Two laboratories report a “dissolved” concentration from the same water. Both used a filter labelled 0.45 µm, yet their results differ. Before deciding that one instrument must be wrong, ask what passed through each filter, what stayed behind, and what the method actually defines as dissolved.
This article explains an operational measurement: a quantity defined partly by the procedure used to obtain it. You will work through an invented element balance, distinguish filtration losses from contamination, and see why a dissolved spike cannot automatically correct the behaviour of colloidal material.
The foundation is The Gold Standard of Chemistry. This lesson also connects to The Gold Standard of Education and How X Works: learning transfers when the definition travels with the number.
eduKateSG · The Gold Standard of Chemistry
Choose your reading route
Define the filtered fraction · Chapters 1–2. Build the quantities before using a formula.
Calculate recovery and composition effects · Chapters 3–5. Follow original examples, assumptions and changed conditions.
Test the method and interpretation · Chapters 6–8. Test transfer, answer common questions and follow connected reading.
Full chapter index · Practice and evidence checks · Return to Chemistry
Chapter index
Define the filtered fraction · Chapters 1–2
Calculate recovery and composition effects · Chapters 3–5
Test the method and interpretation · Chapters 6–8
CHAPTER 1 OF 8 · Define the filtered fraction
1. Ask what the reported word includes
In an introductory particle model, dissolving separates a substance into molecules or ions distributed through a solvent. A water-analysis report can use “dissolved” in a more procedural sense: the material measured in water that has passed through a specified filter under a specified method.
The USGS water-quality glossary gives passage through a 0.45-micrometre filter as an operational definition for dissolved constituents. That is a widely used convention in water studies, not a universal proof that every passing atom exists as a free ion or small molecule. The applicable analytical method must still be identified.
A 0.45 µm opening corresponds to 450 nanometres. Some fine dispersed particles and colloids can enter a filtrate. Conversely, material small enough to pass geometrically can interact with a membrane or with material accumulated on it. The filter is a physical and chemical part of the measurement, not merely a perfect drawing of a sieve.
Keep three questions separate: what chemical species are present, which size-associated fractions the procedure separates, and what the analytical instrument measures after preparation. A filtered total concentration of an element does not identify the individual chemical forms carrying that element. Nor does the word “dissolved” by itself establish mobility, toxicity or biological availability.
The purpose of the procedural definition is reproducibility. It tells another analyst how the fraction was obtained. Problems begin when a method-defined fraction is treated as an exact description of every molecule in the original water.
CHAPTER 2 OF 8 · Define the filtered fraction
2. Build a mass balance before adding filter imperfections
Consider a fictional element E in water. All numbers below refer to micrograms of E per litre of the original sample. The values describe elemental mass, whether E is present as a free ion or attached to a particle. They are not particle masses and are not observations from a real site.
Assume three mutually exclusive pools: 20 µg/L in a small dissolved-species pool, 30 µg/L associated with colloids that pass an idealised first filter, and 50 µg/L associated with larger particles retained by that filter. The original elemental total is 20 + 30 + 50 = 100 µg/L.
| Defined pool or measurement | E concentration | Interpretation in this stipulated model |
|---|---|---|
| Small dissolved species | 20 µg/L | The molecular/ionic pool specified in the example |
| Passing colloid-associated E | 30 µg/L | Particulate association remains possible after filtration |
| Larger-particle-associated E | 50 µg/L | Retained by the ideal first filter |
| First filtrate | 50 µg/L | 20 + 30; not identical to the small-species pool |
| Complete original-sample total | 100 µg/L | Requires a method that actually measures all three pools |
Now imagine a second, ideal separation that retains all of the remaining colloidal E while passing the small-species pool without loss. Its filtrate contains 20 µg/L. The difference between the two filtrates is 30 µg/L under these assumptions. That arithmetic does not establish that an arbitrary finer filter will separate these pools perfectly in practice.
