Mass Balance: Why Assay, Impurities and Water Must Add Up

Take a certificate and do the arithmetic. Assay 99.5 percent, total related substances 0.4 percent, water 0.3 percent, residual solvents not tested. The sum is 100.2. Sometimes it is 98.6. Sometimes it is 101.4. The gap is not a rounding error, and reading it correctly tells you more about the analytical package than reading any single line.

Mass balance is the discipline of accounting for everything in the sample. Where it is done, it converts a list of results into a statement about completeness. Where it is not, a certificate can be internally consistent and still describe only part of the material.

The arithmetic, and what belongs in it

A complete balance for a small-molecule API has five terms: the assay of the main component, the sum of organic impurities, water, residual solvents, and inorganic residue. Each has a measurement method and each has a typical magnitude.

Term	Measured by	Often omitted when
Assay of main component	Titration or chromatographic comparison to a standard	Rarely omitted
Organic impurities	Related substances by HPLC	When only specified impurities are reported
Water	Karl Fischer, or loss on drying as a surrogate	When loss on drying is treated as water
Residual solvents	Gas chromatography	When the batch is released on a reduced panel
Inorganic residue	Sulfated ash or residue on ignition	Almost always, until somebody asks

The last row explains most surprises. Inorganic residue is small for a well-purified organic substance and it is not zero, and it sits in the gap without appearing on any line.

Loss on drying is not water

Loss on drying measures mass lost under stated conditions. That mass may include water, residual solvent and, at higher temperatures, material that decomposes. Using it as the water term in a mass balance is a convenience that works when the solvent residue is negligible and fails when it is not.

Karl Fischer measures water specifically. Where both are reported, the difference between them is informative: a large gap suggests solvent or volatile impurity, which is precisely the term the balance is missing.

Area percent is not weight percent

Most related-substance methods report area percentage, which is the peak area of an impurity divided by the total peak area. That is a statement about the chromatogram. It becomes a statement about the sample only if every component has the same response per unit mass.

For structurally related impurities in a bile acid, responses are often similar but not identical, and a difference of twenty or thirty percent in response is unremarkable. An impurity reported at 0.20 area percent may be 0.15 or 0.26 weight percent. Over several impurities the errors partly cancel and partly accumulate, which is why an uncorrected area sum is a rough estimate rather than a measurement.

Where the gap legitimately sits

A gap of one to two percentage points is normal and has ordinary explanations: an untested residual solvent, an inorganic residue of a few tenths, an impurity below the reporting threshold, a standard whose assigned purity is itself 99.5 percent, and the accumulated rounding of five separate methods each with its own uncertainty.

The important distinction is between a gap that is explained and a gap that is merely present. An explained gap is a closed item. An unexplained gap is an open question about method coverage, and it does not go away by being averaged over several batches.

Assay on the dried basis versus as is

Many assays are reported on the dried basis, which means the result has already been corrected for water. Others are reported as is. Mixing the two in a mass balance produces a double count or a double correction, and the error is easy to make because the certificate does not always say which basis was used.

This is one of the reasons a certificate without a stated basis is a weak document. The number is not wrong; the number is uninterpretable until the basis is known.

When to ask for a mass balance

Three occasions justify it. At qualification, to establish that the analytical package covers the material. During an investigation, when a result does not fit. And when a specification is being rewritten, because the exercise usually reveals that one term has never been measured at all.

It is not a routine release test. Asking for it on every delivery converts a characterisation exercise into a production burden, and the answer you get will be a template rather than an analysis.

What a good certificate discloses

A certificate that supports a mass balance states the assay basis, reports total impurities as well as specified ones, reports water by a named method, reports residual solvents against a named class, and reports inorganic residue. Five lines, all of them ordinary, and together they let a buyer close the arithmetic without asking a question.

The absence of those five lines is not evidence of a problem. It is evidence that nobody has asked, which is a different thing and easier to fix.

How to close the arithmetic yourself

Take the five terms from the certificate, convert them to the same basis, and add. Where a term is missing, write zero and mark it as missing rather than assuming it is negligible. The result is either close to one hundred or it is not, and the size of the gap tells you which term to ask about.

