Parts per million (ppm): definition
The keyword parts per million (ppm) describes a very small proportion of one component in a mixture. It is a ratio scale that states how many “parts” of solute correspond to \(10^6\) parts of the total mixture. Because it is a ratio, ppm is dimensionless; the practical meaning depends on the chosen basis (mass, volume, or amount of substance).
In many general chemistry solution problems, ppm is used on a mass basis (ppmw): “mg of solute per kg of solution.”
Formulas for ppm on common bases
The cleanest definition uses a fraction multiplied by \(10^6\). Three common interpretations are:
| Type | Meaning of ppm | Formula | Typical use |
|---|---|---|---|
| ppmw (mass/mass) | parts by mass | \(\mathrm{ppm}=\dfrac{m_{\text{solute}}}{m_{\text{solution}}}\times 10^6\) | solids, liquids, solutions |
| ppmv (volume/volume) | parts by volume | \(\mathrm{ppm}=\dfrac{V_{\text{solute}}}{V_{\text{mixture}}}\times 10^6\) | gas mixtures, sometimes liquids |
| mole-based (often in gases) | parts by amount (mole fraction) | \(\mathrm{ppm}=\chi_{\text{solute}}\times 10^6=\dfrac{n_{\text{solute}}}{n_{\text{total}}}\times 10^6\) | atmospheric chemistry, ideal gases |
Key conversions
Since ppm is \(10^6\) times a fraction, it connects directly to percent and to mass fraction.
- ppm ↔ fraction: \[ \text{fraction}=\frac{\mathrm{ppm}}{10^6} \quad\text{and}\quad \mathrm{ppm}=10^6\times \text{fraction} \]
- ppm ↔ percent: \[ \% = \left(\frac{\mathrm{ppm}}{10^6}\right)\times 100 \quad\Rightarrow\quad 1\,\mathrm{ppm}=10^{-4}\% \]
Why \(1\,\mathrm{ppm}\approx 1\,\mathrm{mg/L}\) for dilute aqueous solutions
In water-based solutions that are dilute and have density close to \(1.00\,\mathrm{kg/L}\), the following approximation is widely used: \(1\,\mathrm{ppm}\approx 1\,\mathrm{mg/L}\). The reasoning is a unit conversion from mass fraction (mg/kg) to mg/L using density.
Start from the mass definition: \[ 1\,\mathrm{ppm} = 1\,\frac{\mathrm{mg}}{\mathrm{kg}} \] If the solution density is approximately \(1.00\,\mathrm{kg/L}\), then \(1\,\mathrm{L}\) of solution has mass \(\approx 1.00\,\mathrm{kg}\), so: \[ 1\,\frac{\mathrm{mg}}{\mathrm{kg}} \approx 1\,\frac{\mathrm{mg}}{\mathrm{L}} \]
In those cases, ppm should be handled explicitly as \( \mathrm{mg/kg} \) (mass basis) or converted using the actual density.
Visualization: what “one part per million” looks like
Worked examples using parts per million
Example 1 (dilute aqueous, using \( \mathrm{ppm}\approx \mathrm{mg/L} \)): A water sample contains \(3.5\,\mathrm{ppm}\) of fluoride. Find the mass of fluoride in \(1.50\,\mathrm{L}\) of water.
Since \(3.5\,\mathrm{ppm}\approx 3.5\,\mathrm{mg/L}\), \[ m = (3.5\,\mathrm{mg/L})\times (1.50\,\mathrm{L}) = 5.25\,\mathrm{mg} \]
Example 2 (mass basis, solid sample): A soil sample has \(25.0\,\mathrm{ppm}\) of lead by mass. Find the mass of lead in \(500\,\mathrm{g}\) of soil.
Interpret \(25.0\,\mathrm{ppm}\) as \(25.0\,\mathrm{mg/kg}\). Convert \(500\,\mathrm{g}=0.500\,\mathrm{kg}\): \[ m = (25.0\,\mathrm{mg/kg})\times (0.500\,\mathrm{kg}) = 12.5\,\mathrm{mg} \]
Quick reference conversions (common in general chemistry)
| Statement | Equivalent form | Notes |
|---|---|---|
| \(1\,\mathrm{ppm}\) (mass basis) | \(1\times 10^{-6}\) (mass fraction) | \(\mathrm{ppm}=\text{fraction}\times 10^6\) |
| \(1\,\mathrm{ppm}\) | \(10^{-4}\%\) | because \(1\% = 10^4\,\mathrm{ppm}\) |
| \(1\,\mathrm{ppm}\) in dilute water | \(\approx 1\,\mathrm{mg/L}\) | requires density \(\approx 1\,\mathrm{kg/L}\) |
| \(1\,\mathrm{ppm}\) (mass basis) | \(1\,\mathrm{mg/kg}\) | exact identity for ppmw |
| \(1\,\mathrm{ppm}\) in dilute water | \(\approx 1\,\mathrm{\mu g/mL}\) | since \(1\,\mathrm{mg/L}=1\,\mathrm{\mu g/mL}\) |
| \(1\,\mathrm{ppmv}\) in gases | \(1\,\mathrm{\mu mol/mol}\) | mole-fraction interpretation; often used for air pollutants |
Common pitfalls
- Solute/solution vs solute/solvent: ppm is typically defined using the total mixture (solution), not just the solvent.
- Assuming \( \mathrm{ppm}=\mathrm{mg/L} \) without checking density: the shortcut is reliable only for dilute, water-like densities.
- Mixing ppmw and ppmv: mass-based and volume-based ppm are not interchangeable without additional information.
Answer
Parts per million (ppm) is a concentration ratio equal to \(10^6\) times a fraction of a component in a mixture, most commonly \( \mathrm{ppm}=\dfrac{m_{\text{solute}}}{m_{\text{solution}}}\times 10^6 \); for dilute aqueous solutions it is often approximated as \(1\,\mathrm{ppm}\approx 1\,\mathrm{mg/L}\).