Parts-per notation

Parts-per notation (PPN) is a set of pseudo-units used to describe small values of dimensionless quantities, such as mass or mole fraction. These units are used in fields such as chemistry, physics, and environmental science to express the concentration of very dilute solutions. The most common units of parts-per notation are parts-per-million (PPM), parts-per-billion (PPB), and parts-per-trillion (PPT), which denote one part of a substance per one million, one billion, and one trillion parts of the total, respectively.

Overview

Parts-per notation is used when the ratio of solute to solution is very small. It is a convenient method for expressing very small concentrations without the need for large exponents or small decimal fractions. For example, a concentration of 1 PPM means that there is one unit of a substance for every million units of the total, which can be expressed as 1 part in 10^6 parts, or 1 mg of substance per kg of total mass if the context is mass.

Units

• Parts-per-million (PPM): Commonly used to describe the concentration of pollutants in air, water, or soil. It can also be used in describing the concentration of a particular substance in a mixture or solution.
• Parts-per-billion (PPB): This unit is used for even more dilute concentrations. It is often used in environmental science, chemistry, and physics to describe extremely low concentrations of a substance.
• Parts-per-trillion (PPT): Used for extremely low concentrations, often in the context of toxicology or environmental pollutants. PPT is indicative of a very minute quantity of a substance in a larger mixture.

Calculation

The calculation of parts-per notation is straightforward. For mass-based measurements, the formula is:

\[PPM = \frac{\text{mass of solute (mg)}}{\text{mass of solution (kg)}} \times 10^6\]

Similarly, for volume-based measurements:

\[PPM = \frac{\text{volume of solute (mL)}}{\text{volume of solution (L)}} \times 10^6\]

The formulas for PPB and PPT follow the same structure but are multiplied by \(10^9\) and \(10^{12}\), respectively.

Applications

Parts-per notation is widely used in various fields:

• In environmental science, to report the concentration of pollutants in air, water, or soil.
• In chemistry, to describe the concentration of solutions or the purity of materials.
• In physics, to express very small values of physical constants or quantities.
• In medicine and pharmacology, to describe the concentration of drugs or toxins in the blood.

Limitations

While parts-per notation is useful for describing very small quantities, it has limitations. It is a dimensionless quantity and does not specify the type of measurement (mass or volume), which can lead to confusion. Additionally, it assumes a linear relationship between the components, which may not always be accurate, especially in complex mixtures.

See Also

• Concentration
• Dilution (chemistry)
• Mole (unit)
• Environmental science
• Toxicology