Measurement: Derived Units

SI base units are seven fundamental units defined by international agreement: length, mass, time, temperature, electric current, amount of substance, and luminous intensity. Derived units are combinations of one or more base units. For example, volume combines the base unit of length cubed, while density combines mass and length units. Derived units allow us to express complex measurements in chemistry and physics.

Volume measures the space occupied by an object. The SI unit for volume is the cubic meter (m³), derived from the base unit of length. Any unit of length raised to the third power becomes a volume unit, such as cm³ or mm³. A liter, equal to one cubic decimeter, is a common alternative volume unit equal to 1,000 milliliters or 1,000 cubic centimeters.

Density is the ratio of mass to volume. The SI unit for density is kg/m³. However, g/cm³ is often used for solids and liquids, while g/L is used for gases. For example, tin has a density of 7.3 g/cm³, which remains constant regardless of sample size, making density useful for identifying substances.

Intensive properties, such as density, temperature, and boiling point, do not depend on the amount of matter present. They remain constant regardless of sample size, making them reliable identifiers. Extensive properties like mass and volume change with sample size, so they cannot reliably identify a substance. The density of tin, for instance, is always 7.3 g/cm³ whether you have one gram or one kilogram.

Extensive properties depend on the amount of matter present and change with sample size. Mass, volume, and length are primary examples of extensive properties. Because these properties vary with the quantity of substance, they are poor tools for identifying materials. A larger sample of tin will have greater mass and volume than a smaller sample, but both remain tin.

When combining samples, intensive properties remain unchanged. For example, if one liter of milk at 20°C is combined with one cup of milk at 20°C, the resulting mixture stays at 20°C. Extensive properties, however, add together. The combined mass and volume equal the sum of the individual samples. This distinction makes intensive properties valuable for substance identification and physical and chemical properties of matter.

Derived units allow chemists to express complex measurements by combining base units mathematically. This standardized approach enables consistent communication across the scientific community. Volume and density, two essential derived units in chemistry, cannot be expressed using single base units alone. The SI system's derived units provide a universal framework for measuring and comparing properties of matter in experiments and calculations.