Hier die Frage:
"When do you use mass, volume or number of molecules when the unit ppm (parts per million) is given? Is there a rule, e.g. number of molecules when dealing with gaseous concentrations and volumes when dealing with fluids?"

Hier die Antwort:
PPM (parts per million) is a dimensionless ratio expressing a very small concentration: 1 part of something per 1,000,000 parts of the total mixture (or solution/solvent). It can refer to different "parts" depending on context—mass, volume, or number of molecules (moles)—which is why the unit alone can be ambiguous without context or qualifiers like ppmw (by mass/weight), ppmv (by volume), or ppmm (by mole).⁠Wikipedia
General Rules by Phase/Context

There is a common convention (not a strict universal law, but widely followed to avoid confusion):

Gases (especially air pollution, atmospheric chemistry, gas mixtures):
PPM almost always means ppm by volume (ppmv) or by mole (number of molecules).
For ideal gases (most common case at typical temperatures and pressures), volume fraction = mole fraction. So 1 ppmv of a gas in air means 1 molecule of the pollutant per million molecules of air (or 1 volume unit per million volume units).
This is because gas behavior follows the ideal gas law, where equal volumes contain equal numbers of molecules (Avogadro's law). Mass-based ppm would be misleading here due to differing molecular weights.⁠Researchgate
Liquids (especially dilute aqueous solutions, like pollutants in water):
PPM usually means ppm by mass (ppmw), which for water (density ≈ 1 g/mL or 1 kg/L) is numerically equal to mg of solute per liter of solution (mg/L).
Example: 1 ppm of a contaminant in water ≈ 1 mg/L. Volume-based interpretations are less common unless specified (e.g., for immiscible liquids). Mass is preferred because solutions are weighed or because density is close to 1.⁠Wikipedia
Solids (e.g., contaminants in soil, metals, sediments):
Almost always ppm by mass (mg/kg). This is a straightforward weight/weight ratio.

Your suggested rule is close and often correct in practice:

Number of molecules (mole fraction) for gaseous concentrations → yes, standard for gases.
Volume or mass for fluids → for liquids, it's typically mass (or mass/volume like mg/L), not pure volume fraction unless dealing with volume mixing of similar-density liquids.

When to Use Each Basis

Number of molecules (mole fraction × 10⁶):
Best for gases or when reactions/partial pressures matter (e.g., CO₂ in air at ~420 ppm means ~420 molecules of CO₂ per million air molecules). Ideal for comparing molecular-level effects.
Mass (mass fraction × 10⁶):
Used for liquids, solids, or when total weight matters (e.g., trace metals in water or soil). In water, this conveniently matches mg/L.
Volume (volume fraction × 10⁶):
Common for gases (as ppmv). For liquids, it's rarer but appears in some mixing scenarios (e.g., μL/L). Density differences make it less useful than mass for most solutions.

Key Caveats and Best Practices

Always check context or qualifiers: In scientific literature, "ppm" for gases in air pollution is ppmv/mole. For water quality, it's often mg/L (≈ ppm mass). If unspecified, assume the convention for the medium.⁠Wikipedia
Conversions matter when densities or molecular weights differ: For example, converting gas ppmv to mg/m³ requires the molar mass and conditions (temperature, pressure) via the ideal gas law. Mass ppm and volume ppm give different numerical values for the same mixture if components have different densities/masses.
Mixed units: Sometimes you see mg/L called "ppm" even though it's mass/volume (common in water analysis because density ≈ 1 makes them equivalent).
Non-ideal cases: For high-pressure gases or very different densities, revert to explicit mole or mass fractions.

Quick Examples

Gas: 10 ppm CO in air → typically 10 µL CO per liter of air (volume) or 10 molecules CO per million air molecules.
Water: 10 ppm lead in drinking water → 10 mg lead per kg (or liter) of water.
Soil: 5 ppm pesticide → 5 mg pesticide per kg soil.

In summary, the choice depends on the physical state and what property you're interested in (molecular behavior for gases, gravimetric for liquids/solids). When in doubt, specify "ppmv", "ppmw", or convert explicitly using the appropriate basis (mole for gases, mass for condensed phases). This avoids the common ambiguity in the bare "ppm" unit.
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