Notice the denominator: every concentration is referred to the same original sample volume, and we assume no dilution, evaporation or phase conversion. When procedures change volume or digest different aliquots, the measurements must be brought onto a common basis before subtraction. A negative or implausible balance is a reason to investigate the measurement chain, not to rename the discrepancy as a new chemical fraction.
CHAPTER 3 OF 8 · Calculate recovery and composition effects
3. Model transmission, retention and contamination separately
Replace the ideal first filter with a hypothetical imperfect one. It transmits 90% of the small-species E and 70% of the passing-colloid pool. It still retains all of the larger particles. These percentages are chosen to teach the calculation; they are not published performance specifications for any membrane.
The filtrate contains 0.90 × 20 + 0.70 × 30 = 18 + 21 = 39 µg/L. Relative to the ideal 50 µg/L filtrate, 11 µg/L is missing: 2 from the small-species pool and 9 from the colloid-associated pool. A single lower concentration cannot tell you which mechanism produced that loss.
Write the model as Cmeasured = aD + bC + cP + B, where D, C and P are the original pools, a, b and c are their transmission/recovery factors, and B is an added blank contribution on the same concentration basis. The equation is a teaching model. Real procedures can also change species or redistribute material during processing.
If contamination contributes 5 µg/L, the instrument now reports 44 µg/L. Subtracting a representative 5 µg/L blank returns 39 µg/L. It removes the stipulated added contribution, but it does not restore the E retained during filtration. Blank correction and recovery correction address different errors.
USGS researchers Horowitz, Elrick and Colberg’s 1992 filtration study examined how factors beyond nominal pore size can alter filtered trace-element measurements. Its importance here is the mechanism and comparability problem. It is not being presented as a current regulatory sampling instruction.
CHAPTER 4 OF 8 · Calculate recovery and composition effects
4. See why the same filter can produce different biases
Keep the hypothetical transmission factors a = 0.90 and b = 0.70. Compare two samples with the same 50 µg/L total in the two pools that the ideal first filter would pass. Their partitioning differs.
| Quantity | Sample A | Sample B |
|---|---|---|
| Small-species E | 20 µg/L | 40 µg/L |
| Passing-colloid-associated E | 30 µg/L | 10 µg/L |
| Ideal first-filtrate concentration | 50 µg/L | 50 µg/L |
| Hypothetical measured filtrate | 0.9 × 20 + 0.7 × 30 = 39 µg/L | 0.9 × 40 + 0.7 × 10 = 43 µg/L |
Sample B reads 4 µg/L higher even though both ideal filtrates contain 50 µg/L. The model explains that difference through composition-dependent recovery. It does not prove that a real observed difference has this cause; that claim would require evidence about fractions and method performance.
Now add 10 µg/L of E entirely in the small-species form to Sample A before filtration, assuming no redistribution. The measured concentration rises from 39 to 48 µg/L. The increment is 9, so the spike recovery is 90%. That correctly describes the added material in this model.
Dividing the original 39 by 0.90 gives about 43.33 µg/L, still below the ideal 50. Why? The dissolved spike tested factor a, while the native colloidal material followed factor b. A recovery check represents the material and steps it actually challenges. It does not automatically validate every native form of an element.
The standard-additions lesson develops a related distinction: responding correctly to added analyte does not make every background effect or preparation loss disappear. Place the check at the step whose performance you want to investigate.
CHAPTER 5 OF 8 · Calculate recovery and composition effects
5. Keep sample history attached to the result
A filter label alone is an incomplete method record. Depending on the method and question, useful information includes membrane material, nominal pore size, filter geometry, the volume processed, filtration approach, sample handling and elapsed time. These details help distinguish a changed environment from a changed measurement procedure.
The timing matters because the sample can continue to change. Oxidation, precipitation, dissolution and adsorption can redistribute an element between phases. Treating a later filtrate as a perfect snapshot of the collection moment requires evidence. Follow the validated method for the analyte and purpose rather than improvising a universal preservation rule.