The conversion to a common basis is where most manual checks fail. An assay reported on the dried basis must be combined with water in a way that does not double count it. A residual solvent reported in parts per million must be converted to a percentage before it enters the sum.

Three articles here cover the individual terms. An assay above 100 percent explains the most common arithmetic surprise. Assay versus area normalisation explains why the purity figure cannot simply be subtracted. And Loss on drying versus water explains the term that is most often miscounted.

Where the guidance sits

The International Council for Harmonisation publishes the impurity and validation guidance that defines reporting, identification and qualification thresholds, and the analytical procedure guidance that defines what a validated method has demonstrated. The European Pharmacopoeia and the United States Pharmacopeia publish the general chapters on related substances, water determination and residue on ignition that supply the individual measurements.

Together they define the terms. None of them requires a supplier to present a mass balance on a certificate, which is why the exercise is one a buyer performs rather than one a buyer receives.

What to do with an unexplained gap

Ask which term has not been measured. In most cases the answer is residual solvents or inorganic residue, and in most cases the answer is given freely once the question is specific. A gap that closes when one term is added was never a quality problem; it was an incomplete panel.

Where the gap does not close after the obvious terms are added, the next question is about the standard. An assay calculated against a standard whose assigned purity is itself uncertain carries that uncertainty into the result, and the arithmetic will not reconcile until the standard's value is confirmed.

Either way, the resolution is a conversation about method coverage rather than about the batch. That is a much cheaper conversation than the one that follows a rejected delivery, and it can be had before the first order.

A worked example, with illustrative values

Take a hypothetical certificate: assay 99.4 percent on the dried basis, total related substances 0.45 percent, water 0.35 percent by Karl Fischer, residual solvents not tested, residue on ignition not tested. The values here are illustrative and are not taken from any specific batch.

Converting to a single basis, the dried-basis assay already excludes the water, so the water must be added back to reach an as-is figure. That gives roughly 99.1 percent as is, plus 0.35 percent water, plus 0.45 percent impurities, which sums to 99.9 percent and leaves a gap of about 0.1 percent. That gap is small enough to be explained by the untested inorganic residue.

Now change one input. If the assay had been reported as is rather than on the dried basis, the same arithmetic would produce 100.25 percent and a negative gap, which is impossible and therefore informative: the basis statement was wrong, or the water was counted twice.

That is the whole technique. It requires no instrument, only the discipline of putting every term on the same basis and declining to average away an unexplained residual.

Why suppliers rarely volunteer it

A mass balance is a development exercise and it takes time. It is also, in a sense, an admission that the release panel does not cover everything, which is true of every release panel and uncomfortable to say out loud.

Once you have asked once and received a sensible answer, the topic stops being sensitive. The supplier knows what you are checking, you know what the panel covers, and the next batch arrives with the right five lines because somebody now knows why they matter.

Frequently asked questions

What is mass balance in a pharmaceutical analysis?

It is the check that everything in the sample has been accounted for. The assay of the main component plus all measured impurities plus water plus residual solvents plus inorganic residue should come close to one hundred percent. When it does not, something was not measured or was measured with the wrong response.

How close does mass balance need to be?

Common practice accepts a total within about two percentage points of one hundred, with tighter expectations for a well-characterised small molecule. The number matters less than the explanation for the gap. A gap that is understood is acceptable. A gap that is unexplained is a method question.

Why is area percent different from weight percent?

Because a chromatographic detector does not respond equally to every molecule. Area percent assumes all components have the same response per unit mass, which is rarely true for structurally related impurities. Without a response factor, an area percentage is a description of the chromatogram rather than of the sample.

What is a response factor and when is it needed?

It is the ratio between a substance's detector response and that of the reference compound, per unit mass. It is needed whenever an impurity's response differs materially from the main component, which for related substances in a bile acid is common because the chromophore is the same but the environment differs.

Does a mass balance gap mean the batch is bad?

No. It usually means the analytical package is incomplete: residual solvents not tested, inorganic residue not measured, water measured by a method that misses part of it, or an impurity below the reporting threshold but present. The batch can be entirely fine while the arithmetic does not close.

Should I request a mass balance on every batch?

No. It is a characterisation exercise, appropriate at qualification and during an investigation. Routine release uses the specification. Asking for a mass balance on every delivery is asking for development work on a production batch.