decide whether the number you need is a mass of salt, a mass of free base, or a mass on the anhydrous basis. Everything downstream depends on this one sentence.
2. Apply the salt factor. Divide by the free-base fraction when converting from salt to base, multiply when converting back. Do this once, and only if the certificate is not already on the basis you need.
3. Align the water and solvent basis. From anhydrous to as-is, multiply by one minus the water fraction. From as-is to anhydrous, divide by the same.
4. Apply the assigned content. Divide the target mass by the assigned content as a fraction. This is the only step that consumes analytical information, and it is the step that carries the uncertainty of the standard into every result calibrated against it.

A worked sequence. The target is 1.000 mg of free base. The material is the hydrochloride monohydrate, factor 0.8463, assigned content 98.0 per cent on the anhydrous salt basis, water 5.08 per cent. Step two gives 1.000 / 0.8463 = 1.182 mg of anhydrous salt. Step three gives 1.182 / (1 - 0.0508) = 1.245 mg of salt as weighed. Step four gives 1.245 / 0.980 = 1.270 mg on the balance. Skip step two and the standard is prepared 15 per cent strong; skip step three and it is 5 per cent weak; do both in the wrong order and the error is neither, which is the worst outcome because it looks like a mystery.

The place this goes wrong most often is the certificate that assigns content on a basis it does not name. Before trusting any assigned value, the fields on the certificate have to be read together: form, stoichiometry, basis, and the water and counter-ion figures from the same lot. A content of 99.5 per cent means nothing until those four are known.

What to establish before anything is weighed

• The exact form and stoichiometry. Not hydrochloride, but monohydrochloride; not hydrate, but monohydrate or the actual water figure found on the lot. The factor follows from this and from nothing else.
• The basis of the assigned content. As is, anhydrous, or free base. If the certificate does not say, ask; a value without a basis cannot be converted, only guessed at.
• Whether the factor is already inside the number. An assigned content on the free-base basis already contains the salt correction. Applying it again is the most common arithmetic error in standard preparation.
• Water and counter-ion from the same lot as the assigned content. Values borrowed from a different batch, or from a specification rather than a result, do not describe the powder in the vial.
• How the assigned content was obtained. A mass balance and a titrimetric assay carry different uncertainties, and a mass balance carries the uncertainty of every term it subtracts. The difference between a reference standard and an ordinary reagent is exactly this documented chain.
• Whether the material is hygroscopic, and how it was equilibrated before filling. For a solid that takes up water, the as-is content is a moving target and the weighing has to be fast, or done in a controlled atmosphere.

None of this requires a new method or a new instrument. It requires that every number travelling between a certificate, a specification and a balance carries its basis with it. When that happens, the disagreements between laboratories mostly stop being disagreements and turn into two correct answers to two different questions.