The supersaturation and delayed-precipitation guide explains why thermodynamic favourability and the appearance of detectable solid need not coincide. The free-ion and total-solubility guide explains another distinction: total dissolved metal and free-metal concentration can differ even within a filtrate.
Choose the quantity from the question. Studying total elemental transport, comparing a method-defined filtered fraction and investigating chemical speciation are related tasks, but they need not use the same preparation or interpretation. A more finely filtered result is not automatically the more truthful answer to all three.
For a regulated or contractual decision, the specified method and decision rule govern the report. The educational balances here help readers ask better questions of that method; they do not define a substitute compliance procedure or a threshold for safe water.
CHAPTER 6 OF 8 · Test the method and interpretation
6. Test an explanation rather than merely repeating a number
Begin by writing a precise claim: “This procedure measured E in this filtrate,” followed by the method conditions and units. Then ask which alternative explanations could change the number. Contamination, incomplete recovery, changing particle distribution and sample evolution require different checks.
A suitable blank investigates introduced material. A replicate assesses repeatability under the repeated conditions. A spike challenges recovery of the added form at the stage where it was added. A comparison of well-defined fractions can test distribution, provided preparation, recovery and volume accounting are compatible. None alone proves that every part of the method is unbiased.
Transfer task one: after blank subtraction, the fictional result is 39 µg/L rather than 50. Can the discrepancy be fixed by subtracting the blank again? No. The model’s remaining discrepancy is loss, not added contamination. Repeating the subtraction would move the result further away.
Transfer task two: a spike added after filtration recovers 100%. Does it show that filtration recovered native E completely? No. The added material did not experience the filter. It checks later analytical steps under its stated conditions.
Transfer task three: two laboratories agree on a filtered concentration but used no independent recovery evidence. Does agreement prove the molecular/ionic pool was measured? No. Both methods might include a similar colloidal fraction or share a similar loss. Agreement is useful evidence, but its meaning depends on what was varied and what remained common.
A good report states the operational definition, relevant controls and unresolved limitations together. It does not ask the reader to infer a complete chemical story from one concentration and the word “dissolved.”
CHAPTER 7 OF 8 · Test the method and interpretation
7. Frequently asked questions about filtered concentrations
Does clear water contain only dissolved molecules and ions?
No. Visual clarity is not a complete particle-size or speciation measurement. The absence of obvious cloudiness does not establish the absence of colloidal material, nor does it establish water safety.
Is a 0.45 µm filter a universal boundary between dissolved and particulate?
It is a useful operational convention in many water methods. Its meaning depends on the procedure and analyte. It is not a universal physical boundary that classifies every environmental constituent perfectly.
Can I subtract two filtrates to calculate a colloidal concentration?
Only with an adequately defined separation and compatible recoveries, preparation and volume basis. The difference is initially a difference between operational fractions. Giving it a more specific chemical meaning requires additional support.
Does a good dissolved spike validate particle-associated analyte?
Not necessarily. It may fail to represent the native material’s association, equilibration or recovery. State what form was added and which steps it experienced.
CHAPTER 8 OF 8 · Test the method and interpretation
8. Connect the fraction to chemistry and environmental evidence
Chemical forms and changing phases
- Chemistry subject root connects particles, reactions, equilibrium and evidence.
- Free ions and total solubility separates free species from total dissolved amounts.
- Supersaturation and induction time explains why the sample’s phase distribution can evolve.
- Biogeochemistry follows elements between environmental pools and processes.
Analytical checks and defensible reporting
- Standard additions and the x-intercept examines what an added analyte can establish.
- Environmental laboratory testing connects sampling, blanks, method suitability and interpretation.
Authoritative sources
- USGS water-quality glossary provides the operational dissolved-constituent definition used for orientation.
- USGS: membrane filtration artifacts and trace elements describes why nominally similar filtration can yield non-equivalent measurements.
Carry the definition into the conclusion. A useful concentration answers a stated chemical question through a stated method; neither the unit nor the filter label can supply that context on its own.